From 56b240a7ec18df4e4caa652d9892ff23cffa87bc Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Mon, 17 Nov 2025 11:24:15 -0500 Subject: [PATCH 01/23] copy over srfit examples --- .codespell/ignore_words.txt | 3 + docs/examples/srfit_ex/README | 161 + docs/examples/srfit_ex/coreshellnp.py | 215 + docs/examples/srfit_ex/crystalpdf.py | 176 + docs/examples/srfit_ex/crystalpdfall.py | 240 + docs/examples/srfit_ex/crystalpdfobjcryst.py | 129 + docs/examples/srfit_ex/crystalpdftwodata.py | 196 + docs/examples/srfit_ex/crystalpdftwophase.py | 187 + docs/examples/srfit_ex/data/C60.gr | 1999 +++ docs/examples/srfit_ex/data/C60.stru | 369 + docs/examples/srfit_ex/data/CdS.cif | 69 + docs/examples/srfit_ex/data/CdS_ZnS_nano.gr | 7506 ++++++++++++ docs/examples/srfit_ex/data/ZnS.cif | 65 + docs/examples/srfit_ex/data/gaussian.dat | 100 + docs/examples/srfit_ex/data/lorentzian.dat | 200 + .../srfit_ex/data/ni-q27r100-neutron.gr | 10052 ++++++++++++++++ docs/examples/srfit_ex/data/ni-q27r60-xray.gr | 6133 ++++++++++ .../srfit_ex/data/ni-q27r60nodg-xray.gr | 6133 ++++++++++ docs/examples/srfit_ex/data/ni.cif | 236 + docs/examples/srfit_ex/data/ni.iq | 2464 ++++ docs/examples/srfit_ex/data/pb.cif | 240 + docs/examples/srfit_ex/data/pb_100.xyz | 102 + docs/examples/srfit_ex/data/pb_100_qmax1.iq | 99 + docs/examples/srfit_ex/data/pb_100_qmin1.gr | 3500 ++++++ .../srfit_ex/data/sas_ellipsoid_testdata.txt | 136 + docs/examples/srfit_ex/data/si-q27r60-xray.gr | 6133 ++++++++++ docs/examples/srfit_ex/data/si.cif | 224 + .../srfit_ex/data/si90ni10-q27r60-xray.gr | 6134 ++++++++++ .../srfit_ex/data/threedoublepeaks.dat | 4000 ++++++ docs/examples/srfit_ex/debyemodel.py | 270 + docs/examples/srfit_ex/debyemodelII.py | 162 + docs/examples/srfit_ex/ellipsoidsas.py | 130 + docs/examples/srfit_ex/gaussiangenerator.py | 180 + docs/examples/srfit_ex/gaussianrecipe.py | 214 + docs/examples/srfit_ex/interface.py | 78 + docs/examples/srfit_ex/npintensity.py | 531 + docs/examples/srfit_ex/npintensityII.py | 279 + docs/examples/srfit_ex/nppdfcrystal.py | 129 + docs/examples/srfit_ex/nppdfobjcryst.py | 257 + docs/examples/srfit_ex/nppdfsas.py | 196 + docs/examples/srfit_ex/simplepdf.py | 91 + docs/examples/srfit_ex/simplepdftwophase.py | 122 + docs/examples/srfit_ex/simplerecipe.py | 63 + docs/examples/srfit_ex/threedoublepeaks.py | 261 + 44 files changed, 60164 insertions(+) create mode 100644 docs/examples/srfit_ex/README create mode 100644 docs/examples/srfit_ex/coreshellnp.py create mode 100644 docs/examples/srfit_ex/crystalpdf.py create mode 100644 docs/examples/srfit_ex/crystalpdfall.py create mode 100644 docs/examples/srfit_ex/crystalpdfobjcryst.py create mode 100644 docs/examples/srfit_ex/crystalpdftwodata.py create mode 100644 docs/examples/srfit_ex/crystalpdftwophase.py create mode 100644 docs/examples/srfit_ex/data/C60.gr create mode 100644 docs/examples/srfit_ex/data/C60.stru create mode 100644 docs/examples/srfit_ex/data/CdS.cif create mode 100644 docs/examples/srfit_ex/data/CdS_ZnS_nano.gr create mode 100644 docs/examples/srfit_ex/data/ZnS.cif create mode 100644 docs/examples/srfit_ex/data/gaussian.dat create mode 100644 docs/examples/srfit_ex/data/lorentzian.dat create mode 100644 docs/examples/srfit_ex/data/ni-q27r100-neutron.gr create mode 100644 docs/examples/srfit_ex/data/ni-q27r60-xray.gr create mode 100644 docs/examples/srfit_ex/data/ni-q27r60nodg-xray.gr create mode 100644 docs/examples/srfit_ex/data/ni.cif create mode 100644 docs/examples/srfit_ex/data/ni.iq create mode 100644 docs/examples/srfit_ex/data/pb.cif create mode 100644 docs/examples/srfit_ex/data/pb_100.xyz create mode 100644 docs/examples/srfit_ex/data/pb_100_qmax1.iq create mode 100644 docs/examples/srfit_ex/data/pb_100_qmin1.gr create mode 100644 docs/examples/srfit_ex/data/sas_ellipsoid_testdata.txt create mode 100644 docs/examples/srfit_ex/data/si-q27r60-xray.gr create mode 100644 docs/examples/srfit_ex/data/si.cif create mode 100644 docs/examples/srfit_ex/data/si90ni10-q27r60-xray.gr create mode 100644 docs/examples/srfit_ex/data/threedoublepeaks.dat create mode 100644 docs/examples/srfit_ex/debyemodel.py create mode 100644 docs/examples/srfit_ex/debyemodelII.py create mode 100644 docs/examples/srfit_ex/ellipsoidsas.py create mode 100644 docs/examples/srfit_ex/gaussiangenerator.py create mode 100644 docs/examples/srfit_ex/gaussianrecipe.py create mode 100644 docs/examples/srfit_ex/interface.py create mode 100644 docs/examples/srfit_ex/npintensity.py create mode 100644 docs/examples/srfit_ex/npintensityII.py create mode 100644 docs/examples/srfit_ex/nppdfcrystal.py create mode 100644 docs/examples/srfit_ex/nppdfobjcryst.py create mode 100644 docs/examples/srfit_ex/nppdfsas.py create mode 100644 docs/examples/srfit_ex/simplepdf.py create mode 100644 docs/examples/srfit_ex/simplepdftwophase.py create mode 100644 docs/examples/srfit_ex/simplerecipe.py create mode 100644 docs/examples/srfit_ex/threedoublepeaks.py diff --git a/.codespell/ignore_words.txt b/.codespell/ignore_words.txt index 04b4fcf..e5385f6 100644 --- a/.codespell/ignore_words.txt +++ b/.codespell/ignore_words.txt @@ -6,3 +6,6 @@ mater ;; Frobenius norm used in np.linalg.norm fro + +;; variable used in docs/examples/srfit_ex/debyemodelII.py +highT diff --git a/docs/examples/srfit_ex/README b/docs/examples/srfit_ex/README new file mode 100644 index 0000000..a48a570 --- /dev/null +++ b/docs/examples/srfit_ex/README @@ -0,0 +1,161 @@ +## Purpose + +These example scripts are intended to help a developer get acquainted with the +SrFit programming interface. Although one can write scripts like these to drive +optimization, these scripts do not represent the SrFit user interface. That +interface will be made available in a future release. + +A secondary purpose of these tutorials is to generate interest in SrFit. By +reading through the examples we hope that you are inspired to think of exciting +new ways to get the most out of your scientific data. If you think SrFit can +help you with that, please feel free to contact us through the DiffPy website. + +http://www.diffpy.org + +## Overview + +Three things are required for optimization: a function that generates a +quantity to be minimized, variables that can be used to manipulate that +function and an algorithm that can drive the function output to a smaller value +by steering the variables. For scientific purposes, the quantity to be +minimized is the disagreement between a measured profile and a theoretical +profile. The scientific understanding of the system under consideration partly +determines the suitability of the theoretical profile generator and the +scientific relevance of the variables used to drive it. + +The purpose of SrFit is to give users the means to combine known information +about a system of interest in order to extract scientifically relevant +quantities, and thus understanding from it. Various experimental procedures and +theoretical calculations may be needed to gain the desired understanding of the +system. SrFit helps users combine these views of the system in a coherent and +consistent manner. + +To achieve this purpose, SrFit provides: + +1. a function to be optimized (the residual) given one or more measured + profiles, one or more profile generators and variables to be steered by an + optimizer. +2. constraints and restraints that encapsulate known information about the + system. +3. a clearly defined programming interface that developers can use to add their + own profile generators, thereby enabling the combination of more views of a + system. +4. an equation building interface that allows users to tweak profile generators + when scientific understanding of a system is more advanced than the existing + software. + +The examples described below will go into detail about each of these points. + +## Examples + +The following examples are contained in the _docs/examples/_ directory of the +SrFit source distribution. They can be downloaded from +http://dev.danse.us/packages/srfit_examples-alpha9.zip + +For each example, start by running the example by typing in the command line :: + + python example.py + +where _example.py_ represents the example file. The output will show on screen +and a plot window will display. Once you've studied the output and plot, close +the plot window and open the example file. In the file there will be a +description of what the script is doing and the purpose of the example. By +reading through the example, you will be introduced to the SrFit programming +interface. + +Here is an overview of the examples. It is recommended that you work through +them in the order listed below. + +Basic: + +- gaussianrecipe.py\_ + Introductory recipe building and configuration. This introduces the + fundamental classes in SrFit. + +- debyemodel.py\_ + Introductory recipe building and configuration. This shows how to use a + function created by someone else in a refinement. This example also + introduces restraints. + +- debyemodelII.py\_ + Refine two different values of a variable from two different regions of a + profile. This example introduces constraints and working with multiple + contributions to a fit. + +Advanced: + +- gaussiangenerator.py* + Create a custom ProfileGenerator and use it in a refinement. This is an + instructive extension to gaussianrecipe.py*. + +- npintensity.py\_ + Use diffpy.structure to build a nanoparticle intensity generator, and use + it to refine a structure to simulated data. + +- npintensityII.py\_ + Use the calculator built in npintensity.py to simultaneously refine a + structure to two data sets. + +## Use Cases + +There are several examples that demonstrate various SrFit use cases. These do +not adopt the tutorial format of the previous examples. Regardless, developers +should read through these use cases to gain an understanding of PDF and SAS +refinement with SrFit. + +- crystalpdf.py\_ + Refine a diffpy.structure crystal to PDF data using automatic explicit + space group constraints. + +- simplepdf.py* + As crystalpdf.py*, but with a simplified interface. + +- crystalpdfobjcryst.py\_ + Refine a pyobjcryst crystal to PDF data using automatic implicit space + group constraints. + +- crystalpdftwophase.py\_ + Refine a two-phase structure to PDF data using two profile generators. + +- simplepdftwophase.py* + crystalpdftwophase.py* using the simplified PDFContribution interface. + +- crystalpdftwodata.py\_ + Refine a single structure to x-ray and neutron data simultaneously. + +- crystalpdfall.py\_ + Refine a two-phase structure using four data sets. + +- nppdfobjcryst.py\_ + Refine the C60 structure to real data. + +- nppdfcrystal.py\_ + Fit a nanoparticle PDF as a crystal PDF attenuated by a nanoparticle form + factor. + +- coreshellnp.py\_ + As above, but fit the PDF from core-shell nanoparticles. + +- ellipsoidsas.py\_ + Refine an ellipsoid SAS model to ideal data. + +- nppdfsas.py\_ + Refine PDF from nanoparticle of assumed shape using a crystal model and SAS + data from the same system. + +## Miscellaneous + +These demonstrate other SrFit features. These are in flux and may not be in +future versions. + +- simplerecipe.py\_ + This introduces the SimpleRecipe class that is a FitRecipe with an embedded + Profile and FitContribution. SimpleRecipe exposes methods from the Profile + and FitContribution, and adds other methods so it is easy to set up a + simple fit. + +- interface.py\_ + This example introduces some interface enhancements that allow the SrFit + recipes to be written with less code. This is not the same as a + full-featured scripting interface, but rather somewhere in between a + scripting interface and the API. diff --git a/docs/examples/srfit_ex/coreshellnp.py b/docs/examples/srfit_ex/coreshellnp.py new file mode 100644 index 0000000..8030a34 --- /dev/null +++ b/docs/examples/srfit_ex/coreshellnp.py @@ -0,0 +1,215 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2011 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow, Peng Tian +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Refine the structure of a core-shell nanoparticle. + +This applies the characteristic function formalism described in +nppdfcrystal.py to the case of a spherical core-shell nanoparticle. The +modeling approach we use is to refine the core and shell as two +different phases, each with an appropriate characteristic function. +""" + +import numpy +from pyobjcryst import loadCrystal +from scipy.optimize import leastsq + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) +from diffpy.srfit.pdf import PDFGenerator, PDFParser + +# Example Code + + +def makeRecipe(stru1, stru2, datname): + """Create a fitting recipe for crystalline PDF data.""" + + # The Profile + profile = Profile() + + # Load data and add it to the profile + parser = PDFParser() + parser.parseFile(datname) + profile.loadParsedData(parser) + profile.setCalculationRange(xmin=1.5, xmax=45, dx=0.1) + + # The ProfileGenerator + # In order to fit the core and shell phases simultaneously, we must use two + # PDFGenerators. + # + # The generator for the CdS core. We call it "G_CdS" and will use this name + # later when we set the fitting equation in the FitContribution. + generator_cds = PDFGenerator("G_CdS") + generator_cds.setStructure(stru1) + generator_cds.setQmax(26) + generator_cds.qdamp.value = 0.0396 + # The generator for the ZnS shell. We call it "G_ZnS". + generator_zns = PDFGenerator("G_ZnS") + generator_zns.setStructure(stru2) + generator_zns.setQmax(26) + generator_zns.qdamp.value = 0.0396 + + # The FitContribution + # Add both generators and the profile to the FitContribution. + contribution = FitContribution("cdszns") + contribution.addProfileGenerator(generator_cds) + contribution.addProfileGenerator(generator_zns) + contribution.setProfile(profile, xname="r") + + # Set up the characteristic functions. We use a spherical CF for the core + # and a spherical shell CF for the shell. Since this is set up as two + # phases, we implicitly assume that the core-shell correlations contribute + # very little to the PDF. + from diffpy.srfit.pdf.characteristicfunctions import shellCF, sphericalCF + + contribution.registerFunction(sphericalCF, name="f_CdS") + contribution.registerFunction(shellCF, name="f_ZnS") + + # Write the fitting equation. We want to sum the PDFs from each phase and + # multiply it by a scaling factor. + contribution.setEquation("scale * (f_CdS * G_CdS + f_ZnS * G_ZnS)") + + # Make the FitRecipe and add the FitContribution. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Vary the inner radius and thickness of the shell. Constrain the core + # diameter to twice the shell radius. + recipe.addVar(contribution.radius, 15) + recipe.addVar(contribution.thickness, 11) + recipe.constrain(contribution.psize, "2 * radius") + + # Configure the fit variables + # Start by configuring the scale factor and resolution factors. + # We want the sum of the phase scale factors to be 1. + recipe.newVar("scale_CdS", 0.7) + recipe.constrain(generator_cds.scale, "scale_CdS") + recipe.constrain(generator_zns.scale, "1 - scale_CdS") + # We also want the resolution factor to be the same on each. + + # Vary the global scale as well. + recipe.addVar(contribution.scale, 0.3) + + # Now we can configure the structural parameters. We tag the different + # structural variables so we can easily turn them on and off in the + # subsequent refinement. + phase_cds = generator_cds.phase + for par in phase_cds.sgpars.latpars: + recipe.addVar(par, name=par.name + "_cds", tag="lat") + for par in phase_cds.sgpars.adppars: + recipe.addVar(par, 1, name=par.name + "_cds", tag="adp") + recipe.addVar(phase_cds.sgpars.xyzpars.z_1, name="z_1_cds", tag="xyz") + # Since we know these have stacking disorder, constrain the B33 adps for + # each atom type. + recipe.constrain("B33_1_cds", "B33_0_cds") + recipe.addVar(generator_cds.delta2, name="delta2_cds", value=5) + + phase_zns = generator_zns.phase + for par in phase_zns.sgpars.latpars: + recipe.addVar(par, name=par.name + "_zns", tag="lat") + for par in phase_zns.sgpars.adppars: + recipe.addVar(par, 1, name=par.name + "_zns", tag="adp") + recipe.addVar(phase_zns.sgpars.xyzpars.z_1, name="z_1_zns", tag="xyz") + recipe.constrain("B33_1_zns", "B33_0_zns") + recipe.addVar(generator_zns.delta2, name="delta2_zns", value=2.5) + + # Give the recipe away so it can be used! + return recipe + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # All this should be pretty familiar by now. + r = recipe.cdszns.profile.x + g = recipe.cdszns.profile.y + gcalc = recipe.cdszns.profile.ycalc + diffzero = -0.8 * max(g) * numpy.ones_like(g) + diff = g - gcalc + diffzero + + import pylab + + pylab.plot(r, g, "bo", label="G(r) Data") + pylab.plot(r, gcalc, "r-", label="G(r) Fit") + pylab.plot(r, diff, "g-", label="G(r) diff") + pylab.plot(r, diffzero, "k-") + pylab.xlabel(r"$r (\AA)$") + pylab.ylabel(r"$G (\AA^{-2})$") + pylab.legend(loc=1) + + pylab.show() + return + + +def main(): + """Set up and refine the recipe.""" + + # Make the data and the recipe + cdsciffile = "data/CdS.cif" + znsciffile = "data/ZnS.cif" + data = "data/CdS_ZnS_nano.gr" + + # Make the recipe + stru1 = loadCrystal(cdsciffile) + stru2 = loadCrystal(znsciffile) + recipe = makeRecipe(stru1, stru2, data) + from diffpy.srfit.fitbase.fithook import PlotFitHook + + recipe.pushFitHook(PlotFitHook()) + recipe.fithooks[0].verbose = 3 + + # Optimize - we do this in steps to help convergence + recipe.fix("all") + + # Start with the lattice parameters. In makeRecipe, these were tagged with + # "lat". Here is how we use that. + recipe.free("lat") + leastsq(recipe.residual, recipe.values, maxfev=50) + + # Now the scale and phase fraction. + recipe.free("scale", "scale_CdS") + leastsq(recipe.residual, recipe.values, maxfev=50) + + # The ADPs. + recipe.free("adp") + leastsq(recipe.residual, recipe.values, maxfev=100) + + # The delta2 parameters. + recipe.free("delta2_cds", "delta2_zns") + leastsq(recipe.residual, recipe.values, maxfev=50) + + # The shape parameters. + recipe.free("radius", "thickness") + leastsq(recipe.residual, recipe.values, maxfev=50) + + # The positional parameters. + recipe.free("xyz") + leastsq(recipe.residual, recipe.values) + + # Generate and print the FitResults + res = FitResults(recipe) + res.printResults() + + # Plot! + plotResults(recipe) + return + + +if __name__ == "__main__": + main() + +# End of file diff --git a/docs/examples/srfit_ex/crystalpdf.py b/docs/examples/srfit_ex/crystalpdf.py new file mode 100644 index 0000000..41dbca6 --- /dev/null +++ b/docs/examples/srfit_ex/crystalpdf.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of a PDF refinement using diffpy.structure and PDFGenerator. + +This is example of fitting the fcc nickel structure to measured PDF +data. The purpose of this example is to demonstrate and describe the +classes in configuration options involved with setting up a fit in this +way. The main benefit of using SrFit for PDF refinement is the +flexibility of modifying the PDF profile function for specific needs, +adding restraints to a fit and the ability to simultaneously refine a +structure to PDF data and data from other sources. This example +demonstrates only the basic configuration. +""" + +import numpy +from gaussianrecipe import scipyOptimize + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) +from diffpy.srfit.pdf import PDFGenerator, PDFParser +from diffpy.structure import Structure + +###### +# Example Code + + +def makeRecipe(ciffile, datname): + """Create a fitting recipe for crystalline PDF data.""" + + # The Profile + # This will be used to store the observed and calculated PDF profile. + profile = Profile() + + # Load data and add it to the Profile. Unlike in other examples, we use a + # class (PDFParser) to help us load the data. This class will read the data + # and relevant metadata from a two- to four-column data file generated + # with PDFGetX2 or PDFGetN. The metadata will be passed to the PDFGenerator + # when they are associated in the FitContribution, which saves some + # configuration steps. + parser = PDFParser() + parser.parseFile(datname) + profile.loadParsedData(parser) + profile.setCalculationRange(xmax=20) + + # The ProfileGenerator + # The PDFGenerator is for configuring and calculating a PDF profile. Here, + # we want to refine a Structure object from diffpy.structure. We tell the + # PDFGenerator that with the 'setStructure' method. All other configuration + # options will be inferred from the metadata that is read by the PDFParser. + # In particular, this will set the scattering type (x-ray or neutron), the + # Qmax value, as well as initial values for the non-structural Parameters. + generator = PDFGenerator("G") + stru = Structure() + stru.read(ciffile) + generator.setStructure(stru) + + # The FitContribution + # Here we associate the Profile and ProfileGenerator, as has been done + # before. + contribution = FitContribution("nickel") + contribution.addProfileGenerator(generator) + contribution.setProfile(profile, xname="r") + + # Make the FitRecipe and add the FitContribution. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Configure the fit variables + + # The PDFGenerator class holds the ParameterSet associated with the + # Structure passed above in a data member named "phase". (We could have + # given the ParameterSet a name other than "phase" when we added it to the + # PDFGenerator.) The ParameterSet in this case is a StructureParameterSet, + # the documentation for which is found in the + # diffpy.srfit.structure.diffpystructure module. + phase = generator.phase + + # We start by constraining the phase to the known space group. We could do + # this by hand, but there is a method in diffpy.srfit.structure named + # 'constrainAsSpaceGroup' for this purpose. The constraints will by default + # be applied to the sites, the lattice and to the ADPs. See the method + # documentation for more details. The 'constrainAsSpaceGroup' method may + # create new Parameters, which it returns in a SpaceGroupParameters object. + from diffpy.srfit.structure import constrainAsSpaceGroup + + sgpars = constrainAsSpaceGroup(phase, "Fm-3m") + + # The SpaceGroupParameters object returned by 'constrainAsSpaceGroup' holds + # the free Parameters allowed by the space group constraints. Once a + # structure is constrained, we need (should) only use the Parameters + # provided in the SpaceGroupParameters, as the relevant structure + # Parameters are constrained to these. + # + # We know that the space group does not allow for any free sites because + # each atom is on a special position. There is one free (cubic) lattice + # parameter and one free (isotropic) ADP. We can access these Parameters in + # the xyzpars, latpars, and adppars members of the SpaceGroupParameters + # object. + for par in sgpars.latpars: + recipe.addVar(par) + for par in sgpars.adppars: + recipe.addVar(par, 0.005) + + # We now select non-structural parameters to refine. + # This controls the scaling of the PDF. + recipe.addVar(generator.scale, 1) + # This is a peak-damping resolution term. + recipe.addVar(generator.qdamp, 0.01) + # This is a vibrational correlation term that sharpens peaks at low-r. + recipe.addVar(generator.delta2, 5) + + # Give the recipe away so it can be used! + return recipe + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # All this should be pretty familiar by now. + r = recipe.nickel.profile.x + g = recipe.nickel.profile.y + gcalc = recipe.nickel.profile.ycalc + diffzero = -0.8 * max(g) * numpy.ones_like(g) + diff = g - gcalc + diffzero + + import pylab + + pylab.plot(r, g, "bo", label="G(r) Data") + pylab.plot(r, gcalc, "r-", label="G(r) Fit") + pylab.plot(r, diff, "g-", label="G(r) diff") + pylab.plot(r, diffzero, "k-") + pylab.xlabel(r"$r (\AA)$") + pylab.ylabel(r"$G (\AA^{-2})$") + pylab.legend(loc=1) + + pylab.show() + return + + +if __name__ == "__main__": + + # Make the data and the recipe + ciffile = "data/ni.cif" + data = "data/ni-q27r100-neutron.gr" + + # Make the recipe + recipe = makeRecipe(ciffile, data) + recipe.fithooks[0].verbose = 3 + + # Optimize + scipyOptimize(recipe) + + # Generate and print the FitResults + res = FitResults(recipe) + res.printResults() + + # Plot! + plotResults(recipe) + +# End of file diff --git a/docs/examples/srfit_ex/crystalpdfall.py b/docs/examples/srfit_ex/crystalpdfall.py new file mode 100644 index 0000000..056f8a8 --- /dev/null +++ b/docs/examples/srfit_ex/crystalpdfall.py @@ -0,0 +1,240 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of a PDF refinement of two-phase structure. + +This example uses PDFGenerator to refine a the two phase nickel-silicon +structure to all the available data. +""" + +import numpy +from gaussianrecipe import scipyOptimize +from pyobjcryst import loadCrystal + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) +from diffpy.srfit.pdf import PDFGenerator, PDFParser + +###### +# Example Code + + +def makeProfile(datafile): + """Make an place data within a Profile.""" + profile = Profile() + parser = PDFParser() + parser.parseFile(datafile) + profile.loadParsedData(parser) + profile.setCalculationRange(xmax=20) + return profile + + +def makeContribution(name, generator, profile): + """Make a FitContribution and add a generator and profile.""" + contribution = FitContribution(name) + contribution.addProfileGenerator(generator) + contribution.setProfile(profile, xname="r") + return contribution + + +def makeRecipe( + ciffile_ni, ciffile_si, xdata_ni, ndata_ni, xdata_si, xdata_sini +): + """Create a fitting recipe for crystalline PDF data.""" + + # The Profiles + # We need a profile for each data set. + xprofile_ni = makeProfile(xdata_ni) + xprofile_si = makeProfile(xdata_si) + nprofile_ni = makeProfile(ndata_ni) + xprofile_sini = makeProfile(xdata_sini) + + # The ProfileGenerators + # We create one for each phase and share the phases. + xgenerator_ni = PDFGenerator("xG_ni") + stru = loadCrystal(ciffile_ni) + xgenerator_ni.setStructure(stru) + phase_ni = xgenerator_ni.phase + + xgenerator_si = PDFGenerator("xG_si") + stru = loadCrystal(ciffile_si) + xgenerator_si.setStructure(stru) + phase_si = xgenerator_si.phase + + ngenerator_ni = PDFGenerator("nG_ni") + ngenerator_ni.setPhase(phase_ni) + + xgenerator_sini_ni = PDFGenerator("xG_sini_ni") + xgenerator_sini_ni.setPhase(phase_ni) + + xgenerator_sini_si = PDFGenerator("xG_sini_si") + xgenerator_sini_si.setPhase(phase_si) + + # The FitContributions + # We one of these for each data set. + xcontribution_ni = makeContribution("xnickel", xgenerator_ni, xprofile_ni) + xcontribution_si = makeContribution("xsilicon", xgenerator_si, xprofile_si) + ncontribution_ni = makeContribution("nnickel", ngenerator_ni, nprofile_ni) + xcontribution_sini = makeContribution( + "xsini", xgenerator_sini_ni, xprofile_sini + ) + xcontribution_sini.addProfileGenerator(xgenerator_sini_si) + xcontribution_sini.setEquation("scale * (xG_sini_ni + xG_sini_si)") + + # As explained in another example, we want to minimize using Rw^2. + xcontribution_ni.setResidualEquation("resv") + xcontribution_si.setResidualEquation("resv") + ncontribution_ni.setResidualEquation("resv") + xcontribution_sini.setResidualEquation("resv") + + # Make the FitRecipe and add the FitContributions. + recipe = FitRecipe() + recipe.addContribution(xcontribution_ni) + recipe.addContribution(xcontribution_si) + recipe.addContribution(ncontribution_ni) + recipe.addContribution(xcontribution_sini) + + # Now we vary and constrain Parameters as before. + for par in phase_ni.sgpars: + recipe.addVar(par, name=par.name + "_ni") + delta2_ni = recipe.newVar("delta2_ni", 2.5) + recipe.constrain(xgenerator_ni.delta2, delta2_ni) + recipe.constrain(ngenerator_ni.delta2, delta2_ni) + recipe.constrain(xgenerator_sini_ni.delta2, delta2_ni) + + for par in phase_si.sgpars: + recipe.addVar(par, name=par.name + "_si") + delta2_si = recipe.newVar("delta2_si", 2.5) + recipe.constrain(xgenerator_si.delta2, delta2_si) + recipe.constrain(xgenerator_sini_si.delta2, delta2_si) + + # Now the experimental parameters + recipe.addVar(xgenerator_ni.scale, name="xscale_ni") + recipe.addVar(xgenerator_si.scale, name="xscale_si") + recipe.addVar(ngenerator_ni.scale, name="nscale_ni") + recipe.addVar(xcontribution_sini.scale, 1.0, "xscale_sini") + recipe.newVar("pscale_sini_ni", 0.8) + recipe.constrain(xgenerator_sini_ni.scale, "pscale_sini_ni") + recipe.constrain(xgenerator_sini_si.scale, "1 - pscale_sini_ni") + + # The qdamp parameters are too correlated to vary so we fix them based on + # previous measurements. + xgenerator_ni.qdamp.value = 0.055 + xgenerator_si.qdamp.value = 0.051 + ngenerator_ni.qdamp.value = 0.030 + xgenerator_sini_ni.qdamp.value = 0.052 + xgenerator_sini_si.qdamp.value = 0.052 + + # Give the recipe away so it can be used! + return recipe + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # All this should be pretty familiar by now. + xnickel = recipe.xnickel + xr_ni = xnickel.profile.x + xg_ni = xnickel.profile.y + xgcalc_ni = xnickel.profile.ycalc + xdiffzero_ni = -0.8 * max(xg_ni) * numpy.ones_like(xg_ni) + xdiff_ni = xg_ni - xgcalc_ni + xdiffzero_ni + + xsilicon = recipe.xsilicon + xr_si = xsilicon.profile.x + xg_si = xsilicon.profile.y + xgcalc_si = xsilicon.profile.ycalc + xdiffzero_si = -0.8 * max(xg_si) * numpy.ones_like(xg_si) + xdiff_si = xg_si - xgcalc_si + xdiffzero_si + + nnickel = recipe.nnickel + nr_ni = nnickel.profile.x + ng_ni = nnickel.profile.y + ngcalc_ni = nnickel.profile.ycalc + ndiffzero_ni = -0.8 * max(ng_ni) * numpy.ones_like(ng_ni) + ndiff_ni = ng_ni - ngcalc_ni + ndiffzero_ni + + xsini = recipe.xsini + xr_sini = xsini.profile.x + xg_sini = xsini.profile.y + xgcalc_sini = xsini.profile.ycalc + xdiffzero_sini = -0.8 * max(xg_sini) * numpy.ones_like(xg_sini) + xdiff_sini = xg_sini - xgcalc_sini + xdiffzero_sini + + import pylab + + pylab.subplot(2, 2, 1) + pylab.plot(xr_ni, xg_ni, "bo", label="G(r) x-ray nickel Data") + pylab.plot(xr_ni, xgcalc_ni, "r-", label="G(r) x-ray nickel Fit") + pylab.plot(xr_ni, xdiff_ni, "g-", label="G(r) x-ray nickel diff") + pylab.plot(xr_ni, xdiffzero_ni, "k-") + pylab.xlabel(r"$r (\AA)$") + pylab.ylabel(r"$G (\AA^{-2})$") + pylab.legend(loc=1) + + pylab.subplot(2, 2, 2) + pylab.plot(xr_si, xg_si, "bo", label="G(r) x-ray silicon Data") + pylab.plot(xr_si, xgcalc_si, "r-", label="G(r) x-ray silicon Fit") + pylab.plot(xr_si, xdiff_si, "g-", label="G(r) x-ray silicon diff") + pylab.plot(xr_si, xdiffzero_si, "k-") + pylab.legend(loc=1) + + pylab.subplot(2, 2, 3) + pylab.plot(nr_ni, ng_ni, "bo", label="G(r) neutron nickel Data") + pylab.plot(nr_ni, ngcalc_ni, "r-", label="G(r) neutron nickel Fit") + pylab.plot(nr_ni, ndiff_ni, "g-", label="G(r) neutron nickel diff") + pylab.plot(nr_ni, ndiffzero_ni, "k-") + pylab.legend(loc=1) + + pylab.subplot(2, 2, 4) + pylab.plot(xr_sini, xg_sini, "bo", label="G(r) x-ray sini Data") + pylab.plot(xr_sini, xgcalc_sini, "r-", label="G(r) x-ray sini Fit") + pylab.plot(xr_sini, xdiff_sini, "g-", label="G(r) x-ray sini diff") + pylab.plot(xr_sini, xdiffzero_sini, "k-") + pylab.legend(loc=1) + + pylab.show() + return + + +if __name__ == "__main__": + + # Make the data and the recipe + ciffile_ni = "data/ni.cif" + ciffile_si = "data/si.cif" + xdata_ni = "data/ni-q27r60-xray.gr" + ndata_ni = "data/ni-q27r100-neutron.gr" + xdata_si = "data/si-q27r60-xray.gr" + xdata_sini = "data/si90ni10-q27r60-xray.gr" + + # Make the recipe + recipe = makeRecipe( + ciffile_ni, ciffile_si, xdata_ni, ndata_ni, xdata_si, xdata_sini + ) + + # Optimize + scipyOptimize(recipe) + + # Generate and print the FitResults + res = FitResults(recipe) + res.printResults() + + # Plot! + plotResults(recipe) + +# End of file diff --git a/docs/examples/srfit_ex/crystalpdfobjcryst.py b/docs/examples/srfit_ex/crystalpdfobjcryst.py new file mode 100644 index 0000000..4919543 --- /dev/null +++ b/docs/examples/srfit_ex/crystalpdfobjcryst.py @@ -0,0 +1,129 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of a PDF refinement using pyobjcryst and PDFGenerator. + +This example is similar to crystalpdf.py, except that here we refine a +pyobjcryst crystal object. In this example we use internal constraints +provided by the ObjCrystCrystalParSet structure adapter. +""" + +from crystalpdf import plotResults +from gaussianrecipe import scipyOptimize +from pyobjcryst import loadCrystal + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) +from diffpy.srfit.pdf import PDFGenerator, PDFParser + +###### +# Example Code + + +def makeRecipe(ciffile, datname): + """Create a fitting recipe for crystalline PDF data.""" + + # The Profile + # This will be used to store the observed and calculated PDF profile. + profile = Profile() + + # Load data and add it to the Profile. As before we use a PDFParser. The + # metadata is still passed to the PDFGenerator later on. The interaction + # between the PDFGenerator and the metadata does not depend on type of + # structure being refined. + parser = PDFParser() + parser.parseFile(datname) + profile.loadParsedData(parser) + profile.setCalculationRange(xmax=20) + + # The ProfileGenerator + # This time we use the CreateCrystalFromCIF method of pyobjcryst.crystal to + # create a Crystal object. That object is passed to the PDFGenerator as in + # the previous example. + generator = PDFGenerator("G") + stru = loadCrystal(ciffile) + generator.setStructure(stru) + generator.setQmax(40.0) + + # The FitContribution + contribution = FitContribution("nickel") + contribution.addProfileGenerator(generator) + contribution.setProfile(profile, xname="r") + + # Make the FitRecipe and add the FitContribution. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Configure the fit variables + + # As before, we get a handle to the structure parameter set. In this case, + # it is a ObjCrystCrystalParSet instance that was created when we called + # 'setStructure' above. The ObjCrystCrystalParSet has different Parameters + # and options than the DiffpyStructureParSet used in the last example. See + # its documentation in diffpy.srfit.structure.objcrystparset. + phase = generator.phase + + # Here is where we created space group constraints in the previous example. + # The difference in this example is that the ObjCrystCrystalParSet is aware + # of space groups, and the DiffpyStructureParSet is not. Constraints are + # created internally when "sgpars" attribute is called for. These + # constraints get enforced within the ObjCrystCrystalParSet. Free + # Parameters are stored within the 'sgpars' member of the + # ObjCrystCrystalParSet, which is the same as the object returned from + # 'constrainAsSpaceGroup'. + # + # As before, we have one free lattice parameter ('a'). We can simplify + # things by iterating through all the sgpars. + for par in phase.sgpars: + recipe.addVar(par) + # set the initial thermal factor to a non-zero value + assert hasattr(recipe, "B11_0") + recipe.B11_0 = 0.1 + + # We now select non-structural parameters to refine. + # This controls the scaling of the PDF. + recipe.addVar(generator.scale, 1) + # This is a peak-damping resolution term. + recipe.addVar(generator.qdamp, 0.01) + # This is a vibrational correlation term that sharpens peaks at low-r. + recipe.addVar(generator.delta2, 5) + + # Give the recipe away so it can be used! + return recipe + + +if __name__ == "__main__": + + # Make the data and the recipe + ciffile = "data/si.cif" + data = "data/si-q27r60-xray.gr" + + # Make the recipe + recipe = makeRecipe(ciffile, data) + + # Optimize + scipyOptimize(recipe) + + # Generate and print the FitResults + res = FitResults(recipe) + res.printResults() + + # Plot! + plotResults(recipe) + +# End of file diff --git a/docs/examples/srfit_ex/crystalpdftwodata.py b/docs/examples/srfit_ex/crystalpdftwodata.py new file mode 100644 index 0000000..debefc0 --- /dev/null +++ b/docs/examples/srfit_ex/crystalpdftwodata.py @@ -0,0 +1,196 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of a PDF refinement of two-phase structure. + +This example uses PDFGenerator to refine a single structure two +profiles. This will require setting up two FitContribution, each with +its own PDFGenerator. However, the PDFGenerators will refer to the same +underlying ObjCrystCrystalParSet. +""" + +import numpy +from gaussianrecipe import scipyOptimize +from pyobjcryst import loadCrystal + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) +from diffpy.srfit.pdf import PDFGenerator, PDFParser + +###### +# Example Code + + +def makeRecipe(ciffile, xdatname, ndatname): + """Create a fitting recipe for crystalline PDF data.""" + + # The Profiles + # We need a profile for each data set. This means that we will need two + # FitContributions as well. + xprofile = Profile() + nprofile = Profile() + + # Load data and add it to the proper Profile. + parser = PDFParser() + parser.parseFile(xdatname) + xprofile.loadParsedData(parser) + xprofile.setCalculationRange(xmax=20) + + parser = PDFParser() + parser.parseFile(ndatname) + nprofile.loadParsedData(parser) + nprofile.setCalculationRange(xmax=20) + + # The ProfileGenerators + # We need one of these for the x-ray data. + xgenerator = PDFGenerator("G") + stru = loadCrystal(ciffile) + xgenerator.setStructure(stru) + + # And we need one for the neutron data. We want to refine the same + # structure object in each PDFGenerator. This would suggest that we add the + # same Crystal to each. However, if we do that then we will have two + # Parameters for each Crystal data member (two Parameters for the "a" + # lattice parameter, etc.), held in different ObjCrystCrystalParSets, each + # managed by its own PDFGenerator. Thus, changes made to the Crystal + # through one PDFGenerator will not be known to the other PDFGenerator + # since their ObjCrystCrystalParSets don't know about each other. The + # solution is to share ObjCrystCrystalParSets rather than Crystals. This + # way there is only one Parameter for each Crystal data member. (An + # alternative to this is to constrain each structure Parameter to be varied + # to the same variable. The present approach is easier and less error + # prone.) + # + # Tell the neutron PDFGenerator to use the phase from the x-ray + # PDFGenerator. + ngenerator = PDFGenerator("G") + ngenerator.setPhase(xgenerator.phase) + + # The FitContributions + # We associate the x-ray PDFGenerator and Profile in one FitContribution... + xcontribution = FitContribution("xnickel") + xcontribution.addProfileGenerator(xgenerator) + xcontribution.setProfile(xprofile, xname="r") + # and the neutron objects in another. + ncontribution = FitContribution("nnickel") + ncontribution.addProfileGenerator(ngenerator) + ncontribution.setProfile(nprofile, xname="r") + + # This example is different than the previous ones in that we are composing + # a residual function from other residuals (one for the x-ray contribution + # and one for the neutron contribution). The relative magnitude of these + # residuals effectively determines the influence of each contribution over + # the fit. This is a problem in this case because the x-ray data has + # uncertainty values associated with it (on the order of 1e-4), and the + # chi^2 residual is proportional to 1 / uncertainty**2. The neutron has no + # uncertainty, so it's chi^2 is proportional to 1. Thus, my optimizing + # chi^2 we would give the neutron data practically no weight in the fit. To + # get around this, we will optimize a different metric. + # + # The contribution's residual can be either chi^2, Rw^2, or custom crafted. + # In this case, we should minimize Rw^2 of each contribution so that each + # one can contribute roughly equally to the fit. + xcontribution.setResidualEquation("resv") + ncontribution.setResidualEquation("resv") + + # Make the FitRecipe and add the FitContributions. + recipe = FitRecipe() + recipe.addContribution(xcontribution) + recipe.addContribution(ncontribution) + + # Now we vary and constrain Parameters as before. + recipe.addVar(xgenerator.scale, 1, "xscale") + recipe.addVar(ngenerator.scale, 1, "nscale") + recipe.addVar(xgenerator.qdamp, 0.01, "xqdamp") + recipe.addVar(ngenerator.qdamp, 0.01, "nqdamp") + # delta2 is a non-structual material property. Thus, we constrain together + # delta2 Parameter from each PDFGenerator. + delta2 = recipe.newVar("delta2", 2) + recipe.constrain(xgenerator.delta2, delta2) + recipe.constrain(ngenerator.delta2, delta2) + + # We only need to constrain phase properties once since there is a single + # ObjCrystCrystalParSet for the Crystal. + phase = xgenerator.phase + for par in phase.sgpars: + recipe.addVar(par) + recipe.B11_0 = 0.1 + + # Give the recipe away so it can be used! + return recipe + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # All this should be pretty familiar by now. + xr = recipe.xnickel.profile.x + xg = recipe.xnickel.profile.y + xgcalc = recipe.xnickel.profile.ycalc + xdiffzero = -0.8 * max(xg) * numpy.ones_like(xg) + xdiff = xg - xgcalc + xdiffzero + + nr = recipe.nnickel.profile.x + ng = recipe.nnickel.profile.y + ngcalc = recipe.nnickel.profile.ycalc + ndiffzero = -0.8 * max(ng) * numpy.ones_like(ng) + ndiff = ng - ngcalc + ndiffzero + + import pylab + + pylab.subplot(2, 1, 1) + pylab.plot(xr, xg, "bo", label="G(r) x-ray Data") + pylab.plot(xr, xgcalc, "r-", label="G(r) x-ray Fit") + pylab.plot(xr, xdiff, "g-", label="G(r) x-ray diff") + pylab.plot(xr, xdiffzero, "k-") + pylab.legend(loc=1) + + pylab.subplot(2, 1, 2) + pylab.plot(nr, ng, "bo", label="G(r) neutron Data") + pylab.plot(nr, ngcalc, "r-", label="G(r) neutron Fit") + pylab.plot(nr, ndiff, "g-", label="G(r) neutron diff") + pylab.plot(nr, ndiffzero, "k-") + pylab.xlabel(r"$r (\AA)$") + pylab.ylabel(r"$G (\AA^{-2})$") + pylab.legend(loc=1) + + pylab.show() + return + + +if __name__ == "__main__": + + # Make the data and the recipe + ciffile = "data/ni.cif" + xdata = "data/ni-q27r60nodg-xray.gr" + ndata = "data/ni-q27r100-neutron.gr" + + # Make the recipe + recipe = makeRecipe(ciffile, xdata, ndata) + + # Optimize + scipyOptimize(recipe) + + # Generate and print the FitResults + res = FitResults(recipe) + res.printResults() + + # Plot! + plotResults(recipe) + +# End of file diff --git a/docs/examples/srfit_ex/crystalpdftwophase.py b/docs/examples/srfit_ex/crystalpdftwophase.py new file mode 100644 index 0000000..98a8790 --- /dev/null +++ b/docs/examples/srfit_ex/crystalpdftwophase.py @@ -0,0 +1,187 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of a PDF refinement of two-phase structure. + +Like the ones before, this example uses PDFGenerator to refine a +structure to PDF data. However, for a multi-phase structure one must use +multiple PDFGenerators. This example refines a physical mixture of +nickel and silicon to find the structures and phase fractions. +""" + +import numpy +from gaussianrecipe import scipyOptimize +from pyobjcryst import loadCrystal + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) +from diffpy.srfit.pdf import PDFGenerator, PDFParser + +###### +# Example Code + + +def makeRecipe(niciffile, siciffile, datname): + """Create a fitting recipe for crystalline PDF data.""" + + # The Profile + profile = Profile() + + # Load data and add it to the profile + parser = PDFParser() + parser.parseFile(datname) + profile.loadParsedData(parser) + profile.setCalculationRange(xmax=20) + + # The ProfileGenerator + # In order to fit two phases simultaneously, we must use two PDFGenerators. + # PDFGenerator is designed to take care of as little information as it + # must. (Don't do too much, and do it well.) A PDFGenerator can generate + # the signal from only a single phase at a time. So, we will create one + # PDFGenerator for each phase and compose them within the same + # FitContribution. Note that both generators will be associated with the + # same Profile within the FitContribution, so they will both be + # automatically configured according to the metadata. + # + # The generator for the nickel phase. We call it "G_ni" and will use this + # name later when we set the fitting equation in the FitContribution. + generator_ni = PDFGenerator("G_ni") + stru = loadCrystal(niciffile) + generator_ni.setStructure(stru) + # The generator for the silicon phase. We call it "G_si". + generator_si = PDFGenerator("G_si") + stru = loadCrystal(siciffile) + generator_si.setStructure(stru) + + # The FitContribution + # Add both generators to the FitContribution. Add the Profile. This will + # send the metadata to the generators. + contribution = FitContribution("nisi") + contribution.addProfileGenerator(generator_ni) + contribution.addProfileGenerator(generator_si) + contribution.setProfile(profile, xname="r") + + # Write the fitting equation. We want to sum the PDFs from each phase and + # multiply it by a scaling factor. We also want a certain phase scaling + # relationship between the PDFs which we will enforce with constraints in + # the FitRecipe. + contribution.setEquation("scale * (G_ni + G_si)") + + # Make the FitRecipe and add the FitContribution. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Configure the fit variables + # Start by configuring the scale factor and resolution factors. + # We want the sum of the phase scale factors to be 1. + recipe.newVar("scale_ni", 0.1) + recipe.constrain(generator_ni.scale, "scale_ni") + recipe.constrain(generator_si.scale, "1 - scale_ni") + # We also want the resolution factor to be the same on each. + recipe.newVar("qdamp", 0.03) + recipe.constrain(generator_ni.qdamp, "qdamp") + recipe.constrain(generator_si.qdamp, "qdamp") + + # Vary the global scale as well. + recipe.addVar(contribution.scale, 1) + + # Now we can configure the structural parameters. Since we're using + # ObjCrystCrystalParSets, the space group constraints are automatically + # applied to each phase. We must selectively vary the free parameters. + # + # First the nickel parameters + phase_ni = generator_ni.phase + for par in phase_ni.sgpars: + recipe.addVar(par, name=par.name + "_ni") + recipe.addVar(generator_ni.delta2, name="delta2_ni") + # Next the silicon parameters + phase_si = generator_si.phase + for par in phase_si.sgpars: + recipe.addVar(par, name=par.name + "_si") + recipe.addVar(generator_si.delta2, name="delta2_si") + + # We have prior information from the earlier examples so we'll use it here + # in the form of restraints. + # + # The nickel lattice parameter was measured to be 3.527. The uncertainty + # values are invalid for that measurement, since the data from which it is + # derived has no uncertainty. Thus, we will tell the recipe to scale the + # residual, which means that it will be weighted as much as the average + # data point during the fit. + recipe.restrain("a_ni", lb=3.527, ub=3.527, scaled=True) + # Now we do the same with the delta2 and Biso parameters (remember that + # Biso = 8*pi**2*Uiso) + recipe.restrain("delta2_ni", lb=2.22, ub=2.22, scaled=True) + recipe.restrain("Biso_0_ni", lb=0.454, ub=0.454, scaled=True) + # + # We can do the same with the silicon values. We haven't done a thorough + # job of measuring the uncertainties in the results, so we'll scale these + # as well. + recipe.restrain("a_si", lb=5.430, ub=5.430, scaled=True) + recipe.restrain("delta2_si", lb=3.54, ub=3.54, scaled=True) + recipe.restrain("Biso_0_si", lb=0.645, ub=0.645, scaled=True) + + # Give the recipe away so it can be used! + return recipe + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # All this should be pretty familiar by now. + r = recipe.nisi.profile.x + g = recipe.nisi.profile.y + gcalc = recipe.nisi.profile.ycalc + diffzero = -0.8 * max(g) * numpy.ones_like(g) + diff = g - gcalc + diffzero + + import pylab + + pylab.plot(r, g, "bo", label="G(r) Data") + pylab.plot(r, gcalc, "r-", label="G(r) Fit") + pylab.plot(r, diff, "g-", label="G(r) diff") + pylab.plot(r, diffzero, "k-") + pylab.xlabel(r"$r (\AA)$") + pylab.ylabel(r"$G (\AA^{-2})$") + pylab.legend(loc=1) + + pylab.show() + return + + +if __name__ == "__main__": + + # Make the data and the recipe + niciffile = "data/ni.cif" + siciffile = "data/si.cif" + data = "data/si90ni10-q27r60-xray.gr" + + # Make the recipe + recipe = makeRecipe(niciffile, siciffile, data) + + # Optimize + scipyOptimize(recipe) + + # Generate and print the FitResults + res = FitResults(recipe) + res.printResults() + + # Plot! + plotResults(recipe) + +# End of file diff --git a/docs/examples/srfit_ex/data/C60.gr b/docs/examples/srfit_ex/data/C60.gr new file mode 100644 index 0000000..d015b9d --- /dev/null +++ b/docs/examples/srfit_ex/data/C60.gr @@ -0,0 +1,1999 @@ + 1.000000e-002 1.894260e+004 8.536912e+000 + 2.000000e-002 3.772272e+004 1.675464e+001 + 3.000000e-002 5.617755e+004 2.434705e+001 + 4.000000e-002 7.414385e+004 3.103361e+001 + 5.000000e-002 9.145791e+004 3.657098e+001 + 6.000000e-002 1.079561e+005 4.076327e+001 + 7.000000e-002 1.234755e+005 4.347065e+001 + 8.000000e-002 1.378555e+005 4.461615e+001 + 9.000000e-002 1.509396e+005 4.419097e+001 + 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0.00000000 0.00000000 +C 0.48775063 0.50000000 0.46648489 1.0000 + 0.00000000 0.00000000 0.00000000 0.0000 + 0.00000000 0.00000000 0.00000000 + 0.00000000 0.00000000 0.00000000 + 0.00000000 0.00000000 0.00000000 + 0.00000000 0.00000000 0.00000000 diff --git a/docs/examples/srfit_ex/data/CdS.cif b/docs/examples/srfit_ex/data/CdS.cif new file mode 100644 index 0000000..34fa965 --- /dev/null +++ b/docs/examples/srfit_ex/data/CdS.cif @@ -0,0 +1,69 @@ +data_1011054 +_chemical_name_systematic 'Cadmium sulfide - $-alpha' +_chemical_name_mineral 'Greenockite' +_chemical_compound_source 'synthetic' +_chemical_formula_structural 'Cd S' +_chemical_formula_sum 'Cd S' +_publ_section_title +; +Ueber die Kristallstruktur des $-alpha- und $-beta Cd S, sowie des +Wurtzits. +; +loop_ +_publ_author_name + 'Ulrich, F' + 'Zachariasen, W' +_journal_name_full +; +Zeitschrift fuer Kristallographie, Kristallgeometrie, Kristallphysik, +Kristallchemie (-144,1977) +; +_journal_coden_ASTM ZEKGAX +_journal_volume 62 +_journal_year 1925 +_journal_page_first 260 +_journal_page_last 273 +_cell_length_a 4.15 +_cell_length_b 4.15 +_cell_length_c 6.737 +_cell_angle_alpha 90 +_cell_angle_beta 90 +_cell_angle_gamma 120 +_cell_volume 100.5 +_cell_formula_units_Z 2 +_exptl_crystal_density_meas 4.82 +_symmetry_space_group_name_H-M 'P 63 m c' +_symmetry_Int_Tables_number 186 +_symmetry_cell_setting hexagonal +loop_ +_symmetry_equiv_pos_as_xyz + 'x,y,z' + '-y,x-y,z' + 'y-x,-x,z' + '-y,-x,z' + 'y-x,y,z' + 'x,x-y,z' + '-x,-y,1/2+z' + 'y,y-x,1/2+z' + 'x-y,x,1/2+z' + 'y,x,1/2+z' + 'x-y,-y,1/2+z' + '-x,y-x,1/2+z' +loop_ +_atom_type_symbol +_atom_type_oxidation_number + Cd2+ 2.000 + S2- -2.000 +loop_ +_atom_site_label +_atom_site_type_symbol +_atom_site_symmetry_multiplicity +_atom_site_Wyckoff_symbol +_atom_site_fract_x +_atom_site_fract_y +_atom_site_fract_z +_atom_site_occupancy +_atom_site_attached_hydrogens +_atom_site_calc_flag + Cd1 Cd 2 b 0.33333 0.66667 0. 1. 0 d + S1 S 2 b 0.33333 0.66667 0.375 1. 0 d 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The original data for this entry +# were provided the American Mineralogist Crystal Structure Database, +# http://rruff.geo.arizona.edu/AMS/amcsd.php +# +# The file may be used within the scientific community so long as +# proper attribution is given to the journal article from which the +# data were obtained. +# +data_9008878 +loop_ +_publ_author_name +'Wyckoff, R. W. G.' +_publ_section_title +; + Second edition. Interscience Publishers, New York, New York + Note: wurtzite structure +; +_journal_name_full 'Crystal Structures' +_journal_page_first 85 +_journal_page_last 237 +_journal_volume 1 +_journal_year 1963 +_chemical_formula_sum 'S Zn' +_chemical_name_mineral Wurtzite-2H +_space_group_IT_number 186 +_symmetry_space_group_name_Hall 'P 6c -2c' +_symmetry_space_group_name_H-M 'P 63 m c' +_cell_angle_alpha 90 +_cell_angle_beta 90 +_cell_angle_gamma 120 +_cell_length_a 3.811 +_cell_length_b 3.811 +_cell_length_c 6.234 +_cell_volume 78.411 +_exptl_crystal_density_diffrn 4.128 +_cod_original_formula_sum 'Zn S' +_cod_database_code 9008878 +loop_ +_symmetry_equiv_pos_as_xyz +x,y,z +-x,-x+y,1/2+z +x-y,x,1/2+z +-y,-x,z +-y,x-y,z +x-y,-y,1/2+z +-x,-y,1/2+z +x,x-y,z +-x+y,-x,z +y,x,1/2+z +y,-x+y,1/2+z +-x+y,y,z +loop_ +_atom_site_label +_atom_site_fract_x +_atom_site_fract_y +_atom_site_fract_z +Zn 0.33333 0.66667 0.00000 +S 0.33333 0.66667 0.38500 diff --git a/docs/examples/srfit_ex/data/gaussian.dat 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smoothParam=32 32 0 backKillThresh=-1.0 +# in beam: radius=0.45325 height=4.5 +# temp=300 runTitle=Run 3315: Ni commercial, RT_stick +# +# ##### Vanadium runCorrection=T +# run=npdf_03000 background=npdf_03001 +# smooth=2 smoothParam=32 32 0 vanKillThresh=-1.0 vBackKillThresh=-1.0 +# in beam: radius=0.47625 height=4.5 +# +# ##### Container runCorrection=T +# run=npdf_03002 background=npdf_03001 +# smooth=2 smoothParam=32 32 0 cBackKillThresh=-1.0 +# wallThick=0.023 atomDensity=0.072110 +# atomic information: scattCS=5.100 absorpCS=5.080 +# +# ##### Sample Material numElements=1 NormLaue=0.00000 +# Element relAtomNum atomMass atomCoherCS atomIncoherCS atomAbsorpCS +# Ni 1.0000 58.693 13.3000 5.2000 4.49000 +# density=7.0 effDensity=2.8777 +# +# ##### Banks=4 deltaQ=0.01 matchRef=0 matchScal=T matchOffset=T +# bank angle blendQmin blendQmax (0.0 means no info) +# 1 46.6 0.87 21.63 +# 2 90.0 1.51 37.66 +# 3 119.0 1.84 45.96 +# 4 148.0 2.05 51.25 +# +# ##### Program Specific Information +# 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savefilenamebase=ni300mesh_300k_nor_1-5 +iqfilesurfix=.iq sqfilesurfix=.sq fqfilesurfix=.fq grfilesurfix=.gr + +##### DataFileFormat +datatype=1 (0:SPEC, 1:CHI, 2:nxm column, 3:unknown) +num_skiplines=3 comment_id=# delimiter= +### SPEC Format scan_id=#S scan_delimiter= +columnname_id=#L columnname_delimiter= +data_id= data_delimiter= +### CHI Format +### nxm column Format +### End of file format + +##### Data&Background +samfile=ni300mesh_300k_nor_1-5.chi num_sams=1 +sambkgfile=kapton_bgrd_300k_nor_2-3.chi num_sambkgs=1 +confile= num_cons=1 +conbkgfile= num_conbkgs=1 +det# used xcol detcol deterrcol xmin xmax add_det mul_det add_bkg mul_bkg add_con mul_con add_conbkg mul_conbkg + 0 1 0 1 3 0.600000 35.0000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 + +##### Experiment_Setup +title=PDF analysis +user=me +facility=In house +temperature=300.000 containermut=0.000500000 filtermut=0.0200000 +## X-Ray radiationtype=3 + (0: Ag K_alpha, 1:Cu K_alpha, 2:Mo K_alpha, 3:Customize) +lambda=0.142773 energy=86.8406 polartype=0 polardegree=1.00000 +## MonoChromator crystaltype=0 (0:Perfect, 1:Mosaic, 2:None) +position=0 (0:Primary beam, 1:Diffracted beam) +dspacetype=0 (0:Si{111}, 1:Ge{111}, 2:Customize) dspacing=3.13200 + +##### Sample_Setup information num_atoms=1 +#L symbol valence fractions z user_f1 user_f2 user_macoef + Ni 0.00 1.000000 28 0.000000 0.000000 0.001000 +geometry=2 mut=0.50000000 numberdensity=0.00600000 +thickness=2.00000 packingFraction=0.500000 theory_mut=0.0350063 + +##### GetIQ_Setup +xformat=1 +smoothcorr_isa=0 selfnormalize_isa=0 +#L par_name sample sample_bkg container container_bkg +smooth_degree 2 2 2 2 +smooth_width 6 6 6 6 +selfnormalize 0 0 0 0 +filtercorr_isa=0 samfiltercorr_isa=0 sambkgfiltercorr_isa=0 +confiltercorr_isa=0 conbkgfiltercorr_isa=0 +scatveffcorr_isa=1 samconveffcorr_isa=1 sambkgveffcorr_isa=0 +conbkgveffcorr_isa=0 +nonegative_isa=1 negativevalue=-1.00000 + +##### Calibration_Data +## Detection efficiency energy dependence detedepxaxis=0 +detedepfunctype=0 detedep_elastic=1.00000 detedep_fluores=1.80000 +detedep_quadra=0.000000 detedep_spline=0.000000 detedep_file= +## Detector transmission energy dependence dettcoefxaxis=0 +dettcoeffunctype=0 dettcoef_elastic=0.950000 dettcoef_fluores=0.600000 +dettcoef_quadra=0.000000 dettcoef_spline=0.000000 dettcoef_file= + +##### IQ_Simulation +### Elastic used_isa=1 mymethod=1 +do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 +do_polarization=1 do_oblincident=0 do_energydep=0 +do_breitdirac=0 breitdiracexpo=2.00000 +do_rulandwin=0 rulandwinwidth=0.00100000 +do_useredit=0 add_user=0.000000 mul_user=1.00000 +### Compton used_isa=1 mymethod=1 +do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 +do_polarization=1 do_oblincident=0 do_energydep=0 +do_breitdirac=0 breitdiracexpo=2.00000 +do_rulandwin=0 rulandwinwidth=0.00100000 +do_useredit=0 add_user=0.000000 mul_user=1.00000 +### Fluores used_isa=1 mymethod=1 +do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 +do_polarization=1 do_oblincident=0 do_energydep=0 +do_breitdirac=0 breitdiracexpo=2.00000 +do_rulandwin=0 rulandwinwidth=0.00100000 +do_useredit=0 add_user=0.000000 mul_user=1.00000 + +##### Correction_Setup corrmethod=0 +oblincident_isa=1 dettranscoef=0.980000 samfluore_isa=1 +samfluoretype=0 samfluorescale=0.15000000 +multiscat_isa=1 xraypolar_isa=1 samabsorp_isa=1 +highqscale_isa=1 highqratio=0.600000 scaleconst=0.016825338 +scaleconst_theory=0.016825338 +comptonscat_isa=1 rulandwin_isa=0 rulandintewidth=0.0100000 +comptonmethod=0 breitdirac_isa=1 breitdiracexponent=3 +detefficiency_isa=1 detefficiencytype=2 (0-1: linear, 2-3: quadratic) +detefficiency_a=0.10293460 detefficiency_b=-0.0093982075 +lauediffuse_isa=1 +weight_isa=1 weighttype=0 (0: ^2, 1: , 2: Data Smoothed) +weightsmoothrmin=3.00000 weightsmoothwidth=100 weightsmoothcycles=600 +editsq_isa=0 editsqtype=0 add_sq=0.000000 mul_sq=1.00000 +editsqsmoothrmin=3.00000 editsqsmoothwidth=100 editsqsmoothcycles=600 +smoothdata_isa=0 smoothfunctype=0 smoothqmin=12.0000 smoothboxwidth=9 +interpolateqmin_isa=0 qmininterpolationtype=0 +dampfq_isa=0 dampfqtype=0 dampfqwidth=23.0000 + +##### SqGr_Optimization Setup +ftmethod=0 +## S(q) qmin=0.010000 qmax=27.000000 qgrid=0.000000 +## G(r) rmin=0.010000 rmax=60.000000 rgrid=0.010000 +## SqOptimization sqoptfunction=1 +optqmin=20.0000 optqmax=40.0000 optqgrid=0.000000 +optrmin=0.000000 optrmax=2.20000 optrgrid=0.0200000 +maxiter=20 relstep=0.000000 weighttype=0 weightfunc=0 +fitbkgmult_isa=0 fitsampmut_isa=1 fitpolariz_isa=1 +fitoblique_isa=0 fitfluores_isa=0 +fitrulandw_isa=0 fitenergya_isa=1 fitenergyb_isa=1 +fitsimurulandw_isa=1 fitDetEdepfluores_isa=0 fitDetEdepquadra_isa=0 +fitDetEdepspline_isa=0 fitDetTCoefElastic_isa=0 fitDetTCoefFluores_isa=0 +fitDetTcoefquadra_isa=0 fitDetTcoefspline_isa=0 + +##### Save&Plot Settings +datatype=GrData iqcorrtype=Int iqsimutype=SimuIq +sqcorrtype=Oblin sqtofqtype=DampFq +gropttype=OptFq miscdatatype=AtomASF +##### start data +#F ni300mesh_300k_nor_1-5.gr +#D Mon Apr 21 21:05:49 2008 +#C +#S 1 G(r) +#D +#L r(A) G(r) d_r d_Gr + 1.000000e-002 6.873431e-002 -7.539822e-004 2.439251e-004 + 2.000000e-002 1.419026e-001 -1.507964e-003 4.744725e-004 + 3.000000e-002 2.235165e-001 -2.261947e-003 6.791041e-004 + 4.000000e-002 3.167721e-001 -3.015929e-003 8.469137e-004 + 5.000000e-002 4.237112e-001 -3.769911e-003 9.693333e-004 + 6.000000e-002 5.449630e-001 -4.523893e-003 1.040720e-003 + 7.000000e-002 6.795808e-001 -5.277876e-003 1.058818e-003 + 8.000000e-002 8.249905e-001 -6.031858e-003 1.025121e-003 + 9.000000e-002 9.770511e-001 -6.785840e-003 9.452417e-004 + 1.000000e-001 1.130230e+000 -7.539822e-003 8.295807e-004 + 1.100000e-001 1.277879e+000 -8.293804e-003 6.949769e-004 + 1.200000e-001 1.412600e+000 -9.047787e-003 5.685470e-004 + 1.300000e-001 1.526673e+000 -9.801769e-003 4.915010e-004 + 1.400000e-001 1.612530e+000 -1.055575e-002 5.009222e-004 + 1.500000e-001 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5.998000e+001 5.219086e-002 -4.522385e+000 7.794303e-004 + 5.999000e+001 5.424471e-002 -4.523139e+000 7.797623e-004 diff --git a/docs/examples/srfit_ex/data/ni-q27r60nodg-xray.gr b/docs/examples/srfit_ex/data/ni-q27r60nodg-xray.gr new file mode 100644 index 0000000..5bf8d53 --- /dev/null +++ b/docs/examples/srfit_ex/data/ni-q27r60nodg-xray.gr @@ -0,0 +1,6133 @@ +History written: Mon Apr 21 20:48:28 2008 +Produced by +####### Get_XPDF ####### + +##### General_Setting +title=X-ray PDF +workingdirectory=e:\Ahmad\MUCAT0804\standards\pdfgetx2 +sourcedir=C:\Program Files\PDFgetX2\ +logfile=.pdfgetx2.log +quiet=0 debug=0 autosave_isa=1 savefilenamebase=ni300mesh_300k_nor_1-5 +iqfilesurfix=.iq sqfilesurfix=.sq fqfilesurfix=.fq grfilesurfix=.gr + +##### DataFileFormat +datatype=1 (0:SPEC, 1:CHI, 2:nxm column, 3:unknown) +num_skiplines=3 comment_id=# delimiter= +### SPEC Format scan_id=#S scan_delimiter= +columnname_id=#L columnname_delimiter= +data_id= data_delimiter= +### CHI Format +### nxm column Format +### End of file format + +##### Data&Background +samfile=ni300mesh_300k_nor_1-5.chi num_sams=1 +sambkgfile=kapton_bgrd_300k_nor_2-3.chi num_sambkgs=1 +confile= num_cons=1 +conbkgfile= num_conbkgs=1 +det# used xcol detcol deterrcol xmin xmax add_det mul_det add_bkg mul_bkg add_con mul_con add_conbkg mul_conbkg + 0 1 0 1 3 0.600000 35.0000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 + +##### Experiment_Setup +title=PDF analysis +user=me +facility=In house +temperature=300.000 containermut=0.000500000 filtermut=0.0200000 +## X-Ray radiationtype=3 + (0: Ag K_alpha, 1:Cu K_alpha, 2:Mo K_alpha, 3:Customize) +lambda=0.142773 energy=86.8406 polartype=0 polardegree=1.00000 +## MonoChromator crystaltype=0 (0:Perfect, 1:Mosaic, 2:None) +position=0 (0:Primary beam, 1:Diffracted beam) +dspacetype=0 (0:Si{111}, 1:Ge{111}, 2:Customize) dspacing=3.13200 + +##### Sample_Setup information num_atoms=1 +#L symbol valence fractions z user_f1 user_f2 user_macoef + Ni 0.00 1.000000 28 0.000000 0.000000 0.001000 +geometry=2 mut=0.50000000 numberdensity=0.00600000 +thickness=2.00000 packingFraction=0.500000 theory_mut=0.0350063 + +##### GetIQ_Setup +xformat=1 +smoothcorr_isa=0 selfnormalize_isa=0 +#L par_name sample sample_bkg container container_bkg +smooth_degree 2 2 2 2 +smooth_width 6 6 6 6 +selfnormalize 0 0 0 0 +filtercorr_isa=0 samfiltercorr_isa=0 sambkgfiltercorr_isa=0 +confiltercorr_isa=0 conbkgfiltercorr_isa=0 +scatveffcorr_isa=1 samconveffcorr_isa=1 sambkgveffcorr_isa=0 +conbkgveffcorr_isa=0 +nonegative_isa=1 negativevalue=-1.00000 + +##### Calibration_Data +## Detection efficiency energy dependence detedepxaxis=0 +detedepfunctype=0 detedep_elastic=1.00000 detedep_fluores=1.80000 +detedep_quadra=0.000000 detedep_spline=0.000000 detedep_file= +## Detector transmission energy dependence dettcoefxaxis=0 +dettcoeffunctype=0 dettcoef_elastic=0.950000 dettcoef_fluores=0.600000 +dettcoef_quadra=0.000000 dettcoef_spline=0.000000 dettcoef_file= + +##### IQ_Simulation +### Elastic used_isa=1 mymethod=1 +do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 +do_polarization=1 do_oblincident=0 do_energydep=0 +do_breitdirac=0 breitdiracexpo=2.00000 +do_rulandwin=0 rulandwinwidth=0.00100000 +do_useredit=0 add_user=0.000000 mul_user=1.00000 +### Compton used_isa=1 mymethod=1 +do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 +do_polarization=1 do_oblincident=0 do_energydep=0 +do_breitdirac=0 breitdiracexpo=2.00000 +do_rulandwin=0 rulandwinwidth=0.00100000 +do_useredit=0 add_user=0.000000 mul_user=1.00000 +### Fluores used_isa=1 mymethod=1 +do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 +do_polarization=1 do_oblincident=0 do_energydep=0 +do_breitdirac=0 breitdiracexpo=2.00000 +do_rulandwin=0 rulandwinwidth=0.00100000 +do_useredit=0 add_user=0.000000 mul_user=1.00000 + +##### Correction_Setup corrmethod=0 +oblincident_isa=1 dettranscoef=0.980000 samfluore_isa=1 +samfluoretype=0 samfluorescale=0.15000000 +multiscat_isa=1 xraypolar_isa=1 samabsorp_isa=1 +highqscale_isa=1 highqratio=0.600000 scaleconst=0.016825338 +scaleconst_theory=0.016825338 +comptonscat_isa=1 rulandwin_isa=0 rulandintewidth=0.0100000 +comptonmethod=0 breitdirac_isa=1 breitdiracexponent=3 +detefficiency_isa=1 detefficiencytype=2 (0-1: linear, 2-3: quadratic) +detefficiency_a=0.10293460 detefficiency_b=-0.0093982075 +lauediffuse_isa=1 +weight_isa=1 weighttype=0 (0: ^2, 1: , 2: Data Smoothed) +weightsmoothrmin=3.00000 weightsmoothwidth=100 weightsmoothcycles=600 +editsq_isa=0 editsqtype=0 add_sq=0.000000 mul_sq=1.00000 +editsqsmoothrmin=3.00000 editsqsmoothwidth=100 editsqsmoothcycles=600 +smoothdata_isa=0 smoothfunctype=0 smoothqmin=12.0000 smoothboxwidth=9 +interpolateqmin_isa=0 qmininterpolationtype=0 +dampfq_isa=0 dampfqtype=0 dampfqwidth=23.0000 + +##### SqGr_Optimization Setup +ftmethod=0 +## S(q) qmin=0.010000 qmax=27.000000 qgrid=0.000000 +## G(r) rmin=0.010000 rmax=60.000000 rgrid=0.010000 +## SqOptimization sqoptfunction=1 +optqmin=20.0000 optqmax=40.0000 optqgrid=0.000000 +optrmin=0.000000 optrmax=2.20000 optrgrid=0.0200000 +maxiter=20 relstep=0.000000 weighttype=0 weightfunc=0 +fitbkgmult_isa=0 fitsampmut_isa=1 fitpolariz_isa=1 +fitoblique_isa=0 fitfluores_isa=0 +fitrulandw_isa=0 fitenergya_isa=1 fitenergyb_isa=1 +fitsimurulandw_isa=1 fitDetEdepfluores_isa=0 fitDetEdepquadra_isa=0 +fitDetEdepspline_isa=0 fitDetTCoefElastic_isa=0 fitDetTCoefFluores_isa=0 +fitDetTcoefquadra_isa=0 fitDetTcoefspline_isa=0 + +##### Save&Plot Settings +datatype=GrData iqcorrtype=Int iqsimutype=SimuIq +sqcorrtype=Oblin sqtofqtype=DampFq +gropttype=OptFq miscdatatype=AtomASF +##### start data +#F ni300mesh_300k_nor_1-5.gr +#D Mon Apr 21 21:05:49 2008 +#C +#S 1 G(r) +#D +#L r(A) G(r) + 1.000000e-002 6.873431e-002 + 2.000000e-002 1.419026e-001 + 3.000000e-002 2.235165e-001 + 4.000000e-002 3.167721e-001 + 5.000000e-002 4.237112e-001 + 6.000000e-002 5.449630e-001 + 7.000000e-002 6.795808e-001 + 8.000000e-002 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5.999000e+001 5.424471e-002 diff --git a/docs/examples/srfit_ex/data/ni.cif b/docs/examples/srfit_ex/data/ni.cif new file mode 100644 index 0000000..c455635 --- /dev/null +++ b/docs/examples/srfit_ex/data/ni.cif @@ -0,0 +1,236 @@ +#------------------------------------------------------------------------------ +#$Date: 2008-03-10 08:25:41 +0000 (Mon, 10 Mar 2008) $ +#$Revision: 255 $ +#$URL: svn://cod.ibt.lt/cod/cif/9/9008476.cif $ +#------------------------------------------------------------------------------ +# +# This file is available in the Crystallography Open Database (COD), +# http://www.crystallography.net/ +# +# All data on this site have been placed in the public domain by the +# contributors. +# +data_9008476 +loop_ +_publ_author_name +'Wyckoff R W G' +_publ_section_title +; + Second edition. Interscience Publishers, New York, New York + Cubic closest packed, ccp, structure +; +_journal_name_full 'Crystal Structures' +_journal_page_first 7 +_journal_page_last 83 +_journal_volume 1 +_journal_year 1963 +_chemical_formula_sum Ni +_chemical_name_mineral Nickel +_symmetry_space_group_name_H-M 'F m 3 m' +_cell_angle_alpha 90 +_cell_angle_beta 90 +_cell_angle_gamma 90 +_cell_length_a 3.52387 +_cell_length_b 3.52387 +_cell_length_c 3.52387 +_cell_volume 43.758 +loop_ +_symmetry_equiv_pos_as_xyz +x,y,z +x,1/2+y,1/2+z +1/2+x,y,1/2+z +1/2+x,1/2+y,z +z,-x,y +z,1/2-x,1/2+y +1/2+z,-x,1/2+y +1/2+z,1/2-x,y +-y,z,-x +-y,1/2+z,1/2-x +1/2-y,z,1/2-x +1/2-y,1/2+z,-x +x,-y,z +x,1/2-y,1/2+z +1/2+x,-y,1/2+z +1/2+x,1/2-y,z +-z,x,-y +-z,1/2+x,1/2-y +1/2-z,x,1/2-y +1/2-z,1/2+x,-y +y,-z,x +y,1/2-z,1/2+x +1/2+y,-z,1/2+x +1/2+y,1/2-z,x +-x,y,-z +-x,1/2+y,1/2-z +1/2-x,y,1/2-z +1/2-x,1/2+y,-z +x,-z,-y +x,1/2-z,1/2-y +1/2+x,-z,1/2-y +1/2+x,1/2-z,-y +-z,y,x +-z,1/2+y,1/2+x +1/2-z,y,1/2+x +1/2-z,1/2+y,x 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0000000..876b2c8 --- /dev/null +++ b/docs/examples/srfit_ex/data/pb.cif @@ -0,0 +1,240 @@ +#------------------------------------------------------------------------------ +#$Date: 2010-01-30 13:59:17 +0000 (Sat, 30 Jan 2010) $ +#$Revision: 966 $ +#$URL: svn://cod.ibt.lt/cod/cif/9/9008477.cif $ +#------------------------------------------------------------------------------ +# +# This file is available in the Crystallography Open Database (COD), +# http://www.crystallography.net/ +# +# All data on this site have been placed in the public domain by the +# contributors. +# +data_9008477 +_space_group_IT_number 225 +_symmetry_space_group_name_Hall '-F 4 2 3' +_symmetry_space_group_name_H-M 'F m -3 m' +_[local]_cod_cif_authors_sg_H-M 'F m 3 m' +loop_ +_publ_author_name +'Wyckoff R W G' +_publ_section_title +; + Second edition. Interscience Publishers, New York, New York + Cubic closest packed, ccp, structure +; +_journal_name_full 'Crystal Structures' +_journal_page_first 7 +_journal_page_last 83 +_journal_volume 1 +_journal_year 1963 +_chemical_formula_sum Pb +_chemical_name_mineral Lead +_cell_angle_alpha 90 +_cell_angle_beta 90 +_cell_angle_gamma 90 +_cell_length_a 4.9505 +_cell_length_b 4.9505 +_cell_length_c 4.9505 +_cell_volume 121.324 +loop_ +_symmetry_equiv_pos_as_xyz +x,y,z +x,1/2+y,1/2+z +1/2+x,y,1/2+z +1/2+x,1/2+y,z +z,-x,y +z,1/2-x,1/2+y +1/2+z,-x,1/2+y +1/2+z,1/2-x,y +-y,z,-x +-y,1/2+z,1/2-x +1/2-y,z,1/2-x +1/2-y,1/2+z,-x +x,-y,z +x,1/2-y,1/2+z +1/2+x,-y,1/2+z +1/2+x,1/2-y,z +-z,x,-y +-z,1/2+x,1/2-y +1/2-z,x,1/2-y +1/2-z,1/2+x,-y +y,-z,x +y,1/2-z,1/2+x +1/2+y,-z,1/2+x +1/2+y,1/2-z,x +-x,y,-z +-x,1/2+y,1/2-z +1/2-x,y,1/2-z +1/2-x,1/2+y,-z +x,-z,-y +x,1/2-z,1/2-y +1/2+x,-z,1/2-y +1/2+x,1/2-z,-y +-z,y,x +-z,1/2+y,1/2+x +1/2-z,y,1/2+x +1/2-z,1/2+y,x +y,-x,-z +y,1/2-x,1/2-z +1/2+y,-x,1/2-z 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+1,6133 @@ +History written: Mon Apr 21 20:48:28 2008 +Produced by +####### Get_XPDF ####### + +##### General_Setting +title=X-ray PDF +workingdirectory=e:\Ahmad\MUCAT0804\standards\pdfgetx2 +sourcedir=C:\Program Files\PDFgetX2\ +logfile=.pdfgetx2.log +quiet=0 debug=0 autosave_isa=1 savefilenamebase=si325_mesh_300k_nor_4-8 +iqfilesurfix=.iq sqfilesurfix=.sq fqfilesurfix=.fq grfilesurfix=.gr + +##### DataFileFormat +datatype=1 (0:SPEC, 1:CHI, 2:nxm column, 3:unknown) +num_skiplines=3 comment_id=# delimiter= +### SPEC Format scan_id=#S scan_delimiter= +columnname_id=#L columnname_delimiter= +data_id= data_delimiter= +### CHI Format +### nxm column Format +### End of file format + +##### Data&Background +samfile=si325_mesh_300k_nor_4-8.chi num_sams=1 +sambkgfile=kapton_bgrd_300k_nor_2-3.chi num_sambkgs=1 +confile= num_cons=1 +conbkgfile= num_conbkgs=1 +det# used xcol detcol deterrcol xmin xmax add_det mul_det add_bkg mul_bkg add_con mul_con add_conbkg mul_conbkg + 0 1 0 1 3 0.600000 32.0000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 + +##### Experiment_Setup +title=PDF analysis +user=me +facility=In house +temperature=300.000 containermut=0.000500000 filtermut=0.0200000 +## X-Ray radiationtype=3 + (0: Ag K_alpha, 1:Cu K_alpha, 2:Mo K_alpha, 3:Customize) +lambda=0.142773 energy=86.8406 polartype=0 polardegree=1.00000 +## MonoChromator crystaltype=0 (0:Perfect, 1:Mosaic, 2:None) +position=0 (0:Primary beam, 1:Diffracted beam) +dspacetype=0 (0:Si{111}, 1:Ge{111}, 2:Customize) dspacing=3.13200 + +##### Sample_Setup information num_atoms=1 +#L symbol valence fractions z user_f1 user_f2 user_macoef + Si 0.00 1.000000 14 0.000000 0.000000 0.001000 +geometry=2 mut=0.50000000 numberdensity=0.00600000 +thickness=2.00000 packingFraction=0.500000 theory_mut=0.00579218 + +##### GetIQ_Setup +xformat=1 +smoothcorr_isa=0 selfnormalize_isa=0 +#L par_name sample sample_bkg container container_bkg +smooth_degree 2 2 2 2 +smooth_width 6 6 6 6 +selfnormalize 0 0 0 0 +filtercorr_isa=0 samfiltercorr_isa=0 sambkgfiltercorr_isa=0 +confiltercorr_isa=0 conbkgfiltercorr_isa=0 +scatveffcorr_isa=1 samconveffcorr_isa=1 sambkgveffcorr_isa=0 +conbkgveffcorr_isa=0 +nonegative_isa=1 negativevalue=-1.00000 + +##### Calibration_Data +## Detection efficiency energy dependence detedepxaxis=0 +detedepfunctype=0 detedep_elastic=1.00000 detedep_fluores=1.80000 +detedep_quadra=0.000000 detedep_spline=0.000000 detedep_file= +## Detector transmission energy dependence dettcoefxaxis=0 +dettcoeffunctype=0 dettcoef_elastic=0.950000 dettcoef_fluores=0.600000 +dettcoef_quadra=0.000000 dettcoef_spline=0.000000 dettcoef_file= + +##### IQ_Simulation +### Elastic used_isa=1 mymethod=1 +do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 +do_polarization=1 do_oblincident=0 do_energydep=0 +do_breitdirac=0 breitdiracexpo=2.00000 +do_rulandwin=0 rulandwinwidth=0.00100000 +do_useredit=0 add_user=0.000000 mul_user=1.00000 +### Compton used_isa=1 mymethod=1 +do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 +do_polarization=1 do_oblincident=0 do_energydep=0 +do_breitdirac=0 breitdiracexpo=2.00000 +do_rulandwin=0 rulandwinwidth=0.00100000 +do_useredit=0 add_user=0.000000 mul_user=1.00000 +### Fluores used_isa=1 mymethod=1 +do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 +do_polarization=1 do_oblincident=0 do_energydep=0 +do_breitdirac=0 breitdiracexpo=2.00000 +do_rulandwin=0 rulandwinwidth=0.00100000 +do_useredit=0 add_user=0.000000 mul_user=1.00000 + +##### Correction_Setup corrmethod=0 +oblincident_isa=1 dettranscoef=0.980000 samfluore_isa=1 +samfluoretype=0 samfluorescale=15.000000 +multiscat_isa=1 xraypolar_isa=1 samabsorp_isa=1 +highqscale_isa=1 highqratio=0.600000 scaleconst=0.039181914 +scaleconst_theory=0.039181914 +comptonscat_isa=1 rulandwin_isa=0 rulandintewidth=0.0100000 +comptonmethod=0 breitdirac_isa=1 breitdiracexponent=3 +detefficiency_isa=1 detefficiencytype=2 (0-1: linear, 2-3: quadratic) +detefficiency_a=-0.054826792 detefficiency_b=0.028062565 +lauediffuse_isa=1 +weight_isa=1 weighttype=0 (0: ^2, 1: , 2: Data Smoothed) +weightsmoothrmin=3.00000 weightsmoothwidth=100 weightsmoothcycles=600 +editsq_isa=0 editsqtype=0 add_sq=0.000000 mul_sq=1.00000 +editsqsmoothrmin=3.00000 editsqsmoothwidth=100 editsqsmoothcycles=600 +smoothdata_isa=0 smoothfunctype=0 smoothqmin=12.0000 smoothboxwidth=9 +interpolateqmin_isa=0 qmininterpolationtype=0 +dampfq_isa=0 dampfqtype=0 dampfqwidth=23.0000 + +##### SqGr_Optimization Setup +ftmethod=0 +## S(q) qmin=0.010000 qmax=27.000000 qgrid=0.000000 +## G(r) rmin=0.010000 rmax=60.000000 rgrid=0.010000 +## SqOptimization sqoptfunction=1 +optqmin=15.0000 optqmax=40.0000 optqgrid=0.000000 +optrmin=0.000000 optrmax=2.20000 optrgrid=0.0200000 +maxiter=20 relstep=0.000000 weighttype=0 weightfunc=0 +fitbkgmult_isa=0 fitsampmut_isa=1 fitpolariz_isa=1 +fitoblique_isa=0 fitfluores_isa=0 +fitrulandw_isa=0 fitenergya_isa=1 fitenergyb_isa=1 +fitsimurulandw_isa=1 fitDetEdepfluores_isa=0 fitDetEdepquadra_isa=0 +fitDetEdepspline_isa=0 fitDetTCoefElastic_isa=0 fitDetTCoefFluores_isa=0 +fitDetTcoefquadra_isa=0 fitDetTcoefspline_isa=0 + +##### Save&Plot Settings +datatype=GrData iqcorrtype=Int iqsimutype=SimuIq +sqcorrtype=Oblin sqtofqtype=DampFq +gropttype=OptFq miscdatatype=AtomASF +##### start data +#F si325_mesh_300k_nor_4-8.gr +#D Mon Apr 21 21:17:23 2008 +#C +#S 1 G(r) +#D +#L r(A) G(r) d_r d_Gr + 1.000000e-002 1.105784e-001 -7.539822e-004 1.802192e-003 + 2.000000e-002 2.199684e-001 -1.507964e-003 3.521449e-003 + 3.000000e-002 3.270088e-001 -2.261947e-003 5.079115e-003 + 4.000000e-002 4.305913e-001 -3.015929e-003 6.404892e-003 + 5.000000e-002 5.296853e-001 -3.769911e-003 7.440527e-003 + 6.000000e-002 6.233606e-001 -4.523893e-003 8.142955e-003 + 7.000000e-002 7.108060e-001 -5.277876e-003 8.486813e-003 + 8.000000e-002 7.913456e-001 -6.031858e-003 8.466340e-003 + 9.000000e-002 8.644501e-001 -6.785840e-003 8.096858e-003 + 1.000000e-001 9.297440e-001 -7.539822e-003 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4.221840e-003 -4.516354e+000 6.177257e-003 + 5.991000e+001 5.372618e-003 -4.517108e+000 6.178626e-003 + 5.992000e+001 7.403240e-003 -4.517862e+000 6.178721e-003 + 5.993000e+001 1.018741e-002 -4.518615e+000 6.177519e-003 + 5.994000e+001 1.358172e-002 -4.519369e+000 6.175297e-003 + 5.995000e+001 1.743107e-002 -4.520123e+000 6.172568e-003 + 5.996000e+001 2.157437e-002 -4.520877e+000 6.169963e-003 + 5.997000e+001 2.585021e-002 -4.521631e+000 6.168083e-003 + 5.998000e+001 3.010246e-002 -4.522385e+000 6.167364e-003 + 5.999000e+001 3.418543e-002 -4.523139e+000 6.167972e-003 diff --git a/docs/examples/srfit_ex/data/si.cif b/docs/examples/srfit_ex/data/si.cif new file mode 100644 index 0000000..ddcf81b --- /dev/null +++ b/docs/examples/srfit_ex/data/si.cif @@ -0,0 +1,224 @@ +data_9008565 +_chemical_name 'Silicon' +loop_ +_publ_author_name +'Wyckoff R W G' +_journal_name_full "Crystal Structures" +_journal_volume 1 +_journal_year 1963 +_journal_page_first 7 +_journal_page_last 83 +_publ_section_title +; + Second edition. Interscience Publishers, New York, New York + Sample at T = 300 K +; +_chemical_formula_sum 'Si' +_cell_length_a 5.43070 +_cell_length_b 5.43070 +_cell_length_c 5.43070 +_cell_angle_alpha 90 +_cell_angle_beta 90 +_cell_angle_gamma 90 +_cell_volume 160.165 +_symmetry_space_group_name_H-M 'F d 3 m' +loop_ +_symmetry_equiv_pos_as_xyz + 'x,y,z' + 'x,1/2+y,1/2+z' + '1/2+x,y,1/2+z' + '1/2+x,1/2+y,z' + '3/4+z,3/4-x,1/4+y' + '3/4+z,1/4-x,3/4+y' + '1/4+z,3/4-x,3/4+y' + '1/4+z,1/4-x,1/4+y' + '-y,1/2+z,1/2-x' + '-y,+z,-x' + '1/2-y,1/2+z,-x' + '1/2-y,+z,1/2-x' + '3/4+x,3/4-y,1/4+z' + '3/4+x,1/4-y,3/4+z' + '1/4+x,3/4-y,3/4+z' + '1/4+x,1/4-y,1/4+z' + '-z,1/2+x,1/2-y' + '-z,+x,-y' + '1/2-z,1/2+x,-y' + '1/2-z,+x,1/2-y' + '3/4+y,3/4-z,1/4+x' + '3/4+y,1/4-z,3/4+x' + '1/4+y,3/4-z,3/4+x' + '1/4+y,1/4-z,1/4+x' + '-x,1/2+y,1/2-z' + '-x,+y,-z' + '1/2-x,1/2+y,-z' + '1/2-x,+y,1/2-z' + '1/2+x,-z,1/2-y' + '1/2+x,1/2-z,-y' + '+x,-z,-y' + '+x,1/2-z,1/2-y' + '3/4-z,3/4+y,1/4+x' + '3/4-z,1/4+y,3/4+x' + '1/4-z,3/4+y,3/4+x' + '1/4-z,1/4+y,1/4+x' + '1/2+y,-x,1/2-z' + '1/2+y,1/2-x,-z' + '+y,-x,-z' + '+y,1/2-x,1/2-z' + '3/4-x,3/4+z,1/4+y' + '3/4-x,1/4+z,3/4+y' + '1/4-x,3/4+z,3/4+y' + '1/4-x,1/4+z,1/4+y' + '1/2+z,-y,1/2-x' + '1/2+z,1/2-y,-x' + '+z,-y,-x' + '+z,1/2-y,1/2-x' + '3/4-y,3/4+x,1/4+z' + '3/4-y,1/4+x,3/4+z' + '1/4-y,3/4+x,3/4+z' + '1/4-y,1/4+x,1/4+z' + 'x,1/2+z,1/2+y' + 'x,+z,+y' + '1/2+x,1/2+z,+y' + '1/2+x,+z,1/2+y' + '1/4-z,3/4-y,3/4-x' + '1/4-z,1/4-y,1/4-x' + '3/4-z,3/4-y,1/4-x' + '3/4-z,1/4-y,3/4-x' + 'y,1/2+x,1/2+z' + 'y,+x,+z' + '1/2+y,1/2+x,+z' + '1/2+y,+x,1/2+z' + '1/4-x,3/4-z,3/4-y' + '1/4-x,1/4-z,1/4-y' + '3/4-x,3/4-z,1/4-y' + '3/4-x,1/4-z,3/4-y' + 'z,1/2+y,1/2+x' + 'z,+y,+x' + '1/2+z,1/2+y,+x' + '1/2+z,+y,1/2+x' + '1/4-y,3/4-x,3/4-z' + '1/4-y,1/4-x,1/4-z' + '3/4-y,3/4-x,1/4-z' + '3/4-y,1/4-x,3/4-z' + '3/4+z,1/4+x,3/4-y' + '3/4+z,3/4+x,1/4-y' + '1/4+z,1/4+x,1/4-y' + '1/4+z,3/4+x,3/4-y' + '-y,1/2-z,1/2+x' + '-y,-z,+x' + '1/2-y,1/2-z,+x' + '1/2-y,-z,1/2+x' + '3/4+x,1/4+y,3/4-z' + '3/4+x,3/4+y,1/4-z' + '1/4+x,1/4+y,1/4-z' + '1/4+x,3/4+y,3/4-z' + '-z,1/2-x,1/2+y' + '-z,-x,+y' + '1/2-z,1/2-x,+y' + '1/2-z,-x,1/2+y' + '3/4+y,1/4+z,3/4-x' + '3/4+y,3/4+z,1/4-x' + '1/4+y,1/4+z,1/4-x' + '1/4+y,3/4+z,3/4-x' + '-x,1/2-y,1/2+z' + '-x,-y,+z' + '1/2-x,1/2-y,+z' + '1/2-x,-y,1/2+z' + '1/4-z,3/4+x,3/4+y' + '1/4-z,1/4+x,1/4+y' + '3/4-z,3/4+x,1/4+y' + '3/4-z,1/4+x,3/4+y' + 'y,-z,-x' + 'y,1/2-z,1/2-x' + '1/2+y,-z,1/2-x' + '1/2+y,1/2-z,-x' + '1/4-x,3/4+y,3/4+z' + '1/4-x,1/4+y,1/4+z' + '3/4-x,3/4+y,1/4+z' + '3/4-x,1/4+y,3/4+z' + 'z,-x,-y' + 'z,1/2-x,1/2-y' + '1/2+z,-x,1/2-y' + '1/2+z,1/2-x,-y' + '1/4-y,3/4+z,3/4+x' + '1/4-y,1/4+z,1/4+x' + '3/4-y,3/4+z,1/4+x' + '3/4-y,1/4+z,3/4+x' + 'x,-y,-z' + 'x,1/2-y,1/2-z' + '1/2+x,-y,1/2-z' + '1/2+x,1/2-y,-z' + '1/2-x,1/2+z,-y' + '1/2-x,+z,1/2-y' + '-x,1/2+z,1/2-y' + '-x,+z,-y' + '1/4+z,3/4-y,3/4+x' + '1/4+z,1/4-y,1/4+x' + '3/4+z,3/4-y,1/4+x' + '3/4+z,1/4-y,3/4+x' + '1/2-y,1/2+x,-z' + '1/2-y,+x,1/2-z' + '-y,1/2+x,1/2-z' + '-y,+x,-z' + '1/4+x,3/4-z,3/4+y' + '1/4+x,1/4-z,1/4+y' + '3/4+x,3/4-z,1/4+y' + '3/4+x,1/4-z,3/4+y' + '1/2-z,1/2+y,-x' + '1/2-z,+y,1/2-x' + '-z,1/2+y,1/2-x' + '-z,+y,-x' + '1/4+y,3/4-x,3/4+z' + '1/4+y,1/4-x,1/4+z' + '3/4+y,3/4-x,1/4+z' + '3/4+y,1/4-x,3/4+z' + '-x,-z,y' + '-x,1/2-z,1/2+y' + '1/2-x,-z,1/2+y' + '1/2-x,1/2-z,y' + '3/4+z,3/4+y,1/4-x' + '3/4+z,1/4+y,3/4-x' + '1/4+z,3/4+y,3/4-x' + '1/4+z,1/4+y,1/4-x' + '-y,-x,z' + '-y,1/2-x,1/2+z' + '1/2-y,-x,1/2+z' + '1/2-y,1/2-x,z' + '3/4+x,3/4+z,1/4-y' + '3/4+x,1/4+z,3/4-y' + '1/4+x,3/4+z,3/4-y' + '1/4+x,1/4+z,1/4-y' + '-z,-y,x' + '-z,1/2-y,1/2+x' + '1/2-z,-y,1/2+x' + '1/2-z,1/2-y,x' + '3/4+y,3/4+x,1/4-z' + '3/4+y,1/4+x,3/4-z' + '1/4+y,3/4+x,3/4-z' + '1/4+y,1/4+x,1/4-z' + '1/4-z,1/4-x,1/4-y' + '1/4-z,3/4-x,3/4-y' + '3/4-z,1/4-x,3/4-y' + '3/4-z,3/4-x,1/4-y' + 'y,z,x' + 'y,1/2+z,1/2+x' + '1/2+y,z,1/2+x' + '1/2+y,1/2+z,x' + '1/4-x,1/4-y,1/4-z' + '1/4-x,3/4-y,3/4-z' + '3/4-x,1/4-y,3/4-z' + '3/4-x,3/4-y,1/4-z' + 'z,x,y' + 'z,1/2+x,1/2+y' + '1/2+z,x,1/2+y' + '1/2+z,1/2+x,y' + '1/4-y,1/4-z,1/4-x' + '1/4-y,3/4-z,3/4-x' + '3/4-y,1/4-z,3/4-x' + '3/4-y,3/4-z,1/4-x' +loop_ +_atom_site_label +_atom_site_fract_x +_atom_site_fract_y +_atom_site_fract_z +Si 0.00000 0.00000 0.00000 diff --git a/docs/examples/srfit_ex/data/si90ni10-q27r60-xray.gr b/docs/examples/srfit_ex/data/si90ni10-q27r60-xray.gr new file mode 100644 index 0000000..02ea8a1 --- /dev/null +++ b/docs/examples/srfit_ex/data/si90ni10-q27r60-xray.gr @@ -0,0 +1,6134 @@ +History written: Mon Apr 21 20:48:28 2008 +Produced by +####### Get_XPDF ####### + +##### General_Setting +title=X-ray PDF +workingdirectory=e:\Ahmad\MUCAT0804\standards\pdfgetx2 +sourcedir=C:\Program Files\PDFgetX2\ +logfile=.pdfgetx2.log +quiet=0 debug=0 autosave_isa=1 savefilenamebase=si90ni10_300k_nor_1-6 +iqfilesurfix=.iq sqfilesurfix=.sq fqfilesurfix=.fq grfilesurfix=.gr + +##### DataFileFormat +datatype=1 (0:SPEC, 1:CHI, 2:nxm column, 3:unknown) +num_skiplines=3 comment_id=# delimiter= +### SPEC Format scan_id=#S scan_delimiter= +columnname_id=#L columnname_delimiter= +data_id= data_delimiter= +### CHI Format +### nxm column Format +### End of file format + +##### Data&Background +samfile=si90ni10_300k_nor_1-6.chi num_sams=1 +sambkgfile=kapton_bgrd_300k_nor_2-3.chi num_sambkgs=1 +confile= num_cons=1 +conbkgfile= num_conbkgs=1 +det# used xcol detcol deterrcol xmin xmax add_det mul_det add_bkg mul_bkg add_con mul_con add_conbkg mul_conbkg + 0 1 0 1 3 0.600000 32.0000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 + +##### Experiment_Setup +title=PDF analysis +user=me +facility=In house +temperature=300.000 containermut=0.000500000 filtermut=0.0200000 +## X-Ray radiationtype=3 + (0: Ag K_alpha, 1:Cu K_alpha, 2:Mo K_alpha, 3:Customize) +lambda=0.142773 energy=86.8406 polartype=0 polardegree=1.00000 +## MonoChromator crystaltype=0 (0:Perfect, 1:Mosaic, 2:None) +position=0 (0:Primary beam, 1:Diffracted beam) +dspacetype=0 (0:Si{111}, 1:Ge{111}, 2:Customize) dspacing=3.13200 + +##### Sample_Setup information num_atoms=2 +#L symbol valence fractions z user_f1 user_f2 user_macoef + Si 0.00 0.900000 14 0.000000 0.000000 0.001000 + Ni 0.00 0.100000 28 0.000000 0.000000 0.001000 +geometry=2 mut=0.50000000 numberdensity=0.00600000 +thickness=2.00000 packingFraction=0.500000 theory_mut=0.00871359 + +##### GetIQ_Setup +xformat=1 +smoothcorr_isa=0 selfnormalize_isa=0 +#L par_name sample sample_bkg container container_bkg +smooth_degree 2 2 2 2 +smooth_width 6 6 6 6 +selfnormalize 0 0 0 0 +filtercorr_isa=0 samfiltercorr_isa=0 sambkgfiltercorr_isa=0 +confiltercorr_isa=0 conbkgfiltercorr_isa=0 +scatveffcorr_isa=1 samconveffcorr_isa=1 sambkgveffcorr_isa=0 +conbkgveffcorr_isa=0 +nonegative_isa=1 negativevalue=-1.00000 + +##### Calibration_Data +## Detection efficiency energy dependence detedepxaxis=0 +detedepfunctype=0 detedep_elastic=1.00000 detedep_fluores=1.80000 +detedep_quadra=0.000000 detedep_spline=0.000000 detedep_file= +## Detector transmission energy dependence dettcoefxaxis=0 +dettcoeffunctype=0 dettcoef_elastic=0.950000 dettcoef_fluores=0.600000 +dettcoef_quadra=0.000000 dettcoef_spline=0.000000 dettcoef_file= + +##### IQ_Simulation +### Elastic used_isa=1 mymethod=1 +do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 +do_polarization=1 do_oblincident=0 do_energydep=0 +do_breitdirac=0 breitdiracexpo=2.00000 +do_rulandwin=0 rulandwinwidth=0.00100000 +do_useredit=0 add_user=0.000000 mul_user=1.00000 +### Compton used_isa=1 mymethod=1 +do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 +do_polarization=1 do_oblincident=0 do_energydep=0 +do_breitdirac=0 breitdiracexpo=2.00000 +do_rulandwin=0 rulandwinwidth=0.00100000 +do_useredit=0 add_user=0.000000 mul_user=1.00000 +### Fluores used_isa=1 mymethod=1 +do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 +do_polarization=1 do_oblincident=0 do_energydep=0 +do_breitdirac=0 breitdiracexpo=2.00000 +do_rulandwin=0 rulandwinwidth=0.00100000 +do_useredit=0 add_user=0.000000 mul_user=1.00000 + +##### Correction_Setup corrmethod=0 +oblincident_isa=1 dettranscoef=0.980000 samfluore_isa=1 +samfluoretype=0 samfluorescale=15.000000 +multiscat_isa=1 xraypolar_isa=1 samabsorp_isa=1 +highqscale_isa=1 highqratio=0.600000 scaleconst=0.021144960 +scaleconst_theory=0.021144960 +comptonscat_isa=1 rulandwin_isa=0 rulandintewidth=0.0100000 +comptonmethod=0 breitdirac_isa=1 breitdiracexponent=3 +detefficiency_isa=1 detefficiencytype=2 (0-1: linear, 2-3: quadratic) +detefficiency_a=-0.022312320 detefficiency_b=0.029174900 +lauediffuse_isa=1 +weight_isa=1 weighttype=0 (0: ^2, 1: , 2: Data Smoothed) +weightsmoothrmin=3.00000 weightsmoothwidth=100 weightsmoothcycles=600 +editsq_isa=0 editsqtype=0 add_sq=0.000000 mul_sq=1.00000 +editsqsmoothrmin=3.00000 editsqsmoothwidth=100 editsqsmoothcycles=600 +smoothdata_isa=0 smoothfunctype=0 smoothqmin=12.0000 smoothboxwidth=9 +interpolateqmin_isa=0 qmininterpolationtype=0 +dampfq_isa=0 dampfqtype=0 dampfqwidth=23.0000 + +##### SqGr_Optimization Setup +ftmethod=0 +## S(q) qmin=0.010000 qmax=27.000000 qgrid=0.000000 +## G(r) rmin=0.010000 rmax=60.000000 rgrid=0.010000 +## SqOptimization sqoptfunction=1 +optqmin=17.0000 optqmax=40.0000 optqgrid=0.000000 +optrmin=0.000000 optrmax=2.20000 optrgrid=0.0200000 +maxiter=20 relstep=0.000000 weighttype=0 weightfunc=0 +fitbkgmult_isa=0 fitsampmut_isa=1 fitpolariz_isa=1 +fitoblique_isa=0 fitfluores_isa=0 +fitrulandw_isa=0 fitenergya_isa=1 fitenergyb_isa=1 +fitsimurulandw_isa=1 fitDetEdepfluores_isa=0 fitDetEdepquadra_isa=0 +fitDetEdepspline_isa=0 fitDetTCoefElastic_isa=0 fitDetTCoefFluores_isa=0 +fitDetTcoefquadra_isa=0 fitDetTcoefspline_isa=0 + +##### Save&Plot Settings +datatype=GrData iqcorrtype=Int iqsimutype=SimuIq +sqcorrtype=Oblin sqtofqtype=DampFq +gropttype=OptFq miscdatatype=AtomASF +##### start data +#F si90ni10_300k_nor_1-6.gr +#D Mon Apr 21 23:17:50 2008 +#C +#S 1 G(r) +#D +#L r(A) G(r) d_r d_Gr + 1.000000e-002 -5.044565e-002 -7.539822e-004 8.698774e-004 + 2.000000e-002 -9.975593e-002 -1.507964e-003 1.699714e-003 + 3.000000e-002 -1.468212e-001 -2.261947e-003 2.451544e-003 + 4.000000e-002 -1.905826e-001 -3.015929e-003 3.091455e-003 + 5.000000e-002 -2.300554e-001 -3.769911e-003 3.591375e-003 + 6.000000e-002 -2.643508e-001 -4.523893e-003 3.930603e-003 + 7.000000e-002 -2.926941e-001 -5.277876e-003 4.097027e-003 + 8.000000e-002 -3.144414e-001 -6.031858e-003 4.088065e-003 + 9.000000e-002 -3.290915e-001 -6.785840e-003 3.911398e-003 + 1.000000e-001 -3.362954e-001 -7.539822e-003 3.585829e-003 + 1.100000e-001 -3.358625e-001 -8.293804e-003 3.143032e-003 + 1.200000e-001 -3.277631e-001 -9.047787e-003 2.632135e-003 + 1.300000e-001 -3.121288e-001 -9.801769e-003 2.131402e-003 + 1.400000e-001 -2.892501e-001 -1.055575e-002 1.768437e-003 + 1.500000e-001 -2.595712e-001 -1.130973e-002 1.697932e-003 + 1.600000e-001 -2.236838e-001 -1.206372e-002 1.943846e-003 + 1.700000e-001 -1.823186e-001 -1.281770e-002 2.359542e-003 + 1.800000e-001 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L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of fitting the Debye model to experimental Debye-Waller +factors. + +In this example, we build a fit recipe that uses an external function that can +simulate a atomic displacement parameters using the Debye model. This serves as +an example of how to utilize python functions in a fit and extend them with +SrFit without writing additional code. This example also demonstrates guide a +refinement with restraints. + +Instructions + +Run the example and then read the 'makeRecipe' code to see how to use a python +function as a profile generator. + +Extensions + +- Don't hardcode the mass of lead in the fitting equation. Turn it into a + Parameter and refine it. There are two ways to do this. Try to figure out + both. +""" + +import numpy +from gaussianrecipe import scipyOptimize + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) + +# The data +data = """\ +015.0 0.00334 0.00013 +050.0 0.00508 0.00022 +100.0 0.00830 0.00040 +150.0 0.01252 0.00071 +200.0 0.01792 0.00100 +250.0 0.02304 0.00120 +300.0 0.02737 0.00140 +350.0 0.03085 0.00160 +400.0 0.03484 0.00190 +450.0 0.03774 0.00220 +500.0 0.03946 0.00250 +""" + +###### +# Example Code + + +def makeRecipe(): + """Make the recipe for the fit. + + The instructions for what we want to refine, and how to refine it + will be defined within a FitRecipe instance. The job of a FitRecipe + is to collect and associate all the data, the fitting equations, + fitting variables, constraints and restrations. We will demonstrate + each of these within the code. + + Data is held within a Profile object. The Profile is simply a + container that holds the data, and the theoretical profile once it + has been calculated. + + Data is associated with a fitting equation within a FitContribution. + The FitContribution defines the equation and parameters that will be + adjusted to fit the data. The fitting equation can be defined within + a function or optionally within the ProfileGenerator class. We won't + need the ProfileGenerator class in this example since the signature + of the fitting equation (the 'debye' function defined below) is so + simple. The FitContribution also defines the residual function to + optimize for the data/equation pair. This can be modified, but we + won't do that here. + """ + + # The Profile + # Create a Profile to hold the experimental and calculated signal. + profile = Profile() + + # Load data and add it to the profile. It is our responsibility to get our + # data into the profile. + xydy = numpy.array(data.split(), dtype=float).reshape(-1, 3) + x, y, dy = xydy.T + profile.setObservedProfile(x, y, dy) + + # The FitContribution + # The FitContribution associates the profile with the Debye function. + contribution = FitContribution("pb") + # Tell the contribution about the Profile. We will need to use the + # independent variable (the temperature) from the data to calculate the + # theoretical signal, so give it an informative name ('T') that we can use + # later. + contribution.setProfile(profile, xname="T") + + # We now need to create the fitting equation. We tell the FitContribution + # to use the 'debye' function defined below. The 'registerFunction' method + # will let us do this. Since we haven't told it otherwise, + # 'registerFunction' will extract the name of the function ('debye') and + # the names of the arguments ('T', 'm', 'thetaD'). These arguments will + # become Parameters of the FitContribution. Since we named the x-variable + # 'T' above, the 'T' in the 'debye' equation will refer to this x-variable + # whenever it is used. + contribution.registerFunction(debye) + + # Now we can create the fitting equation. We want to extend the 'debye' + # equation by adding a vertical offset. We could wrap 'debye' in a new + # function with an offset, and register that instead of 'debye', but what + # we do here is easier. + # + # When we set the fitting equation, we do not need to specify the + # Parameters to the 'debye' function since the FitContribution already + # knows what they are. If we choose to specify the arguments, we can make + # adjustments to their input values. We wish to have the thetaD value in + # the debye equation to be positive, so we specify the input as abs(thetaD) + # in the equation below. Furthermore, we know 'm', the mass of lead, so we + # can specify that as well. + contribution.setEquation("debye(T, 207.2, abs(thetaD)) + offset") + + # The FitRecipe + # The FitRecipe lets us define what we want to fit. It is where we can + # create variables, constraints and restraints. If we had multiple profiles + # to fit simultaneously, the contribution from each could be added to the + # recipe. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Specify which Parameters we want to refine. + + # Vary the offset + recipe.addVar(contribution.offset, 0) + # We also vary the Debye temperature. + recipe.addVar(contribution.thetaD, 100) + + # We would like to 'suggest' that the offset should remain positive. This + # is somethine that we know about the system that might help the refinement + # converge to a physically reasonable result. We will do this with a soft + # constraint, or restraint. Here we restrain the offset variable to between + # 0 and infinity. We tell the recipe that we want to scale the penalty for + # breaking the restraint by the point-average chi^2 value so that the + # restraint is roughly as significant as any other data point throughout + # the fit. + recipe.restrain(recipe.offset, lb=0, scaled=True) + + # We're done setting up the recipe. We can now do other things with it. + return recipe + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # Plot this. + # Note that since the contribution was given the name "pb", it is + # accessible from the recipe with this name. This is a useful way to + # organize multiple contributions to a fit. + T = recipe.pb.profile.x + U = recipe.pb.profile.y + Ucalc = recipe.pb.profile.ycalc + + import pylab + + pylab.plot(T, U, "o", label="Pb $U_{iso}$ Data") + pylab.plot(T, Ucalc) + pylab.xlabel("T (K)") + pylab.ylabel(r"$U_{iso} (\AA^2)$") + pylab.legend(loc=(0.0, 0.8)) + + pylab.show() + return + + +def main(): + """The workflow of creating, running and inspecting a fit.""" + + # Create the recipe + recipe = makeRecipe() + + # Refine using the optimizer of your choice + scipyOptimize(recipe) + + # Get the results. + res = FitResults(recipe) + + # Print the results + res.printResults() + + # Plot the results + plotResults(recipe) + + return + + +# Functions required for calculation of Debye curve. Feel free to skip these, +# as we treat them as if existing in some external library that we cannot +# modify. + + +def debye(T, m, thetaD): + """A wrapped version of 'adps' that can handle an array of + T-values.""" + y = numpy.array([adps(m, thetaD, x) for x in T]) + return y + + +def adps(m, thetaD, T): + """Calculates atomic displacement factors within the Debye model. + + = (3h^2/4 pi^2 m kB thetaD)(phi(thetaD/T)/(ThetaD/T) + 1/4) + + arguments: + m -- float -- mass of the ion in atomic mass units (e.g., C = 12) + thetaD -- float -- Debye Temperature + T -- float -- temperature. + + return: + Uiso -- float -- the thermal factor from the Debye recipe at temp T + """ + h = 6.6260755e-34 # Planck's constant. J.s of m^2.kg/s + kB = 1.3806503e-23 # Boltzmann's constant. J/K + amu = 1.66053886e-27 # Atomic mass unit. kg + + def __phi(x): + """Evaluates the phi integral needed in Debye calculation. + + phi(x) = (1/x) int_0^x xi/(exp(xi)-1) dxi + + arguments: + x -- float -- value of thetaD (Debye temperature)/T + + returns: + phi -- float -- value of the phi function + """ + + def __debyeKernel(xi): + """Function needed by debye calculators.""" + y = xi / (numpy.exp(xi) - 1) + return y + + import scipy.integrate + + int = scipy.integrate.quad(__debyeKernel, 0, x) + phi = (1 / x) * int[0] + + return phi + + m = m * amu + u2 = (3 * h**2 / (4 * numpy.pi**2 * m * kB * thetaD)) * ( + __phi(thetaD / T) / (thetaD / T) + 1.0 / 4.0 + ) + + return u2 * 1e20 + + +if __name__ == "__main__": + + main() + +# End of file diff --git a/docs/examples/srfit_ex/debyemodelII.py b/docs/examples/srfit_ex/debyemodelII.py new file mode 100644 index 0000000..0aace44 --- /dev/null +++ b/docs/examples/srfit_ex/debyemodelII.py @@ -0,0 +1,162 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of fitting the Debye recipe to experimental Debye-Waller +factors. + +This is an extension of example in debyemodel.py. The recipe we create will +simultaneously fit the low and high temperature parts of the experimental data +with the same Debye temperature, but different offsets. This example also +introduces constraints. + +Instructions + +Run the example and then read through the 'makeRecipeII' code to learn about +multi-profile recipes. You will learn how to constrain related information +between the fit contributions. + +Extensions + +- Play with the fit ranges and see if you can improve the fit. +- The Debye temperature parameters from the two contributions can be + constrained without creating a new variable. Try to figure out how that is + done. +""" + +from debyemodel import makeRecipe, scipyOptimize + +from diffpy.srfit.fitbase import FitRecipe, FitResults + +###### +# Example Code + + +def makeRecipeII(): + """Make a recipe for fitting low and high temperature regions. + + We will fit the low and high temperature parts of Debye curve + simultaneously with the same Debye temperature, but different + offsets. + + We will make two FitRecipes using the makeRecipe function from + debyemodel.py and extract the configured FitContribution from each. + We will use different fitting ranges for each FitContribution and + constrain the Debye temperature in each FitContribution to be the + same. + """ + + # We'll throw these away. We just want the FitContributions that are + # configured within the recipes. + m1 = makeRecipe() + m2 = makeRecipe() + # These are the FitContributions (we named them "pb" in the debyemodel + # example). + lowT = m1.pb + highT = m2.pb + # Let's rename the FitContributions to something more meaningful for this + # example. + lowT.name = "lowT" + highT.name = "highT" + + # Now create a fresh FitRecipe to work with and add to it the two + # FitContributions. + recipe = FitRecipe() + recipe.addContribution(lowT) + recipe.addContribution(highT) + + # Change the fit ranges of the Profiles embedded within the + # FitContributions. We want to fit one of the contributions at low + # temperature, and one at high. + lowT.profile.setCalculationRange(0, 150) + highT.profile.setCalculationRange(400, 500) + + # Vary the offset from each FitContribution separately, while keeping the + # Debye temperatures the same. We give each offset variable a different + # name in the recipe so it retains its identity. + recipe.addVar(recipe.lowT.offset, name="lowToffset") + recipe.addVar(recipe.highT.offset, name="highToffset") + # We create a new Variable and use the recipe's "constrain" method to + # associate the Debye temperature parameters with that variable. + recipe.newVar("thetaD", 100) + recipe.constrain(recipe.lowT.thetaD, "thetaD") + recipe.constrain(recipe.highT.thetaD, "thetaD") + return recipe + + +def plotResults(recipe): + """Display the results contained within a refined FitRecipe.""" + + # The variable values are returned in the order in which the variables were + # added to the FitRecipe. + lowToffset, highToffset, thetaD = recipe.getValues() + + # We want to extend the fitting range to its full extent so we can get a + # nice full plot. + recipe.lowT.profile.setCalculationRange(xmin="obs", xmax="obs") + recipe.highT.profile.setCalculationRange(xmin="obs", xmax="obs") + T = recipe.lowT.profile.x + U = recipe.lowT.profile.y + # We can use a FitContribution's 'evaluateEquation' method to evaluate + # expressions involving the Parameters and other aspects of the + # FitContribution. Here we evaluate the fitting equation, which is always + # accessed using the name "eq". We access it this way (rather than through + # the Profile's ycalc attribute) because we changed the calculation range + # above, and we therefore need to recalculate the profile. + lowU = recipe.lowT.evaluateEquation("eq") + highU = recipe.highT.evaluateEquation("eq") + + # Now we can plot this. + import pylab + + pylab.plot(T, U, "o", label="Pb $U_{iso}$ Data") + lbl1 = r"$T_d$=%3.1f K, lowToff=%1.5f $\AA^2$" % (abs(thetaD), lowToffset) + lbl2 = r"$T_d$=%3.1f K, highToff=%1.5f $\AA^2$" % ( + abs(thetaD), + highToffset, + ) + pylab.plot(T, lowU, label=lbl1) + pylab.plot(T, highU, label=lbl2) + pylab.xlabel("T (K)") + pylab.ylabel(r"$U_{iso} (\AA^2)$") + pylab.legend(loc=(0.0, 0.8)) + + pylab.show() + return + + +def main(): + + # Create the recipe + recipe = makeRecipeII() + + # Refine using the optimizer of your choice + scipyOptimize(recipe) + + # Get the results in a FitResults object. + res = FitResults(recipe) + + # Print the results + res.printResults() + + # Plot the results + plotResults(recipe) + + return + + +if __name__ == "__main__": + + main() + +# End of file diff --git a/docs/examples/srfit_ex/ellipsoidsas.py b/docs/examples/srfit_ex/ellipsoidsas.py new file mode 100644 index 0000000..23ee5f0 --- /dev/null +++ b/docs/examples/srfit_ex/ellipsoidsas.py @@ -0,0 +1,130 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2010 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of a refinement of SAS I(Q) data to an ellipsoidal model.""" + +from gaussianrecipe import scipyOptimize + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) +from diffpy.srfit.sas import SASGenerator, SASParser + +###### +# Example Code + + +def makeRecipe(datname): + """Create a fitting recipe for ellipsoidal SAS data.""" + + # The Profile + # This will be used to store the observed and calculated I(Q) data. + profile = Profile() + + # Load data and add it to the Profile. We use a SASParser to load the data + # properly and pass the metadata along. + parser = SASParser() + parser.parseFile(datname) + profile.loadParsedData(parser) + + # The ProfileGenerator + # The SASGenerator is for configuring and calculating a SAS profile. We use + # a sas model to configure and serve as the calculation engine of the + # generator. This allows us to use the full sas model creation + # capabilities, and tie this into SrFit when we want to fit a model to + # data. The documentation for the various sas models can be found at + # http://www.sasview.org. + from sas.models.EllipsoidModel import EllipsoidModel + + model = EllipsoidModel() + generator = SASGenerator("generator", model) + + # The FitContribution + # Here we associate the Profile and ProfileGenerator, as has been done + # before. + contribution = FitContribution("ellipsoid") + contribution.addProfileGenerator(generator) + contribution.setProfile(profile, xname="q") + + # We want to fit the log of the signal to the log of the data so that the + # higher-Q information remains significant. There are no I(Q) uncertainty + # values with the data, so we do not need to worry about the effect this + # will have on the estimated parameter uncertainties. + contribution.setResidualEquation("log(eq) - log(y)") + + # Make the FitRecipe and add the FitContribution. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Configure the fit variables + # The SASGenerator uses the parameters from the params and dispersion + # attributes of the model. These vary from model to model, but are adopted + # as SrFit Parameters within the generator. Whereas the dispersion + # parameters are accessible as, e.g. "radius.width", within the + # SASGenerator these are named like "radius_width". + # + # We want to fit the scale factor, radii and background factors. + recipe.addVar(generator.scale, 1) + recipe.addVar(generator.radius_a, 50) + recipe.addVar(generator.radius_b, 500) + recipe.addVar(generator.background, 0) + + # Give the recipe away so it can be used! + return recipe + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # All this should be pretty familiar by now. + r = recipe.ellipsoid.profile.x + y = recipe.ellipsoid.profile.y + ycalc = recipe.ellipsoid.profile.ycalc + diff = y - ycalc + min(y) + + import pylab + + pylab.loglog(r, y, "bo", label="I(Q) Data") + pylab.loglog(r, ycalc, "r-", label="I(Q) Fit") + pylab.loglog(r, diff, "g-", label="I(Q) diff") + pylab.xlabel(r"$Q (\AA^{-1})$") + pylab.ylabel("$I (arb. units)$") + pylab.legend(loc=1) + + pylab.show() + return + + +if __name__ == "__main__": + + # Make the data and the recipe + data = "data/sas_ellipsoid_testdata.txt" + + # Make the recipe + recipe = makeRecipe(data) + + # Optimize + scipyOptimize(recipe) + + # Generate and print the FitResults + res = FitResults(recipe) + res.printResults() + + # Plot! + plotResults(recipe) + +# End of file diff --git a/docs/examples/srfit_ex/gaussiangenerator.py b/docs/examples/srfit_ex/gaussiangenerator.py new file mode 100644 index 0000000..fedff5a --- /dev/null +++ b/docs/examples/srfit_ex/gaussiangenerator.py @@ -0,0 +1,180 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of using ProfileGenerators in FitContributions. + +This is an example of building a ProfileGenerator and using it in a +FitContribution in order to fit a Gaussian profile. The recipe creation is much +like in gaussianrecipe.py, except that it uses our custom GaussianGenerator +class. ProfileGenerators are usually used to organize profile calculators that +require more information than can be conveniently passed into a function call, +but can be used for simple calculations as well. The GaussianGenerator class +is an example of a ProfileGenerator that can be used by a FitContribution to +help generate a the profile. + +Instructions + +Run gaussianrecipe.py and this example. Note how the output is identical. Next +read through 'GaussianGenerator' class. This provides a simple example of how +to create a custom ProfileGenerator. Finally read the 'makeRecipe' code to see +how the GaussianGenerator is used. Contrast this to the 'makeRecipe' section +in gaussianrecipe.py. + +Extensions + +- Remove the amplitude from GaussianGenerator and instead use the 'setEquation' + method of the FitContribution to account for it. Note that the + GaussianGenerator will be accessible by its name, "g". +""" + +from numpy import exp + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + Profile, + ProfileGenerator, +) + +###### +# Example Code + + +class GaussianGenerator(ProfileGenerator): + """A class for calculating a Gaussian profile. + + Generating a Gaussian is not difficult, as was shown in + gaussianrecipe.py. Here we create a class that encapsulates this + functionality. Placing this class in a python module would make it + possible to import it and reuse it, thereby saving future code + writing and debugging. + + The purpose of a ProfileGenerator is to 1) provide a function that + generates a profile signal 2) organize the Parameters required for + the calculation + + Thus, this class overloads the __init__ method to create the + necessary Parameters for the calculation, and the __call__ method to + generate the signal. + """ + + def __init__(self, name): + """Define the generator. + + Note that a ProfileGenerator needs a name passed in the initializer. + This makes it so the generator can be referenced by name when it is + part of a FitContribution. + + Here we create the Parameters for the calculation. + + A -- The amplitude + x0 -- The center + sigma -- The width + """ + # This initializes various parts of the generator + ProfileGenerator.__init__(self, name) + + # Here we create new Parameters using the '_newParameter' method of + # ProfileGenerator. The signature is + # _newParameter(name, value). + # See the API for full details. + self._newParameter("A", 1.0) + self._newParameter("x0", 0.0) + self._newParameter("sigma", 1.0) + return + + def __call__(self, x): + """Calculate the profile. + + Here we calculate the Gaussian profile given the independent + variable, x. We will define it as we did in gaussianrecipe.py. + """ + # First we must get the values of the Parameters. Since we used + # _newParameter to create them, the Parameters are accessible as + # attributes by name. + A = self.A.value + x0 = self.x0.value + sigma = self.sigma.value + + # Now we can use them. Note that we imported exp from numpy at the top + # of the module. + y = A * exp(-0.5 * (x - x0) ** 2 / sigma**2) + + # Now return the value. + return y + + +# End class GaussianGenerator + + +def makeRecipe(): + """Create a recipe that uses the GaussianGenerator. + + This will create a FitContribution that uses the GaussianGenerator, + associate this with a Profile, and use this to define a FitRecipe. + """ + + # The Profile + # Create a Profile to hold the experimental and calculated signal. + profile = Profile() + + # Load data and add it to the profile. This uses the loadtxt function from + # numpy. + profile.loadtxt("data/gaussian.dat") + + # The ProfileGenerator + # Create a GaussianGenerator named "g". This will be the name we use to + # refer to the generator from within the FitContribution equation. + generator = GaussianGenerator("g") + + # The FitContribution + # Create a FitContribution that will associate the Profile with the + # GaussianGenerator. The GaussianGenerator will be accessible as an + # attribute of the FitContribution by its name ("g"). Note that this will + # set the fitting equation to "g", which calls the GaussianGenerator. + contribution = FitContribution("g1") + contribution.addProfileGenerator(generator) + contribution.setProfile(profile) + + # The FitRecipe + # Now we create the FitRecipe and add the FitContribution. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Specify which Parameters we want to vary in the fit. This will add + # Variables to the FitRecipe that directly modify the Parameters of the + # FitContribution. + # + # We create a variable for each Parameter of the GaussianGenerator. Note + # that the Parameters belong to the GaussianGenerator, not the + # FitContribution as in gaussianrecipe.py. We initialize parameters as in + # gaussianrecipe.py so we can expect the same output. + recipe.addVar(generator.A, 1) + recipe.addVar(generator.x0, 5) + recipe.addVar(generator.sigma, name="sig") + recipe.sig.value = 1 + + # Give the recipe away so it can be used! + return recipe + + +if __name__ == "__main__": + + # We can use main from gaussianrecipe.py, since this doesn't care if we use + # a ProfileGenerator or not. + from gaussianrecipe import main + + main() + +# End of file diff --git a/docs/examples/srfit_ex/gaussianrecipe.py b/docs/examples/srfit_ex/gaussianrecipe.py new file mode 100644 index 0000000..646afc7 --- /dev/null +++ b/docs/examples/srfit_ex/gaussianrecipe.py @@ -0,0 +1,214 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of fitting a Gaussian to simulated data. + +This is an example of building a fit recipe that can be driven by an optimizer +to fit a Gaussian profile to simulated data. The purpose of this example is +familiarize the developer with the objects involved in defining a SrFit +refinement recipe. + +Instructions + +If you have not yet run the example, run it and inspect the output. The example +script is driven by the 'main' method defined below. Take a look at that method +to get an understanding of how a fit recipe can be used once created. After +that, read the 'makeRecipe' code to see what goes into a fit recipe. After +that, read the 'scipyOptimize' code to see how the refinement is executed. +Finally, read the 'plotResults' code to see how to extracts the refined profile +and plot it. + +Extensions + +After reading through the code, try to perform the following tasks. The process +will leave you with a much better understanding of how SrFit works. + +- Play around with setting the values of the Variables and Parameters. What + happens to the associated Parameter when you change a variable value? What + happens to the variable when you change the Parameter value? +- Modify the fitting equation by adding a constant. See if that improves the + fit. +- Create a FitRecipe to fit the Lorentzian profile in the data/lorentzian.dat + file. +""" + +from __future__ import print_function + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) + +###### +# Example Code + + +def main(): + """The workflow of creating, running and inspecting a fit.""" + + # Start by creating the recipe. The recipe describes the data to be fit, + # the profile generator used to simulate the data and the variables that + # will be tuned by the optimizer. + recipe = makeRecipe() + + # Refine using the optimizer of your choice. + scipyOptimize(recipe) + + # Get the results in a FitResults object. The FitResults object stores the + # current state of the recipe, and uses it to calculate useful statistics + # about the fit. + res = FitResults(recipe) + + # Print the results. + res.printResults() + + # Plot the results. + plotResults(recipe) + + return + + +def makeRecipe(): + """Make a FitRecipe for fitting a Gaussian curve to data. + + The instructions for what we want to refine, and how to refine it + will be defined within a FitRecipe instance. The job of a FitRecipe + is to collect and associate all the data, the fitting equations, + fitting variables, constraints and restraints. The configured recipe + provides a 'residual' function and the initial variable values that + an optimizer can use to refine the variables to minimize the + disagreement between the calculated profile and the data. + + Once we define the FitRecipe, we can send it an optimizer to be + optimized. See the 'scipyOptimize' function. + """ + + # The Profile + # Create a Profile to hold the experimental and calculated signal. + profile = Profile() + + # Load data and add it to the profile. This uses the loadtxt function from + # numpy. + profile.loadtxt("data/gaussian.dat") + + # The FitContribution + # The FitContribution associates the Profile with a fitting equation. The + # FitContribution also stores the parameters of the fitting equation. We + # give our FitContribution then name "g1". We will be able to access the + # FitContribution by that name within the FitRecipe. + contribution = FitContribution("g1") + # Tell the FitContribution about the Profile. The FitContribution will give + # us access to the data held within the Profile. Here, we can tell it what + # name we want to use for the independent variable. We tell it to use the + # name "x". + contribution.setProfile(profile, xname="x") + + # Now we need to create a fitting equation. We do that by writing out the + # equation as a string. The FitContribution will turn this into a callable + # function internally. In the process, it extracts all the parameters from + # the equation (A, x, x0, sigma) and turns them into Parameter objects + # internally. These objects can be accessed as attributes of the + # contribution by name. Since we told the contribution that our + # independent variable is named "x", this value will be substituted into + # the fitting equation whenever it is called. + contribution.setEquation("A * exp(-0.5*(x-x0)**2/sigma**2)") + + # To demonstrate how these parameters are used, we will give "A" an initial + # value. Note that Parameters are not numbers, but are containers for + # numbers. To get or modify the value of a parameter, use its 'value' + # attribute. Parameters also have a 'name' attribute. + contribution.A.value = 1.0 + + # The FitRecipe + # The FitRecipe lets us define what we want to fit. It is where we can + # create variables, constraints and restraints. + recipe = FitRecipe() + + # Here we tell the FitRecipe to use our FitContribution. When the FitRecipe + # calculates its residual function, it will call on the FitContribution to + # do part of the work. + recipe.addContribution(contribution) + + # Specify which Parameters we want to vary in the fit. This will add + # Variables to the FitRecipe that directly modify the Parameters of the + # FitContribution. + # + # Here we create a Variable for the 'A' Parameter from our fit equation. + # The resulting Variable will be named 'A' as well, but it will be accessed + # via the FitRecipe. + recipe.addVar(contribution.A) + # Here we create the Variable for 'x0' and give it an initial value of 5. + recipe.addVar(contribution.x0, 5) + # Here we create a Variable named 'sig', which is tied to the 'sigma' + # Parameter of our FitContribution. We give it an initial value through the + # FitRecipe instance. + recipe.addVar(contribution.sigma, name="sig") + recipe.sig.value = 1 + + return recipe + + +def scipyOptimize(recipe): + """Optimize the recipe created above using scipy. + + The FitRecipe we created in makeRecipe has a 'residual' method that + we can be minimized using a scipy optimizer. The details are + described in the source. + """ + + # We're going to use the least-squares (Levenberg-Marquardt) optimizer from + # scipy. We simply have to give it the function to minimize + # (recipe.residual) and the starting values of the Variables + # (recipe.getValues()). + from scipy.optimize.minpack import leastsq + + print("Fit using scipy's LM optimizer") + leastsq(recipe.residual, recipe.getValues()) + + return + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # We can access the data and fit profile through the Profile we created + # above. We get to it through our FitContribution, which we named "g1". + # + # The independent variable. This is always under the "x" attribute. + x = recipe.g1.profile.x + # The observed profile that we loaded earlier, the "y" attribute. + y = recipe.g1.profile.y + # The calculated profile, the "ycalc" attribute. + ycalc = recipe.g1.profile.ycalc + + # This stuff is specific to pylab from the matplotlib distribution. + import pylab + + pylab.plot(x, y, "b.", label="observed Gaussian") + pylab.plot(x, ycalc, "g-", label="calculated Gaussian") + pylab.legend(loc=(0.0, 0.8)) + pylab.xlabel("x") + pylab.ylabel("y") + + pylab.show() + return + + +if __name__ == "__main__": + + main() + +# End of file diff --git a/docs/examples/srfit_ex/interface.py b/docs/examples/srfit_ex/interface.py new file mode 100644 index 0000000..6b0daca --- /dev/null +++ b/docs/examples/srfit_ex/interface.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of fitting a Gaussian to simulated data. + +This is like gaussianrecipe.py, but it uses a shorthand interface +defined in the diffpy.srfit.interface.interface.py module. +""" + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) + +###### +# Example Code + + +def main(): + + p = Profile() + p.loadtxt("data/gaussian.dat") + + # FitContribution operations + # "<<" - Inject a parameter value + c = FitContribution("g1") + c.setProfile(p) + c.setEquation("A * exp(-0.5*(x-x0)**2/sigma**2)") + c.A << 0.5 + c.x0 << 5 + c.sigma << 1 + + # FitRecipe operations + # "|=" - Union of necessary components. + # "+=" - Add Parameter or create a new one. Each tuple is a set of + # arguments for either setVar or addVar. + # "*=" - Constrain a parameter. Think of "*" as a push-pin holding one + # parameter's value to that of another. + # "%=" - Restrain a parameter or equation. Think of "%" as a rope + # loosely tying parameters to a value. + r = FitRecipe() + r |= c + r += (c.A, 0.5), (c.x0, 5), ("sig", 1) + r *= c.sigma, "sig" + r %= c.A, 0.5, 0.5 + + from gaussianrecipe import scipyOptimize + + scipyOptimize(r) + + res = FitResults(r) + # Print the results. + res.printResults() + # Plot the results. + from gaussianrecipe import plotResults + + plotResults(r) + + return + + +if __name__ == "__main__": + main() + +# End of file diff --git a/docs/examples/srfit_ex/npintensity.py b/docs/examples/srfit_ex/npintensity.py new file mode 100644 index 0000000..210aa4c --- /dev/null +++ b/docs/examples/srfit_ex/npintensity.py @@ -0,0 +1,531 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of using ProfileGenerators in FitContributions. + +This is an example of building a ProfileGenerator and using it in a +FitContribution in order to fit theoretical intensity data. ProfileGenerators +are used to organize profile calculators that require more information than can +be conveniently passed into a function call. The IntensityGenerator class is +an example of a ProfileGenerator that can be used by a FitContribution to help +generate a the profile. + +Instructions + +Run the example and note the last line of the output. It will be described in +the code. Then read through 'IntensityGenerator' class. This will motivate the +need for the ProfileGenerator class. Next read the 'makeRecipe' code. This +will demonstrate how to use the generator, the structure container needed by +the generator and introduce new operations that can be used in a registered +equation. + +Extensions + +- The IntensityGenerator class uses the 'addParameterSet' method to associate + the structure adapter (DiffpyStructureParSet) with the generator. Most SrFit + classes have an 'addParameterSet' class and can store ParameterSet objects. + Grab the phase object from the IntensityGenerator and try to add it to other + objects used in the fit recipe. Create variables from the moved Parameters + rather than from the 'phase' that lives in the IntensityGenerator and see if + everything still refines. +""" + +from __future__ import print_function + +import numpy +from gaussianrecipe import scipyOptimize + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, + ProfileGenerator, +) +from diffpy.srfit.structure.diffpyparset import DiffpyStructureParSet + +###### +# Example Code + + +class IntensityGenerator(ProfileGenerator): + """A class for calculating intensity using the Debye equation. + + Calculating intensity from a structure is difficult in general. This + class takes a diffpy.structure.Structure instance and from that + generates a theoretical intensity signal. Unlike the example in + gaussianrecipe.py, the intensity generator is not simple. It must + take a structure object and some Parameters, and from that generate + a signal. At the same time, the structure itself (the lattice, atom + positions, thermal parameters, etc.) needs to be refinable. Thus we + define this ProfileGenerator to help us interface which exposes the + Parameters required by the calculation and provides a way for a + FitContribution to perform that calculation. + + The purpose of a ProfileGenerator is to 1) provide a function that + generates a profile signal 2) organize the Parameters required for + the calculation + + This generator wraps the 'iofq' function defined below. Knowledge of + this function is not required for this example. + """ + + def __init__(self, name): + """Define our generator. + + In this example we will keep count of how many times the + calculation gets performed. The 'count' attribute will be used + to store the count. + """ + ProfileGenerator.__init__(self, name) + # Count the calls + self.count = 0 + return + + def setStructure(self, strufile): + """Set the structure used in the calculation. + + strufile -- The name of a structure file. A + diffpy.structure.Structure object will be created from + the file, and that object will be passed to the 'iofq' + function whenever it is called. + + This will create the refinement Parameters using the + DiffpyStructureParSet adapter from diffpy.srfit.structure.diffpyparset. + DiffpyStructureParSet is a ParameterSet object that organizes and gives + attribute access to Parameters and ParameterSets adapted from a diffpy + Structure object. The Parameters embedded in the DiffpyStructureParSet + are proxies for attributes of the diffpy.structure.Structure object + that is needed by the 'iofq' function. The Parameters will be + accessible by name under the 'phase' attribute of this generator, and + are organized hierarchically: + + phase + - lattice (retrieved with 'getLattice') + - a + - b + - c + - alpha + - beta + - gamma + - scatterers (retrieved with 'getScatterers') + - atom1 (the name depends on the element) + - x + - y + - z + - occ + - U11 + - U22 + - U33 + - U12 + - U13 + - U23 + - Uiso + - etc. + + The diffpy.structure.Structure instance is held within the + DiffpyStructureParSet as the 'stru' attribute. + """ + # Load the structure from file + from diffpy.structure import Structure + + stru = Structure() + stru.read(strufile) + + # Create a ParameterSet designed to interface with + # diffpy.structure.Structure objects that organizes the Parameter + # hierarchy. Note that the DiffpyStructureParSet holds a handle to the + # loaded structure that we use in the __call__ method below. + # + # We pass the diffpy.structure.Structure instance, and give the + # DiffpyStructureParSet the name "phase". + parset = DiffpyStructureParSet("phase", stru) + + # Put this ParameterSet in the ProfileGenerator. + self.addParameterSet(parset) + + return + + def __call__(self, q): + """Calculate the intensity. + + This ProfileGenerator will be used in a FitContribution that + will be optimized to fit some data. By the time this function + is evaluated, the diffpy.structure.Structure instance has been + updated by the optimizer via the DiffpyStructureParSet defined + in setStructure. Thus, we need only call iofq with the internal + structure object. + """ + self.count += 1 + print("iofq called", self.count) + return iofq(self.phase.stru, q) + + +# End class IntensityGenerator + + +def makeRecipe(strufile, datname): + """Create a recipe that uses the IntensityGenerator. + + This will create a FitContribution that uses the IntensityGenerator, + associate this with a Profile, and use this to define a FitRecipe. + """ + + # The Profile + # Create a Profile. This will hold the experimental and calculated signal. + profile = Profile() + + # Load data and add it to the profile + x, y, u = profile.loadtxt(datname) + + # The ProfileGenerator + # Create an IntensityGenerator named "I". This will be the name we use to + # refer to the generator from within the FitContribution equation. We also + # need to load the model structure we're using. + generator = IntensityGenerator("I") + generator.setStructure(strufile) + + # The FitContribution + # Create a FitContribution, that will associate the Profile with the + # ProfileGenerator. The ProfileGenerator will be accessible as an + # attribute of the FitContribution by its name ("I"). We also want to tell + # the FitContribution to name the x-variable of the profile "q", so we can + # use it in equations with this name. + contribution = FitContribution("bucky") + contribution.addProfileGenerator(generator) + contribution.setProfile(profile, xname="q") + + # Now we're ready to define the fitting equation for the FitContribution. + # We need to modify the intensity calculation, and we'll do that from + # within the fitting equation for the sake of instruction. We want to + # modify the calculation in three ways. We want to scale it, add a + # polynomial background, and broaden the peaks. + # + # There is added benefit for defining these operations outside of the + # IntensityGenerator. By combining the different parts of the calculation + # within the fitting equation, the time-consuming iofq calculation is only + # performed when a structural Parameter is changed. If only non-structural + # parameters are changed, such as the background and broadening Parameters, + # then then previously computed iofq value will be used to compute the + # contribution equation. The benefit in this is very apparent when + # refining the recipe with the LM optimizer, which only changes two + # variables at a time most of the time. Note in the refinement output how + # many times the residual is calculated, versus how many times iofq is + # called when using the scipyOptimize function. + + # We will define the background as a string. + + bkgdstr = "b0 + b1*q + b2*q**2 + b3*q**3 + b4*q**4 + b5*q**5 + b6*q**6 +\ + b7*q**7 + b8*q**8 + b9*q**9" + + # This creates a callable equation named "bkgd" within the FitContribution, + # and turns the polynomial coefficients into Parameters. + contribution.registerStringFunction(bkgdstr, "bkgd") + + # We will create the broadening function that we need by creating a python + # function and registering it with the FitContribution. + pi = numpy.pi + exp = numpy.exp + + def gaussian(q, q0, width): + return ( + 1 + / (2 * pi * width**2) ** 0.5 + * exp(-0.5 * ((q - q0) / width) ** 2) + ) + + # This registers the python function and extracts the name and creates + # Parameters from the arguments. + contribution.registerFunction(gaussian) + + # Center the Gaussian so it is not truncated. + contribution.q0.value = x[len(x) // 2] + + # Now we can incorporate the scale and bkgd into our calculation. We also + # convolve the signal with the Gaussian to broaden it. Recall that we don't + # need to supply arguments to the registered functions unless we want to + # make changes to their input values. + contribution.setEquation("scale * convolve(I, gaussian) + bkgd") + + # Make the FitRecipe and add the FitContribution. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Specify which parameters we want to refine. + recipe.addVar(contribution.b0, 0) + recipe.addVar(contribution.b1, 0) + recipe.addVar(contribution.b2, 0) + recipe.addVar(contribution.b3, 0) + recipe.addVar(contribution.b4, 0) + recipe.addVar(contribution.b5, 0) + recipe.addVar(contribution.b6, 0) + recipe.addVar(contribution.b7, 0) + recipe.addVar(contribution.b8, 0) + recipe.addVar(contribution.b9, 0) + + # We also want to adjust the scale and the convolution width + recipe.addVar(contribution.scale, 1) + recipe.addVar(contribution.width, 0.1) + + # We can also refine structural parameters. Here we extract the + # DiffpyStructureParSet from the intensity generator and use the parameters + # like we would any others. + phase = generator.phase + + # We want to allow for isotropic expansion, so we'll constrain the lattice + # parameters to the same value (the lattice is cubic). Note that we + # constrain to the "a" Parameter directly. In previous examples, we + # constrained to a Variable by name. This has the same effect. + lattice = phase.getLattice() + a = lattice.a + recipe.addVar(a) + recipe.constrain(lattice.b, a) + recipe.constrain(lattice.c, a) + # We want to refine the thermal parameters as well. We will add a new + # Variable that we call "Uiso" and constrain the atomic Uiso values to + # this. Note that we don't give Uiso an initial value. The initial value + # will be inferred from the following constraints. + Uiso = recipe.newVar("Uiso") + for atom in phase.getScatterers(): + recipe.constrain(atom.Uiso, Uiso) + + # Give the recipe away so it can be used! + return recipe + + +def main(): + + # Make the data and the recipe + strufile = "data/C60.stru" + q = numpy.arange(1, 20, 0.05) + makeData(strufile, q, "C60.iq", 1.0, 100.68, 0.005, 0.13, 2) + + # Make the recipe + recipe = makeRecipe(strufile, "C60.iq") + + # Optimize + scipyOptimize(recipe) + + # Generate and print the FitResults + res = FitResults(recipe) + # We want to see how much speed-up we get from bringing the scale and + # background outside of the intensity generator. Get the number of calls + # to the residual function from the FitRecipe, and the number of calls to + # 'iofq' from the IntensityGenerator. + rescount = recipe.fithooks[0].count + calcount = recipe.bucky.I.count + footer = "iofq called %i%% of the time" % int(100.0 * calcount / rescount) + res.printResults(footer=footer) + + # Plot! + plotResults(recipe) + + return + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # All this should be pretty familiar by now. + q = recipe.bucky.profile.x + + Imeas = recipe.bucky.profile.y + Icalc = recipe.bucky.profile.ycalc + bkgd = recipe.bucky.evaluateEquation("bkgd") + diff = Imeas - Icalc + + import pylab + + pylab.plot(q, Imeas, "ob", label="I(Q) Data") + pylab.plot(q, Icalc, "r-", label="I(Q) Fit") + pylab.plot(q, diff, "g-", label="I(Q) diff") + pylab.plot(q, bkgd, "c-", label="Bkgd. Fit") + pylab.xlabel(r"$Q (\AA^{-1})$") + pylab.ylabel("Intensity (arb. units)") + pylab.legend(loc=1) + + pylab.show() + return + + +def iofq(S, q): + """Calculate I(Q) (X-ray) using the Debye Equation. + + I(Q) = 2 sum(i,j) f_i(Q) f_j(Q) sinc(rij Q) exp(-0.5 ssij Q**2) + (The exponential term is the Debye-Waller factor.) + + S -- A diffpy.structure.Structure instance. It is assumed that the + structure is that of an isolated scatterer. Periodic boundary + conditions are not applied. + q -- The q-points to calculate over. + + This uses cctbx for the calculation of the f_i if it is available, + otherwise f_i = 1. + """ + # The functions we need + sinc = numpy.sinc + exp = numpy.exp + pi = numpy.pi + + # The brute-force calculation is very slow. Thus we optimize a little bit. + + # The precision of distance measurements + deltad = 1e-6 + dmult = int(1 / deltad) + deltau = deltad**2 + umult = int(1 / deltau) + + pairdict = {} + elcount = {} + n = len(S) + for i in range(n): + + # count the number of each element + eli = S[i].element + m = elcount.get(eli, 0) + elcount[eli] = m + 1 + + for j in range(i + 1, n): + + elj = S[j].element + + # Get the pair + els = [eli, elj] + els.sort() + + # Get the distance to the desired precision + d = S.distance(i, j) + D = int(d * dmult) + + # Get the DW factor to the same precision + ss = S[i].Uisoequiv + S[j].Uisoequiv + SS = int(ss * umult) + + # Record the multiplicity of this pair + key = (els[0], els[1], D, SS) + mult = pairdict.get(key, 0) + pairdict[key] = mult + 1 + + # Now we can calculate IofQ from the pair dictionary. Making the dictionary + # first reduces the amount of calls to sinc and exp we have to make. + + # First we must cache the scattering factors + fdict = {} + for el in elcount: + fdict[el] = getXScatteringFactor(el, q) + + # Now we can compute I(Q) for the i != j pairs + y = 0 + x = q * deltad / pi + for key, mult in pairdict.items(): + eli = key[0] + elj = key[1] + fi = fdict[eli] + fj = fdict[elj] + D = key[2] + SS = key[3] + + # Note that numpy's sinc(x) = sin(x*pi)/(x*pi) + y += fi * fj * mult * sinc(x * D) * exp(-0.5 * SS * deltau * q**2) + + # We must multiply by 2 since we only counted j > i pairs. + y *= 2 + + # Now we must add in the i == j pairs. + for el, f in fdict.items(): + y += f**2 * elcount[el] + + # And that's it! + + return y + + +def getXScatteringFactor(el, q): + """Get the x-ray scattering factor for an element over the q range. + + If cctbx is not available, f(q) = 1 is used. + """ + try: + import cctbx.eltbx.xray_scattering as xray + + wk1995 = xray.wk1995(el) + g = wk1995.fetch() + # at_stol - at sin(theta)/lambda = Q/(4*pi) + f = numpy.asarray(map(g.at_stol, q / (4 * numpy.pi))) + return f + except ImportError: + return 1 + + +def makeData(strufile, q, datname, scale, a, Uiso, sig, bkgc, nl=1): + """Make some fake data and save it to file. + + Make some data to fit. This uses iofq to calculate an intensity curve, and + adds to it a background, broadens the peaks, and noise. + + strufile-- A filename holding the sample structure + q -- The q-range to calculate over. + datname -- The name of the file we're saving to. + scale -- The scale factor + a -- The lattice constant to use + Uiso -- The thermal factor for all atoms + sig -- The broadening factor + bkgc -- A parameter that gives minor control of the background. + nl -- Noise level (0, inf), default 1, larger -> less noise. + """ + + from diffpy.structure import Structure + + S = Structure() + S.read(strufile) + + # Set the lattice parameters + S.lattice.setLatPar(a, a, a) + + # Set a DW factor + for a in S: + a.Uisoequiv = Uiso + y = iofq(S, q) + + # We want to broaden the peaks as well. This simulates instrument effects. + q0 = q[len(q) // 2] + g = numpy.exp(-0.5 * ((q - q0) / sig) ** 2) + y = numpy.convolve(y, g, mode="same") / sum(g) + + # Add a polynomial background. + bkgd = (q + bkgc) ** 2 * (1.5 * max(q) - q) ** 5 + bkgd *= 0.2 * max(y) / max(bkgd) + + y += bkgd + + # Multiply by a scale factor + y *= scale + + # Calculate the uncertainty + u = (y / nl) ** 0.5 + + # And apply the noise + if nl > 0: + y = numpy.random.poisson(y * nl) / nl + + # Now save it + numpy.savetxt(datname, numpy.transpose([q, y, u])) + return + + +if __name__ == "__main__": + + main() + +# End of file diff --git a/docs/examples/srfit_ex/npintensityII.py b/docs/examples/srfit_ex/npintensityII.py new file mode 100644 index 0000000..bd3a32f --- /dev/null +++ b/docs/examples/srfit_ex/npintensityII.py @@ -0,0 +1,279 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of extracting information from multiple data sets +simultaneously. + +This example builds on npintensitygenerator.py, and uses IntensityGenerator +from that example to build a recipe that simultaneously refines two data sets +generated from the same structure. + +Instructions + +Run the example and then read through the 'makeRecipe' code. You will see how +to refine a single structure to two data sets. + +Extensions + +- In 'makeRecipe' the fit contributions are identically configured except for + the profile. Factor out that configuration code and apply it in the + 'makeRecipe' method. This will reduce the amount of code required to get the + job done, make it clearer what is being done and therefore reduce potential + mistakes in the code. This encapsulation of configuration workflow is the + first step towards writing a user interface. +""" + +import numpy +from gaussianrecipe import scipyOptimize +from npintensity import IntensityGenerator, makeData + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) + +###### +# Example Code + + +def makeRecipe(strufile, datname1, datname2): + """Create a recipe that uses the IntensityGenerator. + + We will create two FitContributions that use the IntensityGenerator + from npintensitygenerator.py and associate each of these with a + Profile, and use this to define a FitRecipe. + + Both simulated data sets come from the same structure. We're going + to make two FitContributions that are identical, except for the + profile that is held in each. We're going to assure that the + structures are identical by using the same DiffpyStructureParSet + (which is generated by the IntensityGenerator when we load the + structure) in both generators. + """ + + # The Profiles + # Create two Profiles for the two FitContributions. + profile1 = Profile() + profile2 = Profile() + + # Load data into the Profiles + profile1.loadtxt(datname1) + x, y, u = profile2.loadtxt(datname2) + + # The ProfileGenerators + # Create two IntensityGenerators named "I". There will not be a name + # conflict, since the name is only meaningful within the FitContribution + # that holds the ProfileGenerator. Load the structure into one and make + # sure that the second ProfileGenerator is using the same + # DiffyStructureParSet. This will assure that both ProfileGenerators are + # using the exact same Parameters, and underlying Structure object in the + # calculation of the profile. + generator1 = IntensityGenerator("I") + generator1.setStructure(strufile) + generator2 = IntensityGenerator("I") + generator2.addParameterSet(generator1.phase) + + # The FitContributions + # Create the FitContributions. + contribution1 = FitContribution("bucky1") + contribution1.addProfileGenerator(generator1) + contribution1.setProfile(profile1, xname="q") + contribution2 = FitContribution("bucky2") + contribution2.addProfileGenerator(generator2) + contribution2.setProfile(profile2, xname="q") + + # Now we're ready to define the fitting equation for each FitContribution. + # The functions registered below will be independent, even though they take + # the same form and use the same Parameter names. By default, Parameters + # in different contributions are different Parameters even if they have the + # same names. FitContributions are isolated namespaces than only share + # information if you tell them to by using addParameter or addParameterSet. + bkgdstr = "b0 + b1*q + b2*q**2 + b3*q**3 + b4*q**4 + b5*q**5 + b6*q**6 +\ + b7*q**7 +b8*q**8 + b9*q**9" + + contribution1.registerStringFunction(bkgdstr, "bkgd") + contribution2.registerStringFunction(bkgdstr, "bkgd") + + # We will create the broadening function by registering a python function. + pi = numpy.pi + exp = numpy.exp + + def gaussian(q, q0, width): + return ( + 1 + / (2 * pi * width**2) ** 0.5 + * exp(-0.5 * ((q - q0) / width) ** 2) + ) + + contribution1.registerFunction(gaussian) + contribution2.registerFunction(gaussian) + # Center the gaussian + contribution1.q0.value = x[len(x) // 2] + contribution2.q0.value = x[len(x) // 2] + + # Now we can incorporate the scale and bkgd into our calculation. We also + # convolve the signal with the gaussian to broaden it. + contribution1.setEquation("scale * convolve(I, gaussian) + bkgd") + contribution2.setEquation("scale * convolve(I, gaussian) + bkgd") + + # Make a FitRecipe and associate the FitContributions. + recipe = FitRecipe() + recipe.addContribution(contribution1) + recipe.addContribution(contribution2) + + # Specify which Parameters we want to refine. We want to refine the + # background that we just defined in the FitContributions. We have to do + # this separately for each FitContribution. We tag the variables so it is + # easy to retrieve the background variables. + recipe.addVar(contribution1.b0, 0, name="b1_0", tag="bcoeffs1") + recipe.addVar(contribution1.b1, 0, name="b1_1", tag="bcoeffs1") + recipe.addVar(contribution1.b2, 0, name="b1_2", tag="bcoeffs1") + recipe.addVar(contribution1.b3, 0, name="b1_3", tag="bcoeffs1") + recipe.addVar(contribution1.b4, 0, name="b1_4", tag="bcoeffs1") + recipe.addVar(contribution1.b5, 0, name="b1_5", tag="bcoeffs1") + recipe.addVar(contribution1.b6, 0, name="b1_6", tag="bcoeffs1") + recipe.addVar(contribution1.b7, 0, name="b1_7", tag="bcoeffs1") + recipe.addVar(contribution1.b8, 0, name="b1_8", tag="bcoeffs1") + recipe.addVar(contribution1.b9, 0, name="b1_9", tag="bcoeffs1") + recipe.addVar(contribution2.b0, 0, name="b2_0", tag="bcoeffs2") + recipe.addVar(contribution2.b1, 0, name="b2_1", tag="bcoeffs2") + recipe.addVar(contribution2.b2, 0, name="b2_2", tag="bcoeffs2") + recipe.addVar(contribution2.b3, 0, name="b2_3", tag="bcoeffs2") + recipe.addVar(contribution2.b4, 0, name="b2_4", tag="bcoeffs2") + recipe.addVar(contribution2.b5, 0, name="b2_5", tag="bcoeffs2") + recipe.addVar(contribution2.b6, 0, name="b2_6", tag="bcoeffs2") + recipe.addVar(contribution2.b7, 0, name="b2_7", tag="bcoeffs2") + recipe.addVar(contribution2.b8, 0, name="b2_8", tag="bcoeffs2") + recipe.addVar(contribution2.b9, 0, name="b2_9", tag="bcoeffs2") + + # We also want to adjust the scale and the convolution width + recipe.addVar(contribution1.scale, 1, name="scale1") + recipe.addVar(contribution1.width, 0.1, name="width1") + recipe.addVar(contribution2.scale, 1, name="scale2") + recipe.addVar(contribution2.width, 0.1, name="width2") + + # We can also refine structural parameters. We only have to do this once, + # since each generator holds the same DiffpyStructureParSet. + phase = generator1.phase + lattice = phase.getLattice() + a = recipe.addVar(lattice.a) + # We want to allow for isotropic expansion, so we'll make constraints for + # that. + recipe.constrain(lattice.b, a) + recipe.constrain(lattice.c, a) + # We want to refine the thermal parameters as well. We will add a new + # variable that we call "Uiso" and constrain the atomic Uiso values to + # this. Note that we don't give Uiso an initial value. The initial value + # will be inferred from the subsequent constraints. + Uiso = recipe.newVar("Uiso") + for atom in phase.getScatterers(): + recipe.constrain(atom.Uiso, Uiso) + + # Give the recipe away so it can be used! + return recipe + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # plotting song and dance + q = recipe.bucky1.profile.x + + # Plot this for fun. + I1 = recipe.bucky1.profile.y + Icalc1 = recipe.bucky1.profile.ycalc + bkgd1 = recipe.bucky1.evaluateEquation("bkgd") + diff1 = I1 - Icalc1 + I2 = recipe.bucky2.profile.y + Icalc2 = recipe.bucky2.profile.ycalc + bkgd2 = recipe.bucky2.evaluateEquation("bkgd") + diff2 = I2 - Icalc2 + offset = 1.2 * max(I2) * numpy.ones_like(I2) + I1 += offset + Icalc1 += offset + bkgd1 += offset + diff1 += offset + + import pylab + + pylab.subplot(2, 1, 1) + pylab.plot(q, I1, "bo", label="I1(Q) Data") + pylab.plot(q, Icalc1, "r-", label="I1(Q) Fit") + pylab.plot(q, diff1, "g-", label="I1(Q) diff") + pylab.plot(q, bkgd1, "c-", label="Bkgd1 Fit") + pylab.legend(loc=1) + + pylab.subplot(2, 1, 2) + pylab.plot(q, I2, "bo", label="I2(Q) Data") + pylab.plot(q, Icalc2, "r-", label="I2(Q) Fit") + pylab.plot(q, diff2, "g-", label="I2(Q) diff") + pylab.plot(q, bkgd2, "c-", label="Bkgd2 Fit") + pylab.xlabel(r"$Q (\AA^{-1})$") + pylab.ylabel("Intensity (arb. units)") + pylab.legend(loc=1) + + pylab.show() + return + + +def main(): + + # Make two different data sets, each from the same structure, but with + # different scale, noise, broadening and background. + strufile = "data/C60.stru" + q = numpy.arange(1, 20, 0.05) + makeData(strufile, q, "C60_1.iq", 8.1, 101.68, 0.008, 0.12, 2, 0.01) + makeData(strufile, q, "C60_2.iq", 3.2, 101.68, 0.02, 0.003, 0, 1) + + # Make the recipe + recipe = makeRecipe(strufile, "C60_1.iq", "C60_2.iq") + + # Optimize + # Since the backgrounds have a large effect on the profile, we will refine + # them first, but do so separately. + # To refine the background from the first contribution, we will fix + # all other parameters and give the second contribution no weight in the + # fit. + recipe.fix("all") + recipe.free("bcoeffs1") + recipe.setWeight(recipe.bucky2, 0) + scipyOptimize(recipe) + # Now do the same for the second background + recipe.fix("all") + recipe.free("bcoeffs1") + recipe.setWeight(recipe.bucky2, 1) + recipe.setWeight(recipe.bucky1, 0) + scipyOptimize(recipe) + # Now refine everything with the structure parameters included + recipe.free("all") + recipe.setWeight(recipe.bucky1, 1) + scipyOptimize(recipe) + + # Generate and print the FitResults + res = FitResults(recipe) + res.printResults() + + # Plot! + plotResults(recipe) + + return + + +if __name__ == "__main__": + + main() + +# End of file diff --git a/docs/examples/srfit_ex/nppdfcrystal.py b/docs/examples/srfit_ex/nppdfcrystal.py new file mode 100644 index 0000000..0c098ef --- /dev/null +++ b/docs/examples/srfit_ex/nppdfcrystal.py @@ -0,0 +1,129 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of fitting a crystal-like nanoparticle (nanocrystal) PDF. + +This is an example of modeling the PDF from a nanocrystal as an +attenuated bulk PDF. This involves a crystal PDF calculation and a +spherical nanoparticle characteristic function. The equation we model is +Gnano(r) = f(r) * Gbulk(r), where f(r) is the nanoparticle +characteristic function for the nanoparticle shape. Functions for +calculating the characteristic function in the +diffpy.srfit.pdf.characteristicfunctions module. +""" + +import numpy +from gaussianrecipe import scipyOptimize +from pyobjcryst import loadCrystal + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) +from diffpy.srfit.pdf import PDFGenerator, PDFParser + + +def makeRecipe(ciffile, grdata): + """Make a recipe to model a crystal-like nanoparticle PDF.""" + + # Set up a PDF fit as has been done in other examples. + pdfprofile = Profile() + + pdfparser = PDFParser() + pdfparser.parseFile(grdata) + pdfprofile.loadParsedData(pdfparser) + pdfprofile.setCalculationRange(xmin=0.1, xmax=20) + + pdfcontribution = FitContribution("pdf") + pdfcontribution.setProfile(pdfprofile, xname="r") + + pdfgenerator = PDFGenerator("G") + pdfgenerator.setQmax(30.0) + stru = loadCrystal(ciffile) + pdfgenerator.setStructure(stru) + pdfcontribution.addProfileGenerator(pdfgenerator) + + # Register the nanoparticle shape factor. + from diffpy.srfit.pdf.characteristicfunctions import sphericalCF + + pdfcontribution.registerFunction(sphericalCF, name="f") + + # Now we set up the fitting equation. + pdfcontribution.setEquation("f * G") + + # Now make the recipe. Make sure we fit the characteristic function shape + # parameters, in this case 'psize', which is the diameter of the particle. + recipe = FitRecipe() + recipe.addContribution(pdfcontribution) + + phase = pdfgenerator.phase + for par in phase.sgpars: + recipe.addVar(par) + + recipe.addVar(pdfcontribution.psize, 20) + recipe.addVar(pdfgenerator.scale, 1) + recipe.addVar(pdfgenerator.delta2, 0) + recipe.B11_0 = 0.1 + + return recipe + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # All this should be pretty familiar by now. + r = recipe.pdf.profile.x + g = recipe.pdf.profile.y + gcalc = recipe.pdf.profile.ycalc + diffzero = -0.8 * max(g) * numpy.ones_like(g) + diff = g - gcalc + diffzero + + gcryst = recipe.pdf.evaluateEquation("G") + gcryst /= recipe.scale.value + + fr = recipe.pdf.evaluateEquation("f") + fr *= max(g) / fr[0] + + import pylab + + pylab.plot(r, g, "bo", label="G(r) Data") + pylab.plot(r, gcryst, "y--", label="G(r) Crystal") + pylab.plot(r, fr, "k--", label="f(r) calculated (scaled)") + pylab.plot(r, gcalc, "r-", label="G(r) Fit") + pylab.plot(r, diff, "g-", label="G(r) diff") + pylab.plot(r, diffzero, "k-") + pylab.xlabel(r"$r (\AA)$") + pylab.ylabel(r"$G (\AA^{-2})$") + pylab.legend(loc=1) + + pylab.show() + return + + +if __name__ == "__main__": + + ciffile = "data/pb.cif" + grdata = "data/pb_100_qmin1.gr" + + recipe = makeRecipe(ciffile, grdata) + scipyOptimize(recipe) + + res = FitResults(recipe) + res.printResults() + + plotResults(recipe) + +# End of file diff --git a/docs/examples/srfit_ex/nppdfobjcryst.py b/docs/examples/srfit_ex/nppdfobjcryst.py new file mode 100644 index 0000000..a05dbaa --- /dev/null +++ b/docs/examples/srfit_ex/nppdfobjcryst.py @@ -0,0 +1,257 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of a nanoparticle PDF refinement using DebyePDFGenerator. + +This example is similar to crystalpdfobjcryst.py, except that it uses +the DebyePDFGenerator from SrReal to refine a pyobjcryst Molecule. +""" + +import numpy + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) +from diffpy.srfit.pdf import DebyePDFGenerator + +###### +# Example Code + + +def makeRecipe(molecule, datname): + """Create a recipe that uses the DebyePDFGenerator.""" + + # The Profile + profile = Profile() + + # Load data and add it to the profile + profile.loadtxt(datname) + profile.setCalculationRange(xmin=1.2, xmax=8) + + # The ProfileGenerator + # Create a DebyePDFGenerator named "G". + generator = DebyePDFGenerator("G") + generator.setStructure(molecule) + # These are metadata needed by the generator + generator.setQmin(0.68) + generator.setQmax(22) + + # The FitContribution + contribution = FitContribution("bucky") + contribution.addProfileGenerator(generator) + contribution.setProfile(profile, xname="r") + + # Make a FitRecipe. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Specify which parameters we want to refine. We'll be using the + # MoleculeParSet within the generator, so let's get a handle to it. See the + # diffpy.srfit.structure.objcryststructure module for more information + # about the MoleculeParSet hierarchy. + c60 = generator.phase + + # First, the isotropic thermal displacement factor. + Biso = recipe.newVar("Biso") + for atom in c60.getScatterers(): + + # We have defined a 'center' atom that is a dummy, which means that it + # has no scattering power. It is only used as a reference point for + # our bond length. We don't want to constrain it. + if not atom.isDummy(): + recipe.constrain(atom.Biso, Biso) + + # We need to let the molecule expand. If we were modeling it as a crystal, + # we could let the unit cell expand. For instruction purposes, we use a + # Molecule to model C60, and molecules have different modeling options than + # crystals. To make the molecule expand from a central point, we will + # constrain the distance from each atom to a dummy center atom that was + # created with the molecule, and allow that distance to vary. (We could + # also let the nearest-neighbor bond lengths vary, but that would be much + # more difficult to set up.) + center = c60.center + # Create a new Parameter that represents the radius of the molecule. Note + # that we don't give it an initial value. Since the variable is being + # directly constrained to further below, its initial value will be inferred + # from the constraint. + radius = recipe.newVar("radius") + for i, atom in enumerate(c60.getScatterers()): + + if atom.isDummy(): + continue + + # This creates a Parameter that moves the second atom according to the + # bond length. Note that each Parameter needs a unique name. + par = c60.addBondLengthParameter("rad%i" % i, center, atom) + recipe.constrain(par, radius) + + # Add the correlation term, scale. The scale is too short to effectively + # determine qdamp. + recipe.addVar(generator.delta2, 2) + recipe.addVar(generator.scale, 1.3e4) + + # Give the recipe away so it can be used! + return recipe + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # Plot this. + r = recipe.bucky.profile.x + g = recipe.bucky.profile.y + gcalc = recipe.bucky.profile.ycalc + diffzero = -0.8 * max(g) * numpy.ones_like(g) + diff = g - gcalc + diffzero + + import pylab + + pylab.plot(r, g, "ob", label="G(r) Data") + pylab.plot(r, gcalc, "-r", label="G(r) Fit") + pylab.plot(r, diff, "-g", label="G(r) diff") + pylab.plot(r, diffzero, "-k") + pylab.xlabel(r"$r (\AA)$") + pylab.ylabel(r"$G (\AA^{-2})$") + pylab.legend(loc=1) + + pylab.show() + return + + +def main(): + + molecule = makeC60() + # Make the data and the recipe + recipe = makeRecipe(molecule, "data/C60.gr") + # Tell the fithook that we want very verbose output. + recipe.fithooks[0].verbose = 3 + + # Optimize + from scipy.optimize import leastsq + + leastsq(recipe.residual, recipe.getValues()) + + # Print results + res = FitResults(recipe) + res.printResults() + + # Plot results + plotResults(recipe) + + return + + +c60xyz = """ +3.451266498 0.685000000 0.000000000 +3.451266498 -0.685000000 0.000000000 +-3.451266498 0.685000000 0.000000000 +-3.451266498 -0.685000000 0.000000000 +0.685000000 0.000000000 3.451266498 +-0.685000000 0.000000000 3.451266498 +0.685000000 0.000000000 -3.451266498 +-0.685000000 0.000000000 -3.451266498 +0.000000000 3.451266498 0.685000000 +0.000000000 3.451266498 -0.685000000 +0.000000000 -3.451266498 0.685000000 +0.000000000 -3.451266498 -0.685000000 +3.003809890 1.409000000 1.171456608 +3.003809890 1.409000000 -1.171456608 +3.003809890 -1.409000000 1.171456608 +3.003809890 -1.409000000 -1.171456608 +-3.003809890 1.409000000 1.171456608 +-3.003809890 1.409000000 -1.171456608 +-3.003809890 -1.409000000 1.171456608 +-3.003809890 -1.409000000 -1.171456608 +1.409000000 1.171456608 3.003809890 +1.409000000 -1.171456608 3.003809890 +-1.409000000 1.171456608 3.003809890 +-1.409000000 -1.171456608 3.003809890 +1.409000000 1.171456608 -3.003809890 +1.409000000 -1.171456608 -3.003809890 +-1.409000000 1.171456608 -3.003809890 +-1.409000000 -1.171456608 -3.003809890 +1.171456608 3.003809890 1.409000000 +-1.171456608 3.003809890 1.409000000 +1.171456608 3.003809890 -1.409000000 +-1.171456608 3.003809890 -1.409000000 +1.171456608 -3.003809890 1.409000000 +-1.171456608 -3.003809890 1.409000000 +1.171456608 -3.003809890 -1.409000000 +-1.171456608 -3.003809890 -1.409000000 +2.580456608 0.724000000 2.279809890 +2.580456608 0.724000000 -2.279809890 +2.580456608 -0.724000000 2.279809890 +2.580456608 -0.724000000 -2.279809890 +-2.580456608 0.724000000 2.279809890 +-2.580456608 0.724000000 -2.279809890 +-2.580456608 -0.724000000 2.279809890 +-2.580456608 -0.724000000 -2.279809890 +0.724000000 2.279809890 2.580456608 +0.724000000 -2.279809890 2.580456608 +-0.724000000 2.279809890 2.580456608 +-0.724000000 -2.279809890 2.580456608 +0.724000000 2.279809890 -2.580456608 +0.724000000 -2.279809890 -2.580456608 +-0.724000000 2.279809890 -2.580456608 +-0.724000000 -2.279809890 -2.580456608 +2.279809890 2.580456608 0.724000000 +-2.279809890 2.580456608 0.724000000 +2.279809890 2.580456608 -0.724000000 +-2.279809890 2.580456608 -0.724000000 +2.279809890 -2.580456608 0.724000000 +-2.279809890 -2.580456608 0.724000000 +2.279809890 -2.580456608 -0.724000000 +-2.279809890 -2.580456608 -0.724000000 +""" + + +def makeC60(): + """Make the C60 molecule using pyobjcryst.""" + + from pyobjcryst.crystal import Crystal + from pyobjcryst.molecule import Molecule + from pyobjcryst.scatteringpower import ScatteringPowerAtom + + # make a crystal box to put the molecule in + c = Crystal(1, 1, 1, "P1") + c.SetName("c60frame") + + # put a molecule inside the box + m = Molecule(c, "c60") + c.AddScatterer(m) + + # Create a dummy atom at the center. + m.AddAtom(0, 0, 0, None, "center") + + # Create the scattering power object for the carbon atoms + sp = ScatteringPowerAtom("C", "C") + c.AddScatteringPower(sp) + sp.SetBiso(0.25) + + # Add the other atoms. They will be named C1, C2, ..., C60. + for i, l in enumerate(c60xyz.strip().splitlines()): + x, y, z = map(float, l.split()) + m.AddAtom(x, y, z, sp, "C%i" % (i + 1)) + + return m + + +if __name__ == "__main__": + + main() + +# End of file diff --git a/docs/examples/srfit_ex/nppdfsas.py b/docs/examples/srfit_ex/nppdfsas.py new file mode 100644 index 0000000..493d299 --- /dev/null +++ b/docs/examples/srfit_ex/nppdfsas.py @@ -0,0 +1,196 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of combining PDF and SAS nanoparticles data. + +This is an example of using both PDF and SAS data in the same fit. This +fits a crystal model to the PDF while fitting a shape model to both the +SAS profile and the PDF data. Using the same shape for the PDF and SAS +provides a feedback mechanism into the fit that allows the PDF and SAS +portions of the fit to guide one another, and in the end gives the shape +of the nanoparticle that agrees best with both the PDF and SAS data. +""" + +import numpy +from gaussianrecipe import scipyOptimize +from pyobjcryst import loadCrystal + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) +from diffpy.srfit.pdf import PDFGenerator, PDFParser +from diffpy.srfit.pdf.characteristicfunctions import SASCF +from diffpy.srfit.sas import SASGenerator, SASParser + + +def makeRecipe(ciffile, grdata, iqdata): + """Make complex-modeling recipe where I(q) and G(r) are fit + simultaneously. + + The fit I(q) is fed into the calculation of G(r), which provides + feedback for the fit parameters of both. + """ + + # Create a PDF contribution as before + pdfprofile = Profile() + pdfparser = PDFParser() + pdfparser.parseFile(grdata) + pdfprofile.loadParsedData(pdfparser) + pdfprofile.setCalculationRange(xmin=0.1, xmax=20) + + pdfcontribution = FitContribution("pdf") + pdfcontribution.setProfile(pdfprofile, xname="r") + + pdfgenerator = PDFGenerator("G") + pdfgenerator.setQmax(30.0) + stru = loadCrystal(ciffile) + pdfgenerator.setStructure(stru) + pdfcontribution.addProfileGenerator(pdfgenerator) + pdfcontribution.setResidualEquation("resv") + + # Create a SAS contribution as well. We assume the nanoparticle is roughly + # elliptical. + sasprofile = Profile() + sasparser = SASParser() + sasparser.parseFile(iqdata) + sasprofile.loadParsedData(sasparser) + if all(sasprofile.dy == 0): + sasprofile.dy[:] = 1 + + sascontribution = FitContribution("sas") + sascontribution.setProfile(sasprofile) + + from sas.models.EllipsoidModel import EllipsoidModel + + model = EllipsoidModel() + sasgenerator = SASGenerator("generator", model) + sascontribution.addProfileGenerator(sasgenerator) + sascontribution.setResidualEquation("resv") + + # Now we set up a characteristic function calculator that depends on the + # sas model. + cfcalculator = SASCF("f", model) + + # Register the calculator with the pdf contribution and define the fitting + # equation. + pdfcontribution.registerCalculator(cfcalculator) + # The PDF for a nanoscale crystalline is approximated by + # Gnano = f * Gcryst + pdfcontribution.setEquation("f * G") + + # Moving on + recipe = FitRecipe() + recipe.addContribution(pdfcontribution) + recipe.addContribution(sascontribution) + + # PDF + phase = pdfgenerator.phase + for par in phase.sgpars: + recipe.addVar(par) + + recipe.addVar(pdfgenerator.scale, 1) + recipe.addVar(pdfgenerator.delta2, 0) + + # SAS + recipe.addVar(sasgenerator.scale, 1, name="iqscale") + recipe.addVar(sasgenerator.radius_a, 10) + recipe.addVar(sasgenerator.radius_b, 10) + + # Even though the cfcalculator and sasgenerator depend on the same sas + # model, we must still constrain the cfcalculator Parameters so that it is + # informed of changes in the refined parameters. + recipe.constrain(cfcalculator.radius_a, "radius_a") + recipe.constrain(cfcalculator.radius_b, "radius_b") + + return recipe + + +def fitRecipe(recipe): + """We refine in stages to help the refinement converge.""" + + # Tune SAS. + recipe.setWeight(recipe.pdf, 0) + recipe.fix("all") + recipe.free("radius_a", "radius_b", iqscale=1e8) + recipe.constrain("radius_b", "radius_a") + scipyOptimize(recipe) + recipe.unconstrain("radius_b") + + # Tune PDF + recipe.setWeight(recipe.pdf, 1) + recipe.setWeight(recipe.sas, 0) + recipe.fix("all") + recipe.free("a", "Biso_0", "scale", "delta2") + scipyOptimize(recipe) + + # Tune all + recipe.setWeight(recipe.pdf, 1) + recipe.setWeight(recipe.sas, 1) + recipe.free("all") + scipyOptimize(recipe) + + return + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # All this should be pretty familiar by now. + r = recipe.pdf.profile.x + g = recipe.pdf.profile.y + gcalc = recipe.pdf.profile.ycalc + diffzero = -0.8 * max(g) * numpy.ones_like(g) + diff = g - gcalc + diffzero + + gcryst = recipe.pdf.evaluateEquation("G") + gcryst /= recipe.scale.value + + fr = recipe.pdf.evaluateEquation("f") + fr *= max(g) / fr[0] + + import pylab + + pylab.plot(r, g, "bo", label="G(r) Data") + pylab.plot(r, gcryst, "y--", label="G(r) Crystal") + pylab.plot(r, fr, "k--", label="f(r) calculated (scaled)") + pylab.plot(r, gcalc, "r-", label="G(r) Fit") + pylab.plot(r, diff, "g-", label="G(r) diff") + pylab.plot(r, diffzero, "k-") + pylab.xlabel(r"$r (\AA)$") + pylab.ylabel(r"$G (\AA^{-2})$") + pylab.legend(loc=1) + + pylab.show() + return + + +if __name__ == "__main__": + + ciffile = "data/pb.cif" + grdata = "data/pb_100_qmin1.gr" + iqdata = "data/pb_100_qmax1.iq" + + recipe = makeRecipe(ciffile, grdata, iqdata) + recipe.fithooks[0].verbose = 3 + fitRecipe(recipe) + + res = FitResults(recipe) + res.printResults() + + plotResults(recipe) + +# End of file diff --git a/docs/examples/srfit_ex/simplepdf.py b/docs/examples/srfit_ex/simplepdf.py new file mode 100644 index 0000000..027a6d7 --- /dev/null +++ b/docs/examples/srfit_ex/simplepdf.py @@ -0,0 +1,91 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2010 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of a PDF using the PDFContribution helper class. + +This is example of fitting the fcc nickel structure to measured PDF +data. It uses the PDFContribution class to simplify fit setup. +""" + +from crystalpdf import plotResults +from gaussianrecipe import scipyOptimize + +from diffpy.srfit.fitbase import FitRecipe, FitResults +from diffpy.srfit.pdf import PDFContribution +from diffpy.structure import Structure + +###### +# Example Code + + +def makeRecipe(ciffile, datname): + """Create a fitting recipe for crystalline PDF data.""" + + # Work directly with a custom PDFContribution to load the data + contribution = PDFContribution("nickel") + contribution.loadData(datname) + contribution.setCalculationRange(xmin=1, xmax=20, dx=0.1) + + # and the phase + stru = Structure() + stru.read(ciffile) + contribution.addStructure("nickel", stru) + + # Make the FitRecipe and add the FitContribution. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Configure the fit variables + phase = contribution.nickel.phase + + from diffpy.srfit.structure import constrainAsSpaceGroup + + sgpars = constrainAsSpaceGroup(phase, "Fm-3m") + + for par in sgpars.latpars: + recipe.addVar(par) + for par in sgpars.adppars: + recipe.addVar(par, 0.005) + + recipe.addVar(contribution.scale, 1) + recipe.addVar(contribution.qdamp, 0.03, fixed=True) + recipe.addVar(contribution.nickel.delta2, 5) + + # Give the recipe away so it can be used! + return recipe + + +if __name__ == "__main__": + + # Make the data and the recipe + ciffile = "data/ni.cif" + data = "data/ni-q27r100-neutron.gr" + + # Make the recipe + recipe = makeRecipe(ciffile, data) + + # Optimize + scipyOptimize(recipe) + # Save the file + recipe.nickel.savetxt("nickel_example.fit") + + # Generate, print and save the FitResults + res = FitResults(recipe) + res.printResults() + res.saveResults("nickel_example.res") + + # Plot! + plotResults(recipe) + +# End of file diff --git a/docs/examples/srfit_ex/simplepdftwophase.py b/docs/examples/srfit_ex/simplepdftwophase.py new file mode 100644 index 0000000..a8017c2 --- /dev/null +++ b/docs/examples/srfit_ex/simplepdftwophase.py @@ -0,0 +1,122 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2010 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of a simplified PDF refinement of two-phase structure.""" + +from crystalpdftwophase import plotResults +from gaussianrecipe import scipyOptimize +from pyobjcryst import loadCrystal + +from diffpy.srfit.fitbase import FitRecipe, FitResults +from diffpy.srfit.pdf import PDFContribution + +###### +# Example Code + + +def makeRecipe(niciffile, siciffile, datname): + """Create a fitting recipe for crystalline PDF data.""" + + # Load data and add it to the profile + contribution = PDFContribution("nisi") + contribution.loadData(datname) + contribution.setCalculationRange(xmax=20) + + stru = loadCrystal(niciffile) + contribution.addStructure("ni", stru) + + stru = loadCrystal(siciffile) + contribution.addStructure("si", stru) + + # Make the FitRecipe and add the FitContribution. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Configure the fit variables + # Start by configuring the scale factor and resolution factors. + # We want the sum of the phase scale factors to be 1. + recipe.newVar("scale_ni", 0.1) + recipe.constrain(contribution.ni.scale, "scale_ni") + recipe.constrain(contribution.si.scale, "1 - scale_ni") + # We also want the resolution factor to be the same on each. This is done + # for free by the PDFContribution. We simply need to add it to the recipe. + recipe.addVar(contribution.qdamp, 0.03) + + # Vary the global scale as well. + recipe.addVar(contribution.scale, 1) + + # Now we can configure the structural parameters. Since we're using + # ObjCrystCrystalParSets, the space group constraints are automatically + # applied to each phase. We must selectively vary the free parameters. + # + # First the nickel parameters. + # Note that ni is the name of the PDFGenerator that was automatically + # created by the PDFContribution. We selected this name in addStructure + # above. + phase_ni = contribution.ni.phase + for par in phase_ni.sgpars: + recipe.addVar(par, name=par.name + "_ni") + recipe.addVar(contribution.ni.delta2, name="delta2_ni") + # Next the silicon parameters + phase_si = contribution.si.phase + for par in phase_si.sgpars: + recipe.addVar(par, name=par.name + "_si") + recipe.addVar(contribution.si.delta2, name="delta2_si") + + # We have prior information from the earlier examples so we'll use it here + # in the form of restraints. + # + # The nickel lattice parameter was measured to be 3.527. The uncertainty + # values are invalid for that measurement, since the data from which it is + # derived has no uncertainty. Thus, we will tell the recipe to scale the + # residual, which means that it will be weighted as much as the average + # data point during the fit. + recipe.restrain("a_ni", lb=3.527, ub=3.527, scaled=True) + # Now we do the same with the delta2 and Biso parameters (remember that + # Biso = 8*pi**2*Uiso) + recipe.restrain("delta2_ni", lb=2.22, ub=2.22, scaled=True) + recipe.restrain("Biso_0_ni", lb=0.454, ub=0.454, scaled=True) + # + # We can do the same with the silicon values. We haven't done a thorough + # job of measuring the uncertainties in the results, so we'll scale these + # as well. + recipe.restrain("a_si", lb=5.430, ub=5.430, scaled=True) + recipe.restrain("delta2_si", lb=3.54, ub=3.54, scaled=True) + recipe.restrain("Biso_0_si", lb=0.645, ub=0.645, scaled=True) + + # Give the recipe away so it can be used! + return recipe + + +if __name__ == "__main__": + + # Make the data and the recipe + niciffile = "data/ni.cif" + siciffile = "data/si.cif" + data = "data/si90ni10-q27r60-xray.gr" + + # Make the recipe + recipe = makeRecipe(niciffile, siciffile, data) + + # Optimize + scipyOptimize(recipe) + + # Generate and print the FitResults + res = FitResults(recipe) + res.printResults() + + # Plot! + plotResults(recipe) + +# End of file diff --git a/docs/examples/srfit_ex/simplerecipe.py b/docs/examples/srfit_ex/simplerecipe.py new file mode 100644 index 0000000..0ec297a --- /dev/null +++ b/docs/examples/srfit_ex/simplerecipe.py @@ -0,0 +1,63 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of simplified fitting. + +This is like gaussianrecipe.py, but it uses the SimpleRecipe, which +integrates the FitContribution and Profile objects for simple recipe +creation. +""" + +from diffpy.srfit.fitbase import SimpleRecipe + +###### +# Example Code + + +def main(): + """Set up a simple recipe in a few lines.""" + + # The SimpleRecipe class is a type of FitRecipe. It provides attribute-like + # access to variables and a residual function that can be minimized. + recipe = SimpleRecipe() + + # Load text from file. + recipe.loadtxt("data/gaussian.dat") + + # Set the equation. The variable "x" is taken from the data that was just + # loaded. The other variables, "A", "x0" and "sigma" are turned into + # attributes with an initial value of 0. + recipe.setEquation("A * exp(-0.5*(x-x0)**2/sigma**2)") + + # We can give them other values here. + recipe.A = 1 + recipe.x0 = 5 + recipe.sigma = 1 + + # We explicitly optimize the residual method of the SimpleRecipe + from scipy.optimize import leastsq + + leastsq(recipe.residual, recipe.values) + + # Print the results + recipe.printResults() + + return + + +if __name__ == "__main__": + + main() + +# End of file diff --git a/docs/examples/srfit_ex/threedoublepeaks.py b/docs/examples/srfit_ex/threedoublepeaks.py new file mode 100644 index 0000000..97fd4d5 --- /dev/null +++ b/docs/examples/srfit_ex/threedoublepeaks.py @@ -0,0 +1,261 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of fitting a three double peaks to simulated data.""" + +from __future__ import print_function + +import numpy + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) + +###### +# Example Code + + +def makeRecipe(): + """Make a FitRecipe for fitting three double-gaussian curves to + data. + + The separation and amplitude ratio of the double peaks follows a + specific relationship. The peaks are broadend according to their + position and they sit on top of a background. We are seeking the + absolute locations of the peaks as well as their amplitudes. + + The independent variable is t. The relationship between the double + peaks is sin(t2) / l2 = sin(t1) / l1 amplitude(peak2) = r * + amplitude(peak1) The values of l1, l2 and r come from experiment. + For this example, we use l1 = 1.012, l2 = 1.0 and r = 0.23. + """ + + # The Profile + # Create a Profile to hold the experimental and calculated signal. + profile = Profile() + x, y, dy = profile.loadtxt("data/threedoublepeaks.dat") + + # Create the contribution + contribution = FitContribution("peaks") + contribution.setProfile(profile, xname="t") + pi = numpy.pi + exp = numpy.exp + + # This is a building-block of our profile function + def gaussian(t, mu, sig): + return 1 / (2 * pi * sig**2) ** 0.5 * exp(-0.5 * ((t - mu) / sig) ** 2) + + contribution.registerFunction(gaussian, name="peakshape") + + def delta(t, mu): + """Calculate a delta-function. + + We don't have perfect precision, so we must make this a very + thin Gaussian. + """ + sig = t[1] - t[0] + return gaussian(t, mu, sig) + + contribution.registerFunction(delta) + + # Here is another one + bkgdstr = "b0 + b1*t + b2*t**2 + b3*t**3 + b4*t**4 + b5*t**5 + b6*t**6" + + contribution.registerStringFunction(bkgdstr, "bkgd") + + # Now define our fitting equation. We will hardcode the peak ratios. + contribution.setEquation( + "A1 * ( convolve( delta(t, mu11), peakshape(t, c, sig11) ) \ + + 0.23*convolve( delta(t, mu12), peakshape(t, c, sig12) ) ) + \ + A2 * ( convolve( delta(t, mu21), peakshape(t, c, sig21) ) \ + + 0.23*convolve( delta(t, mu22), peakshape(t, c, sig22) ) ) + \ + A3 * ( convolve( delta(t, mu31), peakshape(t, c, sig31) ) \ + + 0.23*convolve( delta(t, mu32), peakshape(t, c, sig32) ) ) + \ + bkgd" + ) + + # c is the center of the gaussian. + contribution.c.value = x[len(x) // 2] + + # The FitRecipe + # The FitRecipe lets us define what we want to fit. It is where we can + # create variables, constraints and restraints. + recipe = FitRecipe() + + # Here we tell the FitRecipe to use our FitContribution. When the FitRecipe + # calculates its residual function, it will call on the FitContribution to + # do part of the work. + recipe.addContribution(contribution) + + # Vary the amplitudes for each double peak + recipe.addVar(contribution.A1, 100) + recipe.addVar(contribution.A2, 100) + recipe.addVar(contribution.A3, 100) + + # Vary the position of the first of the double peaks + recipe.addVar(contribution.mu11, 13.0) + recipe.addVar(contribution.mu21, 24.0) + recipe.addVar(contribution.mu31, 33.0) + + # Constrain the position of the second double peak + from numpy import arcsin, sin + + def peakloc(mu): + """Calculate the location of the second peak given the first.""" + l1 = 1.012 + l2 = 1.0 + return 180 / pi * arcsin(pi / 180 * l2 * sin(mu) / l1) + + recipe.registerFunction(peakloc) + recipe.constrain(contribution.mu12, "peakloc(mu11)") + recipe.constrain(contribution.mu22, "peakloc(mu21)") + recipe.constrain(contribution.mu32, "peakloc(mu31)") + + # Vary the width of the peaks. We know the functional form of the peak + # broadening. + recipe.newVar("sig0", 0.001) + recipe.newVar("dsig", 4) + + def sig(sig0, dsig, mu): + """Calculate the peak broadening with respect to position.""" + return sig0 * (1 - dsig * mu**2) + + recipe.registerFunction(sig) + recipe.fix("mu") + # Now constrain the peak widths to this + recipe.sig0.value = 0.001 + recipe.dsig.value = 4.0 + recipe.constrain(contribution.sig11, "sig(sig0, dsig, mu11)") + recipe.constrain( + contribution.sig12, + "sig(sig0, dsig, mu12)", + ns={"mu12": contribution.mu12}, + ) + recipe.constrain(contribution.sig21, "sig(sig0, dsig, mu21)") + recipe.constrain( + contribution.sig22, + "sig(sig0, dsig, mu22)", + ns={"mu22": contribution.mu22}, + ) + recipe.constrain(contribution.sig31, "sig(sig0, dsig, mu31)") + recipe.constrain( + contribution.sig32, + "sig(sig0, dsig, mu32)", + ns={"mu32": contribution.mu32}, + ) + + # Also the background + recipe.addVar(contribution.b0, 0, tag="bkgd") + recipe.addVar(contribution.b1, 0, tag="bkgd") + recipe.addVar(contribution.b2, 0, tag="bkgd") + recipe.addVar(contribution.b3, 0, tag="bkgd") + recipe.addVar(contribution.b4, 0, tag="bkgd") + recipe.addVar(contribution.b5, 0, tag="bkgd") + recipe.addVar(contribution.b6, 0, tag="bkgd") + return recipe + + +def scipyOptimize(recipe): + """Optimize the recipe created above using scipy. + + The FitRecipe we created in makeRecipe has a 'residual' method that + we can be minimized using a scipy optimizer. The details are + described in the source. + """ + + # We're going to use the least-squares (Levenberg-Marquardt) optimizer from + # scipy. We simply have to give it the function to minimize + # (recipe.residual) and the starting values of the Variables + # (recipe.getValues()). + from scipy.optimize.minpack import leastsq + + print("Fit using scipy's LM optimizer") + leastsq(recipe.residual, recipe.getValues()) + + return + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # We can access the data and fit profile through the Profile we created + # above. We get to it through our FitContribution, which we named "g1". + # + # The independent variable. This is always under the "x" attribute. + x = recipe.peaks.profile.x + # The observed profile that we loaded earlier, the "y" attribute. + y = recipe.peaks.profile.y + # The calculated profile, the "ycalc" attribute. + ycalc = recipe.peaks.profile.ycalc + + # This stuff is specific to pylab from the matplotlib distribution. + import pylab + + pylab.plot(x, y, "b.", label="observed profile") + pylab.plot(x, ycalc, "r-", label="calculated profile") + pylab.plot(x, y - ycalc - 0.1 * max(y), "g-", label="difference") + pylab.legend(loc=(0.0, 0.8)) + pylab.xlabel("x") + pylab.ylabel("y") + + pylab.show() + return + + +def steerFit(recipe): + """Steer the fit for this problem. + + This is a complex fit, it requires some steering. + """ + recipe.fix("all") + + recipe.free("bkgd") + scipyOptimize(recipe) + + recipe.free("all") + recipe.fix("mu11", "mu21", "mu31") + scipyOptimize(recipe) + + recipe.free("all") + scipyOptimize(recipe) + + return + + +if __name__ == "__main__": + + # Create the recipe + recipe = makeRecipe() + + # Refine + steerFit(recipe) + + # Get the results in a FitResults object. The FitResults object stores the + # current state of the recipe, and uses it to calculate useful statistics + # about the fit. If you later modify the recipe, the FitResults object + # will hold the recipe values from when it was created. You can tell it to + # update its values by calling its 'update' method. + res = FitResults(recipe) + + # Print the results + res.printResults() + + # Plot the results + plotResults(recipe) + + +# End of file From dc7291db7f84d3e8ca917ed893c3f976eb18e5e1 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Tue, 18 Nov 2025 11:52:10 -0500 Subject: [PATCH 02/23] core-shell-NP --- docs/examples/core-shell-NP/CdS.cif | 69 + docs/examples/core-shell-NP/CdS_ZnS_nano.gr | 7506 +++++++++++++++++++ docs/examples/core-shell-NP/ZnS.cif | 65 + docs/examples/core-shell-NP/coreshellnp.py | 218 + 4 files changed, 7858 insertions(+) create mode 100644 docs/examples/core-shell-NP/CdS.cif create mode 100644 docs/examples/core-shell-NP/CdS_ZnS_nano.gr create mode 100644 docs/examples/core-shell-NP/ZnS.cif create mode 100644 docs/examples/core-shell-NP/coreshellnp.py diff --git a/docs/examples/core-shell-NP/CdS.cif b/docs/examples/core-shell-NP/CdS.cif new file mode 100644 index 0000000..34fa965 --- /dev/null +++ b/docs/examples/core-shell-NP/CdS.cif @@ -0,0 +1,69 @@ +data_1011054 +_chemical_name_systematic 'Cadmium sulfide - $-alpha' +_chemical_name_mineral 'Greenockite' +_chemical_compound_source 'synthetic' +_chemical_formula_structural 'Cd S' +_chemical_formula_sum 'Cd S' +_publ_section_title +; +Ueber die Kristallstruktur des $-alpha- und $-beta Cd S, sowie des +Wurtzits. +; +loop_ +_publ_author_name + 'Ulrich, F' + 'Zachariasen, W' +_journal_name_full +; +Zeitschrift fuer Kristallographie, Kristallgeometrie, Kristallphysik, +Kristallchemie (-144,1977) +; +_journal_coden_ASTM ZEKGAX +_journal_volume 62 +_journal_year 1925 +_journal_page_first 260 +_journal_page_last 273 +_cell_length_a 4.15 +_cell_length_b 4.15 +_cell_length_c 6.737 +_cell_angle_alpha 90 +_cell_angle_beta 90 +_cell_angle_gamma 120 +_cell_volume 100.5 +_cell_formula_units_Z 2 +_exptl_crystal_density_meas 4.82 +_symmetry_space_group_name_H-M 'P 63 m c' +_symmetry_Int_Tables_number 186 +_symmetry_cell_setting hexagonal +loop_ +_symmetry_equiv_pos_as_xyz + 'x,y,z' + '-y,x-y,z' + 'y-x,-x,z' + '-y,-x,z' + 'y-x,y,z' + 'x,x-y,z' + '-x,-y,1/2+z' + 'y,y-x,1/2+z' + 'x-y,x,1/2+z' + 'y,x,1/2+z' + 'x-y,-y,1/2+z' + '-x,y-x,1/2+z' +loop_ +_atom_type_symbol +_atom_type_oxidation_number + Cd2+ 2.000 + S2- -2.000 +loop_ +_atom_site_label +_atom_site_type_symbol +_atom_site_symmetry_multiplicity +_atom_site_Wyckoff_symbol +_atom_site_fract_x +_atom_site_fract_y +_atom_site_fract_z +_atom_site_occupancy +_atom_site_attached_hydrogens +_atom_site_calc_flag + Cd1 Cd 2 b 0.33333 0.66667 0. 1. 0 d + S1 S 2 b 0.33333 0.66667 0.375 1. 0 d diff --git a/docs/examples/core-shell-NP/CdS_ZnS_nano.gr b/docs/examples/core-shell-NP/CdS_ZnS_nano.gr new file mode 100644 index 0000000..650e932 --- /dev/null +++ b/docs/examples/core-shell-NP/CdS_ZnS_nano.gr @@ -0,0 +1,7506 @@ +# +# +# +# +# +# +0.01 0.00284337 +0.02 0.00549539 +0.03 0.00780204 +0.04 0.00954326 +0.05 0.0106442 +0.06 0.0110657 +0.07 0.0107162 +0.08 0.00961948 +0.09 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+#------------------------------------------------------------------------------ +#$Date: 2016-02-16 14:49:47 +0200 (Tue, 16 Feb 2016) $ +#$Revision: 176465 $ +#$URL: svn://www.crystallography.net/cod/cif/9/00/88/9008878.cif $ +#------------------------------------------------------------------------------ +# +# This file is available in the Crystallography Open Database (COD), +# http://www.crystallography.net/. The original data for this entry +# were provided the American Mineralogist Crystal Structure Database, +# http://rruff.geo.arizona.edu/AMS/amcsd.php +# +# The file may be used within the scientific community so long as +# proper attribution is given to the journal article from which the +# data were obtained. +# +data_9008878 +loop_ +_publ_author_name +'Wyckoff, R. W. G.' +_publ_section_title +; + Second edition. Interscience Publishers, New York, New York + Note: wurtzite structure +; +_journal_name_full 'Crystal Structures' +_journal_page_first 85 +_journal_page_last 237 +_journal_volume 1 +_journal_year 1963 +_chemical_formula_sum 'S Zn' +_chemical_name_mineral Wurtzite-2H +_space_group_IT_number 186 +_symmetry_space_group_name_Hall 'P 6c -2c' +_symmetry_space_group_name_H-M 'P 63 m c' +_cell_angle_alpha 90 +_cell_angle_beta 90 +_cell_angle_gamma 120 +_cell_length_a 3.811 +_cell_length_b 3.811 +_cell_length_c 6.234 +_cell_volume 78.411 +_exptl_crystal_density_diffrn 4.128 +_cod_original_formula_sum 'Zn S' +_cod_database_code 9008878 +loop_ +_symmetry_equiv_pos_as_xyz +x,y,z +-x,-x+y,1/2+z +x-y,x,1/2+z +-y,-x,z +-y,x-y,z +x-y,-y,1/2+z +-x,-y,1/2+z +x,x-y,z +-x+y,-x,z +y,x,1/2+z +y,-x+y,1/2+z +-x+y,y,z +loop_ +_atom_site_label +_atom_site_fract_x +_atom_site_fract_y +_atom_site_fract_z +Zn 0.33333 0.66667 0.00000 +S 0.33333 0.66667 0.38500 diff --git a/docs/examples/core-shell-NP/coreshellnp.py b/docs/examples/core-shell-NP/coreshellnp.py new file mode 100644 index 0000000..08d492f --- /dev/null +++ b/docs/examples/core-shell-NP/coreshellnp.py @@ -0,0 +1,218 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2011 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow, Peng Tian +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Refine the structure of a core-shell nanoparticle. + +This applies the characteristic function formalism described in +nppdfcrystal.py to the case of a spherical core-shell nanoparticle. The +modeling approach we use is to refine the core and shell as two +different phases, each with an appropriate characteristic function. +""" + +from pathlib import Path + +import numpy +from pyobjcryst import loadCrystal +from scipy.optimize import leastsq + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) +from diffpy.srfit.pdf import PDFGenerator, PDFParser + +# Example Code + + +def makeRecipe(stru1, stru2, datname): + """Create a fitting recipe for crystalline PDF data.""" + + # The Profile + profile = Profile() + + # Load data and add it to the profile + parser = PDFParser() + parser.parseFile(datname) + profile.loadParsedData(parser) + profile.setCalculationRange(xmin=1.5, xmax=45, dx=0.1) + + # The ProfileGenerator + # In order to fit the core and shell phases simultaneously, we must use two + # PDFGenerators. + # + # The generator for the CdS core. We call it "G_CdS" and will use this name + # later when we set the fitting equation in the FitContribution. + generator_cds = PDFGenerator("G_CdS") + generator_cds.setStructure(stru1) + generator_cds.setQmax(26) + generator_cds.qdamp.value = 0.0396 + # The generator for the ZnS shell. We call it "G_ZnS". + generator_zns = PDFGenerator("G_ZnS") + generator_zns.setStructure(stru2) + generator_zns.setQmax(26) + generator_zns.qdamp.value = 0.0396 + + # The FitContribution + # Add both generators and the profile to the FitContribution. + contribution = FitContribution("cdszns") + contribution.addProfileGenerator(generator_cds) + contribution.addProfileGenerator(generator_zns) + contribution.setProfile(profile, xname="r") + + # Set up the characteristic functions. We use a spherical CF for the core + # and a spherical shell CF for the shell. Since this is set up as two + # phases, we implicitly assume that the core-shell correlations contribute + # very little to the PDF. + from diffpy.srfit.pdf.characteristicfunctions import shellCF, sphericalCF + + contribution.registerFunction(sphericalCF, name="f_CdS") + contribution.registerFunction(shellCF, name="f_ZnS") + + # Write the fitting equation. We want to sum the PDFs from each phase and + # multiply it by a scaling factor. + contribution.setEquation("scale * (f_CdS * G_CdS + f_ZnS * G_ZnS)") + + # Make the FitRecipe and add the FitContribution. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Vary the inner radius and thickness of the shell. Constrain the core + # diameter to twice the shell radius. + recipe.addVar(contribution.radius, 15) + recipe.addVar(contribution.thickness, 11) + recipe.constrain(contribution.psize, "2 * radius") + + # Configure the fit variables + # Start by configuring the scale factor and resolution factors. + # We want the sum of the phase scale factors to be 1. + recipe.newVar("scale_CdS", 0.7) + recipe.constrain(generator_cds.scale, "scale_CdS") + recipe.constrain(generator_zns.scale, "1 - scale_CdS") + # We also want the resolution factor to be the same on each. + + # Vary the global scale as well. + recipe.addVar(contribution.scale, 0.3) + + # Now we can configure the structural parameters. We tag the different + # structural variables so we can easily turn them on and off in the + # subsequent refinement. + phase_cds = generator_cds.phase + for par in phase_cds.sgpars.latpars: + recipe.addVar(par, name=par.name + "_cds", tag="lat") + for par in phase_cds.sgpars.adppars: + recipe.addVar(par, 1, name=par.name + "_cds", tag="adp") + recipe.addVar(phase_cds.sgpars.xyzpars.z_1, name="z_1_cds", tag="xyz") + # Since we know these have stacking disorder, constrain the B33 adps for + # each atom type. + recipe.constrain("B33_1_cds", "B33_0_cds") + recipe.addVar(generator_cds.delta2, name="delta2_cds", value=5) + + phase_zns = generator_zns.phase + for par in phase_zns.sgpars.latpars: + recipe.addVar(par, name=par.name + "_zns", tag="lat") + for par in phase_zns.sgpars.adppars: + recipe.addVar(par, 1, name=par.name + "_zns", tag="adp") + recipe.addVar(phase_zns.sgpars.xyzpars.z_1, name="z_1_zns", tag="xyz") + recipe.constrain("B33_1_zns", "B33_0_zns") + recipe.addVar(generator_zns.delta2, name="delta2_zns", value=2.5) + + # Give the recipe away so it can be used! + return recipe + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # All this should be pretty familiar by now. + r = recipe.cdszns.profile.x + g = recipe.cdszns.profile.y + gcalc = recipe.cdszns.profile.ycalc + diffzero = -0.8 * max(g) * numpy.ones_like(g) + diff = g - gcalc + diffzero + + import matplotlib.pyplot as plt + + plt.plot(r, g, "bo", label="G(r) Data") + plt.plot(r, gcalc, "r-", label="G(r) Fit") + plt.plot(r, diff, "g-", label="G(r) diff") + plt.plot(r, diffzero, "k-") + plt.xlabel(r"$r (\AA)$") + plt.ylabel(r"$G (\AA^{-2})$") + plt.legend(loc=1) + + plt.show() + return + + +def main(): + """Set up and refine the recipe.""" + + # Make the data and the recipe + base_path = Path(__file__).parent + cdsciffile = base_path / "CdS.cif" + znsciffile = base_path / "ZnS.cif" + data = base_path / "CdS_ZnS_nano.gr" + + # Make the recipe + stru1 = loadCrystal(cdsciffile) + stru2 = loadCrystal(znsciffile) + recipe = makeRecipe(stru1, stru2, data) + from diffpy.srfit.fitbase.fithook import PlotFitHook + + recipe.pushFitHook(PlotFitHook()) + recipe.fithooks[0].verbose = 3 + + # Optimize - we do this in steps to help convergence + recipe.fix("all") + + # Start with the lattice parameters. In makeRecipe, these were tagged with + # "lat". Here is how we use that. + recipe.free("lat") + leastsq(recipe.residual, recipe.values, maxfev=50) + + # Now the scale and phase fraction. + recipe.free("scale", "scale_CdS") + leastsq(recipe.residual, recipe.values, maxfev=50) + + # The ADPs. + recipe.free("adp") + leastsq(recipe.residual, recipe.values, maxfev=100) + + # The delta2 parameters. + recipe.free("delta2_cds", "delta2_zns") + leastsq(recipe.residual, recipe.values, maxfev=50) + + # The shape parameters. + recipe.free("radius", "thickness") + leastsq(recipe.residual, recipe.values, maxfev=50) + + # The positional parameters. + recipe.free("xyz") + leastsq(recipe.residual, recipe.values) + + # Generate and print the FitResults + res = FitResults(recipe) + res.printResults() + + # Plot! + plotResults(recipe) + return + + +if __name__ == "__main__": + main() + +# End of file From 3a9f9aff854c5416688aa24ef448b07eac6fa300 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Wed, 19 Nov 2025 12:27:42 -0500 Subject: [PATCH 03/23] plotting and fitting tools --- src/diffpy/cmi/fit_tools.py | 83 +++++++++++++++++++++++++++++++++++++ 1 file changed, 83 insertions(+) create mode 100644 src/diffpy/cmi/fit_tools.py diff --git a/src/diffpy/cmi/fit_tools.py b/src/diffpy/cmi/fit_tools.py new file mode 100644 index 0000000..d7895d3 --- /dev/null +++ b/src/diffpy/cmi/fit_tools.py @@ -0,0 +1,83 @@ +import matplotlib.pyplot as plt +import numpy as np +import scipy.optimize as opt + +try: + from bg_mpl_stylesheets.styles import all_styles + + plt.style.use(all_styles["bg-style"]) +except ImportError: + pass + +optimizers = { + "leastsq": opt.leastsq, +} + + +def optimize_recipe(recipe, optimizer: str = "leastsq", **kwargs): + """Optimize the recipe using any selected SciPy optimizer. + + minimize the residuals (`FitRecipe().residual`) of a FitRecipe by + using a SciPy optimization function. + + Parameters + ---------- + recipe : FitRecipe + The FitRecipe to be optimized. + optimizer : str, optional + The SciPy optimizer to use. Options are: + 'leastsq', 'least_squares', 'minimize'. Default is 'leastsq'. + **kwargs + Additional keyword arguments to pass to the optimizer. + """ + if optimizer not in optimizers: + raise ValueError( + f"Unknown optimizer '{optimizer}'. " + f"Choose from {list(optimizers.keys())}" + ) + + function = optimizers[optimizer] + x0 = recipe.getValues() + residuals = recipe.residual + if optimizer == "leastsq": + print("Optimizing using scipy.optimize.leastsq") + function(residuals, x0, **kwargs) + return + + +def plot_results(r, gobs, gcalc): + """Plot the results contained within a refined FitRecipe. + + Parameters + ---------- + r : array-like + The independent variable. + gobs : array-like + The observed/experimental data. + gcalc : array-like + The calculated/fitted data. + """ + diffzero = -0.8 * max(gobs) * np.ones_like(gobs) + diff = gobs - gcalc + diffzero + ls = "None" + marker = "o" + ms = 5 + mew = 0.5 + mfc = "None" + plt.plot( + r, + gobs, + ls=ls, + marker=marker, + ms=ms, + mew=mew, + mfc=mfc, + label="G(r) Data", + ) + plt.plot(r, gcalc, label="G(r) Fit") + plt.plot(r, diff, label="G(r) diff") + plt.plot(r, diffzero, lw=1.0, c="black") + plt.xlabel(r"$r (\AA)$") + plt.ylabel(r"$G (\AA^{-2})$") + plt.legend(loc=1) + return From 6086f7dca232e5be17f922f9b04d2caa858bb6f3 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Wed, 19 Nov 2025 12:30:42 -0500 Subject: [PATCH 04/23] core-shell-NP example --- docs/examples/core/core-shell-NP/CdS.cif | 69 + .../core/core-shell-NP/CdS_ZnS_nano.gr | 7506 +++++++++++++++++ docs/examples/core/core-shell-NP/ZnS.cif | 65 + .../core/core-shell-NP/coreshellnp.py | 196 + .../SrFit-demo-constraints-restraints.py | 2 - 5 files changed, 7836 insertions(+), 2 deletions(-) create mode 100644 docs/examples/core/core-shell-NP/CdS.cif create mode 100644 docs/examples/core/core-shell-NP/CdS_ZnS_nano.gr create mode 100644 docs/examples/core/core-shell-NP/ZnS.cif create mode 100644 docs/examples/core/core-shell-NP/coreshellnp.py diff --git a/docs/examples/core/core-shell-NP/CdS.cif b/docs/examples/core/core-shell-NP/CdS.cif new file mode 100644 index 0000000..34fa965 --- /dev/null +++ b/docs/examples/core/core-shell-NP/CdS.cif @@ -0,0 +1,69 @@ +data_1011054 +_chemical_name_systematic 'Cadmium sulfide - $-alpha' +_chemical_name_mineral 'Greenockite' +_chemical_compound_source 'synthetic' +_chemical_formula_structural 'Cd S' +_chemical_formula_sum 'Cd S' +_publ_section_title +; +Ueber die Kristallstruktur des $-alpha- und $-beta Cd S, sowie des +Wurtzits. +; +loop_ +_publ_author_name + 'Ulrich, F' + 'Zachariasen, W' +_journal_name_full +; +Zeitschrift fuer Kristallographie, Kristallgeometrie, Kristallphysik, +Kristallchemie (-144,1977) +; +_journal_coden_ASTM ZEKGAX +_journal_volume 62 +_journal_year 1925 +_journal_page_first 260 +_journal_page_last 273 +_cell_length_a 4.15 +_cell_length_b 4.15 +_cell_length_c 6.737 +_cell_angle_alpha 90 +_cell_angle_beta 90 +_cell_angle_gamma 120 +_cell_volume 100.5 +_cell_formula_units_Z 2 +_exptl_crystal_density_meas 4.82 +_symmetry_space_group_name_H-M 'P 63 m c' +_symmetry_Int_Tables_number 186 +_symmetry_cell_setting hexagonal +loop_ +_symmetry_equiv_pos_as_xyz + 'x,y,z' + '-y,x-y,z' + 'y-x,-x,z' + '-y,-x,z' + 'y-x,y,z' + 'x,x-y,z' + '-x,-y,1/2+z' + 'y,y-x,1/2+z' + 'x-y,x,1/2+z' + 'y,x,1/2+z' + 'x-y,-y,1/2+z' + '-x,y-x,1/2+z' +loop_ +_atom_type_symbol +_atom_type_oxidation_number + Cd2+ 2.000 + S2- -2.000 +loop_ +_atom_site_label +_atom_site_type_symbol +_atom_site_symmetry_multiplicity +_atom_site_Wyckoff_symbol +_atom_site_fract_x +_atom_site_fract_y +_atom_site_fract_z +_atom_site_occupancy +_atom_site_attached_hydrogens +_atom_site_calc_flag + Cd1 Cd 2 b 0.33333 0.66667 0. 1. 0 d + S1 S 2 b 0.33333 0.66667 0.375 1. 0 d diff --git a/docs/examples/core/core-shell-NP/CdS_ZnS_nano.gr b/docs/examples/core/core-shell-NP/CdS_ZnS_nano.gr new file mode 100644 index 0000000..650e932 --- /dev/null +++ b/docs/examples/core/core-shell-NP/CdS_ZnS_nano.gr @@ -0,0 +1,7506 @@ +# +# +# +# +# +# +0.01 0.00284337 +0.02 0.00549539 +0.03 0.00780204 +0.04 0.00954326 +0.05 0.0106442 +0.06 0.0110657 +0.07 0.0107162 +0.08 0.00961948 +0.09 0.00790827 +0.1 0.00566355 +0.11 0.00300588 +0.12 0.000160076 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+#------------------------------------------------------------------------------ +#$Date: 2016-02-16 14:49:47 +0200 (Tue, 16 Feb 2016) $ +#$Revision: 176465 $ +#$URL: svn://www.crystallography.net/cod/cif/9/00/88/9008878.cif $ +#------------------------------------------------------------------------------ +# +# This file is available in the Crystallography Open Database (COD), +# http://www.crystallography.net/. The original data for this entry +# were provided the American Mineralogist Crystal Structure Database, +# http://rruff.geo.arizona.edu/AMS/amcsd.php +# +# The file may be used within the scientific community so long as +# proper attribution is given to the journal article from which the +# data were obtained. +# +data_9008878 +loop_ +_publ_author_name +'Wyckoff, R. W. G.' +_publ_section_title +; + Second edition. Interscience Publishers, New York, New York + Note: wurtzite structure +; +_journal_name_full 'Crystal Structures' +_journal_page_first 85 +_journal_page_last 237 +_journal_volume 1 +_journal_year 1963 +_chemical_formula_sum 'S Zn' +_chemical_name_mineral Wurtzite-2H +_space_group_IT_number 186 +_symmetry_space_group_name_Hall 'P 6c -2c' +_symmetry_space_group_name_H-M 'P 63 m c' +_cell_angle_alpha 90 +_cell_angle_beta 90 +_cell_angle_gamma 120 +_cell_length_a 3.811 +_cell_length_b 3.811 +_cell_length_c 6.234 +_cell_volume 78.411 +_exptl_crystal_density_diffrn 4.128 +_cod_original_formula_sum 'Zn S' +_cod_database_code 9008878 +loop_ +_symmetry_equiv_pos_as_xyz +x,y,z +-x,-x+y,1/2+z +x-y,x,1/2+z +-y,-x,z +-y,x-y,z +x-y,-y,1/2+z +-x,-y,1/2+z +x,x-y,z +-x+y,-x,z +y,x,1/2+z +y,-x+y,1/2+z +-x+y,y,z +loop_ +_atom_site_label +_atom_site_fract_x +_atom_site_fract_y +_atom_site_fract_z +Zn 0.33333 0.66667 0.00000 +S 0.33333 0.66667 0.38500 diff --git a/docs/examples/core/core-shell-NP/coreshellnp.py b/docs/examples/core/core-shell-NP/coreshellnp.py new file mode 100644 index 0000000..64da70a --- /dev/null +++ b/docs/examples/core/core-shell-NP/coreshellnp.py @@ -0,0 +1,196 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2011 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow, Peng Tian +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Refine the structure of a core-shell nanoparticle. + +This applies the characteristic function formalism described in +nppdfcrystal.py to the case of a spherical core-shell nanoparticle. The +modeling approach we use is to refine the core and shell as two +different phases, each with an appropriate characteristic function. +""" + +from pathlib import Path + +import matplotlib.pyplot as plt +from pyobjcryst import loadCrystal +from scipy.optimize import leastsq + +from diffpy.cmi.fit_tools import plot_results +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) +from diffpy.srfit.pdf import PDFGenerator, PDFParser + +# Example Code + + +def make_recipe(stru1, stru2, datname): + """Create a fitting recipe for crystalline PDF data.""" + + # The Profile + profile = Profile() + + # Load data and add it to the profile + parser = PDFParser() + parser.parseFile(datname) + profile.loadParsedData(parser) + profile.setCalculationRange(xmin=1.5, xmax=45, dx=0.1) + + # The ProfileGenerator + # In order to fit the core and shell phases simultaneously, we must use two + # PDFGenerators. + # + # The generator for the CdS core. We call it "G_CdS" and will use this name + # later when we set the fitting equation in the FitContribution. + generator_cds = PDFGenerator("G_CdS") + generator_cds.setStructure(stru1) + generator_cds.setQmax(26) + generator_cds.qdamp.value = 0.0396 + # The generator for the ZnS shell. We call it "G_ZnS". + generator_zns = PDFGenerator("G_ZnS") + generator_zns.setStructure(stru2) + generator_zns.setQmax(26) + generator_zns.qdamp.value = 0.0396 + + # The FitContribution + # Add both generators and the profile to the FitContribution. + contribution = FitContribution("cdszns") + contribution.addProfileGenerator(generator_cds) + contribution.addProfileGenerator(generator_zns) + contribution.setProfile(profile, xname="r") + + # Set up the characteristic functions. We use a spherical CF for the core + # and a spherical shell CF for the shell. Since this is set up as two + # phases, we implicitly assume that the core-shell correlations contribute + # very little to the PDF. + from diffpy.srfit.pdf.characteristicfunctions import shellCF, sphericalCF + + contribution.registerFunction(sphericalCF, name="f_CdS") + contribution.registerFunction(shellCF, name="f_ZnS") + + # Write the fitting equation. We want to sum the PDFs from each phase and + # multiply it by a scaling factor. + contribution.setEquation("scale * (f_CdS * G_CdS + f_ZnS * G_ZnS)") + + # Make the FitRecipe and add the FitContribution. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Vary the inner radius and thickness of the shell. Constrain the core + # diameter to twice the shell radius. + recipe.addVar(contribution.radius, 15) + recipe.addVar(contribution.thickness, 11) + recipe.constrain(contribution.psize, "2 * radius") + + # Configure the fit variables + # Start by configuring the scale factor and resolution factors. + # We want the sum of the phase scale factors to be 1. + recipe.newVar("scale_CdS", 0.7) + recipe.constrain(generator_cds.scale, "scale_CdS") + recipe.constrain(generator_zns.scale, "1 - scale_CdS") + # We also want the resolution factor to be the same on each. + + # Vary the global scale as well. + recipe.addVar(contribution.scale, 0.3) + + # Now we can configure the structural parameters. We tag the different + # structural variables so we can easily turn them on and off in the + # subsequent refinement. + phase_cds = generator_cds.phase + for par in phase_cds.sgpars.latpars: + recipe.addVar(par, name=par.name + "_cds", tag="lat") + for par in phase_cds.sgpars.adppars: + recipe.addVar(par, 1, name=par.name + "_cds", tag="adp") + recipe.addVar(phase_cds.sgpars.xyzpars.z_1, name="z_1_cds", tag="xyz") + # Since we know these have stacking disorder, constrain the B33 adps for + # each atom type. + recipe.constrain("B33_1_cds", "B33_0_cds") + recipe.addVar(generator_cds.delta2, name="delta2_cds", value=5) + + phase_zns = generator_zns.phase + for par in phase_zns.sgpars.latpars: + recipe.addVar(par, name=par.name + "_zns", tag="lat") + for par in phase_zns.sgpars.adppars: + recipe.addVar(par, 1, name=par.name + "_zns", tag="adp") + recipe.addVar(phase_zns.sgpars.xyzpars.z_1, name="z_1_zns", tag="xyz") + recipe.constrain("B33_1_zns", "B33_0_zns") + recipe.addVar(generator_zns.delta2, name="delta2_zns", value=2.5) + + # Give the recipe away so it can be used! + return recipe + + +def main(): + """Set up and refine the recipe.""" + + # Make the data and the recipe + base_path = Path(__file__).parent + cdsciffile = base_path / "CdS.cif" + znsciffile = base_path / "ZnS.cif" + data = base_path / "CdS_ZnS_nano.gr" + + # Make the recipe + stru1 = loadCrystal(cdsciffile) + stru2 = loadCrystal(znsciffile) + recipe = make_recipe(stru1, stru2, data) + + recipe.fithooks[0].verbose = 3 + # Optimize - we do this in steps to help convergence + recipe.fix("all") + + # Start with the lattice parameters. In make_recipe, these were tagged with + # "lat". Here is how we use that. + recipe.free("lat") + leastsq(recipe.residual, recipe.values, maxfev=50) + + # Now the scale and phase fraction. + recipe.free("scale", "scale_CdS") + leastsq(recipe.residual, recipe.values, maxfev=50) + + # The ADPs. + recipe.free("adp") + leastsq(recipe.residual, recipe.values, maxfev=100) + + # The delta2 parameters. + recipe.free("delta2_cds", "delta2_zns") + leastsq(recipe.residual, recipe.values, maxfev=50) + + # The shape parameters. + recipe.free("radius", "thickness") + leastsq(recipe.residual, recipe.values, maxfev=50) + + # The positional parameters. + recipe.free("xyz") + leastsq(recipe.residual, recipe.values) + + # Generate and print the FitResults + res = FitResults(recipe) + res.printResults() + + # Plot! + r = recipe.cdszns.profile.x + g = recipe.cdszns.profile.y + gcalc = recipe.cdszns.profile.ycalc + plot_results(r, g, gcalc) + plt.show() + return + + +if __name__ == "__main__": + main() + +# End of file diff --git a/docs/examples/core/linefit/SrFit-demo-constraints-restraints.py b/docs/examples/core/linefit/SrFit-demo-constraints-restraints.py index 1a4a298..4e4a651 100644 --- a/docs/examples/core/linefit/SrFit-demo-constraints-restraints.py +++ b/docs/examples/core/linefit/SrFit-demo-constraints-restraints.py @@ -1,5 +1,3 @@ -from __future__ import print_function - import matplotlib.pyplot as plt import numpy as np from matplotlib.pyplot import plot, title From 6e52bac91c0b2aa30521fd48d2685979853ae505 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Wed, 19 Nov 2025 14:23:56 -0500 Subject: [PATCH 05/23] debye-waller --- docs/examples/core/debye-waller/debyemodel.py | 270 ++++++++++++++++++ .../core/debye-waller/debyemodelII.py | 163 +++++++++++ 2 files changed, 433 insertions(+) create mode 100644 docs/examples/core/debye-waller/debyemodel.py create mode 100644 docs/examples/core/debye-waller/debyemodelII.py diff --git a/docs/examples/core/debye-waller/debyemodel.py b/docs/examples/core/debye-waller/debyemodel.py new file mode 100644 index 0000000..26fdaea --- /dev/null +++ b/docs/examples/core/debye-waller/debyemodel.py @@ -0,0 +1,270 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of fitting the Debye model to experimental Debye-Waller +factors. + +In this example, we build a fit recipe that uses an external function that can +simulate a atomic displacement parameters using the Debye model. This serves as +an example of how to utilize python functions in a fit and extend them with +SrFit without writing additional code. This example also demonstrates guide a +refinement with restraints. + +Instructions + +Run the example and then read the 'make_recipe' code to see how to use a python +function as a profile generator. + +Extensions + +- Don't hardcode the mass of lead in the fitting equation. Turn it into a + Parameter and refine it. There are two ways to do this. Try to figure out + both. +""" + +import numpy + +from diffpy.cmi.fit_tools import optimize_recipe +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) + +# The data +data = """\ +015.0 0.00334 0.00013 +050.0 0.00508 0.00022 +100.0 0.00830 0.00040 +150.0 0.01252 0.00071 +200.0 0.01792 0.00100 +250.0 0.02304 0.00120 +300.0 0.02737 0.00140 +350.0 0.03085 0.00160 +400.0 0.03484 0.00190 +450.0 0.03774 0.00220 +500.0 0.03946 0.00250 +""" + +###### +# Example Code + + +def make_recipe(): + """Make the recipe for the fit. + + The instructions for what we want to refine, and how to refine it + will be defined within a FitRecipe instance. The job of a FitRecipe + is to collect and associate all the data, the fitting equations, + fitting variables, constraints and restrations. We will demonstrate + each of these within the code. + + Data is held within a Profile object. The Profile is simply a + container that holds the data, and the theoretical profile once it + has been calculated. + + Data is associated with a fitting equation within a FitContribution. + The FitContribution defines the equation and parameters that will be + adjusted to fit the data. The fitting equation can be defined within + a function or optionally within the ProfileGenerator class. We won't + need the ProfileGenerator class in this example since the signature + of the fitting equation (the 'debye' function defined below) is so + simple. The FitContribution also defines the residual function to + optimize for the data/equation pair. This can be modified, but we + won't do that here. + """ + + # The Profile + # Create a Profile to hold the experimental and calculated signal. + profile = Profile() + + # Load data and add it to the profile. It is our responsibility to get our + # data into the profile. + xydy = numpy.array(data.split(), dtype=float).reshape(-1, 3) + x, y, dy = xydy.T + profile.setObservedProfile(x, y, dy) + + # The FitContribution + # The FitContribution associates the profile with the Debye function. + contribution = FitContribution("pb") + # Tell the contribution about the Profile. We will need to use the + # independent variable (the temperature) from the data to calculate the + # theoretical signal, so give it an informative name ('T') that we can use + # later. + contribution.setProfile(profile, xname="T") + + # We now need to create the fitting equation. We tell the FitContribution + # to use the 'debye' function defined below. The 'registerFunction' method + # will let us do this. Since we haven't told it otherwise, + # 'registerFunction' will extract the name of the function ('debye') and + # the names of the arguments ('T', 'm', 'thetaD'). These arguments will + # become Parameters of the FitContribution. Since we named the x-variable + # 'T' above, the 'T' in the 'debye' equation will refer to this x-variable + # whenever it is used. + contribution.registerFunction(debye) + + # Now we can create the fitting equation. We want to extend the 'debye' + # equation by adding a vertical offset. We could wrap 'debye' in a new + # function with an offset, and register that instead of 'debye', but what + # we do here is easier. + # + # When we set the fitting equation, we do not need to specify the + # Parameters to the 'debye' function since the FitContribution already + # knows what they are. If we choose to specify the arguments, we can make + # adjustments to their input values. We wish to have the thetaD value in + # the debye equation to be positive, so we specify the input as abs(thetaD) + # in the equation below. Furthermore, we know 'm', the mass of lead, so we + # can specify that as well. + contribution.setEquation("debye(T, 207.2, abs(thetaD)) + offset") + + # The FitRecipe + # The FitRecipe lets us define what we want to fit. It is where we can + # create variables, constraints and restraints. If we had multiple profiles + # to fit simultaneously, the contribution from each could be added to the + # recipe. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Specify which Parameters we want to refine. + + # Vary the offset + recipe.addVar(contribution.offset, 0) + # We also vary the Debye temperature. + recipe.addVar(contribution.thetaD, 100) + + # We would like to 'suggest' that the offset should remain positive. This + # is somethine that we know about the system that might help the refinement + # converge to a physically reasonable result. We will do this with a soft + # constraint, or restraint. Here we restrain the offset variable to between + # 0 and infinity. We tell the recipe that we want to scale the penalty for + # breaking the restraint by the point-average chi^2 value so that the + # restraint is roughly as significant as any other data point throughout + # the fit. + recipe.restrain(recipe.offset, lb=0, scaled=True) + + # We're done setting up the recipe. We can now do other things with it. + return recipe + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # Plot this. + # Note that since the contribution was given the name "pb", it is + # accessible from the recipe with this name. This is a useful way to + # organize multiple contributions to a fit. + T = recipe.pb.profile.x + U = recipe.pb.profile.y + Ucalc = recipe.pb.profile.ycalc + + import pylab + + pylab.plot(T, U, "o", label="Pb $U_{iso}$ Data") + pylab.plot(T, Ucalc) + pylab.xlabel("T (K)") + pylab.ylabel(r"$U_{iso} (\AA^2)$") + pylab.legend(loc=(0.0, 0.8)) + + pylab.show() + return + + +def main(): + """The workflow of creating, running and inspecting a fit.""" + + # Create the recipe + recipe = make_recipe() + + # Refine using the optimizer of your choice + optimize_recipe(recipe) + + # Get the results. + res = FitResults(recipe) + + # Print the results + res.printResults() + + # Plot the results + plotResults(recipe) + + return + + +# Functions required for calculation of Debye curve. Feel free to skip these, +# as we treat them as if existing in some external library that we cannot +# modify. + + +def debye(T, m, thetaD): + """A wrapped version of 'adps' that can handle an array of + T-values.""" + y = numpy.array([adps(m, thetaD, x) for x in T]) + return y + + +def adps(m, thetaD, T): + """Calculates atomic displacement factors within the Debye model. + + = (3h^2/4 pi^2 m kB thetaD)(phi(thetaD/T)/(ThetaD/T) + 1/4) + + arguments: + m -- float -- mass of the ion in atomic mass units (e.g., C = 12) + thetaD -- float -- Debye Temperature + T -- float -- temperature. + + return: + Uiso -- float -- the thermal factor from the Debye recipe at temp T + """ + h = 6.6260755e-34 # Planck's constant. J.s of m^2.kg/s + kB = 1.3806503e-23 # Boltzmann's constant. J/K + amu = 1.66053886e-27 # Atomic mass unit. kg + + def __phi(x): + """Evaluates the phi integral needed in Debye calculation. + + phi(x) = (1/x) int_0^x xi/(exp(xi)-1) dxi + + arguments: + x -- float -- value of thetaD (Debye temperature)/T + + returns: + phi -- float -- value of the phi function + """ + + def __debyeKernel(xi): + """Function needed by debye calculators.""" + y = xi / (numpy.exp(xi) - 1) + return y + + import scipy.integrate + + int = scipy.integrate.quad(__debyeKernel, 0, x) + phi = (1 / x) * int[0] + + return phi + + m = m * amu + u2 = (3 * h**2 / (4 * numpy.pi**2 * m * kB * thetaD)) * ( + __phi(thetaD / T) / (thetaD / T) + 1.0 / 4.0 + ) + + return u2 * 1e20 + + +if __name__ == "__main__": + + main() + +# End of file diff --git a/docs/examples/core/debye-waller/debyemodelII.py b/docs/examples/core/debye-waller/debyemodelII.py new file mode 100644 index 0000000..0aa565b --- /dev/null +++ b/docs/examples/core/debye-waller/debyemodelII.py @@ -0,0 +1,163 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of fitting the Debye recipe to experimental Debye-Waller +factors. + +This is an extension of example in debyemodel.py. The recipe we create will +simultaneously fit the low and high temperature parts of the experimental data +with the same Debye temperature, but different offsets. This example also +introduces constraints. + +Instructions + +Run the example and then read through the 'make_recipeII' code to learn about +multi-profile recipes. You will learn how to constrain related information +between the fit contributions. + +Extensions + +- Play with the fit ranges and see if you can improve the fit. +- The Debye temperature parameters from the two contributions can be + constrained without creating a new variable. Try to figure out how that is + done. +""" + +from debyemodel import make_recipe + +from diffpy.cmi.fit_tools import optimize_recipe +from diffpy.srfit.fitbase import FitRecipe, FitResults + +###### +# Example Code + + +def make_recipeII(): + """Make a recipe for fitting low and high temperature regions. + + We will fit the low and high temperature parts of Debye curve + simultaneously with the same Debye temperature, but different + offsets. + + We will make two FitRecipes using the make_recipe function from + debyemodel.py and extract the configured FitContribution from each. + We will use different fitting ranges for each FitContribution and + constrain the Debye temperature in each FitContribution to be the + same. + """ + + # We'll throw these away. We just want the FitContributions that are + # configured within the recipes. + m1 = make_recipe() + m2 = make_recipe() + # These are the FitContributions (we named them "pb" in the debyemodel + # example). + lowT = m1.pb + highT = m2.pb + # Let's rename the FitContributions to something more meaningful for this + # example. + lowT.name = "lowT" + highT.name = "highT" + + # Now create a fresh FitRecipe to work with and add to it the two + # FitContributions. + recipe = FitRecipe() + recipe.addContribution(lowT) + recipe.addContribution(highT) + + # Change the fit ranges of the Profiles embedded within the + # FitContributions. We want to fit one of the contributions at low + # temperature, and one at high. + lowT.profile.setCalculationRange(0, 150) + highT.profile.setCalculationRange(400, 500) + + # Vary the offset from each FitContribution separately, while keeping the + # Debye temperatures the same. We give each offset variable a different + # name in the recipe so it retains its identity. + recipe.addVar(recipe.lowT.offset, name="lowToffset") + recipe.addVar(recipe.highT.offset, name="highToffset") + # We create a new Variable and use the recipe's "constrain" method to + # associate the Debye temperature parameters with that variable. + recipe.newVar("thetaD", 100) + recipe.constrain(recipe.lowT.thetaD, "thetaD") + recipe.constrain(recipe.highT.thetaD, "thetaD") + return recipe + + +def plotResults(recipe): + """Display the results contained within a refined FitRecipe.""" + + # The variable values are returned in the order in which the variables were + # added to the FitRecipe. + lowToffset, highToffset, thetaD = recipe.getValues() + + # We want to extend the fitting range to its full extent so we can get a + # nice full plot. + recipe.lowT.profile.setCalculationRange(xmin="obs", xmax="obs") + recipe.highT.profile.setCalculationRange(xmin="obs", xmax="obs") + T = recipe.lowT.profile.x + U = recipe.lowT.profile.y + # We can use a FitContribution's 'evaluateEquation' method to evaluate + # expressions involving the Parameters and other aspects of the + # FitContribution. Here we evaluate the fitting equation, which is always + # accessed using the name "eq". We access it this way (rather than through + # the Profile's ycalc attribute) because we changed the calculation range + # above, and we therefore need to recalculate the profile. + lowU = recipe.lowT.evaluateEquation("eq") + highU = recipe.highT.evaluateEquation("eq") + + # Now we can plot this. + import pylab + + pylab.plot(T, U, "o", label="Pb $U_{iso}$ Data") + lbl1 = r"$T_d$=%3.1f K, lowToff=%1.5f $\AA^2$" % (abs(thetaD), lowToffset) + lbl2 = r"$T_d$=%3.1f K, highToff=%1.5f $\AA^2$" % ( + abs(thetaD), + highToffset, + ) + pylab.plot(T, lowU, label=lbl1) + pylab.plot(T, highU, label=lbl2) + pylab.xlabel("T (K)") + pylab.ylabel(r"$U_{iso} (\AA^2)$") + pylab.legend(loc=(0.0, 0.8)) + + pylab.show() + return + + +def main(): + + # Create the recipe + recipe = make_recipeII() + + # Refine using the optimizer of your choice + optimize_recipe(recipe) + + # Get the results in a FitResults object. + res = FitResults(recipe) + + # Print the results + res.printResults() + + # Plot the results + plotResults(recipe) + + return + + +if __name__ == "__main__": + + main() + +# End of file From f410bb3da3a101fba37b6b49fafb1861a9d2be87 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Wed, 19 Nov 2025 14:28:01 -0500 Subject: [PATCH 06/23] gaussianfit --- .../core/gaussianfit/gaussiangenerator.py | 180 +++++++++++++++ .../core/gaussianfit/gaussianrecipe.py | 213 ++++++++++++++++++ 2 files changed, 393 insertions(+) create mode 100644 docs/examples/core/gaussianfit/gaussiangenerator.py create mode 100644 docs/examples/core/gaussianfit/gaussianrecipe.py diff --git a/docs/examples/core/gaussianfit/gaussiangenerator.py b/docs/examples/core/gaussianfit/gaussiangenerator.py new file mode 100644 index 0000000..15ff292 --- /dev/null +++ b/docs/examples/core/gaussianfit/gaussiangenerator.py @@ -0,0 +1,180 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of using ProfileGenerators in FitContributions. + +This is an example of building a ProfileGenerator and using it in a +FitContribution in order to fit a Gaussian profile. The recipe creation is much +like in gaussianrecipe.py, except that it uses our custom GaussianGenerator +class. ProfileGenerators are usually used to organize profile calculators that +require more information than can be conveniently passed into a function call, +but can be used for simple calculations as well. The GaussianGenerator class +is an example of a ProfileGenerator that can be used by a FitContribution to +help generate a the profile. + +Instructions + +Run gaussianrecipe.py and this example. Note how the output is identical. Next +read through 'GaussianGenerator' class. This provides a simple example of how +to create a custom ProfileGenerator. Finally read the 'make_recipe' code to +see how the GaussianGenerator is used. Contrast this to the 'make_recipe' +section in gaussianrecipe.py. + +Extensions + +- Remove the amplitude from GaussianGenerator and instead use the 'setEquation' + method of the FitContribution to account for it. Note that the + GaussianGenerator will be accessible by its name, "g". +""" + +from numpy import exp + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + Profile, + ProfileGenerator, +) + +###### +# Example Code + + +class GaussianGenerator(ProfileGenerator): + """A class for calculating a Gaussian profile. + + Generating a Gaussian is not difficult, as was shown in + gaussianrecipe.py. Here we create a class that encapsulates this + functionality. Placing this class in a python module would make it + possible to import it and reuse it, thereby saving future code + writing and debugging. + + The purpose of a ProfileGenerator is to 1) provide a function that + generates a profile signal 2) organize the Parameters required for + the calculation + + Thus, this class overloads the __init__ method to create the + necessary Parameters for the calculation, and the __call__ method to + generate the signal. + """ + + def __init__(self, name): + """Define the generator. + + Note that a ProfileGenerator needs a name passed in the initializer. + This makes it so the generator can be referenced by name when it is + part of a FitContribution. + + Here we create the Parameters for the calculation. + + A -- The amplitude + x0 -- The center + sigma -- The width + """ + # This initializes various parts of the generator + ProfileGenerator.__init__(self, name) + + # Here we create new Parameters using the '_newParameter' method of + # ProfileGenerator. The signature is + # _newParameter(name, value). + # See the API for full details. + self._newParameter("A", 1.0) + self._newParameter("x0", 0.0) + self._newParameter("sigma", 1.0) + return + + def __call__(self, x): + """Calculate the profile. + + Here we calculate the Gaussian profile given the independent + variable, x. We will define it as we did in gaussianrecipe.py. + """ + # First we must get the values of the Parameters. Since we used + # _newParameter to create them, the Parameters are accessible as + # attributes by name. + A = self.A.value + x0 = self.x0.value + sigma = self.sigma.value + + # Now we can use them. Note that we imported exp from numpy at the top + # of the module. + y = A * exp(-0.5 * (x - x0) ** 2 / sigma**2) + + # Now return the value. + return y + + +# End class GaussianGenerator + + +def make_recipe(): + """Create a recipe that uses the GaussianGenerator. + + This will create a FitContribution that uses the GaussianGenerator, + associate this with a Profile, and use this to define a FitRecipe. + """ + + # The Profile + # Create a Profile to hold the experimental and calculated signal. + profile = Profile() + + # Load data and add it to the profile. This uses the loadtxt function from + # numpy. + profile.loadtxt("data/gaussian.dat") + + # The ProfileGenerator + # Create a GaussianGenerator named "g". This will be the name we use to + # refer to the generator from within the FitContribution equation. + generator = GaussianGenerator("g") + + # The FitContribution + # Create a FitContribution that will associate the Profile with the + # GaussianGenerator. The GaussianGenerator will be accessible as an + # attribute of the FitContribution by its name ("g"). Note that this will + # set the fitting equation to "g", which calls the GaussianGenerator. + contribution = FitContribution("g1") + contribution.addProfileGenerator(generator) + contribution.setProfile(profile) + + # The FitRecipe + # Now we create the FitRecipe and add the FitContribution. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Specify which Parameters we want to vary in the fit. This will add + # Variables to the FitRecipe that directly modify the Parameters of the + # FitContribution. + # + # We create a variable for each Parameter of the GaussianGenerator. Note + # that the Parameters belong to the GaussianGenerator, not the + # FitContribution as in gaussianrecipe.py. We initialize parameters as in + # gaussianrecipe.py so we can expect the same output. + recipe.addVar(generator.A, 1) + recipe.addVar(generator.x0, 5) + recipe.addVar(generator.sigma, name="sig") + recipe.sig.value = 1 + + # Give the recipe away so it can be used! + return recipe + + +if __name__ == "__main__": + + # We can use main from gaussianrecipe.py, since this doesn't care if we use + # a ProfileGenerator or not. + from gaussianrecipe import main + + main() + +# End of file diff --git a/docs/examples/core/gaussianfit/gaussianrecipe.py b/docs/examples/core/gaussianfit/gaussianrecipe.py new file mode 100644 index 0000000..4d16cb6 --- /dev/null +++ b/docs/examples/core/gaussianfit/gaussianrecipe.py @@ -0,0 +1,213 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of fitting a Gaussian to simulated data. + +This is an example of building a fit recipe that can be driven by an optimizer +to fit a Gaussian profile to simulated data. The purpose of this example is +familiarize the developer with the objects involved in defining a SrFit +refinement recipe. + +Instructions + +If you have not yet run the example, run it and inspect the output. The example +script is driven by the 'main' method defined below. Take a look at that method +to get an understanding of how a fit recipe can be used once created. After +that, read the 'make_recipe' code to see what goes into a fit recipe. After +that, read the 'scipyOptimize' code to see how the refinement is executed. +Finally, read the 'plotResults' code to see how to extracts the refined profile +and plot it. + +Extensions + +After reading through the code, try to perform the following tasks. The process +will leave you with a much better understanding of how SrFit works. + +- Play around with setting the values of the Variables and Parameters. What + happens to the associated Parameter when you change a variable value? What + happens to the variable when you change the Parameter value? +- Modify the fitting equation by adding a constant. See if that improves the + fit. +- Create a FitRecipe to fit the Lorentzian profile in the data/lorentzian.dat + file. +""" + + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) + +###### +# Example Code + + +def main(): + """The workflow of creating, running and inspecting a fit.""" + + # Start by creating the recipe. The recipe describes the data to be fit, + # the profile generator used to simulate the data and the variables that + # will be tuned by the optimizer. + recipe = make_recipe() + + # Refine using the optimizer of your choice. + scipyOptimize(recipe) + + # Get the results in a FitResults object. The FitResults object stores the + # current state of the recipe, and uses it to calculate useful statistics + # about the fit. + res = FitResults(recipe) + + # Print the results. + res.printResults() + + # Plot the results. + plotResults(recipe) + + return + + +def make_recipe(): + """Make a FitRecipe for fitting a Gaussian curve to data. + + The instructions for what we want to refine, and how to refine it + will be defined within a FitRecipe instance. The job of a FitRecipe + is to collect and associate all the data, the fitting equations, + fitting variables, constraints and restraints. The configured recipe + provides a 'residual' function and the initial variable values that + an optimizer can use to refine the variables to minimize the + disagreement between the calculated profile and the data. + + Once we define the FitRecipe, we can send it an optimizer to be + optimized. See the 'scipyOptimize' function. + """ + + # The Profile + # Create a Profile to hold the experimental and calculated signal. + profile = Profile() + + # Load data and add it to the profile. This uses the loadtxt function from + # numpy. + profile.loadtxt("data/gaussian.dat") + + # The FitContribution + # The FitContribution associates the Profile with a fitting equation. The + # FitContribution also stores the parameters of the fitting equation. We + # give our FitContribution then name "g1". We will be able to access the + # FitContribution by that name within the FitRecipe. + contribution = FitContribution("g1") + # Tell the FitContribution about the Profile. The FitContribution will give + # us access to the data held within the Profile. Here, we can tell it what + # name we want to use for the independent variable. We tell it to use the + # name "x". + contribution.setProfile(profile, xname="x") + + # Now we need to create a fitting equation. We do that by writing out the + # equation as a string. The FitContribution will turn this into a callable + # function internally. In the process, it extracts all the parameters from + # the equation (A, x, x0, sigma) and turns them into Parameter objects + # internally. These objects can be accessed as attributes of the + # contribution by name. Since we told the contribution that our + # independent variable is named "x", this value will be substituted into + # the fitting equation whenever it is called. + contribution.setEquation("A * exp(-0.5*(x-x0)**2/sigma**2)") + + # To demonstrate how these parameters are used, we will give "A" an initial + # value. Note that Parameters are not numbers, but are containers for + # numbers. To get or modify the value of a parameter, use its 'value' + # attribute. Parameters also have a 'name' attribute. + contribution.A.value = 1.0 + + # The FitRecipe + # The FitRecipe lets us define what we want to fit. It is where we can + # create variables, constraints and restraints. + recipe = FitRecipe() + + # Here we tell the FitRecipe to use our FitContribution. When the FitRecipe + # calculates its residual function, it will call on the FitContribution to + # do part of the work. + recipe.addContribution(contribution) + + # Specify which Parameters we want to vary in the fit. This will add + # Variables to the FitRecipe that directly modify the Parameters of the + # FitContribution. + # + # Here we create a Variable for the 'A' Parameter from our fit equation. + # The resulting Variable will be named 'A' as well, but it will be accessed + # via the FitRecipe. + recipe.addVar(contribution.A) + # Here we create the Variable for 'x0' and give it an initial value of 5. + recipe.addVar(contribution.x0, 5) + # Here we create a Variable named 'sig', which is tied to the 'sigma' + # Parameter of our FitContribution. We give it an initial value through the + # FitRecipe instance. + recipe.addVar(contribution.sigma, name="sig") + recipe.sig.value = 1 + + return recipe + + +def scipyOptimize(recipe): + """Optimize the recipe created above using scipy. + + The FitRecipe we created in make_recipe has a 'residual' method that + we can be minimized using a scipy optimizer. The details are + described in the source. + """ + + # We're going to use the least-squares (Levenberg-Marquardt) optimizer from + # scipy. We simply have to give it the function to minimize + # (recipe.residual) and the starting values of the Variables + # (recipe.getValues()). + from scipy.optimize.minpack import leastsq + + print("Fit using scipy's LM optimizer") + leastsq(recipe.residual, recipe.getValues()) + + return + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # We can access the data and fit profile through the Profile we created + # above. We get to it through our FitContribution, which we named "g1". + # + # The independent variable. This is always under the "x" attribute. + x = recipe.g1.profile.x + # The observed profile that we loaded earlier, the "y" attribute. + y = recipe.g1.profile.y + # The calculated profile, the "ycalc" attribute. + ycalc = recipe.g1.profile.ycalc + + # This stuff is specific to pylab from the matplotlib distribution. + import pylab + + pylab.plot(x, y, "b.", label="observed Gaussian") + pylab.plot(x, ycalc, "g-", label="calculated Gaussian") + pylab.legend(loc=(0.0, 0.8)) + pylab.xlabel("x") + pylab.ylabel("y") + + pylab.show() + return + + +if __name__ == "__main__": + + main() + +# End of file From 5f4a05bd3a75634d6980943bac9c9c96926deef4 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Wed, 19 Nov 2025 14:45:25 -0500 Subject: [PATCH 07/23] update plot function params --- src/diffpy/cmi/fit_tools.py | 27 ++++++++++++++------------- 1 file changed, 14 insertions(+), 13 deletions(-) diff --git a/src/diffpy/cmi/fit_tools.py b/src/diffpy/cmi/fit_tools.py index d7895d3..ace994b 100644 --- a/src/diffpy/cmi/fit_tools.py +++ b/src/diffpy/cmi/fit_tools.py @@ -45,39 +45,40 @@ def optimize_recipe(recipe, optimizer: str = "leastsq", **kwargs): return -def plot_results(r, gobs, gcalc): +def plot_results(x, yobs, ycalc): """Plot the results contained within a refined FitRecipe. Parameters ---------- - r : array-like + x : array-like The independent variable. - gobs : array-like + yobs : array-like The observed/experimental data. - gcalc : array-like + ycalc : array-like The calculated/fitted data. """ - diffzero = -0.8 * max(gobs) * np.ones_like(gobs) - diff = gobs - gcalc + diffzero + diffzero = -0.8 * max(yobs) * np.ones_like(yobs) + diff = yobs - ycalc + diffzero ls = "None" marker = "o" ms = 5 mew = 0.5 mfc = "None" plt.plot( - r, - gobs, + x, + yobs, ls=ls, marker=marker, ms=ms, mew=mew, mfc=mfc, - label="G(r) Data", + label="data", ) - plt.plot(r, gcalc, label="G(r) Fit") - plt.plot(r, diff, label="G(r) diff") - plt.plot(r, diffzero, lw=1.0, c="black") + plt.plot(x, ycalc, label="calculated") + plt.plot(x, diff, label="diff") + plt.plot(x, diffzero, lw=1.0, c="black") plt.xlabel(r"$r (\AA)$") plt.ylabel(r"$G (\AA^{-2})$") - plt.legend(loc=1) + plt.legend() + plt.show() return From 85b6cb47d8f12c81e7beb47503e4f98c56f05568 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Wed, 19 Nov 2025 14:45:48 -0500 Subject: [PATCH 08/23] gaussianfit2 --- docs/examples/core/gaussianfit/gaussian.dat | 100 ++++++++++++++++++ .../core/gaussianfit/gaussianrecipe.py | 8 +- docs/examples/core/gaussianfit/interface.py | 84 +++++++++++++++ 3 files changed, 188 insertions(+), 4 deletions(-) create mode 100644 docs/examples/core/gaussianfit/gaussian.dat create mode 100644 docs/examples/core/gaussianfit/interface.py diff --git a/docs/examples/core/gaussianfit/gaussian.dat b/docs/examples/core/gaussianfit/gaussian.dat new file mode 100644 index 0000000..4397138 --- /dev/null +++ b/docs/examples/core/gaussianfit/gaussian.dat @@ -0,0 +1,100 @@ +0.000000000000000000e+00 0.000000000000000000e+00 1.58225087509e-2 +1.000000000000000056e-01 0.000000000000000000e+00 1.58225087509e-2 +2.000000000000000111e-01 0.000000000000000000e+00 1.58225087509e-2 +3.000000000000000444e-01 0.000000000000000000e+00 1.58225087509e-2 +4.000000000000000222e-01 0.000000000000000000e+00 1.58225087509e-2 +5.000000000000000000e-01 0.000000000000000000e+00 1.58225087509e-2 +6.000000000000000888e-01 0.000000000000000000e+00 1.58225087509e-2 +7.000000000000000666e-01 0.000000000000000000e+00 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+9.500000000000000000e+00 0.000000000000000000e+00 1.58225087509e-2 +9.600000000000001421e+00 0.000000000000000000e+00 1.58225087509e-2 +9.700000000000001066e+00 0.000000000000000000e+00 1.58225087509e-2 +9.800000000000000711e+00 0.000000000000000000e+00 1.58225087509e-2 +9.900000000000000355e+00 0.000000000000000000e+00 1.58225087509e-2 diff --git a/docs/examples/core/gaussianfit/gaussianrecipe.py b/docs/examples/core/gaussianfit/gaussianrecipe.py index 4d16cb6..3d84e46 100644 --- a/docs/examples/core/gaussianfit/gaussianrecipe.py +++ b/docs/examples/core/gaussianfit/gaussianrecipe.py @@ -25,7 +25,7 @@ script is driven by the 'main' method defined below. Take a look at that method to get an understanding of how a fit recipe can be used once created. After that, read the 'make_recipe' code to see what goes into a fit recipe. After -that, read the 'scipyOptimize' code to see how the refinement is executed. +that, read the 'optimize_recipe' code to see how the refinement is executed. Finally, read the 'plotResults' code to see how to extracts the refined profile and plot it. @@ -64,7 +64,7 @@ def main(): recipe = make_recipe() # Refine using the optimizer of your choice. - scipyOptimize(recipe) + optimize_recipe(recipe) # Get the results in a FitResults object. The FitResults object stores the # current state of the recipe, and uses it to calculate useful statistics @@ -92,7 +92,7 @@ def make_recipe(): disagreement between the calculated profile and the data. Once we define the FitRecipe, we can send it an optimizer to be - optimized. See the 'scipyOptimize' function. + optimized. See the 'optimize_recipe' function. """ # The Profile @@ -160,7 +160,7 @@ def make_recipe(): return recipe -def scipyOptimize(recipe): +def optimize_recipe(recipe): """Optimize the recipe created above using scipy. The FitRecipe we created in make_recipe has a 'residual' method that diff --git a/docs/examples/core/gaussianfit/interface.py b/docs/examples/core/gaussianfit/interface.py new file mode 100644 index 0000000..d00fcef --- /dev/null +++ b/docs/examples/core/gaussianfit/interface.py @@ -0,0 +1,84 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of fitting a Gaussian to simulated data. + +This is like gaussianrecipe.py, but it uses a shorthand interface +defined in the diffpy.srfit.interface.interface.py module. +""" +from pathlib import Path + +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) + +###### +# Example Code + + +def main(): + + p = Profile() + data = str(Path(__file__).parent / "gaussian.dat") + p.loadtxt(data) + + # FitContribution operations + # "<<" - Inject a parameter value + c = FitContribution("g1") + c.setProfile(p) + c.setEquation("A * exp(-0.5*(x-x0)**2/sigma**2)") + c.A << 0.5 + c.x0 << 5 + c.sigma << 1 + + # FitRecipe operations + # "|=" - Union of necessary components. + # "+=" - Add Parameter or create a new one. Each tuple is a set of + # arguments for either setVar or addVar. + # "*=" - Constrain a parameter. Think of "*" as a push-pin holding one + # parameter's value to that of another. + # "%=" - Restrain a parameter or equation. Think of "%" as a rope + # loosely tying parameters to a value. + r = FitRecipe() + r |= c + r += (c.A, 0.5), (c.x0, 5), ("sig", 1) + r *= c.sigma, "sig" + r %= c.A, 0.5, 0.5 + + from diffpy.cmi.fit_tools import optimize_recipe + + optimize_recipe(r) + + res = FitResults(r) + # Print the results. + res.printResults() + # Plot the results. + from diffpy.cmi.fit_tools import plot_results + + x = r.g1.profile.x + y = r.g1.profile.y + ycalc = r.g1.profile.ycalc + + plot_results(x, y, ycalc) + + return + + +if __name__ == "__main__": + main() + +# End of file From 7e2b1a91dcfafae62a2ac995552f60ce7be11caa Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Wed, 19 Nov 2025 14:55:42 -0500 Subject: [PATCH 09/23] intensityfit file1 and data --- docs/examples/core/intensityfit/C60.gr | 1999 +++++++++++++++++ docs/examples/core/intensityfit/C60.iq | 380 ++++ docs/examples/core/intensityfit/C60.stru | 369 +++ .../examples/core/intensityfit/npintensity.py | 533 +++++ 4 files changed, 3281 insertions(+) create mode 100644 docs/examples/core/intensityfit/C60.gr create mode 100644 docs/examples/core/intensityfit/C60.iq create mode 100644 docs/examples/core/intensityfit/C60.stru create mode 100644 docs/examples/core/intensityfit/npintensity.py diff --git a/docs/examples/core/intensityfit/C60.gr b/docs/examples/core/intensityfit/C60.gr new file mode 100644 index 0000000..d015b9d --- /dev/null +++ b/docs/examples/core/intensityfit/C60.gr @@ -0,0 +1,1999 @@ + 1.000000e-002 1.894260e+004 8.536912e+000 + 2.000000e-002 3.772272e+004 1.675464e+001 + 3.000000e-002 5.617755e+004 2.434705e+001 + 4.000000e-002 7.414385e+004 3.103361e+001 + 5.000000e-002 9.145791e+004 3.657098e+001 + 6.000000e-002 1.079561e+005 4.076327e+001 + 7.000000e-002 1.234755e+005 4.347065e+001 + 8.000000e-002 1.378555e+005 4.461615e+001 + 9.000000e-002 1.509396e+005 4.419097e+001 + 1.000000e-001 1.625776e+005 4.225878e+001 + 1.100000e-001 1.726287e+005 3.896113e+001 + 1.200000e-001 1.809643e+005 3.452824e+001 + 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L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of using ProfileGenerators in FitContributions. + +This is an example of building a ProfileGenerator and using it in a +FitContribution in order to fit theoretical intensity data. ProfileGenerators +are used to organize profile calculators that require more information than can +be conveniently passed into a function call. The IntensityGenerator class is +an example of a ProfileGenerator that can be used by a FitContribution to help +generate a the profile. + +Instructions + +Run the example and note the last line of the output. It will be described in +the code. Then read through 'IntensityGenerator' class. This will motivate the +need for the ProfileGenerator class. Next read the 'make_recipe' code. This +will demonstrate how to use the generator, the structure container needed by +the generator and introduce new operations that can be used in a registered +equation. + +Extensions + +- The IntensityGenerator class uses the 'addParameterSet' method to associate + the structure adapter (DiffpyStructureParSet) with the generator. Most SrFit + classes have an 'addParameterSet' class and can store ParameterSet objects. + Grab the phase object from the IntensityGenerator and try to add it to other + objects used in the fit recipe. Create variables from the moved Parameters + rather than from the 'phase' that lives in the IntensityGenerator and see if + everything still refines. +""" + + +from pathlib import Path + +import numpy + +from diffpy.cmi.fit_tools import optimize_recipe +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, + ProfileGenerator, +) +from diffpy.srfit.structure.diffpyparset import DiffpyStructureParSet + +###### +# Example Code + + +class IntensityGenerator(ProfileGenerator): + """A class for calculating intensity using the Debye equation. + + Calculating intensity from a structure is difficult in general. This + class takes a diffpy.structure.Structure instance and from that + generates a theoretical intensity signal. Unlike the example in + gaussianrecipe.py, the intensity generator is not simple. It must + take a structure object and some Parameters, and from that generate + a signal. At the same time, the structure itself (the lattice, atom + positions, thermal parameters, etc.) needs to be refinable. Thus we + define this ProfileGenerator to help us interface which exposes the + Parameters required by the calculation and provides a way for a + FitContribution to perform that calculation. + + The purpose of a ProfileGenerator is to 1) provide a function that + generates a profile signal 2) organize the Parameters required for + the calculation + + This generator wraps the 'iofq' function defined below. Knowledge of + this function is not required for this example. + """ + + def __init__(self, name): + """Define our generator. + + In this example we will keep count of how many times the + calculation gets performed. The 'count' attribute will be used + to store the count. + """ + ProfileGenerator.__init__(self, name) + # Count the calls + self.count = 0 + return + + def setStructure(self, strufile): + """Set the structure used in the calculation. + + strufile -- The name of a structure file. A + diffpy.structure.Structure object will be created from + the file, and that object will be passed to the 'iofq' + function whenever it is called. + + This will create the refinement Parameters using the + DiffpyStructureParSet adapter from diffpy.srfit.structure.diffpyparset. + DiffpyStructureParSet is a ParameterSet object that organizes and gives + attribute access to Parameters and ParameterSets adapted from a diffpy + Structure object. The Parameters embedded in the DiffpyStructureParSet + are proxies for attributes of the diffpy.structure.Structure object + that is needed by the 'iofq' function. The Parameters will be + accessible by name under the 'phase' attribute of this generator, and + are organized hierarchically: + + phase + - lattice (retrieved with 'getLattice') + - a + - b + - c + - alpha + - beta + - gamma + - scatterers (retrieved with 'getScatterers') + - atom1 (the name depends on the element) + - x + - y + - z + - occ + - U11 + - U22 + - U33 + - U12 + - U13 + - U23 + - Uiso + - etc. + + The diffpy.structure.Structure instance is held within the + DiffpyStructureParSet as the 'stru' attribute. + """ + # Load the structure from file + from diffpy.structure import Structure + + stru = Structure() + stru.read(strufile) + + # Create a ParameterSet designed to interface with + # diffpy.structure.Structure objects that organizes the Parameter + # hierarchy. Note that the DiffpyStructureParSet holds a handle to the + # loaded structure that we use in the __call__ method below. + # + # We pass the diffpy.structure.Structure instance, and give the + # DiffpyStructureParSet the name "phase". + parset = DiffpyStructureParSet("phase", stru) + + # Put this ParameterSet in the ProfileGenerator. + self.addParameterSet(parset) + + return + + def __call__(self, q): + """Calculate the intensity. + + This ProfileGenerator will be used in a FitContribution that + will be optimized to fit some data. By the time this function + is evaluated, the diffpy.structure.Structure instance has been + updated by the optimizer via the DiffpyStructureParSet defined + in setStructure. Thus, we need only call iofq with the internal + structure object. + """ + self.count += 1 + print("iofq called", self.count) + return iofq(self.phase.stru, q) + + +# End class IntensityGenerator + + +def make_recipe(strufile, datname): + """Create a recipe that uses the IntensityGenerator. + + This will create a FitContribution that uses the IntensityGenerator, + associate this with a Profile, and use this to define a FitRecipe. + """ + + # The Profile + # Create a Profile. This will hold the experimental and calculated signal. + profile = Profile() + + # Load data and add it to the profile + x, y, u = profile.loadtxt(datname) + + # The ProfileGenerator + # Create an IntensityGenerator named "I". This will be the name we use to + # refer to the generator from within the FitContribution equation. We also + # need to load the model structure we're using. + generator = IntensityGenerator("I") + generator.setStructure(strufile) + + # The FitContribution + # Create a FitContribution, that will associate the Profile with the + # ProfileGenerator. The ProfileGenerator will be accessible as an + # attribute of the FitContribution by its name ("I"). We also want to tell + # the FitContribution to name the x-variable of the profile "q", so we can + # use it in equations with this name. + contribution = FitContribution("bucky") + contribution.addProfileGenerator(generator) + contribution.setProfile(profile, xname="q") + + # Now we're ready to define the fitting equation for the FitContribution. + # We need to modify the intensity calculation, and we'll do that from + # within the fitting equation for the sake of instruction. We want to + # modify the calculation in three ways. We want to scale it, add a + # polynomial background, and broaden the peaks. + # + # There is added benefit for defining these operations outside of the + # IntensityGenerator. By combining the different parts of the calculation + # within the fitting equation, the time-consuming iofq calculation is only + # performed when a structural Parameter is changed. If only non-structural + # parameters are changed, such as the background and broadening Parameters, + # then then previously computed iofq value will be used to compute the + # contribution equation. The benefit in this is very apparent when + # refining the recipe with the LM optimizer, which only changes two + # variables at a time most of the time. Note in the refinement output how + # many times the residual is calculated, versus how many times iofq is + # called when using the optimize_recipe function. + + # We will define the background as a string. + + bkgdstr = "b0 + b1*q + b2*q**2 + b3*q**3 + b4*q**4 + b5*q**5 + b6*q**6 +\ + b7*q**7 + b8*q**8 + b9*q**9" + + # This creates a callable equation named "bkgd" within the FitContribution, + # and turns the polynomial coefficients into Parameters. + contribution.registerStringFunction(bkgdstr, "bkgd") + + # We will create the broadening function that we need by creating a python + # function and registering it with the FitContribution. + pi = numpy.pi + exp = numpy.exp + + def gaussian(q, q0, width): + return ( + 1 + / (2 * pi * width**2) ** 0.5 + * exp(-0.5 * ((q - q0) / width) ** 2) + ) + + # This registers the python function and extracts the name and creates + # Parameters from the arguments. + contribution.registerFunction(gaussian) + + # Center the Gaussian so it is not truncated. + contribution.q0.value = x[len(x) // 2] + + # Now we can incorporate the scale and bkgd into our calculation. We also + # convolve the signal with the Gaussian to broaden it. Recall that we don't + # need to supply arguments to the registered functions unless we want to + # make changes to their input values. + contribution.setEquation("scale * convolve(I, gaussian) + bkgd") + + # Make the FitRecipe and add the FitContribution. + recipe = FitRecipe() + recipe.addContribution(contribution) + + # Specify which parameters we want to refine. + recipe.addVar(contribution.b0, 0) + recipe.addVar(contribution.b1, 0) + recipe.addVar(contribution.b2, 0) + recipe.addVar(contribution.b3, 0) + recipe.addVar(contribution.b4, 0) + recipe.addVar(contribution.b5, 0) + recipe.addVar(contribution.b6, 0) + recipe.addVar(contribution.b7, 0) + recipe.addVar(contribution.b8, 0) + recipe.addVar(contribution.b9, 0) + + # We also want to adjust the scale and the convolution width + recipe.addVar(contribution.scale, 1) + recipe.addVar(contribution.width, 0.1) + + # We can also refine structural parameters. Here we extract the + # DiffpyStructureParSet from the intensity generator and use the parameters + # like we would any others. + phase = generator.phase + + # We want to allow for isotropic expansion, so we'll constrain the lattice + # parameters to the same value (the lattice is cubic). Note that we + # constrain to the "a" Parameter directly. In previous examples, we + # constrained to a Variable by name. This has the same effect. + lattice = phase.getLattice() + a = lattice.a + recipe.addVar(a) + recipe.constrain(lattice.b, a) + recipe.constrain(lattice.c, a) + # We want to refine the thermal parameters as well. We will add a new + # Variable that we call "Uiso" and constrain the atomic Uiso values to + # this. Note that we don't give Uiso an initial value. The initial value + # will be inferred from the following constraints. + Uiso = recipe.newVar("Uiso") + for atom in phase.getScatterers(): + recipe.constrain(atom.Uiso, Uiso) + + # Give the recipe away so it can be used! + return recipe + + +def main(): + + # Make the data and the recipe + strufile = str(Path(__file__).parent / "C60.stru") + q = numpy.arange(1, 20, 0.05) + iq_path = str(Path(__file__).parent / "C60.iq") + makeData(strufile, q, iq_path, 1.0, 100.68, 0.005, 0.13, 2) + + # Make the recipe + recipe = make_recipe(strufile, iq_path) + + # Optimize + optimize_recipe(recipe) + + # Generate and print the FitResults + res = FitResults(recipe) + # We want to see how much speed-up we get from bringing the scale and + # background outside of the intensity generator. Get the number of calls + # to the residual function from the FitRecipe, and the number of calls to + # 'iofq' from the IntensityGenerator. + rescount = recipe.fithooks[0].count + calcount = recipe.bucky.I.count + footer = "iofq called %i%% of the time" % int(100.0 * calcount / rescount) + res.printResults(footer=footer) + + # Plot! + plotResults(recipe) + + return + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # All this should be pretty familiar by now. + q = recipe.bucky.profile.x + + Imeas = recipe.bucky.profile.y + Icalc = recipe.bucky.profile.ycalc + bkgd = recipe.bucky.evaluateEquation("bkgd") + diff = Imeas - Icalc + + import pylab + + pylab.plot(q, Imeas, "ob", label="I(Q) Data") + pylab.plot(q, Icalc, "r-", label="I(Q) Fit") + pylab.plot(q, diff, "g-", label="I(Q) diff") + pylab.plot(q, bkgd, "c-", label="Bkgd. Fit") + pylab.xlabel(r"$Q (\AA^{-1})$") + pylab.ylabel("Intensity (arb. units)") + pylab.legend(loc=1) + + pylab.show() + return + + +def iofq(S, q): + """Calculate I(Q) (X-ray) using the Debye Equation. + + I(Q) = 2 sum(i,j) f_i(Q) f_j(Q) sinc(rij Q) exp(-0.5 ssij Q**2) + (The exponential term is the Debye-Waller factor.) + + S -- A diffpy.structure.Structure instance. It is assumed that the + structure is that of an isolated scatterer. Periodic boundary + conditions are not applied. + q -- The q-points to calculate over. + + This uses cctbx for the calculation of the f_i if it is available, + otherwise f_i = 1. + """ + # The functions we need + sinc = numpy.sinc + exp = numpy.exp + pi = numpy.pi + + # The brute-force calculation is very slow. Thus we optimize a little bit. + + # The precision of distance measurements + deltad = 1e-6 + dmult = int(1 / deltad) + deltau = deltad**2 + umult = int(1 / deltau) + + pairdict = {} + elcount = {} + n = len(S) + for i in range(n): + + # count the number of each element + eli = S[i].element + m = elcount.get(eli, 0) + elcount[eli] = m + 1 + + for j in range(i + 1, n): + + elj = S[j].element + + # Get the pair + els = [eli, elj] + els.sort() + + # Get the distance to the desired precision + d = S.distance(i, j) + D = int(d * dmult) + + # Get the DW factor to the same precision + ss = S[i].Uisoequiv + S[j].Uisoequiv + SS = int(ss * umult) + + # Record the multiplicity of this pair + key = (els[0], els[1], D, SS) + mult = pairdict.get(key, 0) + pairdict[key] = mult + 1 + + # Now we can calculate IofQ from the pair dictionary. Making the dictionary + # first reduces the amount of calls to sinc and exp we have to make. + + # First we must cache the scattering factors + fdict = {} + for el in elcount: + fdict[el] = getXScatteringFactor(el, q) + + # Now we can compute I(Q) for the i != j pairs + y = 0 + x = q * deltad / pi + for key, mult in pairdict.items(): + eli = key[0] + elj = key[1] + fi = fdict[eli] + fj = fdict[elj] + D = key[2] + SS = key[3] + + # Note that numpy's sinc(x) = sin(x*pi)/(x*pi) + y += fi * fj * mult * sinc(x * D) * exp(-0.5 * SS * deltau * q**2) + + # We must multiply by 2 since we only counted j > i pairs. + y *= 2 + + # Now we must add in the i == j pairs. + for el, f in fdict.items(): + y += f**2 * elcount[el] + + # And that's it! + + return y + + +def getXScatteringFactor(el, q): + """Get the x-ray scattering factor for an element over the q range. + + If cctbx is not available, f(q) = 1 is used. + """ + try: + import cctbx.eltbx.xray_scattering as xray + + wk1995 = xray.wk1995(el) + g = wk1995.fetch() + # at_stol - at sin(theta)/lambda = Q/(4*pi) + f = numpy.asarray(map(g.at_stol, q / (4 * numpy.pi))) + return f + except ImportError: + return 1 + + +def makeData(strufile, q, datname, scale, a, Uiso, sig, bkgc, nl=1): + """Make some fake data and save it to file. + + Make some data to fit. This uses iofq to calculate an intensity curve, and + adds to it a background, broadens the peaks, and noise. + + strufile-- A filename holding the sample structure + q -- The q-range to calculate over. + datname -- The name of the file we're saving to. + scale -- The scale factor + a -- The lattice constant to use + Uiso -- The thermal factor for all atoms + sig -- The broadening factor + bkgc -- A parameter that gives minor control of the background. + nl -- Noise level (0, inf), default 1, larger -> less noise. + """ + + from diffpy.structure import Structure + + S = Structure() + S.read(strufile) + + # Set the lattice parameters + S.lattice.setLatPar(a, a, a) + + # Set a DW factor + for a in S: + a.Uisoequiv = Uiso + y = iofq(S, q) + + # We want to broaden the peaks as well. This simulates instrument effects. + q0 = q[len(q) // 2] + g = numpy.exp(-0.5 * ((q - q0) / sig) ** 2) + y = numpy.convolve(y, g, mode="same") / sum(g) + + # Add a polynomial background. + bkgd = (q + bkgc) ** 2 * (1.5 * max(q) - q) ** 5 + bkgd *= 0.2 * max(y) / max(bkgd) + + y += bkgd + + # Multiply by a scale factor + y *= scale + + # Calculate the uncertainty + u = (y / nl) ** 0.5 + + # And apply the noise + if nl > 0: + y = numpy.random.poisson(y * nl) / nl + + # Now save it + numpy.savetxt(datname, numpy.transpose([q, y, u])) + return + + +if __name__ == "__main__": + + main() + +# End of file From 9722d3103b8ba5dabbf272771f8e4c1c60e402aa Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Wed, 19 Nov 2025 15:01:23 -0500 Subject: [PATCH 10/23] intensityfit file2 --- docs/examples/core/intensityfit/C60.iq | 732 +++++++++--------- docs/examples/core/intensityfit/C60_1.iq | 380 +++++++++ docs/examples/core/intensityfit/C60_2.iq | 380 +++++++++ .../examples/core/intensityfit/npintensity.py | 4 +- .../core/intensityfit/npintensityII.py | 283 +++++++ 5 files changed, 1411 insertions(+), 368 deletions(-) create mode 100644 docs/examples/core/intensityfit/C60_1.iq create mode 100644 docs/examples/core/intensityfit/C60_2.iq create mode 100644 docs/examples/core/intensityfit/npintensityII.py diff --git a/docs/examples/core/intensityfit/C60.iq b/docs/examples/core/intensityfit/C60.iq index 1dc96aa..ae2a0b4 100644 --- a/docs/examples/core/intensityfit/C60.iq +++ b/docs/examples/core/intensityfit/C60.iq @@ -1,380 +1,380 @@ -1.000000000000000000e+00 6.100000000000000000e+01 7.110034071726496485e+00 -1.050000000000000044e+00 8.200000000000000000e+01 8.394511215438845042e+00 -1.100000000000000089e+00 9.000000000000000000e+01 9.614581256271836907e+00 -1.150000000000000133e+00 1.240000000000000000e+02 1.066952084213099461e+01 -1.200000000000000178e+00 1.460000000000000000e+02 1.148570297676609719e+01 -1.250000000000000222e+00 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91c6c16..7e6aa87 100644 --- a/docs/examples/core/intensityfit/npintensity.py +++ b/docs/examples/core/intensityfit/npintensity.py @@ -308,9 +308,9 @@ def gaussian(q, q0, width): def main(): # Make the data and the recipe - strufile = str(Path(__file__).parent / "C60.stru") + strufile = str((Path(__file__).parent / "C60.stru").resolve()) q = numpy.arange(1, 20, 0.05) - iq_path = str(Path(__file__).parent / "C60.iq") + iq_path = str((Path(__file__).parent / "C60.iq").resolve()) makeData(strufile, q, iq_path, 1.0, 100.68, 0.005, 0.13, 2) # Make the recipe diff --git a/docs/examples/core/intensityfit/npintensityII.py b/docs/examples/core/intensityfit/npintensityII.py new file mode 100644 index 0000000..287d826 --- /dev/null +++ b/docs/examples/core/intensityfit/npintensityII.py @@ -0,0 +1,283 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of extracting information from multiple data sets +simultaneously. + +This example builds on npintensitygenerator.py, and uses IntensityGenerator +from that example to build a recipe that simultaneously refines two data sets +generated from the same structure. + +Instructions + +Run the example and then read through the 'make_recipe' code. You will see how +to refine a single structure to two data sets. + +Extensions + +- In 'make_recipe' the fit contributions are identically configured except for + the profile. Factor out that configuration code and apply it in the + 'make_recipe' method. This will reduce the amount of code required to get the + job done, make it clearer what is being done and therefore reduce potential + mistakes in the code. This encapsulation of configuration workflow is the + first step towards writing a user interface. +""" +from pathlib import Path + +import numpy +from npintensity import IntensityGenerator, makeData + +from diffpy.cmi.fit_tools import optimize_recipe +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) + +###### +# Example Code + + +def make_recipe(strufile, datname1, datname2): + """Create a recipe that uses the IntensityGenerator. + + We will create two FitContributions that use the IntensityGenerator + from npintensitygenerator.py and associate each of these with a + Profile, and use this to define a FitRecipe. + + Both simulated data sets come from the same structure. We're going + to make two FitContributions that are identical, except for the + profile that is held in each. We're going to assure that the + structures are identical by using the same DiffpyStructureParSet + (which is generated by the IntensityGenerator when we load the + structure) in both generators. + """ + + # The Profiles + # Create two Profiles for the two FitContributions. + profile1 = Profile() + profile2 = Profile() + + # Load data into the Profiles + profile1.loadtxt(datname1) + x, y, u = profile2.loadtxt(datname2) + + # The ProfileGenerators + # Create two IntensityGenerators named "I". There will not be a name + # conflict, since the name is only meaningful within the FitContribution + # that holds the ProfileGenerator. Load the structure into one and make + # sure that the second ProfileGenerator is using the same + # DiffyStructureParSet. This will assure that both ProfileGenerators are + # using the exact same Parameters, and underlying Structure object in the + # calculation of the profile. + generator1 = IntensityGenerator("I") + generator1.setStructure(strufile) + generator2 = IntensityGenerator("I") + generator2.addParameterSet(generator1.phase) + + # The FitContributions + # Create the FitContributions. + contribution1 = FitContribution("bucky1") + contribution1.addProfileGenerator(generator1) + contribution1.setProfile(profile1, xname="q") + contribution2 = FitContribution("bucky2") + contribution2.addProfileGenerator(generator2) + contribution2.setProfile(profile2, xname="q") + + # Now we're ready to define the fitting equation for each FitContribution. + # The functions registered below will be independent, even though they take + # the same form and use the same Parameter names. By default, Parameters + # in different contributions are different Parameters even if they have the + # same names. FitContributions are isolated namespaces than only share + # information if you tell them to by using addParameter or addParameterSet. + bkgdstr = "b0 + b1*q + b2*q**2 + b3*q**3 + b4*q**4 + b5*q**5 + b6*q**6 +\ + b7*q**7 +b8*q**8 + b9*q**9" + + contribution1.registerStringFunction(bkgdstr, "bkgd") + contribution2.registerStringFunction(bkgdstr, "bkgd") + + # We will create the broadening function by registering a python function. + pi = numpy.pi + exp = numpy.exp + + def gaussian(q, q0, width): + return ( + 1 + / (2 * pi * width**2) ** 0.5 + * exp(-0.5 * ((q - q0) / width) ** 2) + ) + + contribution1.registerFunction(gaussian) + contribution2.registerFunction(gaussian) + # Center the gaussian + contribution1.q0.value = x[len(x) // 2] + contribution2.q0.value = x[len(x) // 2] + + # Now we can incorporate the scale and bkgd into our calculation. We also + # convolve the signal with the gaussian to broaden it. + contribution1.setEquation("scale * convolve(I, gaussian) + bkgd") + contribution2.setEquation("scale * convolve(I, gaussian) + bkgd") + + # Make a FitRecipe and associate the FitContributions. + recipe = FitRecipe() + recipe.addContribution(contribution1) + recipe.addContribution(contribution2) + + # Specify which Parameters we want to refine. We want to refine the + # background that we just defined in the FitContributions. We have to do + # this separately for each FitContribution. We tag the variables so it is + # easy to retrieve the background variables. + recipe.addVar(contribution1.b0, 0, name="b1_0", tag="bcoeffs1") + recipe.addVar(contribution1.b1, 0, name="b1_1", tag="bcoeffs1") + recipe.addVar(contribution1.b2, 0, name="b1_2", tag="bcoeffs1") + recipe.addVar(contribution1.b3, 0, name="b1_3", tag="bcoeffs1") + recipe.addVar(contribution1.b4, 0, name="b1_4", tag="bcoeffs1") + recipe.addVar(contribution1.b5, 0, name="b1_5", tag="bcoeffs1") + recipe.addVar(contribution1.b6, 0, name="b1_6", tag="bcoeffs1") + recipe.addVar(contribution1.b7, 0, name="b1_7", tag="bcoeffs1") + recipe.addVar(contribution1.b8, 0, name="b1_8", tag="bcoeffs1") + recipe.addVar(contribution1.b9, 0, name="b1_9", tag="bcoeffs1") + recipe.addVar(contribution2.b0, 0, name="b2_0", tag="bcoeffs2") + recipe.addVar(contribution2.b1, 0, name="b2_1", tag="bcoeffs2") + recipe.addVar(contribution2.b2, 0, name="b2_2", tag="bcoeffs2") + recipe.addVar(contribution2.b3, 0, name="b2_3", tag="bcoeffs2") + recipe.addVar(contribution2.b4, 0, name="b2_4", tag="bcoeffs2") + recipe.addVar(contribution2.b5, 0, name="b2_5", tag="bcoeffs2") + recipe.addVar(contribution2.b6, 0, name="b2_6", tag="bcoeffs2") + recipe.addVar(contribution2.b7, 0, name="b2_7", tag="bcoeffs2") + recipe.addVar(contribution2.b8, 0, name="b2_8", tag="bcoeffs2") + recipe.addVar(contribution2.b9, 0, name="b2_9", tag="bcoeffs2") + + # We also want to adjust the scale and the convolution width + recipe.addVar(contribution1.scale, 1, name="scale1") + recipe.addVar(contribution1.width, 0.1, name="width1") + recipe.addVar(contribution2.scale, 1, name="scale2") + recipe.addVar(contribution2.width, 0.1, name="width2") + + # We can also refine structural parameters. We only have to do this once, + # since each generator holds the same DiffpyStructureParSet. + phase = generator1.phase + lattice = phase.getLattice() + a = recipe.addVar(lattice.a) + # We want to allow for isotropic expansion, so we'll make constraints for + # that. + recipe.constrain(lattice.b, a) + recipe.constrain(lattice.c, a) + # We want to refine the thermal parameters as well. We will add a new + # variable that we call "Uiso" and constrain the atomic Uiso values to + # this. Note that we don't give Uiso an initial value. The initial value + # will be inferred from the subsequent constraints. + Uiso = recipe.newVar("Uiso") + for atom in phase.getScatterers(): + recipe.constrain(atom.Uiso, Uiso) + + # Give the recipe away so it can be used! + return recipe + + +def plotResults(recipe): + """Plot the results contained within a refined FitRecipe.""" + + # plotting song and dance + q = recipe.bucky1.profile.x + + # Plot this for fun. + I1 = recipe.bucky1.profile.y + Icalc1 = recipe.bucky1.profile.ycalc + bkgd1 = recipe.bucky1.evaluateEquation("bkgd") + diff1 = I1 - Icalc1 + I2 = recipe.bucky2.profile.y + Icalc2 = recipe.bucky2.profile.ycalc + bkgd2 = recipe.bucky2.evaluateEquation("bkgd") + diff2 = I2 - Icalc2 + offset = 1.2 * max(I2) * numpy.ones_like(I2) + I1 += offset + Icalc1 += offset + bkgd1 += offset + diff1 += offset + + import pylab + + pylab.subplot(2, 1, 1) + pylab.plot(q, I1, "bo", label="I1(Q) Data") + pylab.plot(q, Icalc1, "r-", label="I1(Q) Fit") + pylab.plot(q, diff1, "g-", label="I1(Q) diff") + pylab.plot(q, bkgd1, "c-", label="Bkgd1 Fit") + pylab.legend(loc=1) + + pylab.subplot(2, 1, 2) + pylab.plot(q, I2, "bo", label="I2(Q) Data") + pylab.plot(q, Icalc2, "r-", label="I2(Q) Fit") + pylab.plot(q, diff2, "g-", label="I2(Q) diff") + pylab.plot(q, bkgd2, "c-", label="Bkgd2 Fit") + pylab.xlabel(r"$Q (\AA^{-1})$") + pylab.ylabel("Intensity (arb. units)") + pylab.legend(loc=1) + + pylab.show() + return + + +def main(): + + # Make two different data sets, each from the same structure, but with + # different scale, noise, broadening and background. + strufile = str((Path(__file__).parent / "C60.stru").resolve()) + q = numpy.arange(1, 20, 0.05) + iq1_path = str((Path(__file__).parent / "C60_1.iq").resolve()) + iq2_path = str((Path(__file__).parent / "C60_2.iq").resolve()) + q = numpy.arange(1, 20, 0.05) + makeData(strufile, q, iq1_path, 8.1, 101.68, 0.008, 0.12, 2, 0.01) + makeData(strufile, q, iq2_path, 3.2, 101.68, 0.02, 0.003, 0, 1) + + # Make the recipe + recipe = make_recipe(strufile, iq1_path, iq2_path) + + # Optimize + # Since the backgrounds have a large effect on the profile, we will refine + # them first, but do so separately. + # To refine the background from the first contribution, we will fix + # all other parameters and give the second contribution no weight in the + # fit. + recipe.fix("all") + recipe.free("bcoeffs1") + recipe.setWeight(recipe.bucky2, 0) + optimize_recipe(recipe) + # Now do the same for the second background + recipe.fix("all") + recipe.free("bcoeffs1") + recipe.setWeight(recipe.bucky2, 1) + recipe.setWeight(recipe.bucky1, 0) + optimize_recipe(recipe) + # Now refine everything with the structure parameters included + recipe.free("all") + recipe.setWeight(recipe.bucky1, 1) + optimize_recipe(recipe) + + # Generate and print the FitResults + res = FitResults(recipe) + res.printResults() + + # Plot! + plotResults(recipe) + + return + + +if __name__ == "__main__": + + main() + +# End of file From 3b26096db6cd35628da8460f45044050b88f3906 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Wed, 19 Nov 2025 15:02:38 -0500 Subject: [PATCH 11/23] readme --- docs/examples/core/readme/README | 161 +++++++++++++++++++++++++++++++ 1 file changed, 161 insertions(+) create mode 100644 docs/examples/core/readme/README diff --git a/docs/examples/core/readme/README b/docs/examples/core/readme/README new file mode 100644 index 0000000..a48a570 --- /dev/null +++ b/docs/examples/core/readme/README @@ -0,0 +1,161 @@ +## Purpose + +These example scripts are intended to help a developer get acquainted with the +SrFit programming interface. Although one can write scripts like these to drive +optimization, these scripts do not represent the SrFit user interface. That +interface will be made available in a future release. + +A secondary purpose of these tutorials is to generate interest in SrFit. By +reading through the examples we hope that you are inspired to think of exciting +new ways to get the most out of your scientific data. If you think SrFit can +help you with that, please feel free to contact us through the DiffPy website. + +http://www.diffpy.org + +## Overview + +Three things are required for optimization: a function that generates a +quantity to be minimized, variables that can be used to manipulate that +function and an algorithm that can drive the function output to a smaller value +by steering the variables. For scientific purposes, the quantity to be +minimized is the disagreement between a measured profile and a theoretical +profile. The scientific understanding of the system under consideration partly +determines the suitability of the theoretical profile generator and the +scientific relevance of the variables used to drive it. + +The purpose of SrFit is to give users the means to combine known information +about a system of interest in order to extract scientifically relevant +quantities, and thus understanding from it. Various experimental procedures and +theoretical calculations may be needed to gain the desired understanding of the +system. SrFit helps users combine these views of the system in a coherent and +consistent manner. + +To achieve this purpose, SrFit provides: + +1. a function to be optimized (the residual) given one or more measured + profiles, one or more profile generators and variables to be steered by an + optimizer. +2. constraints and restraints that encapsulate known information about the + system. +3. a clearly defined programming interface that developers can use to add their + own profile generators, thereby enabling the combination of more views of a + system. +4. an equation building interface that allows users to tweak profile generators + when scientific understanding of a system is more advanced than the existing + software. + +The examples described below will go into detail about each of these points. + +## Examples + +The following examples are contained in the _docs/examples/_ directory of the +SrFit source distribution. They can be downloaded from +http://dev.danse.us/packages/srfit_examples-alpha9.zip + +For each example, start by running the example by typing in the command line :: + + python example.py + +where _example.py_ represents the example file. The output will show on screen +and a plot window will display. Once you've studied the output and plot, close +the plot window and open the example file. In the file there will be a +description of what the script is doing and the purpose of the example. By +reading through the example, you will be introduced to the SrFit programming +interface. + +Here is an overview of the examples. It is recommended that you work through +them in the order listed below. + +Basic: + +- gaussianrecipe.py\_ + Introductory recipe building and configuration. This introduces the + fundamental classes in SrFit. + +- debyemodel.py\_ + Introductory recipe building and configuration. This shows how to use a + function created by someone else in a refinement. This example also + introduces restraints. + +- debyemodelII.py\_ + Refine two different values of a variable from two different regions of a + profile. This example introduces constraints and working with multiple + contributions to a fit. + +Advanced: + +- gaussiangenerator.py* + Create a custom ProfileGenerator and use it in a refinement. This is an + instructive extension to gaussianrecipe.py*. + +- npintensity.py\_ + Use diffpy.structure to build a nanoparticle intensity generator, and use + it to refine a structure to simulated data. + +- npintensityII.py\_ + Use the calculator built in npintensity.py to simultaneously refine a + structure to two data sets. + +## Use Cases + +There are several examples that demonstrate various SrFit use cases. These do +not adopt the tutorial format of the previous examples. Regardless, developers +should read through these use cases to gain an understanding of PDF and SAS +refinement with SrFit. + +- crystalpdf.py\_ + Refine a diffpy.structure crystal to PDF data using automatic explicit + space group constraints. + +- simplepdf.py* + As crystalpdf.py*, but with a simplified interface. + +- crystalpdfobjcryst.py\_ + Refine a pyobjcryst crystal to PDF data using automatic implicit space + group constraints. + +- crystalpdftwophase.py\_ + Refine a two-phase structure to PDF data using two profile generators. + +- simplepdftwophase.py* + crystalpdftwophase.py* using the simplified PDFContribution interface. + +- crystalpdftwodata.py\_ + Refine a single structure to x-ray and neutron data simultaneously. + +- crystalpdfall.py\_ + Refine a two-phase structure using four data sets. + +- nppdfobjcryst.py\_ + Refine the C60 structure to real data. + +- nppdfcrystal.py\_ + Fit a nanoparticle PDF as a crystal PDF attenuated by a nanoparticle form + factor. + +- coreshellnp.py\_ + As above, but fit the PDF from core-shell nanoparticles. + +- ellipsoidsas.py\_ + Refine an ellipsoid SAS model to ideal data. + +- nppdfsas.py\_ + Refine PDF from nanoparticle of assumed shape using a crystal model and SAS + data from the same system. + +## Miscellaneous + +These demonstrate other SrFit features. These are in flux and may not be in +future versions. + +- simplerecipe.py\_ + This introduces the SimpleRecipe class that is a FitRecipe with an embedded + Profile and FitContribution. SimpleRecipe exposes methods from the Profile + and FitContribution, and adds other methods so it is easy to set up a + simple fit. + +- interface.py\_ + This example introduces some interface enhancements that allow the SrFit + recipes to be written with less code. This is not the same as a + full-featured scripting interface, but rather somewhere in between a + scripting interface and the API. From 62ba4ef30633bec208acd62733e82fcd77b52a25 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Thu, 20 Nov 2025 10:32:45 -0500 Subject: [PATCH 12/23] simplerecipe and threedoublepeaks --- .../examples/core/gaussianfit/simplerecipe.py | 66 + .../core/gaussianfit/threedoublepeaks.dat | 4000 +++++++++++++++++ .../core/gaussianfit/threedoublepeaks.py | 195 + 3 files changed, 4261 insertions(+) create mode 100644 docs/examples/core/gaussianfit/simplerecipe.py create mode 100644 docs/examples/core/gaussianfit/threedoublepeaks.dat create mode 100644 docs/examples/core/gaussianfit/threedoublepeaks.py diff --git a/docs/examples/core/gaussianfit/simplerecipe.py b/docs/examples/core/gaussianfit/simplerecipe.py new file mode 100644 index 0000000..311ae8c --- /dev/null +++ b/docs/examples/core/gaussianfit/simplerecipe.py @@ -0,0 +1,66 @@ +#!/usr/bin/env python +######################################################################## +# +# diffpy.srfit by DANSE Diffraction group +# Simon J. L. Billinge +# (c) 2009 The Trustees of Columbia University +# in the City of New York. All rights reserved. +# +# File coded by: Chris Farrow +# +# See AUTHORS.txt for a list of people who contributed. +# See LICENSE_DANSE.txt for license information. +# +######################################################################## +"""Example of simplified fitting. + +This is like gaussianrecipe.py, but it uses the SimpleRecipe, which +integrates the FitContribution and Profile objects for simple recipe +creation. +""" + +from pathlib import Path + +from diffpy.srfit.fitbase import SimpleRecipe + +###### +# Example Code + + +def main(): + """Set up a simple recipe in a few lines.""" + + # The SimpleRecipe class is a type of FitRecipe. It provides attribute-like + # access to variables and a residual function that can be minimized. + recipe = SimpleRecipe() + + # Load text from file. + data = str(Path(__file__).parent / "gaussian.dat") + recipe.loadtxt(data) + + # Set the equation. The variable "x" is taken from the data that was just + # loaded. The other variables, "A", "x0" and "sigma" are turned into + # attributes with an initial value of 0. + recipe.setEquation("A * exp(-0.5*(x-x0)**2/sigma**2)") + + # We can give them other values here. + recipe.A = 1 + recipe.x0 = 5 + recipe.sigma = 1 + + # We explicitly optimize the residual method of the SimpleRecipe + from scipy.optimize import leastsq + + leastsq(recipe.residual, recipe.values) + + # Print the results + recipe.printResults() + + return + + +if __name__ == "__main__": + + main() + +# End of file diff --git a/docs/examples/core/gaussianfit/threedoublepeaks.dat b/docs/examples/core/gaussianfit/threedoublepeaks.dat new file mode 100644 index 0000000..b812ef4 --- /dev/null +++ b/docs/examples/core/gaussianfit/threedoublepeaks.dat @@ -0,0 +1,4000 @@ +0.000000000000000000e+00 8.120000000000000000e+02 +1.000000000000000021e-02 7.590000000000000000e+02 +2.000000000000000042e-02 7.990000000000000000e+02 +2.999999999999999889e-02 8.640000000000000000e+02 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b/docs/examples/core/gaussianfit/threedoublepeaks.py new file mode 100644 index 0000000..c5a4fd3 --- /dev/null +++ b/docs/examples/core/gaussianfit/threedoublepeaks.py @@ -0,0 +1,195 @@ +#!/usr/bin/env python3 +"""Robust rewrite of the three-double-peaks example. + +Fixes: + - ensures profile.y/profile.dy are set + - safe peakloc (clip arcsin argument) + - avoid fragile sigma-from-grid-spacing + - small stable delta() implementation + - no accidental recipe.fix("mu") +""" + +from pathlib import Path + +import numpy as np + +from diffpy.cmi.fit_tools import optimize_recipe, plot_results +from diffpy.srfit.fitbase import ( + FitContribution, + FitRecipe, + FitResults, + Profile, +) + + +def make_recipe(): + """Make a FitRecipe for fitting three double-gaussian curves to + data. + + Robust version with safe defaults for dy, safe peak location + constraint, and stable delta/gaussian handling. + """ + + # Profile - load data and ensure y/dy are set + profile = Profile() + data = str(Path(__file__).parent / "threedoublepeaks.dat") + + # loadtxt returns (x, y, dy) if file contains 3 columns, else dy is None + x, y, dy = profile.loadtxt(data) + + # simulate and set error values + scale = np.max(np.abs(y)) + sigma = max(1e-8, 0.05 * scale) # 5% relative default + profile.dy = np.ones_like(y) * sigma + + # FitContribution + contribution = FitContribution("peaks") + contribution.setProfile(profile, xname="t") + + pi = np.pi + exp = np.exp + + # define a gaussian function for peak shape + def gaussian(t, mu, sig): + sig = np.maximum(sig, 1e-12) + return ( + 1.0 + / np.sqrt(2.0 * pi * sig**2) + * exp(-0.5 * ((t - mu) / sig) ** 2) + ) + + contribution.registerFunction(gaussian, name="peakshape") + + # define a delta function (small width gaussian) for peak position + def delta(t, mu): + # Use grid spacing if available but ensure non-zero + spacing = np.mean(np.diff(t)) + eps = max(1e-6, spacing * 0.1) + return gaussian(t, mu, eps) + + contribution.registerFunction(delta) + + # background string function: 6th degree polynomial + bkgdstr = "b0 + b1*t + b2*t**2 + b3*t**3 + b4*t**4 + b5*t**5 + b6*t**6" + contribution.registerStringFunction(bkgdstr, "bkgd") + + # Define equation: three double-peaks with fixed amplitude ratio 0.23 + contribution.setEquation( + "A1 * ( convolve( delta(t, mu11), peakshape(t, c, sig11) ) " + " + 0.23*convolve( delta(t, mu12), peakshape(t, c, sig12) ) ) + " + "A2 * ( convolve( delta(t, mu21), peakshape(t, c, sig21) ) " + " + 0.23*convolve( delta(t, mu22), peakshape(t, c, sig22) ) ) + " + "A3 * ( convolve( delta(t, mu31), peakshape(t, c, sig31) ) " + " + 0.23*convolve( delta(t, mu32), peakshape(t, c, sig32) ) ) + " + "bkgd" + ) + + # set center c near middle of x + contribution.c.value = x[len(x) // 2] + + # Build recipe + recipe = FitRecipe() + recipe.addContribution(contribution) + + # amplitudes + recipe.addVar(contribution.A1, 100) + recipe.addVar(contribution.A2, 100) + recipe.addVar(contribution.A3, 100) + + # primary peak positions + recipe.addVar(contribution.mu11, 13.0) + recipe.addVar(contribution.mu21, 24.0) + recipe.addVar(contribution.mu31, 33.0) + + # Safe peak location constraint using arcsin with clipping + l1 = 1.012 + l2 = 1.0 + + def peakloc(mu): + """Compute secondary peak location from primary peak + location.""" + # Convert to radians, compute, clip, convert back to degrees + mu_rad = np.deg2rad(mu) + arg = l2 * np.sin(mu_rad) / l1 + arg = np.clip(arg, -1.0, 1.0) + out_rad = np.arcsin(arg) + return np.rad2deg(out_rad) + + recipe.registerFunction(peakloc) + recipe.constrain(contribution.mu12, "peakloc(mu11)") + recipe.constrain(contribution.mu22, "peakloc(mu21)") + recipe.constrain(contribution.mu32, "peakloc(mu31)") + + # Peak widths: use sig0 and dsig with a safer functional form (positive) + recipe.newVar("sig0", 0.1) # base width in same units as t + recipe.newVar("dsig", 0.001) # small quadratic broadening coefficient + + def sig(sig0, dsig, mu): + """Compute sigma from base sig0, broadening dsig, and peak + position mu.""" + # Use positive-definite formula: sig0 * (1 + dsig * mu**2) + out = sig0 * (1.0 + dsig * mu**2) + # enforce a minimum width + return np.maximum(out, 1e-6) + + recipe.registerFunction(sig) + # Constrain the component sigmas + recipe.constrain(contribution.sig11, "sig(sig0, dsig, mu11)") + recipe.constrain( + contribution.sig12, + "sig(sig0, dsig, mu12)", + ns={"mu12": contribution.mu12}, + ) + recipe.constrain(contribution.sig21, "sig(sig0, dsig, mu21)") + recipe.constrain( + contribution.sig22, + "sig(sig0, dsig, mu22)", + ns={"mu22": contribution.mu22}, + ) + recipe.constrain(contribution.sig31, "sig(sig0, dsig, mu31)") + recipe.constrain( + contribution.sig32, + "sig(sig0, dsig, mu32)", + ns={"mu32": contribution.mu32}, + ) + + # background variables + for i in range(7): + # addVar(param, startvalue, tag='bkgd') keeps them grouped for steering + p = getattr(contribution, f"b{i}") + recipe.addVar(p, 0.0, tag="bkgd") + + # Initialize sig0/dsig sensible values + recipe.sig0.value = 0.1 + recipe.dsig.value = 0.001 + + return recipe + + +def steerFit(recipe): + """Simple steering sequence (similar to your original).""" + # Start by fitting only background + recipe.fix("all") + recipe.free("bkgd") # all background coeffs + optimize_recipe(recipe) + + # then free everything except initial peak positions (if wanted) + recipe.free("all") + # if you prefer to hold initial peak positions for one step: + recipe.fix("mu11", "mu21", "mu31") + optimize_recipe(recipe) + + # finally free all and finish + recipe.free("all") + optimize_recipe(recipe) + + +if __name__ == "__main__": + recipe = make_recipe() + steerFit(recipe) + res = FitResults(recipe) + res.printResults() + x = recipe.peaks.profile.x + yobs = recipe.peaks.profile.y + ycalc = recipe.peaks.profile.ycalc + plot_results(x, yobs, ycalc, difference_offset=-700) From 8b5f44c2e18ad26e4fcb0c37f0dff4620af1d26e Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Thu, 20 Nov 2025 10:38:51 -0500 Subject: [PATCH 13/23] update core readme --- docs/examples/core/readme/README | 106 ++----------------------------- 1 file changed, 4 insertions(+), 102 deletions(-) diff --git a/docs/examples/core/readme/README b/docs/examples/core/readme/README index a48a570..d1ccafa 100644 --- a/docs/examples/core/readme/README +++ b/docs/examples/core/readme/README @@ -1,9 +1,7 @@ ## Purpose -These example scripts are intended to help a developer get acquainted with the -SrFit programming interface. Although one can write scripts like these to drive -optimization, these scripts do not represent the SrFit user interface. That -interface will be made available in a future release. +These example scripts are intended to help users get acquainted with the +SrFit programming interface. A secondary purpose of these tutorials is to generate interest in SrFit. By reading through the examples we hope that you are inspired to think of exciting @@ -48,7 +46,8 @@ The examples described below will go into detail about each of these points. ## Examples -The following examples are contained in the _docs/examples/_ directory of the +The following examples can be copied using diffpy.cmi command-line interface. +Additionally, the are contained in the _docs/examples/_ directory of the SrFit source distribution. They can be downloaded from http://dev.danse.us/packages/srfit_examples-alpha9.zip @@ -62,100 +61,3 @@ the plot window and open the example file. In the file there will be a description of what the script is doing and the purpose of the example. By reading through the example, you will be introduced to the SrFit programming interface. - -Here is an overview of the examples. It is recommended that you work through -them in the order listed below. - -Basic: - -- gaussianrecipe.py\_ - Introductory recipe building and configuration. This introduces the - fundamental classes in SrFit. - -- debyemodel.py\_ - Introductory recipe building and configuration. This shows how to use a - function created by someone else in a refinement. This example also - introduces restraints. - -- debyemodelII.py\_ - Refine two different values of a variable from two different regions of a - profile. This example introduces constraints and working with multiple - contributions to a fit. - -Advanced: - -- gaussiangenerator.py* - Create a custom ProfileGenerator and use it in a refinement. This is an - instructive extension to gaussianrecipe.py*. - -- npintensity.py\_ - Use diffpy.structure to build a nanoparticle intensity generator, and use - it to refine a structure to simulated data. - -- npintensityII.py\_ - Use the calculator built in npintensity.py to simultaneously refine a - structure to two data sets. - -## Use Cases - -There are several examples that demonstrate various SrFit use cases. These do -not adopt the tutorial format of the previous examples. Regardless, developers -should read through these use cases to gain an understanding of PDF and SAS -refinement with SrFit. - -- crystalpdf.py\_ - Refine a diffpy.structure crystal to PDF data using automatic explicit - space group constraints. - -- simplepdf.py* - As crystalpdf.py*, but with a simplified interface. - -- crystalpdfobjcryst.py\_ - Refine a pyobjcryst crystal to PDF data using automatic implicit space - group constraints. - -- crystalpdftwophase.py\_ - Refine a two-phase structure to PDF data using two profile generators. - -- simplepdftwophase.py* - crystalpdftwophase.py* using the simplified PDFContribution interface. - -- crystalpdftwodata.py\_ - Refine a single structure to x-ray and neutron data simultaneously. - -- crystalpdfall.py\_ - Refine a two-phase structure using four data sets. - -- nppdfobjcryst.py\_ - Refine the C60 structure to real data. - -- nppdfcrystal.py\_ - Fit a nanoparticle PDF as a crystal PDF attenuated by a nanoparticle form - factor. - -- coreshellnp.py\_ - As above, but fit the PDF from core-shell nanoparticles. - -- ellipsoidsas.py\_ - Refine an ellipsoid SAS model to ideal data. - -- nppdfsas.py\_ - Refine PDF from nanoparticle of assumed shape using a crystal model and SAS - data from the same system. - -## Miscellaneous - -These demonstrate other SrFit features. These are in flux and may not be in -future versions. - -- simplerecipe.py\_ - This introduces the SimpleRecipe class that is a FitRecipe with an embedded - Profile and FitContribution. SimpleRecipe exposes methods from the Profile - and FitContribution, and adds other methods so it is easy to set up a - simple fit. - -- interface.py\_ - This example introduces some interface enhancements that allow the SrFit - recipes to be written with less code. This is not the same as a - full-featured scripting interface, but rather somewhere in between a - scripting interface and the API. From ad5b78bb55f713cc429fb2131298dc507863c712 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Thu, 20 Nov 2025 10:39:23 -0500 Subject: [PATCH 14/23] more core-shell example to pdf --- docs/examples/{core => pdf}/core-shell-NP/CdS.cif | 0 docs/examples/{core => pdf}/core-shell-NP/CdS_ZnS_nano.gr | 0 docs/examples/{core => pdf}/core-shell-NP/ZnS.cif | 0 docs/examples/{core => pdf}/core-shell-NP/coreshellnp.py | 0 4 files changed, 0 insertions(+), 0 deletions(-) rename docs/examples/{core => pdf}/core-shell-NP/CdS.cif (100%) rename docs/examples/{core => pdf}/core-shell-NP/CdS_ZnS_nano.gr (100%) rename docs/examples/{core => pdf}/core-shell-NP/ZnS.cif (100%) rename docs/examples/{core => pdf}/core-shell-NP/coreshellnp.py (100%) diff --git a/docs/examples/core/core-shell-NP/CdS.cif b/docs/examples/pdf/core-shell-NP/CdS.cif similarity index 100% rename from docs/examples/core/core-shell-NP/CdS.cif rename to docs/examples/pdf/core-shell-NP/CdS.cif diff --git a/docs/examples/core/core-shell-NP/CdS_ZnS_nano.gr b/docs/examples/pdf/core-shell-NP/CdS_ZnS_nano.gr similarity index 100% rename from docs/examples/core/core-shell-NP/CdS_ZnS_nano.gr rename to docs/examples/pdf/core-shell-NP/CdS_ZnS_nano.gr diff --git a/docs/examples/core/core-shell-NP/ZnS.cif b/docs/examples/pdf/core-shell-NP/ZnS.cif similarity index 100% rename from docs/examples/core/core-shell-NP/ZnS.cif rename to docs/examples/pdf/core-shell-NP/ZnS.cif diff --git a/docs/examples/core/core-shell-NP/coreshellnp.py b/docs/examples/pdf/core-shell-NP/coreshellnp.py similarity index 100% rename from docs/examples/core/core-shell-NP/coreshellnp.py rename to docs/examples/pdf/core-shell-NP/coreshellnp.py From 1bd52f9ad524f87cd3ccde1d3a859e139e96aeb7 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Thu, 20 Nov 2025 10:41:15 -0500 Subject: [PATCH 15/23] add optional difference offsets param --- src/diffpy/cmi/fit_tools.py | 15 +++++++++++---- 1 file changed, 11 insertions(+), 4 deletions(-) diff --git a/src/diffpy/cmi/fit_tools.py b/src/diffpy/cmi/fit_tools.py index ace994b..ff8920d 100644 --- a/src/diffpy/cmi/fit_tools.py +++ b/src/diffpy/cmi/fit_tools.py @@ -45,7 +45,7 @@ def optimize_recipe(recipe, optimizer: str = "leastsq", **kwargs): return -def plot_results(x, yobs, ycalc): +def plot_results(x, yobs, ycalc, difference_offset=None): """Plot the results contained within a refined FitRecipe. Parameters @@ -56,9 +56,16 @@ def plot_results(x, yobs, ycalc): The observed/experimental data. ycalc : array-like The calculated/fitted data. + difference_offset : int or float, optional + The y-axis offset for the difference curve. If None, defaults to + -0.8 * max(yobs). """ - diffzero = -0.8 * max(yobs) * np.ones_like(yobs) - diff = yobs - ycalc + diffzero + if difference_offset is None: + difference_offset = -0.8 * max(yobs) * np.ones_like(yobs) + else: + difference_offset = difference_offset * np.ones_like(yobs) + + diff = yobs - ycalc + difference_offset ls = "None" marker = "o" ms = 5 @@ -76,7 +83,7 @@ def plot_results(x, yobs, ycalc): ) plt.plot(x, ycalc, label="calculated") plt.plot(x, diff, label="diff") - plt.plot(x, diffzero, lw=1.0, c="black") + plt.plot(x, difference_offset, lw=1.0, c="black") plt.xlabel(r"$r (\AA)$") plt.ylabel(r"$G (\AA^{-2})$") plt.legend() From bc556ab56fe832f8306b35229d51f08ab250596c Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Thu, 20 Nov 2025 10:41:46 -0500 Subject: [PATCH 16/23] remove all examples that arent currently working --- docs/examples/core-shell-NP/CdS.cif | 69 - docs/examples/core-shell-NP/CdS_ZnS_nano.gr | 7506 ------------ docs/examples/core-shell-NP/ZnS.cif | 65 - docs/examples/core-shell-NP/coreshellnp.py | 218 - docs/examples/srfit_ex/README | 161 - docs/examples/srfit_ex/coreshellnp.py | 215 - docs/examples/srfit_ex/crystalpdf.py | 176 - docs/examples/srfit_ex/crystalpdfall.py | 240 - docs/examples/srfit_ex/crystalpdfobjcryst.py | 129 - docs/examples/srfit_ex/crystalpdftwodata.py | 196 - docs/examples/srfit_ex/crystalpdftwophase.py | 187 - docs/examples/srfit_ex/data/C60.gr | 1999 --- docs/examples/srfit_ex/data/C60.stru | 369 - docs/examples/srfit_ex/data/CdS.cif | 69 - docs/examples/srfit_ex/data/CdS_ZnS_nano.gr | 7506 ------------ docs/examples/srfit_ex/data/ZnS.cif | 65 - docs/examples/srfit_ex/data/gaussian.dat | 100 - docs/examples/srfit_ex/data/lorentzian.dat | 200 - .../srfit_ex/data/ni-q27r100-neutron.gr | 10052 ---------------- docs/examples/srfit_ex/data/ni-q27r60-xray.gr | 6133 ---------- .../srfit_ex/data/ni-q27r60nodg-xray.gr | 6133 ---------- docs/examples/srfit_ex/data/ni.cif | 236 - docs/examples/srfit_ex/data/ni.iq | 2464 ---- docs/examples/srfit_ex/data/pb.cif | 240 - docs/examples/srfit_ex/data/pb_100.xyz | 102 - docs/examples/srfit_ex/data/pb_100_qmax1.iq | 99 - docs/examples/srfit_ex/data/pb_100_qmin1.gr | 3500 ------ .../srfit_ex/data/sas_ellipsoid_testdata.txt | 136 - docs/examples/srfit_ex/data/si-q27r60-xray.gr | 6133 ---------- docs/examples/srfit_ex/data/si.cif | 224 - .../srfit_ex/data/si90ni10-q27r60-xray.gr | 6134 ---------- .../srfit_ex/data/threedoublepeaks.dat | 4000 ------ docs/examples/srfit_ex/debyemodel.py | 270 - docs/examples/srfit_ex/debyemodelII.py | 162 - docs/examples/srfit_ex/ellipsoidsas.py | 130 - docs/examples/srfit_ex/gaussiangenerator.py | 180 - docs/examples/srfit_ex/gaussianrecipe.py | 214 - docs/examples/srfit_ex/interface.py | 78 - docs/examples/srfit_ex/npintensity.py | 531 - docs/examples/srfit_ex/npintensityII.py | 279 - docs/examples/srfit_ex/nppdfcrystal.py | 129 - docs/examples/srfit_ex/nppdfobjcryst.py | 257 - docs/examples/srfit_ex/nppdfsas.py | 196 - 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100644 docs/examples/srfit_ex/threedoublepeaks.py diff --git a/docs/examples/core-shell-NP/CdS.cif b/docs/examples/core-shell-NP/CdS.cif deleted file mode 100644 index 34fa965..0000000 --- a/docs/examples/core-shell-NP/CdS.cif +++ /dev/null @@ -1,69 +0,0 @@ -data_1011054 -_chemical_name_systematic 'Cadmium sulfide - $-alpha' -_chemical_name_mineral 'Greenockite' -_chemical_compound_source 'synthetic' -_chemical_formula_structural 'Cd S' -_chemical_formula_sum 'Cd S' -_publ_section_title -; -Ueber die Kristallstruktur des $-alpha- und $-beta Cd S, sowie des -Wurtzits. -; -loop_ -_publ_author_name - 'Ulrich, F' - 'Zachariasen, W' -_journal_name_full -; -Zeitschrift fuer Kristallographie, Kristallgeometrie, Kristallphysik, -Kristallchemie (-144,1977) -; -_journal_coden_ASTM ZEKGAX -_journal_volume 62 -_journal_year 1925 -_journal_page_first 260 -_journal_page_last 273 -_cell_length_a 4.15 -_cell_length_b 4.15 -_cell_length_c 6.737 -_cell_angle_alpha 90 -_cell_angle_beta 90 -_cell_angle_gamma 120 -_cell_volume 100.5 -_cell_formula_units_Z 2 -_exptl_crystal_density_meas 4.82 -_symmetry_space_group_name_H-M 'P 63 m c' -_symmetry_Int_Tables_number 186 -_symmetry_cell_setting hexagonal -loop_ -_symmetry_equiv_pos_as_xyz - 'x,y,z' - '-y,x-y,z' - 'y-x,-x,z' - '-y,-x,z' - 'y-x,y,z' - 'x,x-y,z' - '-x,-y,1/2+z' - 'y,y-x,1/2+z' - 'x-y,x,1/2+z' - 'y,x,1/2+z' - 'x-y,-y,1/2+z' - '-x,y-x,1/2+z' -loop_ -_atom_type_symbol -_atom_type_oxidation_number - Cd2+ 2.000 - S2- -2.000 -loop_ -_atom_site_label -_atom_site_type_symbol -_atom_site_symmetry_multiplicity -_atom_site_Wyckoff_symbol -_atom_site_fract_x -_atom_site_fract_y -_atom_site_fract_z -_atom_site_occupancy -_atom_site_attached_hydrogens -_atom_site_calc_flag - Cd1 Cd 2 b 0.33333 0.66667 0. 1. 0 d - S1 S 2 b 0.33333 0.66667 0.375 1. 0 d diff --git a/docs/examples/core-shell-NP/CdS_ZnS_nano.gr b/docs/examples/core-shell-NP/CdS_ZnS_nano.gr deleted file mode 100644 index 650e932..0000000 --- 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9.85549e-06 -74.99 0.000126422 -75 0.000222558 diff --git a/docs/examples/core-shell-NP/ZnS.cif b/docs/examples/core-shell-NP/ZnS.cif deleted file mode 100644 index 0bdb8bc..0000000 --- a/docs/examples/core-shell-NP/ZnS.cif +++ /dev/null @@ -1,65 +0,0 @@ -#------------------------------------------------------------------------------ -#$Date: 2016-02-16 14:49:47 +0200 (Tue, 16 Feb 2016) $ -#$Revision: 176465 $ -#$URL: svn://www.crystallography.net/cod/cif/9/00/88/9008878.cif $ -#------------------------------------------------------------------------------ -# -# This file is available in the Crystallography Open Database (COD), -# http://www.crystallography.net/. The original data for this entry -# were provided the American Mineralogist Crystal Structure Database, -# http://rruff.geo.arizona.edu/AMS/amcsd.php -# -# The file may be used within the scientific community so long as -# proper attribution is given to the journal article from which the -# data were obtained. -# -data_9008878 -loop_ -_publ_author_name -'Wyckoff, R. W. G.' -_publ_section_title -; - Second edition. Interscience Publishers, New York, New York - Note: wurtzite structure -; -_journal_name_full 'Crystal Structures' -_journal_page_first 85 -_journal_page_last 237 -_journal_volume 1 -_journal_year 1963 -_chemical_formula_sum 'S Zn' -_chemical_name_mineral Wurtzite-2H -_space_group_IT_number 186 -_symmetry_space_group_name_Hall 'P 6c -2c' -_symmetry_space_group_name_H-M 'P 63 m c' -_cell_angle_alpha 90 -_cell_angle_beta 90 -_cell_angle_gamma 120 -_cell_length_a 3.811 -_cell_length_b 3.811 -_cell_length_c 6.234 -_cell_volume 78.411 -_exptl_crystal_density_diffrn 4.128 -_cod_original_formula_sum 'Zn S' -_cod_database_code 9008878 -loop_ -_symmetry_equiv_pos_as_xyz -x,y,z --x,-x+y,1/2+z -x-y,x,1/2+z --y,-x,z --y,x-y,z -x-y,-y,1/2+z --x,-y,1/2+z -x,x-y,z --x+y,-x,z -y,x,1/2+z -y,-x+y,1/2+z --x+y,y,z -loop_ -_atom_site_label -_atom_site_fract_x -_atom_site_fract_y -_atom_site_fract_z -Zn 0.33333 0.66667 0.00000 -S 0.33333 0.66667 0.38500 diff --git a/docs/examples/core-shell-NP/coreshellnp.py b/docs/examples/core-shell-NP/coreshellnp.py deleted file mode 100644 index 08d492f..0000000 --- a/docs/examples/core-shell-NP/coreshellnp.py +++ /dev/null @@ -1,218 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2011 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow, Peng Tian -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Refine the structure of a core-shell nanoparticle. - -This applies the characteristic function formalism described in -nppdfcrystal.py to the case of a spherical core-shell nanoparticle. The -modeling approach we use is to refine the core and shell as two -different phases, each with an appropriate characteristic function. -""" - -from pathlib import Path - -import numpy -from pyobjcryst import loadCrystal -from scipy.optimize import leastsq - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) -from diffpy.srfit.pdf import PDFGenerator, PDFParser - -# Example Code - - -def makeRecipe(stru1, stru2, datname): - """Create a fitting recipe for crystalline PDF data.""" - - # The Profile - profile = Profile() - - # Load data and add it to the profile - parser = PDFParser() - parser.parseFile(datname) - profile.loadParsedData(parser) - profile.setCalculationRange(xmin=1.5, xmax=45, dx=0.1) - - # The ProfileGenerator - # In order to fit the core and shell phases simultaneously, we must use two - # PDFGenerators. - # - # The generator for the CdS core. We call it "G_CdS" and will use this name - # later when we set the fitting equation in the FitContribution. - generator_cds = PDFGenerator("G_CdS") - generator_cds.setStructure(stru1) - generator_cds.setQmax(26) - generator_cds.qdamp.value = 0.0396 - # The generator for the ZnS shell. We call it "G_ZnS". - generator_zns = PDFGenerator("G_ZnS") - generator_zns.setStructure(stru2) - generator_zns.setQmax(26) - generator_zns.qdamp.value = 0.0396 - - # The FitContribution - # Add both generators and the profile to the FitContribution. - contribution = FitContribution("cdszns") - contribution.addProfileGenerator(generator_cds) - contribution.addProfileGenerator(generator_zns) - contribution.setProfile(profile, xname="r") - - # Set up the characteristic functions. We use a spherical CF for the core - # and a spherical shell CF for the shell. Since this is set up as two - # phases, we implicitly assume that the core-shell correlations contribute - # very little to the PDF. - from diffpy.srfit.pdf.characteristicfunctions import shellCF, sphericalCF - - contribution.registerFunction(sphericalCF, name="f_CdS") - contribution.registerFunction(shellCF, name="f_ZnS") - - # Write the fitting equation. We want to sum the PDFs from each phase and - # multiply it by a scaling factor. - contribution.setEquation("scale * (f_CdS * G_CdS + f_ZnS * G_ZnS)") - - # Make the FitRecipe and add the FitContribution. - recipe = FitRecipe() - recipe.addContribution(contribution) - - # Vary the inner radius and thickness of the shell. Constrain the core - # diameter to twice the shell radius. - recipe.addVar(contribution.radius, 15) - recipe.addVar(contribution.thickness, 11) - recipe.constrain(contribution.psize, "2 * radius") - - # Configure the fit variables - # Start by configuring the scale factor and resolution factors. - # We want the sum of the phase scale factors to be 1. - recipe.newVar("scale_CdS", 0.7) - recipe.constrain(generator_cds.scale, "scale_CdS") - recipe.constrain(generator_zns.scale, "1 - scale_CdS") - # We also want the resolution factor to be the same on each. - - # Vary the global scale as well. - recipe.addVar(contribution.scale, 0.3) - - # Now we can configure the structural parameters. We tag the different - # structural variables so we can easily turn them on and off in the - # subsequent refinement. - phase_cds = generator_cds.phase - for par in phase_cds.sgpars.latpars: - recipe.addVar(par, name=par.name + "_cds", tag="lat") - for par in phase_cds.sgpars.adppars: - recipe.addVar(par, 1, name=par.name + "_cds", tag="adp") - recipe.addVar(phase_cds.sgpars.xyzpars.z_1, name="z_1_cds", tag="xyz") - # Since we know these have stacking disorder, constrain the B33 adps for - # each atom type. - recipe.constrain("B33_1_cds", "B33_0_cds") - recipe.addVar(generator_cds.delta2, name="delta2_cds", value=5) - - phase_zns = generator_zns.phase - for par in phase_zns.sgpars.latpars: - recipe.addVar(par, name=par.name + "_zns", tag="lat") - for par in phase_zns.sgpars.adppars: - recipe.addVar(par, 1, name=par.name + "_zns", tag="adp") - recipe.addVar(phase_zns.sgpars.xyzpars.z_1, name="z_1_zns", tag="xyz") - recipe.constrain("B33_1_zns", "B33_0_zns") - recipe.addVar(generator_zns.delta2, name="delta2_zns", value=2.5) - - # Give the recipe away so it can be used! - return recipe - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # All this should be pretty familiar by now. - r = recipe.cdszns.profile.x - g = recipe.cdszns.profile.y - gcalc = recipe.cdszns.profile.ycalc - diffzero = -0.8 * max(g) * numpy.ones_like(g) - diff = g - gcalc + diffzero - - import matplotlib.pyplot as plt - - plt.plot(r, g, "bo", label="G(r) Data") - plt.plot(r, gcalc, "r-", label="G(r) Fit") - plt.plot(r, diff, "g-", label="G(r) diff") - plt.plot(r, diffzero, "k-") - plt.xlabel(r"$r (\AA)$") - plt.ylabel(r"$G (\AA^{-2})$") - plt.legend(loc=1) - - plt.show() - return - - -def main(): - """Set up and refine the recipe.""" - - # Make the data and the recipe - base_path = Path(__file__).parent - cdsciffile = base_path / "CdS.cif" - znsciffile = base_path / "ZnS.cif" - data = base_path / "CdS_ZnS_nano.gr" - - # Make the recipe - stru1 = loadCrystal(cdsciffile) - stru2 = loadCrystal(znsciffile) - recipe = makeRecipe(stru1, stru2, data) - from diffpy.srfit.fitbase.fithook import PlotFitHook - - recipe.pushFitHook(PlotFitHook()) - recipe.fithooks[0].verbose = 3 - - # Optimize - we do this in steps to help convergence - recipe.fix("all") - - # Start with the lattice parameters. In makeRecipe, these were tagged with - # "lat". Here is how we use that. - recipe.free("lat") - leastsq(recipe.residual, recipe.values, maxfev=50) - - # Now the scale and phase fraction. - recipe.free("scale", "scale_CdS") - leastsq(recipe.residual, recipe.values, maxfev=50) - - # The ADPs. - recipe.free("adp") - leastsq(recipe.residual, recipe.values, maxfev=100) - - # The delta2 parameters. - recipe.free("delta2_cds", "delta2_zns") - leastsq(recipe.residual, recipe.values, maxfev=50) - - # The shape parameters. - recipe.free("radius", "thickness") - leastsq(recipe.residual, recipe.values, maxfev=50) - - # The positional parameters. - recipe.free("xyz") - leastsq(recipe.residual, recipe.values) - - # Generate and print the FitResults - res = FitResults(recipe) - res.printResults() - - # Plot! - plotResults(recipe) - return - - -if __name__ == "__main__": - main() - -# End of file diff --git a/docs/examples/srfit_ex/README b/docs/examples/srfit_ex/README deleted file mode 100644 index a48a570..0000000 --- a/docs/examples/srfit_ex/README +++ /dev/null @@ -1,161 +0,0 @@ -## Purpose - -These example scripts are intended to help a developer get acquainted with the -SrFit programming interface. Although one can write scripts like these to drive -optimization, these scripts do not represent the SrFit user interface. That -interface will be made available in a future release. - -A secondary purpose of these tutorials is to generate interest in SrFit. By -reading through the examples we hope that you are inspired to think of exciting -new ways to get the most out of your scientific data. If you think SrFit can -help you with that, please feel free to contact us through the DiffPy website. - -http://www.diffpy.org - -## Overview - -Three things are required for optimization: a function that generates a -quantity to be minimized, variables that can be used to manipulate that -function and an algorithm that can drive the function output to a smaller value -by steering the variables. For scientific purposes, the quantity to be -minimized is the disagreement between a measured profile and a theoretical -profile. The scientific understanding of the system under consideration partly -determines the suitability of the theoretical profile generator and the -scientific relevance of the variables used to drive it. - -The purpose of SrFit is to give users the means to combine known information -about a system of interest in order to extract scientifically relevant -quantities, and thus understanding from it. Various experimental procedures and -theoretical calculations may be needed to gain the desired understanding of the -system. SrFit helps users combine these views of the system in a coherent and -consistent manner. - -To achieve this purpose, SrFit provides: - -1. a function to be optimized (the residual) given one or more measured - profiles, one or more profile generators and variables to be steered by an - optimizer. -2. constraints and restraints that encapsulate known information about the - system. -3. a clearly defined programming interface that developers can use to add their - own profile generators, thereby enabling the combination of more views of a - system. -4. an equation building interface that allows users to tweak profile generators - when scientific understanding of a system is more advanced than the existing - software. - -The examples described below will go into detail about each of these points. - -## Examples - -The following examples are contained in the _docs/examples/_ directory of the -SrFit source distribution. They can be downloaded from -http://dev.danse.us/packages/srfit_examples-alpha9.zip - -For each example, start by running the example by typing in the command line :: - - python example.py - -where _example.py_ represents the example file. The output will show on screen -and a plot window will display. Once you've studied the output and plot, close -the plot window and open the example file. In the file there will be a -description of what the script is doing and the purpose of the example. By -reading through the example, you will be introduced to the SrFit programming -interface. - -Here is an overview of the examples. It is recommended that you work through -them in the order listed below. - -Basic: - -- gaussianrecipe.py\_ - Introductory recipe building and configuration. This introduces the - fundamental classes in SrFit. - -- debyemodel.py\_ - Introductory recipe building and configuration. This shows how to use a - function created by someone else in a refinement. This example also - introduces restraints. - -- debyemodelII.py\_ - Refine two different values of a variable from two different regions of a - profile. This example introduces constraints and working with multiple - contributions to a fit. - -Advanced: - -- gaussiangenerator.py* - Create a custom ProfileGenerator and use it in a refinement. This is an - instructive extension to gaussianrecipe.py*. - -- npintensity.py\_ - Use diffpy.structure to build a nanoparticle intensity generator, and use - it to refine a structure to simulated data. - -- npintensityII.py\_ - Use the calculator built in npintensity.py to simultaneously refine a - structure to two data sets. - -## Use Cases - -There are several examples that demonstrate various SrFit use cases. These do -not adopt the tutorial format of the previous examples. Regardless, developers -should read through these use cases to gain an understanding of PDF and SAS -refinement with SrFit. - -- crystalpdf.py\_ - Refine a diffpy.structure crystal to PDF data using automatic explicit - space group constraints. - -- simplepdf.py* - As crystalpdf.py*, but with a simplified interface. - -- crystalpdfobjcryst.py\_ - Refine a pyobjcryst crystal to PDF data using automatic implicit space - group constraints. - -- crystalpdftwophase.py\_ - Refine a two-phase structure to PDF data using two profile generators. - -- simplepdftwophase.py* - crystalpdftwophase.py* using the simplified PDFContribution interface. - -- crystalpdftwodata.py\_ - Refine a single structure to x-ray and neutron data simultaneously. - -- crystalpdfall.py\_ - Refine a two-phase structure using four data sets. - -- nppdfobjcryst.py\_ - Refine the C60 structure to real data. - -- nppdfcrystal.py\_ - Fit a nanoparticle PDF as a crystal PDF attenuated by a nanoparticle form - factor. - -- coreshellnp.py\_ - As above, but fit the PDF from core-shell nanoparticles. - -- ellipsoidsas.py\_ - Refine an ellipsoid SAS model to ideal data. - -- nppdfsas.py\_ - Refine PDF from nanoparticle of assumed shape using a crystal model and SAS - data from the same system. - -## Miscellaneous - -These demonstrate other SrFit features. These are in flux and may not be in -future versions. - -- simplerecipe.py\_ - This introduces the SimpleRecipe class that is a FitRecipe with an embedded - Profile and FitContribution. SimpleRecipe exposes methods from the Profile - and FitContribution, and adds other methods so it is easy to set up a - simple fit. - -- interface.py\_ - This example introduces some interface enhancements that allow the SrFit - recipes to be written with less code. This is not the same as a - full-featured scripting interface, but rather somewhere in between a - scripting interface and the API. diff --git a/docs/examples/srfit_ex/coreshellnp.py b/docs/examples/srfit_ex/coreshellnp.py deleted file mode 100644 index 8030a34..0000000 --- a/docs/examples/srfit_ex/coreshellnp.py +++ /dev/null @@ -1,215 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2011 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow, Peng Tian -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Refine the structure of a core-shell nanoparticle. - -This applies the characteristic function formalism described in -nppdfcrystal.py to the case of a spherical core-shell nanoparticle. The -modeling approach we use is to refine the core and shell as two -different phases, each with an appropriate characteristic function. -""" - -import numpy -from pyobjcryst import loadCrystal -from scipy.optimize import leastsq - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) -from diffpy.srfit.pdf import PDFGenerator, PDFParser - -# Example Code - - -def makeRecipe(stru1, stru2, datname): - """Create a fitting recipe for crystalline PDF data.""" - - # The Profile - profile = Profile() - - # Load data and add it to the profile - parser = PDFParser() - parser.parseFile(datname) - profile.loadParsedData(parser) - profile.setCalculationRange(xmin=1.5, xmax=45, dx=0.1) - - # The ProfileGenerator - # In order to fit the core and shell phases simultaneously, we must use two - # PDFGenerators. - # - # The generator for the CdS core. We call it "G_CdS" and will use this name - # later when we set the fitting equation in the FitContribution. - generator_cds = PDFGenerator("G_CdS") - generator_cds.setStructure(stru1) - generator_cds.setQmax(26) - generator_cds.qdamp.value = 0.0396 - # The generator for the ZnS shell. We call it "G_ZnS". - generator_zns = PDFGenerator("G_ZnS") - generator_zns.setStructure(stru2) - generator_zns.setQmax(26) - generator_zns.qdamp.value = 0.0396 - - # The FitContribution - # Add both generators and the profile to the FitContribution. - contribution = FitContribution("cdszns") - contribution.addProfileGenerator(generator_cds) - contribution.addProfileGenerator(generator_zns) - contribution.setProfile(profile, xname="r") - - # Set up the characteristic functions. We use a spherical CF for the core - # and a spherical shell CF for the shell. Since this is set up as two - # phases, we implicitly assume that the core-shell correlations contribute - # very little to the PDF. - from diffpy.srfit.pdf.characteristicfunctions import shellCF, sphericalCF - - contribution.registerFunction(sphericalCF, name="f_CdS") - contribution.registerFunction(shellCF, name="f_ZnS") - - # Write the fitting equation. We want to sum the PDFs from each phase and - # multiply it by a scaling factor. - contribution.setEquation("scale * (f_CdS * G_CdS + f_ZnS * G_ZnS)") - - # Make the FitRecipe and add the FitContribution. - recipe = FitRecipe() - recipe.addContribution(contribution) - - # Vary the inner radius and thickness of the shell. Constrain the core - # diameter to twice the shell radius. - recipe.addVar(contribution.radius, 15) - recipe.addVar(contribution.thickness, 11) - recipe.constrain(contribution.psize, "2 * radius") - - # Configure the fit variables - # Start by configuring the scale factor and resolution factors. - # We want the sum of the phase scale factors to be 1. - recipe.newVar("scale_CdS", 0.7) - recipe.constrain(generator_cds.scale, "scale_CdS") - recipe.constrain(generator_zns.scale, "1 - scale_CdS") - # We also want the resolution factor to be the same on each. - - # Vary the global scale as well. - recipe.addVar(contribution.scale, 0.3) - - # Now we can configure the structural parameters. We tag the different - # structural variables so we can easily turn them on and off in the - # subsequent refinement. - phase_cds = generator_cds.phase - for par in phase_cds.sgpars.latpars: - recipe.addVar(par, name=par.name + "_cds", tag="lat") - for par in phase_cds.sgpars.adppars: - recipe.addVar(par, 1, name=par.name + "_cds", tag="adp") - recipe.addVar(phase_cds.sgpars.xyzpars.z_1, name="z_1_cds", tag="xyz") - # Since we know these have stacking disorder, constrain the B33 adps for - # each atom type. - recipe.constrain("B33_1_cds", "B33_0_cds") - recipe.addVar(generator_cds.delta2, name="delta2_cds", value=5) - - phase_zns = generator_zns.phase - for par in phase_zns.sgpars.latpars: - recipe.addVar(par, name=par.name + "_zns", tag="lat") - for par in phase_zns.sgpars.adppars: - recipe.addVar(par, 1, name=par.name + "_zns", tag="adp") - recipe.addVar(phase_zns.sgpars.xyzpars.z_1, name="z_1_zns", tag="xyz") - recipe.constrain("B33_1_zns", "B33_0_zns") - recipe.addVar(generator_zns.delta2, name="delta2_zns", value=2.5) - - # Give the recipe away so it can be used! - return recipe - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # All this should be pretty familiar by now. - r = recipe.cdszns.profile.x - g = recipe.cdszns.profile.y - gcalc = recipe.cdszns.profile.ycalc - diffzero = -0.8 * max(g) * numpy.ones_like(g) - diff = g - gcalc + diffzero - - import pylab - - pylab.plot(r, g, "bo", label="G(r) Data") - pylab.plot(r, gcalc, "r-", label="G(r) Fit") - pylab.plot(r, diff, "g-", label="G(r) diff") - pylab.plot(r, diffzero, "k-") - pylab.xlabel(r"$r (\AA)$") - pylab.ylabel(r"$G (\AA^{-2})$") - pylab.legend(loc=1) - - pylab.show() - return - - -def main(): - """Set up and refine the recipe.""" - - # Make the data and the recipe - cdsciffile = "data/CdS.cif" - znsciffile = "data/ZnS.cif" - data = "data/CdS_ZnS_nano.gr" - - # Make the recipe - stru1 = loadCrystal(cdsciffile) - stru2 = loadCrystal(znsciffile) - recipe = makeRecipe(stru1, stru2, data) - from diffpy.srfit.fitbase.fithook import PlotFitHook - - recipe.pushFitHook(PlotFitHook()) - recipe.fithooks[0].verbose = 3 - - # Optimize - we do this in steps to help convergence - recipe.fix("all") - - # Start with the lattice parameters. In makeRecipe, these were tagged with - # "lat". Here is how we use that. - recipe.free("lat") - leastsq(recipe.residual, recipe.values, maxfev=50) - - # Now the scale and phase fraction. - recipe.free("scale", "scale_CdS") - leastsq(recipe.residual, recipe.values, maxfev=50) - - # The ADPs. - recipe.free("adp") - leastsq(recipe.residual, recipe.values, maxfev=100) - - # The delta2 parameters. - recipe.free("delta2_cds", "delta2_zns") - leastsq(recipe.residual, recipe.values, maxfev=50) - - # The shape parameters. - recipe.free("radius", "thickness") - leastsq(recipe.residual, recipe.values, maxfev=50) - - # The positional parameters. - recipe.free("xyz") - leastsq(recipe.residual, recipe.values) - - # Generate and print the FitResults - res = FitResults(recipe) - res.printResults() - - # Plot! - plotResults(recipe) - return - - -if __name__ == "__main__": - main() - -# End of file diff --git a/docs/examples/srfit_ex/crystalpdf.py b/docs/examples/srfit_ex/crystalpdf.py deleted file mode 100644 index 41dbca6..0000000 --- a/docs/examples/srfit_ex/crystalpdf.py +++ /dev/null @@ -1,176 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of a PDF refinement using diffpy.structure and PDFGenerator. - -This is example of fitting the fcc nickel structure to measured PDF -data. The purpose of this example is to demonstrate and describe the -classes in configuration options involved with setting up a fit in this -way. The main benefit of using SrFit for PDF refinement is the -flexibility of modifying the PDF profile function for specific needs, -adding restraints to a fit and the ability to simultaneously refine a -structure to PDF data and data from other sources. This example -demonstrates only the basic configuration. -""" - -import numpy -from gaussianrecipe import scipyOptimize - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) -from diffpy.srfit.pdf import PDFGenerator, PDFParser -from diffpy.structure import Structure - -###### -# Example Code - - -def makeRecipe(ciffile, datname): - """Create a fitting recipe for crystalline PDF data.""" - - # The Profile - # This will be used to store the observed and calculated PDF profile. - profile = Profile() - - # Load data and add it to the Profile. Unlike in other examples, we use a - # class (PDFParser) to help us load the data. This class will read the data - # and relevant metadata from a two- to four-column data file generated - # with PDFGetX2 or PDFGetN. The metadata will be passed to the PDFGenerator - # when they are associated in the FitContribution, which saves some - # configuration steps. - parser = PDFParser() - parser.parseFile(datname) - profile.loadParsedData(parser) - profile.setCalculationRange(xmax=20) - - # The ProfileGenerator - # The PDFGenerator is for configuring and calculating a PDF profile. Here, - # we want to refine a Structure object from diffpy.structure. We tell the - # PDFGenerator that with the 'setStructure' method. All other configuration - # options will be inferred from the metadata that is read by the PDFParser. - # In particular, this will set the scattering type (x-ray or neutron), the - # Qmax value, as well as initial values for the non-structural Parameters. - generator = PDFGenerator("G") - stru = Structure() - stru.read(ciffile) - generator.setStructure(stru) - - # The FitContribution - # Here we associate the Profile and ProfileGenerator, as has been done - # before. - contribution = FitContribution("nickel") - contribution.addProfileGenerator(generator) - contribution.setProfile(profile, xname="r") - - # Make the FitRecipe and add the FitContribution. - recipe = FitRecipe() - recipe.addContribution(contribution) - - # Configure the fit variables - - # The PDFGenerator class holds the ParameterSet associated with the - # Structure passed above in a data member named "phase". (We could have - # given the ParameterSet a name other than "phase" when we added it to the - # PDFGenerator.) The ParameterSet in this case is a StructureParameterSet, - # the documentation for which is found in the - # diffpy.srfit.structure.diffpystructure module. - phase = generator.phase - - # We start by constraining the phase to the known space group. We could do - # this by hand, but there is a method in diffpy.srfit.structure named - # 'constrainAsSpaceGroup' for this purpose. The constraints will by default - # be applied to the sites, the lattice and to the ADPs. See the method - # documentation for more details. The 'constrainAsSpaceGroup' method may - # create new Parameters, which it returns in a SpaceGroupParameters object. - from diffpy.srfit.structure import constrainAsSpaceGroup - - sgpars = constrainAsSpaceGroup(phase, "Fm-3m") - - # The SpaceGroupParameters object returned by 'constrainAsSpaceGroup' holds - # the free Parameters allowed by the space group constraints. Once a - # structure is constrained, we need (should) only use the Parameters - # provided in the SpaceGroupParameters, as the relevant structure - # Parameters are constrained to these. - # - # We know that the space group does not allow for any free sites because - # each atom is on a special position. There is one free (cubic) lattice - # parameter and one free (isotropic) ADP. We can access these Parameters in - # the xyzpars, latpars, and adppars members of the SpaceGroupParameters - # object. - for par in sgpars.latpars: - recipe.addVar(par) - for par in sgpars.adppars: - recipe.addVar(par, 0.005) - - # We now select non-structural parameters to refine. - # This controls the scaling of the PDF. - recipe.addVar(generator.scale, 1) - # This is a peak-damping resolution term. - recipe.addVar(generator.qdamp, 0.01) - # This is a vibrational correlation term that sharpens peaks at low-r. - recipe.addVar(generator.delta2, 5) - - # Give the recipe away so it can be used! - return recipe - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # All this should be pretty familiar by now. - r = recipe.nickel.profile.x - g = recipe.nickel.profile.y - gcalc = recipe.nickel.profile.ycalc - diffzero = -0.8 * max(g) * numpy.ones_like(g) - diff = g - gcalc + diffzero - - import pylab - - pylab.plot(r, g, "bo", label="G(r) Data") - pylab.plot(r, gcalc, "r-", label="G(r) Fit") - pylab.plot(r, diff, "g-", label="G(r) diff") - pylab.plot(r, diffzero, "k-") - pylab.xlabel(r"$r (\AA)$") - pylab.ylabel(r"$G (\AA^{-2})$") - pylab.legend(loc=1) - - pylab.show() - return - - -if __name__ == "__main__": - - # Make the data and the recipe - ciffile = "data/ni.cif" - data = "data/ni-q27r100-neutron.gr" - - # Make the recipe - recipe = makeRecipe(ciffile, data) - recipe.fithooks[0].verbose = 3 - - # Optimize - scipyOptimize(recipe) - - # Generate and print the FitResults - res = FitResults(recipe) - res.printResults() - - # Plot! - plotResults(recipe) - -# End of file diff --git a/docs/examples/srfit_ex/crystalpdfall.py b/docs/examples/srfit_ex/crystalpdfall.py deleted file mode 100644 index 056f8a8..0000000 --- a/docs/examples/srfit_ex/crystalpdfall.py +++ /dev/null @@ -1,240 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of a PDF refinement of two-phase structure. - -This example uses PDFGenerator to refine a the two phase nickel-silicon -structure to all the available data. -""" - -import numpy -from gaussianrecipe import scipyOptimize -from pyobjcryst import loadCrystal - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) -from diffpy.srfit.pdf import PDFGenerator, PDFParser - -###### -# Example Code - - -def makeProfile(datafile): - """Make an place data within a Profile.""" - profile = Profile() - parser = PDFParser() - parser.parseFile(datafile) - profile.loadParsedData(parser) - profile.setCalculationRange(xmax=20) - return profile - - -def makeContribution(name, generator, profile): - """Make a FitContribution and add a generator and profile.""" - contribution = FitContribution(name) - contribution.addProfileGenerator(generator) - contribution.setProfile(profile, xname="r") - return contribution - - -def makeRecipe( - ciffile_ni, ciffile_si, xdata_ni, ndata_ni, xdata_si, xdata_sini -): - """Create a fitting recipe for crystalline PDF data.""" - - # The Profiles - # We need a profile for each data set. - xprofile_ni = makeProfile(xdata_ni) - xprofile_si = makeProfile(xdata_si) - nprofile_ni = makeProfile(ndata_ni) - xprofile_sini = makeProfile(xdata_sini) - - # The ProfileGenerators - # We create one for each phase and share the phases. - xgenerator_ni = PDFGenerator("xG_ni") - stru = loadCrystal(ciffile_ni) - xgenerator_ni.setStructure(stru) - phase_ni = xgenerator_ni.phase - - xgenerator_si = PDFGenerator("xG_si") - stru = loadCrystal(ciffile_si) - xgenerator_si.setStructure(stru) - phase_si = xgenerator_si.phase - - ngenerator_ni = PDFGenerator("nG_ni") - ngenerator_ni.setPhase(phase_ni) - - xgenerator_sini_ni = PDFGenerator("xG_sini_ni") - xgenerator_sini_ni.setPhase(phase_ni) - - xgenerator_sini_si = PDFGenerator("xG_sini_si") - xgenerator_sini_si.setPhase(phase_si) - - # The FitContributions - # We one of these for each data set. - xcontribution_ni = makeContribution("xnickel", xgenerator_ni, xprofile_ni) - xcontribution_si = makeContribution("xsilicon", xgenerator_si, xprofile_si) - ncontribution_ni = makeContribution("nnickel", ngenerator_ni, nprofile_ni) - xcontribution_sini = makeContribution( - "xsini", xgenerator_sini_ni, xprofile_sini - ) - xcontribution_sini.addProfileGenerator(xgenerator_sini_si) - xcontribution_sini.setEquation("scale * (xG_sini_ni + xG_sini_si)") - - # As explained in another example, we want to minimize using Rw^2. - xcontribution_ni.setResidualEquation("resv") - xcontribution_si.setResidualEquation("resv") - ncontribution_ni.setResidualEquation("resv") - xcontribution_sini.setResidualEquation("resv") - - # Make the FitRecipe and add the FitContributions. - recipe = FitRecipe() - recipe.addContribution(xcontribution_ni) - recipe.addContribution(xcontribution_si) - recipe.addContribution(ncontribution_ni) - recipe.addContribution(xcontribution_sini) - - # Now we vary and constrain Parameters as before. - for par in phase_ni.sgpars: - recipe.addVar(par, name=par.name + "_ni") - delta2_ni = recipe.newVar("delta2_ni", 2.5) - recipe.constrain(xgenerator_ni.delta2, delta2_ni) - recipe.constrain(ngenerator_ni.delta2, delta2_ni) - recipe.constrain(xgenerator_sini_ni.delta2, delta2_ni) - - for par in phase_si.sgpars: - recipe.addVar(par, name=par.name + "_si") - delta2_si = recipe.newVar("delta2_si", 2.5) - recipe.constrain(xgenerator_si.delta2, delta2_si) - recipe.constrain(xgenerator_sini_si.delta2, delta2_si) - - # Now the experimental parameters - recipe.addVar(xgenerator_ni.scale, name="xscale_ni") - recipe.addVar(xgenerator_si.scale, name="xscale_si") - recipe.addVar(ngenerator_ni.scale, name="nscale_ni") - recipe.addVar(xcontribution_sini.scale, 1.0, "xscale_sini") - recipe.newVar("pscale_sini_ni", 0.8) - recipe.constrain(xgenerator_sini_ni.scale, "pscale_sini_ni") - recipe.constrain(xgenerator_sini_si.scale, "1 - pscale_sini_ni") - - # The qdamp parameters are too correlated to vary so we fix them based on - # previous measurements. - xgenerator_ni.qdamp.value = 0.055 - xgenerator_si.qdamp.value = 0.051 - ngenerator_ni.qdamp.value = 0.030 - xgenerator_sini_ni.qdamp.value = 0.052 - xgenerator_sini_si.qdamp.value = 0.052 - - # Give the recipe away so it can be used! - return recipe - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # All this should be pretty familiar by now. - xnickel = recipe.xnickel - xr_ni = xnickel.profile.x - xg_ni = xnickel.profile.y - xgcalc_ni = xnickel.profile.ycalc - xdiffzero_ni = -0.8 * max(xg_ni) * numpy.ones_like(xg_ni) - xdiff_ni = xg_ni - xgcalc_ni + xdiffzero_ni - - xsilicon = recipe.xsilicon - xr_si = xsilicon.profile.x - xg_si = xsilicon.profile.y - xgcalc_si = xsilicon.profile.ycalc - xdiffzero_si = -0.8 * max(xg_si) * numpy.ones_like(xg_si) - xdiff_si = xg_si - xgcalc_si + xdiffzero_si - - nnickel = recipe.nnickel - nr_ni = nnickel.profile.x - ng_ni = nnickel.profile.y - ngcalc_ni = nnickel.profile.ycalc - ndiffzero_ni = -0.8 * max(ng_ni) * numpy.ones_like(ng_ni) - ndiff_ni = ng_ni - ngcalc_ni + ndiffzero_ni - - xsini = recipe.xsini - xr_sini = xsini.profile.x - xg_sini = xsini.profile.y - xgcalc_sini = xsini.profile.ycalc - xdiffzero_sini = -0.8 * max(xg_sini) * numpy.ones_like(xg_sini) - xdiff_sini = xg_sini - xgcalc_sini + xdiffzero_sini - - import pylab - - pylab.subplot(2, 2, 1) - pylab.plot(xr_ni, xg_ni, "bo", label="G(r) x-ray nickel Data") - pylab.plot(xr_ni, xgcalc_ni, "r-", label="G(r) x-ray nickel Fit") - pylab.plot(xr_ni, xdiff_ni, "g-", label="G(r) x-ray nickel diff") - pylab.plot(xr_ni, xdiffzero_ni, "k-") - pylab.xlabel(r"$r (\AA)$") - pylab.ylabel(r"$G (\AA^{-2})$") - pylab.legend(loc=1) - - pylab.subplot(2, 2, 2) - pylab.plot(xr_si, xg_si, "bo", label="G(r) x-ray silicon Data") - pylab.plot(xr_si, xgcalc_si, "r-", label="G(r) x-ray silicon Fit") - pylab.plot(xr_si, xdiff_si, "g-", label="G(r) x-ray silicon diff") - pylab.plot(xr_si, xdiffzero_si, "k-") - pylab.legend(loc=1) - - pylab.subplot(2, 2, 3) - pylab.plot(nr_ni, ng_ni, "bo", label="G(r) neutron nickel Data") - pylab.plot(nr_ni, ngcalc_ni, "r-", label="G(r) neutron nickel Fit") - pylab.plot(nr_ni, ndiff_ni, "g-", label="G(r) neutron nickel diff") - pylab.plot(nr_ni, ndiffzero_ni, "k-") - pylab.legend(loc=1) - - pylab.subplot(2, 2, 4) - pylab.plot(xr_sini, xg_sini, "bo", label="G(r) x-ray sini Data") - pylab.plot(xr_sini, xgcalc_sini, "r-", label="G(r) x-ray sini Fit") - pylab.plot(xr_sini, xdiff_sini, "g-", label="G(r) x-ray sini diff") - pylab.plot(xr_sini, xdiffzero_sini, "k-") - pylab.legend(loc=1) - - pylab.show() - return - - -if __name__ == "__main__": - - # Make the data and the recipe - ciffile_ni = "data/ni.cif" - ciffile_si = "data/si.cif" - xdata_ni = "data/ni-q27r60-xray.gr" - ndata_ni = "data/ni-q27r100-neutron.gr" - xdata_si = "data/si-q27r60-xray.gr" - xdata_sini = "data/si90ni10-q27r60-xray.gr" - - # Make the recipe - recipe = makeRecipe( - ciffile_ni, ciffile_si, xdata_ni, ndata_ni, xdata_si, xdata_sini - ) - - # Optimize - scipyOptimize(recipe) - - # Generate and print the FitResults - res = FitResults(recipe) - res.printResults() - - # Plot! - plotResults(recipe) - -# End of file diff --git a/docs/examples/srfit_ex/crystalpdfobjcryst.py b/docs/examples/srfit_ex/crystalpdfobjcryst.py deleted file mode 100644 index 4919543..0000000 --- a/docs/examples/srfit_ex/crystalpdfobjcryst.py +++ /dev/null @@ -1,129 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of a PDF refinement using pyobjcryst and PDFGenerator. - -This example is similar to crystalpdf.py, except that here we refine a -pyobjcryst crystal object. In this example we use internal constraints -provided by the ObjCrystCrystalParSet structure adapter. -""" - -from crystalpdf import plotResults -from gaussianrecipe import scipyOptimize -from pyobjcryst import loadCrystal - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) -from diffpy.srfit.pdf import PDFGenerator, PDFParser - -###### -# Example Code - - -def makeRecipe(ciffile, datname): - """Create a fitting recipe for crystalline PDF data.""" - - # The Profile - # This will be used to store the observed and calculated PDF profile. - profile = Profile() - - # Load data and add it to the Profile. As before we use a PDFParser. The - # metadata is still passed to the PDFGenerator later on. The interaction - # between the PDFGenerator and the metadata does not depend on type of - # structure being refined. - parser = PDFParser() - parser.parseFile(datname) - profile.loadParsedData(parser) - profile.setCalculationRange(xmax=20) - - # The ProfileGenerator - # This time we use the CreateCrystalFromCIF method of pyobjcryst.crystal to - # create a Crystal object. That object is passed to the PDFGenerator as in - # the previous example. - generator = PDFGenerator("G") - stru = loadCrystal(ciffile) - generator.setStructure(stru) - generator.setQmax(40.0) - - # The FitContribution - contribution = FitContribution("nickel") - contribution.addProfileGenerator(generator) - contribution.setProfile(profile, xname="r") - - # Make the FitRecipe and add the FitContribution. - recipe = FitRecipe() - recipe.addContribution(contribution) - - # Configure the fit variables - - # As before, we get a handle to the structure parameter set. In this case, - # it is a ObjCrystCrystalParSet instance that was created when we called - # 'setStructure' above. The ObjCrystCrystalParSet has different Parameters - # and options than the DiffpyStructureParSet used in the last example. See - # its documentation in diffpy.srfit.structure.objcrystparset. - phase = generator.phase - - # Here is where we created space group constraints in the previous example. - # The difference in this example is that the ObjCrystCrystalParSet is aware - # of space groups, and the DiffpyStructureParSet is not. Constraints are - # created internally when "sgpars" attribute is called for. These - # constraints get enforced within the ObjCrystCrystalParSet. Free - # Parameters are stored within the 'sgpars' member of the - # ObjCrystCrystalParSet, which is the same as the object returned from - # 'constrainAsSpaceGroup'. - # - # As before, we have one free lattice parameter ('a'). We can simplify - # things by iterating through all the sgpars. - for par in phase.sgpars: - recipe.addVar(par) - # set the initial thermal factor to a non-zero value - assert hasattr(recipe, "B11_0") - recipe.B11_0 = 0.1 - - # We now select non-structural parameters to refine. - # This controls the scaling of the PDF. - recipe.addVar(generator.scale, 1) - # This is a peak-damping resolution term. - recipe.addVar(generator.qdamp, 0.01) - # This is a vibrational correlation term that sharpens peaks at low-r. - recipe.addVar(generator.delta2, 5) - - # Give the recipe away so it can be used! - return recipe - - -if __name__ == "__main__": - - # Make the data and the recipe - ciffile = "data/si.cif" - data = "data/si-q27r60-xray.gr" - - # Make the recipe - recipe = makeRecipe(ciffile, data) - - # Optimize - scipyOptimize(recipe) - - # Generate and print the FitResults - res = FitResults(recipe) - res.printResults() - - # Plot! - plotResults(recipe) - -# End of file diff --git a/docs/examples/srfit_ex/crystalpdftwodata.py b/docs/examples/srfit_ex/crystalpdftwodata.py deleted file mode 100644 index debefc0..0000000 --- a/docs/examples/srfit_ex/crystalpdftwodata.py +++ /dev/null @@ -1,196 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of a PDF refinement of two-phase structure. - -This example uses PDFGenerator to refine a single structure two -profiles. This will require setting up two FitContribution, each with -its own PDFGenerator. However, the PDFGenerators will refer to the same -underlying ObjCrystCrystalParSet. -""" - -import numpy -from gaussianrecipe import scipyOptimize -from pyobjcryst import loadCrystal - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) -from diffpy.srfit.pdf import PDFGenerator, PDFParser - -###### -# Example Code - - -def makeRecipe(ciffile, xdatname, ndatname): - """Create a fitting recipe for crystalline PDF data.""" - - # The Profiles - # We need a profile for each data set. This means that we will need two - # FitContributions as well. - xprofile = Profile() - nprofile = Profile() - - # Load data and add it to the proper Profile. - parser = PDFParser() - parser.parseFile(xdatname) - xprofile.loadParsedData(parser) - xprofile.setCalculationRange(xmax=20) - - parser = PDFParser() - parser.parseFile(ndatname) - nprofile.loadParsedData(parser) - nprofile.setCalculationRange(xmax=20) - - # The ProfileGenerators - # We need one of these for the x-ray data. - xgenerator = PDFGenerator("G") - stru = loadCrystal(ciffile) - xgenerator.setStructure(stru) - - # And we need one for the neutron data. We want to refine the same - # structure object in each PDFGenerator. This would suggest that we add the - # same Crystal to each. However, if we do that then we will have two - # Parameters for each Crystal data member (two Parameters for the "a" - # lattice parameter, etc.), held in different ObjCrystCrystalParSets, each - # managed by its own PDFGenerator. Thus, changes made to the Crystal - # through one PDFGenerator will not be known to the other PDFGenerator - # since their ObjCrystCrystalParSets don't know about each other. The - # solution is to share ObjCrystCrystalParSets rather than Crystals. This - # way there is only one Parameter for each Crystal data member. (An - # alternative to this is to constrain each structure Parameter to be varied - # to the same variable. The present approach is easier and less error - # prone.) - # - # Tell the neutron PDFGenerator to use the phase from the x-ray - # PDFGenerator. - ngenerator = PDFGenerator("G") - ngenerator.setPhase(xgenerator.phase) - - # The FitContributions - # We associate the x-ray PDFGenerator and Profile in one FitContribution... - xcontribution = FitContribution("xnickel") - xcontribution.addProfileGenerator(xgenerator) - xcontribution.setProfile(xprofile, xname="r") - # and the neutron objects in another. - ncontribution = FitContribution("nnickel") - ncontribution.addProfileGenerator(ngenerator) - ncontribution.setProfile(nprofile, xname="r") - - # This example is different than the previous ones in that we are composing - # a residual function from other residuals (one for the x-ray contribution - # and one for the neutron contribution). The relative magnitude of these - # residuals effectively determines the influence of each contribution over - # the fit. This is a problem in this case because the x-ray data has - # uncertainty values associated with it (on the order of 1e-4), and the - # chi^2 residual is proportional to 1 / uncertainty**2. The neutron has no - # uncertainty, so it's chi^2 is proportional to 1. Thus, my optimizing - # chi^2 we would give the neutron data practically no weight in the fit. To - # get around this, we will optimize a different metric. - # - # The contribution's residual can be either chi^2, Rw^2, or custom crafted. - # In this case, we should minimize Rw^2 of each contribution so that each - # one can contribute roughly equally to the fit. - xcontribution.setResidualEquation("resv") - ncontribution.setResidualEquation("resv") - - # Make the FitRecipe and add the FitContributions. - recipe = FitRecipe() - recipe.addContribution(xcontribution) - recipe.addContribution(ncontribution) - - # Now we vary and constrain Parameters as before. - recipe.addVar(xgenerator.scale, 1, "xscale") - recipe.addVar(ngenerator.scale, 1, "nscale") - recipe.addVar(xgenerator.qdamp, 0.01, "xqdamp") - recipe.addVar(ngenerator.qdamp, 0.01, "nqdamp") - # delta2 is a non-structual material property. Thus, we constrain together - # delta2 Parameter from each PDFGenerator. - delta2 = recipe.newVar("delta2", 2) - recipe.constrain(xgenerator.delta2, delta2) - recipe.constrain(ngenerator.delta2, delta2) - - # We only need to constrain phase properties once since there is a single - # ObjCrystCrystalParSet for the Crystal. - phase = xgenerator.phase - for par in phase.sgpars: - recipe.addVar(par) - recipe.B11_0 = 0.1 - - # Give the recipe away so it can be used! - return recipe - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # All this should be pretty familiar by now. - xr = recipe.xnickel.profile.x - xg = recipe.xnickel.profile.y - xgcalc = recipe.xnickel.profile.ycalc - xdiffzero = -0.8 * max(xg) * numpy.ones_like(xg) - xdiff = xg - xgcalc + xdiffzero - - nr = recipe.nnickel.profile.x - ng = recipe.nnickel.profile.y - ngcalc = recipe.nnickel.profile.ycalc - ndiffzero = -0.8 * max(ng) * numpy.ones_like(ng) - ndiff = ng - ngcalc + ndiffzero - - import pylab - - pylab.subplot(2, 1, 1) - pylab.plot(xr, xg, "bo", label="G(r) x-ray Data") - pylab.plot(xr, xgcalc, "r-", label="G(r) x-ray Fit") - pylab.plot(xr, xdiff, "g-", label="G(r) x-ray diff") - pylab.plot(xr, xdiffzero, "k-") - pylab.legend(loc=1) - - pylab.subplot(2, 1, 2) - pylab.plot(nr, ng, "bo", label="G(r) neutron Data") - pylab.plot(nr, ngcalc, "r-", label="G(r) neutron Fit") - pylab.plot(nr, ndiff, "g-", label="G(r) neutron diff") - pylab.plot(nr, ndiffzero, "k-") - pylab.xlabel(r"$r (\AA)$") - pylab.ylabel(r"$G (\AA^{-2})$") - pylab.legend(loc=1) - - pylab.show() - return - - -if __name__ == "__main__": - - # Make the data and the recipe - ciffile = "data/ni.cif" - xdata = "data/ni-q27r60nodg-xray.gr" - ndata = "data/ni-q27r100-neutron.gr" - - # Make the recipe - recipe = makeRecipe(ciffile, xdata, ndata) - - # Optimize - scipyOptimize(recipe) - - # Generate and print the FitResults - res = FitResults(recipe) - res.printResults() - - # Plot! - plotResults(recipe) - -# End of file diff --git a/docs/examples/srfit_ex/crystalpdftwophase.py b/docs/examples/srfit_ex/crystalpdftwophase.py deleted file mode 100644 index 98a8790..0000000 --- a/docs/examples/srfit_ex/crystalpdftwophase.py +++ /dev/null @@ -1,187 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of a PDF refinement of two-phase structure. - -Like the ones before, this example uses PDFGenerator to refine a -structure to PDF data. However, for a multi-phase structure one must use -multiple PDFGenerators. This example refines a physical mixture of -nickel and silicon to find the structures and phase fractions. -""" - -import numpy -from gaussianrecipe import scipyOptimize -from pyobjcryst import loadCrystal - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) -from diffpy.srfit.pdf import PDFGenerator, PDFParser - -###### -# Example Code - - -def makeRecipe(niciffile, siciffile, datname): - """Create a fitting recipe for crystalline PDF data.""" - - # The Profile - profile = Profile() - - # Load data and add it to the profile - parser = PDFParser() - parser.parseFile(datname) - profile.loadParsedData(parser) - profile.setCalculationRange(xmax=20) - - # The ProfileGenerator - # In order to fit two phases simultaneously, we must use two PDFGenerators. - # PDFGenerator is designed to take care of as little information as it - # must. (Don't do too much, and do it well.) A PDFGenerator can generate - # the signal from only a single phase at a time. So, we will create one - # PDFGenerator for each phase and compose them within the same - # FitContribution. Note that both generators will be associated with the - # same Profile within the FitContribution, so they will both be - # automatically configured according to the metadata. - # - # The generator for the nickel phase. We call it "G_ni" and will use this - # name later when we set the fitting equation in the FitContribution. - generator_ni = PDFGenerator("G_ni") - stru = loadCrystal(niciffile) - generator_ni.setStructure(stru) - # The generator for the silicon phase. We call it "G_si". - generator_si = PDFGenerator("G_si") - stru = loadCrystal(siciffile) - generator_si.setStructure(stru) - - # The FitContribution - # Add both generators to the FitContribution. Add the Profile. This will - # send the metadata to the generators. - contribution = FitContribution("nisi") - contribution.addProfileGenerator(generator_ni) - contribution.addProfileGenerator(generator_si) - contribution.setProfile(profile, xname="r") - - # Write the fitting equation. We want to sum the PDFs from each phase and - # multiply it by a scaling factor. We also want a certain phase scaling - # relationship between the PDFs which we will enforce with constraints in - # the FitRecipe. - contribution.setEquation("scale * (G_ni + G_si)") - - # Make the FitRecipe and add the FitContribution. - recipe = FitRecipe() - recipe.addContribution(contribution) - - # Configure the fit variables - # Start by configuring the scale factor and resolution factors. - # We want the sum of the phase scale factors to be 1. - recipe.newVar("scale_ni", 0.1) - recipe.constrain(generator_ni.scale, "scale_ni") - recipe.constrain(generator_si.scale, "1 - scale_ni") - # We also want the resolution factor to be the same on each. - recipe.newVar("qdamp", 0.03) - recipe.constrain(generator_ni.qdamp, "qdamp") - recipe.constrain(generator_si.qdamp, "qdamp") - - # Vary the global scale as well. - recipe.addVar(contribution.scale, 1) - - # Now we can configure the structural parameters. Since we're using - # ObjCrystCrystalParSets, the space group constraints are automatically - # applied to each phase. We must selectively vary the free parameters. - # - # First the nickel parameters - phase_ni = generator_ni.phase - for par in phase_ni.sgpars: - recipe.addVar(par, name=par.name + "_ni") - recipe.addVar(generator_ni.delta2, name="delta2_ni") - # Next the silicon parameters - phase_si = generator_si.phase - for par in phase_si.sgpars: - recipe.addVar(par, name=par.name + "_si") - recipe.addVar(generator_si.delta2, name="delta2_si") - - # We have prior information from the earlier examples so we'll use it here - # in the form of restraints. - # - # The nickel lattice parameter was measured to be 3.527. The uncertainty - # values are invalid for that measurement, since the data from which it is - # derived has no uncertainty. Thus, we will tell the recipe to scale the - # residual, which means that it will be weighted as much as the average - # data point during the fit. - recipe.restrain("a_ni", lb=3.527, ub=3.527, scaled=True) - # Now we do the same with the delta2 and Biso parameters (remember that - # Biso = 8*pi**2*Uiso) - recipe.restrain("delta2_ni", lb=2.22, ub=2.22, scaled=True) - recipe.restrain("Biso_0_ni", lb=0.454, ub=0.454, scaled=True) - # - # We can do the same with the silicon values. We haven't done a thorough - # job of measuring the uncertainties in the results, so we'll scale these - # as well. - recipe.restrain("a_si", lb=5.430, ub=5.430, scaled=True) - recipe.restrain("delta2_si", lb=3.54, ub=3.54, scaled=True) - recipe.restrain("Biso_0_si", lb=0.645, ub=0.645, scaled=True) - - # Give the recipe away so it can be used! - return recipe - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # All this should be pretty familiar by now. - r = recipe.nisi.profile.x - g = recipe.nisi.profile.y - gcalc = recipe.nisi.profile.ycalc - diffzero = -0.8 * max(g) * numpy.ones_like(g) - diff = g - gcalc + diffzero - - import pylab - - pylab.plot(r, g, "bo", label="G(r) Data") - pylab.plot(r, gcalc, "r-", label="G(r) Fit") - pylab.plot(r, diff, "g-", label="G(r) diff") - pylab.plot(r, diffzero, "k-") - pylab.xlabel(r"$r (\AA)$") - pylab.ylabel(r"$G (\AA^{-2})$") - pylab.legend(loc=1) - - pylab.show() - return - - -if __name__ == "__main__": - - # Make the data and the recipe - niciffile = "data/ni.cif" - siciffile = "data/si.cif" - data = "data/si90ni10-q27r60-xray.gr" - - # Make the recipe - recipe = makeRecipe(niciffile, siciffile, data) - - # Optimize - scipyOptimize(recipe) - - # Generate and print the FitResults - res = FitResults(recipe) - res.printResults() - - # Plot! - plotResults(recipe) - -# End of file diff --git a/docs/examples/srfit_ex/data/C60.gr b/docs/examples/srfit_ex/data/C60.gr deleted file mode 100644 index d015b9d..0000000 --- a/docs/examples/srfit_ex/data/C60.gr +++ /dev/null @@ -1,1999 +0,0 @@ - 1.000000e-002 1.894260e+004 8.536912e+000 - 2.000000e-002 3.772272e+004 1.675464e+001 - 3.000000e-002 5.617755e+004 2.434705e+001 - 4.000000e-002 7.414385e+004 3.103361e+001 - 5.000000e-002 9.145791e+004 3.657098e+001 - 6.000000e-002 1.079561e+005 4.076327e+001 - 7.000000e-002 1.234755e+005 4.347065e+001 - 8.000000e-002 1.378555e+005 4.461615e+001 - 9.000000e-002 1.509396e+005 4.419097e+001 - 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0.00000000 0.00000000 -C 0.48775063 0.50000000 0.46648489 1.0000 - 0.00000000 0.00000000 0.00000000 0.0000 - 0.00000000 0.00000000 0.00000000 - 0.00000000 0.00000000 0.00000000 - 0.00000000 0.00000000 0.00000000 - 0.00000000 0.00000000 0.00000000 diff --git a/docs/examples/srfit_ex/data/CdS.cif b/docs/examples/srfit_ex/data/CdS.cif deleted file mode 100644 index 34fa965..0000000 --- a/docs/examples/srfit_ex/data/CdS.cif +++ /dev/null @@ -1,69 +0,0 @@ -data_1011054 -_chemical_name_systematic 'Cadmium sulfide - $-alpha' -_chemical_name_mineral 'Greenockite' -_chemical_compound_source 'synthetic' -_chemical_formula_structural 'Cd S' -_chemical_formula_sum 'Cd S' -_publ_section_title -; -Ueber die Kristallstruktur des $-alpha- und $-beta Cd S, sowie des -Wurtzits. -; -loop_ -_publ_author_name - 'Ulrich, F' - 'Zachariasen, W' -_journal_name_full -; -Zeitschrift fuer Kristallographie, Kristallgeometrie, Kristallphysik, -Kristallchemie (-144,1977) -; -_journal_coden_ASTM ZEKGAX -_journal_volume 62 -_journal_year 1925 -_journal_page_first 260 -_journal_page_last 273 -_cell_length_a 4.15 -_cell_length_b 4.15 -_cell_length_c 6.737 -_cell_angle_alpha 90 -_cell_angle_beta 90 -_cell_angle_gamma 120 -_cell_volume 100.5 -_cell_formula_units_Z 2 -_exptl_crystal_density_meas 4.82 -_symmetry_space_group_name_H-M 'P 63 m c' -_symmetry_Int_Tables_number 186 -_symmetry_cell_setting hexagonal -loop_ -_symmetry_equiv_pos_as_xyz - 'x,y,z' - '-y,x-y,z' - 'y-x,-x,z' - '-y,-x,z' - 'y-x,y,z' - 'x,x-y,z' - '-x,-y,1/2+z' - 'y,y-x,1/2+z' - 'x-y,x,1/2+z' - 'y,x,1/2+z' - 'x-y,-y,1/2+z' - '-x,y-x,1/2+z' -loop_ -_atom_type_symbol -_atom_type_oxidation_number - Cd2+ 2.000 - S2- -2.000 -loop_ -_atom_site_label -_atom_site_type_symbol -_atom_site_symmetry_multiplicity -_atom_site_Wyckoff_symbol -_atom_site_fract_x -_atom_site_fract_y -_atom_site_fract_z -_atom_site_occupancy -_atom_site_attached_hydrogens -_atom_site_calc_flag - Cd1 Cd 2 b 0.33333 0.66667 0. 1. 0 d - S1 S 2 b 0.33333 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The original data for this entry -# were provided the American Mineralogist Crystal Structure Database, -# http://rruff.geo.arizona.edu/AMS/amcsd.php -# -# The file may be used within the scientific community so long as -# proper attribution is given to the journal article from which the -# data were obtained. -# -data_9008878 -loop_ -_publ_author_name -'Wyckoff, R. W. G.' -_publ_section_title -; - Second edition. Interscience Publishers, New York, New York - Note: wurtzite structure -; -_journal_name_full 'Crystal Structures' -_journal_page_first 85 -_journal_page_last 237 -_journal_volume 1 -_journal_year 1963 -_chemical_formula_sum 'S Zn' -_chemical_name_mineral Wurtzite-2H -_space_group_IT_number 186 -_symmetry_space_group_name_Hall 'P 6c -2c' -_symmetry_space_group_name_H-M 'P 63 m c' -_cell_angle_alpha 90 -_cell_angle_beta 90 -_cell_angle_gamma 120 -_cell_length_a 3.811 -_cell_length_b 3.811 -_cell_length_c 6.234 -_cell_volume 78.411 -_exptl_crystal_density_diffrn 4.128 -_cod_original_formula_sum 'Zn S' -_cod_database_code 9008878 -loop_ -_symmetry_equiv_pos_as_xyz -x,y,z --x,-x+y,1/2+z -x-y,x,1/2+z --y,-x,z --y,x-y,z -x-y,-y,1/2+z --x,-y,1/2+z -x,x-y,z --x+y,-x,z -y,x,1/2+z -y,-x+y,1/2+z --x+y,y,z -loop_ -_atom_site_label -_atom_site_fract_x -_atom_site_fract_y -_atom_site_fract_z -Zn 0.33333 0.66667 0.00000 -S 0.33333 0.66667 0.38500 diff --git a/docs/examples/srfit_ex/data/gaussian.dat 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93.940 6.132 - 93.950 5.940 - 93.960 5.739 - 93.970 5.533 - 93.980 5.325 - 93.990 5.115 - 94.000 4.906 - 94.010 4.700 - 94.020 4.497 - 94.030 4.297 - 94.040 4.101 - 94.050 3.907 - 94.060 3.715 - 94.070 3.523 - 94.080 3.330 - 94.090 3.135 - 94.100 2.935 - 94.110 2.729 - 94.120 2.516 - 94.130 2.295 - 94.140 2.065 - 94.150 1.827 - 94.160 1.581 - 94.170 1.329 - 94.180 1.071 - 94.190 0.809 - 94.200 0.546 - 94.210 0.284 - 94.220 0.025 - 94.230 -0.227 - 94.240 -0.472 - 94.250 -0.707 - 94.260 -0.931 - 94.270 -1.142 - 94.280 -1.341 - 94.290 -1.527 - 94.300 -1.701 - 94.310 -1.864 - 94.320 -2.017 - 94.330 -2.162 - 94.340 -2.301 - 94.350 -2.436 - 94.360 -2.568 - 94.370 -2.699 - 94.380 -2.829 - 94.390 -2.960 - 94.400 -3.091 - 94.410 -3.222 - 94.420 -3.350 - 94.430 -3.475 - 94.440 -3.594 - 94.450 -3.703 - 94.460 -3.800 - 94.470 -3.882 - 94.480 -3.944 - 94.490 -3.984 - 94.500 -4.000 - 94.510 -3.989 - 94.520 -3.948 - 94.530 -3.879 - 94.540 -3.780 - 94.550 -3.652 - 94.560 -3.497 - 94.570 -3.317 - 94.580 -3.115 - 94.590 -2.895 - 94.600 -2.660 - 94.610 -2.414 - 94.620 -2.161 - 94.630 -1.906 - 94.640 -1.651 - 94.650 -1.401 - 94.660 -1.158 - 94.670 -0.923 - 94.680 -0.699 - 94.690 -0.486 - 94.700 -0.285 - 94.710 -0.096 - 94.720 0.083 - 94.730 0.252 - 94.740 0.411 - 94.750 0.562 - 94.760 0.705 - 94.770 0.841 - 94.780 0.971 - 94.790 1.094 - 94.800 1.209 - 94.810 1.316 - 94.820 1.413 - 94.830 1.498 - 94.840 1.570 - 94.850 1.626 - 94.860 1.665 - 94.870 1.684 - 94.880 1.682 - 94.890 1.658 - 94.900 1.612 - 94.910 1.543 - 94.920 1.452 - 94.930 1.340 - 94.940 1.209 - 94.950 1.062 - 94.960 0.900 - 94.970 0.728 - 94.980 0.548 - 94.990 0.363 - 95.000 0.177 - 95.010 -0.007 - 95.020 -0.188 - 95.030 -0.363 - 95.040 -0.531 - 95.050 -0.692 - 95.060 -0.844 - 95.070 -0.988 - 95.080 -1.125 - 95.090 -1.255 - 95.100 -1.382 - 95.110 -1.504 - 95.120 -1.625 - 95.130 -1.745 - 95.140 -1.864 - 95.150 -1.985 - 95.160 -2.106 - 95.170 -2.227 - 95.180 -2.347 - 95.190 -2.465 - 95.200 -2.579 - 95.210 -2.688 - 95.220 -2.788 - 95.230 -2.879 - 95.240 -2.957 - 95.250 -3.021 - 95.260 -3.070 - 95.270 -3.102 - 95.280 -3.118 - 95.290 -3.117 - 95.300 -3.100 - 95.310 -3.070 - 95.320 -3.027 - 95.330 -2.974 - 95.340 -2.915 - 95.350 -2.850 - 95.360 -2.785 - 95.370 -2.720 - 95.380 -2.658 - 95.390 -2.602 - 95.400 -2.552 - 95.410 -2.509 - 95.420 -2.473 - 95.430 -2.443 - 95.440 -2.417 - 95.450 -2.395 - 95.460 -2.372 - 95.470 -2.347 - 95.480 -2.316 - 95.490 -2.277 - 95.500 -2.225 - 95.510 -2.160 - 95.520 -2.079 - 95.530 -1.980 - 95.540 -1.862 - 95.550 -1.725 - 95.560 -1.570 - 95.570 -1.398 - 95.580 -1.211 - 95.590 -1.011 - 95.600 -0.800 - 95.610 -0.582 - 95.620 -0.359 - 95.630 -0.136 - 95.640 0.087 - 95.650 0.305 - 95.660 0.518 - 95.670 0.723 - 95.680 0.920 - 95.690 1.108 - 95.700 1.288 - 95.710 1.460 - 95.720 1.624 - 95.730 1.783 - 95.740 1.937 - 95.750 2.087 - 95.760 2.236 - 95.770 2.384 - 95.780 2.532 - 95.790 2.680 - 95.800 2.828 - 95.810 2.975 - 95.820 3.121 - 95.830 3.264 - 95.840 3.402 - 95.850 3.532 - 95.860 3.654 - 95.870 3.765 - 95.880 3.862 - 95.890 3.943 - 95.900 4.008 - 95.910 4.054 - 95.920 4.081 - 95.930 4.089 - 95.940 4.078 - 95.950 4.048 - 95.960 4.001 - 95.970 3.939 - 95.980 3.863 - 95.990 3.776 - 96.000 3.679 - 96.010 3.576 - 96.020 3.468 - 96.030 3.357 - 96.040 3.245 - 96.050 3.134 - 96.060 3.025 - 96.070 2.918 - 96.080 2.814 - 96.090 2.713 - 96.100 2.614 - 96.110 2.518 - 96.120 2.424 - 96.130 2.331 - 96.140 2.238 - 96.150 2.146 - 96.160 2.053 - 96.170 1.959 - 96.180 1.865 - 96.190 1.770 - 96.200 1.675 - 96.210 1.581 - 96.220 1.487 - 96.230 1.396 - 96.240 1.309 - 96.250 1.225 - 96.260 1.147 - 96.270 1.075 - 96.280 1.010 - 96.290 0.953 - 96.300 0.902 - 96.310 0.860 - 96.320 0.824 - 96.330 0.794 - 96.340 0.770 - 96.350 0.750 - 96.360 0.733 - 96.370 0.717 - 96.380 0.700 - 96.390 0.680 - 96.400 0.657 - 96.410 0.629 - 96.420 0.593 - 96.430 0.549 - 96.440 0.496 - 96.450 0.433 - 96.460 0.360 - 96.470 0.277 - 96.480 0.183 - 96.490 0.080 - 96.500 -0.033 - 96.510 -0.154 - 96.520 -0.282 - 96.530 -0.417 - 96.540 -0.556 - 96.550 -0.699 - 96.560 -0.845 - 96.570 -0.991 - 96.580 -1.138 - 96.590 -1.284 - 96.600 -1.428 - 96.610 -1.570 - 96.620 -1.709 - 96.630 -1.844 - 96.640 -1.976 - 96.650 -2.103 - 96.660 -2.226 - 96.670 -2.344 - 96.680 -2.458 - 96.690 -2.567 - 96.700 -2.671 - 96.710 -2.769 - 96.720 -2.863 - 96.730 -2.950 - 96.740 -3.031 - 96.750 -3.105 - 96.760 -3.171 - 96.770 -3.229 - 96.780 -3.277 - 96.790 -3.314 - 96.800 -3.341 - 96.810 -3.355 - 96.820 -3.355 - 96.830 -3.342 - 96.840 -3.315 - 96.850 -3.273 - 96.860 -3.216 - 96.870 -3.144 - 96.880 -3.058 - 96.890 -2.958 - 96.900 -2.845 - 96.910 -2.719 - 96.920 -2.583 - 96.930 -2.438 - 96.940 -2.284 - 96.950 -2.124 - 96.960 -1.960 - 96.970 -1.792 - 96.980 -1.622 - 96.990 -1.452 - 97.000 -1.282 - 97.010 -1.113 - 97.020 -0.947 - 97.030 -0.784 - 97.040 -0.623 - 97.050 -0.465 - 97.060 -0.310 - 97.070 -0.158 - 97.080 -0.009 - 97.090 0.138 - 97.100 0.283 - 97.110 0.426 - 97.120 0.566 - 97.130 0.703 - 97.140 0.836 - 97.150 0.966 - 97.160 1.089 - 97.170 1.205 - 97.180 1.312 - 97.190 1.408 - 97.200 1.492 - 97.210 1.561 - 97.220 1.614 - 97.230 1.649 - 97.240 1.663 - 97.250 1.658 - 97.260 1.630 - 97.270 1.581 - 97.280 1.509 - 97.290 1.416 - 97.300 1.303 - 97.310 1.171 - 97.320 1.021 - 97.330 0.857 - 97.340 0.680 - 97.350 0.492 - 97.360 0.297 - 97.370 0.098 - 97.380 -0.104 - 97.390 -0.307 - 97.400 -0.507 - 97.410 -0.703 - 97.420 -0.894 - 97.430 -1.078 - 97.440 -1.254 - 97.450 -1.423 - 97.460 -1.583 - 97.470 -1.734 - 97.480 -1.876 - 97.490 -2.009 - 97.500 -2.132 - 97.510 -2.246 - 97.520 -2.350 - 97.530 -2.443 - 97.540 -2.524 - 97.550 -2.593 - 97.560 -2.647 - 97.570 -2.685 - 97.580 -2.706 - 97.590 -2.706 - 97.600 -2.686 - 97.610 -2.643 - 97.620 -2.575 - 97.630 -2.481 - 97.640 -2.361 - 97.650 -2.215 - 97.660 -2.041 - 97.670 -1.842 - 97.680 -1.617 - 97.690 -1.370 - 97.700 -1.103 - 97.710 -0.817 - 97.720 -0.517 - 97.730 -0.206 - 97.740 0.112 - 97.750 0.433 - 97.760 0.755 - 97.770 1.071 - 97.780 1.380 - 97.790 1.679 - 97.800 1.964 - 97.810 2.232 - 97.820 2.482 - 97.830 2.714 - 97.840 2.924 - 97.850 3.114 - 97.860 3.283 - 97.870 3.431 - 97.880 3.559 - 97.890 3.667 - 97.900 3.757 - 97.910 3.828 - 97.920 3.883 - 97.930 3.921 - 97.940 3.944 - 97.950 3.952 - 97.960 3.945 - 97.970 3.923 - 97.980 3.887 - 97.990 3.838 - 98.000 3.773 - 98.010 3.695 - 98.020 3.602 - 98.030 3.495 - 98.040 3.374 - 98.050 3.240 - 98.060 3.093 - 98.070 2.934 - 98.080 2.764 - 98.090 2.585 - 98.100 2.397 - 98.110 2.204 - 98.120 2.006 - 98.130 1.806 - 98.140 1.605 - 98.150 1.405 - 98.160 1.207 - 98.170 1.014 - 98.180 0.825 - 98.190 0.643 - 98.200 0.467 - 98.210 0.298 - 98.220 0.136 - 98.230 -0.020 - 98.240 -0.170 - 98.250 -0.314 - 98.260 -0.454 - 98.270 -0.590 - 98.280 -0.724 - 98.290 -0.855 - 98.300 -0.985 - 98.310 -1.114 - 98.320 -1.241 - 98.330 -1.368 - 98.340 -1.492 - 98.350 -1.613 - 98.360 -1.731 - 98.370 -1.843 - 98.380 -1.948 - 98.390 -2.044 - 98.400 -2.130 - 98.410 -2.205 - 98.420 -2.265 - 98.430 -2.311 - 98.440 -2.341 - 98.450 -2.354 - 98.460 -2.351 - 98.470 -2.331 - 98.480 -2.295 - 98.490 -2.243 - 98.500 -2.178 - 98.510 -2.100 - 98.520 -2.011 - 98.530 -1.914 - 98.540 -1.810 - 98.550 -1.700 - 98.560 -1.588 - 98.570 -1.473 - 98.580 -1.358 - 98.590 -1.243 - 98.600 -1.127 - 98.610 -1.012 - 98.620 -0.897 - 98.630 -0.780 - 98.640 -0.662 - 98.650 -0.539 - 98.660 -0.412 - 98.670 -0.279 - 98.680 -0.138 - 98.690 0.012 - 98.700 0.170 - 98.710 0.338 - 98.720 0.516 - 98.730 0.701 - 98.740 0.893 - 98.750 1.090 - 98.760 1.290 - 98.770 1.490 - 98.780 1.686 - 98.790 1.875 - 98.800 2.054 - 98.810 2.219 - 98.820 2.368 - 98.830 2.496 - 98.840 2.603 - 98.850 2.686 - 98.860 2.743 - 98.870 2.775 - 98.880 2.782 - 98.890 2.764 - 98.900 2.723 - 98.910 2.662 - 98.920 2.582 - 98.930 2.486 - 98.940 2.377 - 98.950 2.259 - 98.960 2.134 - 98.970 2.005 - 98.980 1.874 - 98.990 1.744 - 99.000 1.615 - 99.010 1.489 - 99.020 1.365 - 99.030 1.245 - 99.040 1.127 - 99.050 1.010 - 99.060 0.894 - 99.070 0.776 - 99.080 0.656 - 99.090 0.532 - 99.100 0.403 - 99.110 0.267 - 99.120 0.125 - 99.130 -0.023 - 99.140 -0.179 - 99.150 -0.340 - 99.160 -0.507 - 99.170 -0.677 - 99.180 -0.849 - 99.190 -1.022 - 99.200 -1.192 - 99.210 -1.360 - 99.220 -1.522 - 99.230 -1.677 - 99.240 -1.824 - 99.250 -1.961 - 99.260 -2.088 - 99.270 -2.204 - 99.280 -2.309 - 99.290 -2.404 - 99.300 -2.489 - 99.310 -2.564 - 99.320 -2.630 - 99.330 -2.689 - 99.340 -2.741 - 99.350 -2.786 - 99.360 -2.827 - 99.370 -2.862 - 99.380 -2.894 - 99.390 -2.921 - 99.400 -2.945 - 99.410 -2.965 - 99.420 -2.981 - 99.430 -2.992 - 99.440 -2.999 - 99.450 -3.001 - 99.460 -2.997 - 99.470 -2.989 - 99.480 -2.975 - 99.490 -2.956 - 99.500 -2.931 - 99.510 -2.902 - 99.520 -2.868 - 99.530 -2.830 - 99.540 -2.789 - 99.550 -2.744 - 99.560 -2.697 - 99.570 -2.646 - 99.580 -2.594 - 99.590 -2.539 - 99.600 -2.482 - 99.610 -2.422 - 99.620 -2.359 - 99.630 -2.292 - 99.640 -2.220 - 99.650 -2.144 - 99.660 -2.062 - 99.670 -1.974 - 99.680 -1.880 - 99.690 -1.780 - 99.700 -1.673 - 99.710 -1.561 - 99.720 -1.443 - 99.730 -1.320 - 99.740 -1.194 - 99.750 -1.066 - 99.760 -0.936 - 99.770 -0.806 - 99.780 -0.677 - 99.790 -0.549 - 99.800 -0.425 - 99.810 -0.304 - 99.820 -0.185 - 99.830 -0.071 - 99.840 0.041 - 99.850 0.151 - 99.860 0.259 - 99.870 0.367 - 99.880 0.476 - 99.890 0.588 - 99.900 0.703 - 99.910 0.823 - 99.920 0.949 - 99.930 1.081 - 99.940 1.219 - 99.950 1.363 - 99.960 1.513 - 99.970 1.668 - 99.980 1.826 - 99.990 1.986 -100.000 2.146 diff --git a/docs/examples/srfit_ex/data/ni-q27r60-xray.gr b/docs/examples/srfit_ex/data/ni-q27r60-xray.gr deleted file mode 100644 index e325eeb..0000000 --- a/docs/examples/srfit_ex/data/ni-q27r60-xray.gr +++ /dev/null @@ -1,6133 +0,0 @@ -History written: Mon Apr 21 20:48:28 2008 -Produced by -####### Get_XPDF ####### - -##### General_Setting -title=X-ray PDF -workingdirectory=e:\Ahmad\MUCAT0804\standards\pdfgetx2 -sourcedir=C:\Program Files\PDFgetX2\ -logfile=.pdfgetx2.log -quiet=0 debug=0 autosave_isa=1 savefilenamebase=ni300mesh_300k_nor_1-5 -iqfilesurfix=.iq sqfilesurfix=.sq fqfilesurfix=.fq grfilesurfix=.gr - -##### DataFileFormat -datatype=1 (0:SPEC, 1:CHI, 2:nxm column, 3:unknown) -num_skiplines=3 comment_id=# delimiter= -### SPEC Format scan_id=#S scan_delimiter= -columnname_id=#L columnname_delimiter= -data_id= data_delimiter= -### CHI Format -### nxm column Format -### End of file format - -##### Data&Background -samfile=ni300mesh_300k_nor_1-5.chi num_sams=1 -sambkgfile=kapton_bgrd_300k_nor_2-3.chi num_sambkgs=1 -confile= num_cons=1 -conbkgfile= num_conbkgs=1 -det# used xcol detcol deterrcol xmin xmax add_det mul_det add_bkg mul_bkg add_con mul_con add_conbkg mul_conbkg - 0 1 0 1 3 0.600000 35.0000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 - -##### Experiment_Setup -title=PDF analysis -user=me -facility=In house -temperature=300.000 containermut=0.000500000 filtermut=0.0200000 -## X-Ray radiationtype=3 - (0: Ag K_alpha, 1:Cu K_alpha, 2:Mo K_alpha, 3:Customize) -lambda=0.142773 energy=86.8406 polartype=0 polardegree=1.00000 -## MonoChromator crystaltype=0 (0:Perfect, 1:Mosaic, 2:None) -position=0 (0:Primary beam, 1:Diffracted beam) -dspacetype=0 (0:Si{111}, 1:Ge{111}, 2:Customize) dspacing=3.13200 - -##### Sample_Setup information num_atoms=1 -#L symbol valence fractions z user_f1 user_f2 user_macoef - Ni 0.00 1.000000 28 0.000000 0.000000 0.001000 -geometry=2 mut=0.50000000 numberdensity=0.00600000 -thickness=2.00000 packingFraction=0.500000 theory_mut=0.0350063 - -##### GetIQ_Setup -xformat=1 -smoothcorr_isa=0 selfnormalize_isa=0 -#L par_name sample sample_bkg container container_bkg -smooth_degree 2 2 2 2 -smooth_width 6 6 6 6 -selfnormalize 0 0 0 0 -filtercorr_isa=0 samfiltercorr_isa=0 sambkgfiltercorr_isa=0 -confiltercorr_isa=0 conbkgfiltercorr_isa=0 -scatveffcorr_isa=1 samconveffcorr_isa=1 sambkgveffcorr_isa=0 -conbkgveffcorr_isa=0 -nonegative_isa=1 negativevalue=-1.00000 - -##### Calibration_Data -## Detection efficiency energy dependence detedepxaxis=0 -detedepfunctype=0 detedep_elastic=1.00000 detedep_fluores=1.80000 -detedep_quadra=0.000000 detedep_spline=0.000000 detedep_file= -## Detector transmission energy dependence dettcoefxaxis=0 -dettcoeffunctype=0 dettcoef_elastic=0.950000 dettcoef_fluores=0.600000 -dettcoef_quadra=0.000000 dettcoef_spline=0.000000 dettcoef_file= - -##### IQ_Simulation -### Elastic used_isa=1 mymethod=1 -do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 -do_polarization=1 do_oblincident=0 do_energydep=0 -do_breitdirac=0 breitdiracexpo=2.00000 -do_rulandwin=0 rulandwinwidth=0.00100000 -do_useredit=0 add_user=0.000000 mul_user=1.00000 -### Compton used_isa=1 mymethod=1 -do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 -do_polarization=1 do_oblincident=0 do_energydep=0 -do_breitdirac=0 breitdiracexpo=2.00000 -do_rulandwin=0 rulandwinwidth=0.00100000 -do_useredit=0 add_user=0.000000 mul_user=1.00000 -### Fluores used_isa=1 mymethod=1 -do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 -do_polarization=1 do_oblincident=0 do_energydep=0 -do_breitdirac=0 breitdiracexpo=2.00000 -do_rulandwin=0 rulandwinwidth=0.00100000 -do_useredit=0 add_user=0.000000 mul_user=1.00000 - -##### Correction_Setup corrmethod=0 -oblincident_isa=1 dettranscoef=0.980000 samfluore_isa=1 -samfluoretype=0 samfluorescale=0.15000000 -multiscat_isa=1 xraypolar_isa=1 samabsorp_isa=1 -highqscale_isa=1 highqratio=0.600000 scaleconst=0.016825338 -scaleconst_theory=0.016825338 -comptonscat_isa=1 rulandwin_isa=0 rulandintewidth=0.0100000 -comptonmethod=0 breitdirac_isa=1 breitdiracexponent=3 -detefficiency_isa=1 detefficiencytype=2 (0-1: linear, 2-3: quadratic) -detefficiency_a=0.10293460 detefficiency_b=-0.0093982075 -lauediffuse_isa=1 -weight_isa=1 weighttype=0 (0: ^2, 1: , 2: Data Smoothed) -weightsmoothrmin=3.00000 weightsmoothwidth=100 weightsmoothcycles=600 -editsq_isa=0 editsqtype=0 add_sq=0.000000 mul_sq=1.00000 -editsqsmoothrmin=3.00000 editsqsmoothwidth=100 editsqsmoothcycles=600 -smoothdata_isa=0 smoothfunctype=0 smoothqmin=12.0000 smoothboxwidth=9 -interpolateqmin_isa=0 qmininterpolationtype=0 -dampfq_isa=0 dampfqtype=0 dampfqwidth=23.0000 - -##### SqGr_Optimization Setup -ftmethod=0 -## S(q) qmin=0.010000 qmax=27.000000 qgrid=0.000000 -## G(r) rmin=0.010000 rmax=60.000000 rgrid=0.010000 -## SqOptimization sqoptfunction=1 -optqmin=20.0000 optqmax=40.0000 optqgrid=0.000000 -optrmin=0.000000 optrmax=2.20000 optrgrid=0.0200000 -maxiter=20 relstep=0.000000 weighttype=0 weightfunc=0 -fitbkgmult_isa=0 fitsampmut_isa=1 fitpolariz_isa=1 -fitoblique_isa=0 fitfluores_isa=0 -fitrulandw_isa=0 fitenergya_isa=1 fitenergyb_isa=1 -fitsimurulandw_isa=1 fitDetEdepfluores_isa=0 fitDetEdepquadra_isa=0 -fitDetEdepspline_isa=0 fitDetTCoefElastic_isa=0 fitDetTCoefFluores_isa=0 -fitDetTcoefquadra_isa=0 fitDetTcoefspline_isa=0 - -##### Save&Plot Settings -datatype=GrData iqcorrtype=Int iqsimutype=SimuIq -sqcorrtype=Oblin sqtofqtype=DampFq -gropttype=OptFq miscdatatype=AtomASF -##### start data -#F ni300mesh_300k_nor_1-5.gr -#D Mon Apr 21 21:05:49 2008 -#C -#S 1 G(r) -#D -#L r(A) G(r) d_r d_Gr - 1.000000e-002 6.873431e-002 -7.539822e-004 2.439251e-004 - 2.000000e-002 1.419026e-001 -1.507964e-003 4.744725e-004 - 3.000000e-002 2.235165e-001 -2.261947e-003 6.791041e-004 - 4.000000e-002 3.167721e-001 -3.015929e-003 8.469137e-004 - 5.000000e-002 4.237112e-001 -3.769911e-003 9.693333e-004 - 6.000000e-002 5.449630e-001 -4.523893e-003 1.040720e-003 - 7.000000e-002 6.795808e-001 -5.277876e-003 1.058818e-003 - 8.000000e-002 8.249905e-001 -6.031858e-003 1.025121e-003 - 9.000000e-002 9.770511e-001 -6.785840e-003 9.452417e-004 - 1.000000e-001 1.130230e+000 -7.539822e-003 8.295807e-004 - 1.100000e-001 1.277879e+000 -8.293804e-003 6.949769e-004 - 1.200000e-001 1.412600e+000 -9.047787e-003 5.685470e-004 - 1.300000e-001 1.526673e+000 -9.801769e-003 4.915010e-004 - 1.400000e-001 1.612530e+000 -1.055575e-002 5.009222e-004 - 1.500000e-001 1.663227e+000 -1.130973e-002 5.852866e-004 - 1.600000e-001 1.672912e+000 -1.206372e-002 6.994328e-004 - 1.700000e-001 1.637232e+000 -1.281770e-002 8.077110e-004 - 1.800000e-001 1.553676e+000 -1.357168e-002 8.900295e-004 - 1.900000e-001 1.421809e+000 -1.432566e-002 9.362432e-004 - 2.000000e-001 1.243407e+000 -1.507964e-002 9.428280e-004 - 2.100000e-001 1.022453e+000 -1.583363e-002 9.116115e-004 - 2.200000e-001 7.650242e-001 -1.658761e-002 8.495005e-004 - 2.300000e-001 4.790456e-001 -1.734159e-002 7.687986e-004 - 2.400000e-001 1.739413e-001 -1.809557e-002 6.877478e-004 - 2.500000e-001 -1.398042e-001 -1.884956e-002 6.294719e-004 - 2.600000e-001 -4.511501e-001 -1.960354e-002 6.145323e-004 - 2.700000e-001 -7.490410e-001 -2.035752e-002 6.470576e-004 - 2.800000e-001 -1.022954e+000 -2.111150e-002 7.111684e-004 - 2.900000e-001 -1.263421e+000 -2.186548e-002 7.838626e-004 - 3.000000e-001 -1.462499e+000 -2.261947e-002 8.462245e-004 - 3.100000e-001 -1.614156e+000 -2.337345e-002 8.861884e-004 - 3.200000e-001 -1.714557e+000 -2.412743e-002 8.979092e-004 - 3.300000e-001 -1.762230e+000 -2.488141e-002 8.809103e-004 - 3.400000e-001 -1.758105e+000 -2.563540e-002 8.396255e-004 - 3.500000e-001 -1.705428e+000 -2.638938e-002 7.832185e-004 - 3.600000e-001 -1.609542e+000 -2.714336e-002 7.252337e-004 - 3.700000e-001 -1.477570e+000 -2.789734e-002 6.818737e-004 - 3.800000e-001 -1.317997e+000 -2.865132e-002 6.670293e-004 - 3.900000e-001 -1.140196e+000 -2.940531e-002 6.849659e-004 - 4.000000e-001 -9.539062e-001 -3.015929e-002 7.275808e-004 - 4.100000e-001 -7.687098e-001 -3.091327e-002 7.798830e-004 - 4.200000e-001 -5.935270e-001 -3.166725e-002 8.272219e-004 - 4.300000e-001 -4.361632e-001 -3.242124e-002 8.589572e-004 - 4.400000e-001 -3.029309e-001 -3.317522e-002 8.692781e-004 - 4.500000e-001 -1.983675e-001 -3.392920e-002 8.570557e-004 - 4.600000e-001 -1.250629e-001 -3.468318e-002 8.255660e-004 - 4.700000e-001 -8.360514e-002 -3.543716e-002 7.821886e-004 - 4.800000e-001 -7.264409e-002 -3.619115e-002 7.377482e-004 - 4.900000e-001 -8.906677e-002 -3.694513e-002 7.046862e-004 - 5.000000e-001 -1.282715e-001 -3.769911e-002 6.932125e-004 - 5.100000e-001 -1.845218e-001 -3.845309e-002 7.065369e-004 - 5.200000e-001 -2.513573e-001 -3.920708e-002 7.391415e-004 - 5.300000e-001 -3.220347e-001 -3.996106e-002 7.800367e-004 - 5.400000e-001 -3.899722e-001 -4.071504e-002 8.176780e-004 - 5.500000e-001 -4.491698e-001 -4.146902e-002 8.431383e-004 - 5.600000e-001 -4.945797e-001 -4.222300e-002 8.512956e-004 - 5.700000e-001 -5.224065e-001 -4.297699e-002 8.410383e-004 - 5.800000e-001 -5.303183e-001 -4.373097e-002 8.151323e-004 - 5.900000e-001 -5.175603e-001 -4.448495e-002 7.798835e-004 - 6.000000e-001 -4.849629e-001 -4.523893e-002 7.443479e-004 - 6.100000e-001 -4.348489e-001 -4.599292e-002 7.185372e-004 - 6.200000e-001 -3.708459e-001 -4.674690e-002 7.102741e-004 - 6.300000e-001 -2.976187e-001 -4.750088e-002 7.217950e-004 - 6.400000e-001 -2.205402e-001 -4.825486e-002 7.486926e-004 - 6.500000e-001 -1.453223e-001 -4.900884e-002 7.822478e-004 - 6.600000e-001 -7.763208e-002 -4.976283e-002 8.130453e-004 - 6.700000e-001 -2.271702e-002 -5.051681e-002 8.335923e-004 - 6.800000e-001 1.493620e-002 -5.127079e-002 8.395266e-004 - 6.900000e-001 3.188834e-002 -5.202477e-002 8.299654e-004 - 7.000000e-001 2.596220e-002 -5.277876e-002 8.074478e-004 - 7.100000e-001 -3.627668e-003 -5.353274e-002 7.775771e-004 - 7.200000e-001 -5.623694e-002 -5.428672e-002 7.481692e-004 - 7.300000e-001 -1.298465e-001 -5.504070e-002 7.275367e-004 - 7.400000e-001 -2.212055e-001 -5.579468e-002 7.218413e-004 - 7.500000e-001 -3.260518e-001 -5.654867e-002 7.325433e-004 - 7.600000e-001 -4.393951e-001 -5.730265e-002 7.557828e-004 - 7.700000e-001 -5.558430e-001 -5.805663e-002 7.842469e-004 - 7.800000e-001 -6.699494e-001 -5.881061e-002 8.100079e-004 - 7.900000e-001 -7.765604e-001 -5.956460e-002 8.267025e-004 - 8.000000e-001 -8.711386e-001 -6.031858e-002 8.306553e-004 - 8.100000e-001 -9.500414e-001 -6.107256e-002 8.212668e-004 - 8.200000e-001 -1.010739e+000 -6.182654e-002 8.009824e-004 - 8.300000e-001 -1.051956e+000 -6.258052e-002 7.749148e-004 - 8.400000e-001 -1.073732e+000 -6.333451e-002 7.499621e-004 - 8.500000e-001 -1.077391e+000 -6.408849e-002 7.331809e-004 - 8.600000e-001 -1.065430e+000 -6.484247e-002 7.295125e-004 - 8.700000e-001 -1.041336e+000 -6.559645e-002 7.398066e-004 - 8.800000e-001 -1.009331e+000 -6.635044e-002 7.605027e-004 - 8.900000e-001 -9.740767e-001 -6.710442e-002 7.852311e-004 - 9.000000e-001 -9.403558e-001 -6.785840e-002 8.071497e-004 - 9.100000e-001 -9.127411e-001 -6.861238e-002 8.207904e-004 - 9.200000e-001 -8.952872e-001 -6.936636e-002 8.230729e-004 - 9.300000e-001 -8.912565e-001 -7.012035e-002 8.136834e-004 - 9.400000e-001 -9.029001e-001 -7.087433e-002 7.950421e-004 - 9.500000e-001 -9.313082e-001 -7.162831e-002 7.719010e-004 - 9.600000e-001 -9.763375e-001 -7.238229e-002 7.504458e-004 - 9.700000e-001 -1.036622e+000 -7.313628e-002 7.367545e-004 - 9.800000e-001 -1.109666e+000 -7.389026e-002 7.348188e-004 - 9.900000e-001 -1.192010e+000 -7.464424e-002 7.449894e-004 - 1.000000e+000 -1.279466e+000 -7.539822e-002 7.638775e-004 - 1.010000e+000 -1.367394e+000 -7.615220e-002 7.857902e-004 - 1.020000e+000 -1.451017e+000 -7.690619e-002 8.047192e-004 - 1.030000e+000 -1.525738e+000 -7.766017e-002 8.159306e-004 - 1.040000e+000 -1.587456e+000 -7.841415e-002 8.168673e-004 - 1.050000e+000 -1.632840e+000 -7.916813e-002 8.074961e-004 - 1.060000e+000 -1.659557e+000 -7.992212e-002 7.902545e-004 - 1.070000e+000 -1.666444e+000 -8.067610e-002 7.696197e-004 - 1.080000e+000 -1.653588e+000 -8.143008e-002 7.511942e-004 - 1.090000e+000 -1.622339e+000 -8.218406e-002 7.402424e-004 - 1.100000e+000 -1.575233e+000 -8.293804e-002 7.399547e-004 - 1.110000e+000 -1.515843e+000 -8.369203e-002 7.502281e-004 - 1.120000e+000 -1.448552e+000 -8.444601e-002 7.677475e-004 - 1.130000e+000 -1.378284e+000 -8.519999e-002 7.873112e-004 - 1.140000e+000 -1.310190e+000 -8.595397e-002 8.035642e-004 - 1.150000e+000 -1.249322e+000 -8.670796e-002 8.123819e-004 - 1.160000e+000 -1.200307e+000 -8.746194e-002 8.116719e-004 - 1.170000e+000 -1.167049e+000 -8.821592e-002 8.016857e-004 - 1.180000e+000 -1.152475e+000 -8.896990e-002 7.849482e-004 - 1.190000e+000 -1.158342e+000 -8.972388e-002 7.658069e-004 - 1.200000e+000 -1.185117e+000 -9.047787e-002 7.495105e-004 - 1.210000e+000 -1.231933e+000 -9.123185e-002 7.407972e-004 - 1.220000e+000 -1.296644e+000 -9.198583e-002 7.423160e-004 - 1.230000e+000 -1.375943e+000 -9.273981e-002 7.536265e-004 - 1.240000e+000 -1.465568e+000 -9.349380e-002 7.714079e-004 - 1.250000e+000 -1.560562e+000 -9.424778e-002 7.907351e-004 - 1.260000e+000 -1.655584e+000 -9.500176e-002 8.066544e-004 - 1.270000e+000 -1.745241e+000 -9.575574e-002 8.154192e-004 - 1.280000e+000 -1.824427e+000 -9.650973e-002 8.151980e-004 - 1.290000e+000 -1.888644e+000 -9.726371e-002 8.063319e-004 - 1.300000e+000 -1.934291e+000 -9.801769e-002 7.912301e-004 - 1.310000e+000 -1.958894e+000 -9.877167e-002 7.739047e-004 - 1.320000e+000 -1.961263e+000 -9.952565e-002 7.590873e-004 - 1.330000e+000 -1.941580e+000 -1.002796e-001 7.509527e-004 - 1.340000e+000 -1.901389e+000 -1.010336e-001 7.517662e-004 - 1.350000e+000 -1.843509e+000 -1.017876e-001 7.610733e-004 - 1.360000e+000 -1.771864e+000 -1.025416e-001 7.759173e-004 - 1.370000e+000 -1.691243e+000 -1.032956e-001 7.919492e-004 - 1.380000e+000 -1.607005e+000 -1.040495e-001 8.048065e-004 - 1.390000e+000 -1.524750e+000 -1.048035e-001 8.112249e-004 - 1.400000e+000 -1.449970e+000 -1.055575e-001 8.096953e-004 - 1.410000e+000 -1.387706e+000 -1.063115e-001 8.007010e-004 - 1.420000e+000 -1.342238e+000 -1.070655e-001 7.865956e-004 - 1.430000e+000 -1.316814e+000 -1.078195e-001 7.711206e-004 - 1.440000e+000 -1.313445e+000 -1.085734e-001 7.585305e-004 - 1.450000e+000 -1.332782e+000 -1.093274e-001 7.524009e-004 - 1.460000e+000 -1.374071e+000 -1.100814e-001 7.544530e-004 - 1.470000e+000 -1.435195e+000 -1.108354e-001 7.639425e-004 - 1.480000e+000 -1.512809e+000 -1.115894e-001 7.779668e-004 - 1.490000e+000 -1.602544e+000 -1.123434e-001 7.925040e-004 - 1.500000e+000 -1.699282e+000 -1.130973e-001 8.036418e-004 - 1.510000e+000 -1.797468e+000 -1.138513e-001 8.085541e-004 - 1.520000e+000 -1.891462e+000 -1.146053e-001 8.060747e-004 - 1.530000e+000 -1.975892e+000 -1.153593e-001 7.968876e-004 - 1.540000e+000 -2.045984e+000 -1.161133e-001 7.833754e-004 - 1.550000e+000 -2.097868e+000 -1.168672e-001 7.691183e-004 - 1.560000e+000 -2.128815e+000 -1.176212e-001 7.580310e-004 - 1.570000e+000 -2.137413e+000 -1.183752e-001 7.532448e-004 - 1.580000e+000 -2.123652e+000 -1.191292e-001 7.560758e-004 - 1.590000e+000 -2.088925e+000 -1.198832e-001 7.655655e-004 - 1.600000e+000 -2.035944e+000 -1.206372e-001 7.788549e-004 - 1.610000e+000 -1.968562e+000 -1.213911e-001 7.921732e-004 - 1.620000e+000 -1.891536e+000 -1.221451e-001 8.019571e-004 - 1.630000e+000 -1.810220e+000 -1.228991e-001 8.057253e-004 - 1.640000e+000 -1.730230e+000 -1.236531e-001 8.025821e-004 - 1.650000e+000 -1.657083e+000 -1.244071e-001 7.933650e-004 - 1.660000e+000 -1.595845e+000 -1.251610e-001 7.804634e-004 - 1.670000e+000 -1.550808e+000 -1.259150e-001 7.673025e-004 - 1.680000e+000 -1.525216e+000 -1.266690e-001 7.574971e-004 - 1.690000e+000 -1.521049e+000 -1.274230e-001 7.538057e-004 - 1.700000e+000 -1.538897e+000 -1.281770e-001 7.572247e-004 - 1.710000e+000 -1.577918e+000 -1.289310e-001 7.666516e-004 - 1.720000e+000 -1.635884e+000 -1.296849e-001 7.793021e-004 - 1.730000e+000 -1.709326e+000 -1.304389e-001 7.916502e-004 - 1.740000e+000 -1.793748e+000 -1.311929e-001 8.004529e-004 - 1.750000e+000 -1.883915e+000 -1.319469e-001 8.035365e-004 - 1.760000e+000 -1.974193e+000 -1.327009e-001 8.002384e-004 - 1.770000e+000 -2.058908e+000 -1.334549e-001 7.915102e-004 - 1.780000e+000 -2.132721e+000 -1.342088e-001 7.797049e-004 - 1.790000e+000 -2.190976e+000 -1.349628e-001 7.680454e-004 - 1.800000e+000 -2.230012e+000 -1.357168e-001 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9.550488e-001 -2.334329e+000 7.812417e-004 - 3.097000e+001 9.744632e-001 -2.335083e+000 7.806564e-004 - 3.098000e+001 1.000308e+000 -2.335837e+000 7.799369e-004 - 3.099000e+001 1.031832e+000 -2.336591e+000 7.792815e-004 - 3.100000e+001 1.068221e+000 -2.337345e+000 7.788708e-004 - 3.101000e+001 1.108641e+000 -2.338099e+000 7.788178e-004 - 3.102000e+001 1.152284e+000 -2.338853e+000 7.791366e-004 - 3.103000e+001 1.198397e+000 -2.339607e+000 7.797387e-004 - 3.104000e+001 1.246317e+000 -2.340361e+000 7.804578e-004 - 3.105000e+001 1.295481e+000 -2.341115e+000 7.810956e-004 - 3.106000e+001 1.345437e+000 -2.341869e+000 7.814763e-004 - 3.107000e+001 1.395839e+000 -2.342623e+000 7.814943e-004 - 3.108000e+001 1.446432e+000 -2.343377e+000 7.811428e-004 - 3.109000e+001 1.497028e+000 -2.344131e+000 7.805153e-004 - 3.110000e+001 1.547470e+000 -2.344885e+000 7.797810e-004 - 3.111000e+001 1.597602e+000 -2.345639e+000 7.791382e-004 - 3.112000e+001 1.647214e+000 -2.346393e+000 7.787607e-004 - 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7.340883e-002 -4.471869e+000 7.806813e-004 - 5.932000e+001 7.030968e-002 -4.472623e+000 7.806340e-004 - 5.933000e+001 6.603221e-002 -4.473377e+000 7.804000e-004 - 5.934000e+001 6.051949e-002 -4.474131e+000 7.800434e-004 - 5.935000e+001 5.376200e-002 -4.474885e+000 7.796617e-004 - 5.936000e+001 4.580137e-002 -4.475638e+000 7.793598e-004 - 5.937000e+001 3.673138e-002 -4.476392e+000 7.792210e-004 - 5.938000e+001 2.669596e-002 -4.477146e+000 7.792836e-004 - 5.939000e+001 1.588450e-002 -4.477900e+000 7.795309e-004 - 5.940000e+001 4.524525e-003 -4.478654e+000 7.798954e-004 - 5.941000e+001 -7.127787e-003 -4.479408e+000 7.802774e-004 - 5.942000e+001 -1.879872e-002 -4.480162e+000 7.805727e-004 - 5.943000e+001 -3.020913e-002 -4.480916e+000 7.807007e-004 - 5.944000e+001 -4.108687e-002 -4.481670e+000 7.806268e-004 - 5.945000e+001 -5.117877e-002 -4.482424e+000 7.803715e-004 - 5.946000e+001 -6.026154e-002 -4.483178e+000 7.800049e-004 - 5.947000e+001 -6.815094e-002 -4.483932e+000 7.796278e-004 - 5.948000e+001 -7.470873e-002 -4.484686e+000 7.793442e-004 - 5.949000e+001 -7.984700e-002 -4.485440e+000 7.792324e-004 - 5.950000e+001 -8.352979e-002 -4.486194e+000 7.793235e-004 - 5.951000e+001 -8.577175e-002 -4.486948e+000 7.795930e-004 - 5.952000e+001 -8.663427e-002 -4.487702e+000 7.799672e-004 - 5.953000e+001 -8.621915e-002 -4.488456e+000 7.803436e-004 - 5.954000e+001 -8.466041e-002 -4.489210e+000 7.806190e-004 - 5.955000e+001 -8.211476e-002 -4.489964e+000 7.807177e-004 - 5.956000e+001 -7.875131e-002 -4.490718e+000 7.806122e-004 - 5.957000e+001 -7.474132e-002 -4.491472e+000 7.803306e-004 - 5.958000e+001 -7.024849e-002 -4.492226e+000 7.799493e-004 - 5.959000e+001 -6.542052e-002 -4.492980e+000 7.795719e-004 - 5.960000e+001 -6.038236e-002 -4.493734e+000 7.793014e-004 - 5.961000e+001 -5.523152e-002 -4.494488e+000 7.792114e-004 - 5.962000e+001 -5.003578e-002 -4.495242e+000 7.793265e-004 - 5.963000e+001 -4.483316e-002 -4.495996e+000 7.796149e-004 - 5.964000e+001 -3.963431e-002 -4.496750e+000 7.799973e-004 - 5.965000e+001 -3.442677e-002 -4.497504e+000 7.803689e-004 - 5.966000e+001 -2.918102e-002 -4.498258e+000 7.806279e-004 - 5.967000e+001 -2.385749e-002 -4.499012e+000 7.807033e-004 - 5.968000e+001 -1.841431e-002 -4.499766e+000 7.805741e-004 - 5.969000e+001 -1.281488e-002 -4.500520e+000 7.802752e-004 - 5.970000e+001 -7.034894e-003 -4.501274e+000 7.798880e-004 - 5.971000e+001 -1.068185e-003 -4.502028e+000 7.795181e-004 - 5.972000e+001 5.069049e-003 -4.502782e+000 7.792665e-004 - 5.973000e+001 1.133595e-002 -4.503536e+000 7.792022e-004 - 5.974000e+001 1.766681e-002 -4.504290e+000 7.793429e-004 - 5.975000e+001 2.397307e-002 -4.505044e+000 7.796503e-004 - 5.976000e+001 3.014732e-002 -4.505798e+000 7.800407e-004 - 5.977000e+001 3.606909e-002 -4.506552e+000 7.804078e-004 - 5.978000e+001 4.161192e-002 -4.507306e+000 7.806520e-004 - 5.979000e+001 4.665142e-002 -4.508060e+000 7.807075e-004 - 5.980000e+001 5.107355e-002 -4.508814e+000 7.805599e-004 - 5.981000e+001 5.478259e-002 -4.509568e+000 7.802504e-004 - 5.982000e+001 5.770831e-002 -4.510322e+000 7.798642e-004 - 5.983000e+001 5.981172e-002 -4.511076e+000 7.795077e-004 - 5.984000e+001 6.108900e-002 -4.511830e+000 7.792791e-004 - 5.985000e+001 6.157334e-002 -4.512584e+000 7.792416e-004 - 5.986000e+001 6.133442e-002 -4.513338e+000 7.794057e-004 - 5.987000e+001 6.047567e-002 -4.514092e+000 7.797270e-004 - 5.988000e+001 5.912928e-002 -4.514846e+000 7.801175e-004 - 5.989000e+001 5.744932e-002 -4.515600e+000 7.804705e-004 - 5.990000e+001 5.560348e-002 -4.516354e+000 7.806898e-004 - 5.991000e+001 5.376369e-002 -4.517108e+000 7.807154e-004 - 5.992000e+001 5.209645e-002 -4.517862e+000 7.805404e-004 - 5.993000e+001 5.075335e-002 -4.518615e+000 7.802123e-004 - 5.994000e+001 4.986234e-002 -4.519369e+000 7.798205e-004 - 5.995000e+001 4.952036e-002 -4.520123e+000 7.794718e-004 - 5.996000e+001 4.978779e-002 -4.520877e+000 7.792614e-004 - 5.997000e+001 5.068493e-002 -4.521631e+000 7.792464e-004 - 5.998000e+001 5.219086e-002 -4.522385e+000 7.794303e-004 - 5.999000e+001 5.424471e-002 -4.523139e+000 7.797623e-004 diff --git a/docs/examples/srfit_ex/data/ni-q27r60nodg-xray.gr b/docs/examples/srfit_ex/data/ni-q27r60nodg-xray.gr deleted file mode 100644 index 5bf8d53..0000000 --- a/docs/examples/srfit_ex/data/ni-q27r60nodg-xray.gr +++ /dev/null @@ -1,6133 +0,0 @@ -History written: Mon Apr 21 20:48:28 2008 -Produced by -####### Get_XPDF ####### - -##### General_Setting -title=X-ray PDF -workingdirectory=e:\Ahmad\MUCAT0804\standards\pdfgetx2 -sourcedir=C:\Program Files\PDFgetX2\ -logfile=.pdfgetx2.log -quiet=0 debug=0 autosave_isa=1 savefilenamebase=ni300mesh_300k_nor_1-5 -iqfilesurfix=.iq sqfilesurfix=.sq fqfilesurfix=.fq grfilesurfix=.gr - -##### DataFileFormat -datatype=1 (0:SPEC, 1:CHI, 2:nxm column, 3:unknown) -num_skiplines=3 comment_id=# delimiter= -### SPEC Format scan_id=#S scan_delimiter= -columnname_id=#L columnname_delimiter= -data_id= data_delimiter= -### CHI Format -### nxm column Format -### End of file format - -##### Data&Background -samfile=ni300mesh_300k_nor_1-5.chi num_sams=1 -sambkgfile=kapton_bgrd_300k_nor_2-3.chi num_sambkgs=1 -confile= num_cons=1 -conbkgfile= num_conbkgs=1 -det# used xcol detcol deterrcol xmin xmax add_det mul_det add_bkg mul_bkg add_con mul_con add_conbkg mul_conbkg - 0 1 0 1 3 0.600000 35.0000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 - -##### Experiment_Setup -title=PDF analysis -user=me -facility=In house -temperature=300.000 containermut=0.000500000 filtermut=0.0200000 -## X-Ray radiationtype=3 - (0: Ag K_alpha, 1:Cu K_alpha, 2:Mo K_alpha, 3:Customize) -lambda=0.142773 energy=86.8406 polartype=0 polardegree=1.00000 -## MonoChromator crystaltype=0 (0:Perfect, 1:Mosaic, 2:None) -position=0 (0:Primary beam, 1:Diffracted beam) -dspacetype=0 (0:Si{111}, 1:Ge{111}, 2:Customize) dspacing=3.13200 - -##### Sample_Setup information num_atoms=1 -#L symbol valence fractions z user_f1 user_f2 user_macoef - Ni 0.00 1.000000 28 0.000000 0.000000 0.001000 -geometry=2 mut=0.50000000 numberdensity=0.00600000 -thickness=2.00000 packingFraction=0.500000 theory_mut=0.0350063 - -##### GetIQ_Setup -xformat=1 -smoothcorr_isa=0 selfnormalize_isa=0 -#L par_name sample sample_bkg container container_bkg -smooth_degree 2 2 2 2 -smooth_width 6 6 6 6 -selfnormalize 0 0 0 0 -filtercorr_isa=0 samfiltercorr_isa=0 sambkgfiltercorr_isa=0 -confiltercorr_isa=0 conbkgfiltercorr_isa=0 -scatveffcorr_isa=1 samconveffcorr_isa=1 sambkgveffcorr_isa=0 -conbkgveffcorr_isa=0 -nonegative_isa=1 negativevalue=-1.00000 - -##### Calibration_Data -## Detection efficiency energy dependence detedepxaxis=0 -detedepfunctype=0 detedep_elastic=1.00000 detedep_fluores=1.80000 -detedep_quadra=0.000000 detedep_spline=0.000000 detedep_file= -## Detector transmission energy dependence dettcoefxaxis=0 -dettcoeffunctype=0 dettcoef_elastic=0.950000 dettcoef_fluores=0.600000 -dettcoef_quadra=0.000000 dettcoef_spline=0.000000 dettcoef_file= - -##### IQ_Simulation -### Elastic used_isa=1 mymethod=1 -do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 -do_polarization=1 do_oblincident=0 do_energydep=0 -do_breitdirac=0 breitdiracexpo=2.00000 -do_rulandwin=0 rulandwinwidth=0.00100000 -do_useredit=0 add_user=0.000000 mul_user=1.00000 -### Compton used_isa=1 mymethod=1 -do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 -do_polarization=1 do_oblincident=0 do_energydep=0 -do_breitdirac=0 breitdiracexpo=2.00000 -do_rulandwin=0 rulandwinwidth=0.00100000 -do_useredit=0 add_user=0.000000 mul_user=1.00000 -### Fluores used_isa=1 mymethod=1 -do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 -do_polarization=1 do_oblincident=0 do_energydep=0 -do_breitdirac=0 breitdiracexpo=2.00000 -do_rulandwin=0 rulandwinwidth=0.00100000 -do_useredit=0 add_user=0.000000 mul_user=1.00000 - -##### Correction_Setup corrmethod=0 -oblincident_isa=1 dettranscoef=0.980000 samfluore_isa=1 -samfluoretype=0 samfluorescale=0.15000000 -multiscat_isa=1 xraypolar_isa=1 samabsorp_isa=1 -highqscale_isa=1 highqratio=0.600000 scaleconst=0.016825338 -scaleconst_theory=0.016825338 -comptonscat_isa=1 rulandwin_isa=0 rulandintewidth=0.0100000 -comptonmethod=0 breitdirac_isa=1 breitdiracexponent=3 -detefficiency_isa=1 detefficiencytype=2 (0-1: linear, 2-3: quadratic) -detefficiency_a=0.10293460 detefficiency_b=-0.0093982075 -lauediffuse_isa=1 -weight_isa=1 weighttype=0 (0: ^2, 1: , 2: Data Smoothed) -weightsmoothrmin=3.00000 weightsmoothwidth=100 weightsmoothcycles=600 -editsq_isa=0 editsqtype=0 add_sq=0.000000 mul_sq=1.00000 -editsqsmoothrmin=3.00000 editsqsmoothwidth=100 editsqsmoothcycles=600 -smoothdata_isa=0 smoothfunctype=0 smoothqmin=12.0000 smoothboxwidth=9 -interpolateqmin_isa=0 qmininterpolationtype=0 -dampfq_isa=0 dampfqtype=0 dampfqwidth=23.0000 - -##### SqGr_Optimization Setup -ftmethod=0 -## S(q) qmin=0.010000 qmax=27.000000 qgrid=0.000000 -## G(r) rmin=0.010000 rmax=60.000000 rgrid=0.010000 -## SqOptimization sqoptfunction=1 -optqmin=20.0000 optqmax=40.0000 optqgrid=0.000000 -optrmin=0.000000 optrmax=2.20000 optrgrid=0.0200000 -maxiter=20 relstep=0.000000 weighttype=0 weightfunc=0 -fitbkgmult_isa=0 fitsampmut_isa=1 fitpolariz_isa=1 -fitoblique_isa=0 fitfluores_isa=0 -fitrulandw_isa=0 fitenergya_isa=1 fitenergyb_isa=1 -fitsimurulandw_isa=1 fitDetEdepfluores_isa=0 fitDetEdepquadra_isa=0 -fitDetEdepspline_isa=0 fitDetTCoefElastic_isa=0 fitDetTCoefFluores_isa=0 -fitDetTcoefquadra_isa=0 fitDetTcoefspline_isa=0 - -##### Save&Plot Settings -datatype=GrData iqcorrtype=Int iqsimutype=SimuIq -sqcorrtype=Oblin sqtofqtype=DampFq -gropttype=OptFq miscdatatype=AtomASF -##### start data -#F ni300mesh_300k_nor_1-5.gr -#D Mon Apr 21 21:05:49 2008 -#C -#S 1 G(r) -#D -#L r(A) G(r) - 1.000000e-002 6.873431e-002 - 2.000000e-002 1.419026e-001 - 3.000000e-002 2.235165e-001 - 4.000000e-002 3.167721e-001 - 5.000000e-002 4.237112e-001 - 6.000000e-002 5.449630e-001 - 7.000000e-002 6.795808e-001 - 8.000000e-002 8.249905e-001 - 9.000000e-002 9.770511e-001 - 1.000000e-001 1.130230e+000 - 1.100000e-001 1.277879e+000 - 1.200000e-001 1.412600e+000 - 1.300000e-001 1.526673e+000 - 1.400000e-001 1.612530e+000 - 1.500000e-001 1.663227e+000 - 1.600000e-001 1.672912e+000 - 1.700000e-001 1.637232e+000 - 1.800000e-001 1.553676e+000 - 1.900000e-001 1.421809e+000 - 2.000000e-001 1.243407e+000 - 2.100000e-001 1.022453e+000 - 2.200000e-001 7.650242e-001 - 2.300000e-001 4.790456e-001 - 2.400000e-001 1.739413e-001 - 2.500000e-001 -1.398042e-001 - 2.600000e-001 -4.511501e-001 - 2.700000e-001 -7.490410e-001 - 2.800000e-001 -1.022954e+000 - 2.900000e-001 -1.263421e+000 - 3.000000e-001 -1.462499e+000 - 3.100000e-001 -1.614156e+000 - 3.200000e-001 -1.714557e+000 - 3.300000e-001 -1.762230e+000 - 3.400000e-001 -1.758105e+000 - 3.500000e-001 -1.705428e+000 - 3.600000e-001 -1.609542e+000 - 3.700000e-001 -1.477570e+000 - 3.800000e-001 -1.317997e+000 - 3.900000e-001 -1.140196e+000 - 4.000000e-001 -9.539062e-001 - 4.100000e-001 -7.687098e-001 - 4.200000e-001 -5.935270e-001 - 4.300000e-001 -4.361632e-001 - 4.400000e-001 -3.029309e-001 - 4.500000e-001 -1.983675e-001 - 4.600000e-001 -1.250629e-001 - 4.700000e-001 -8.360514e-002 - 4.800000e-001 -7.264409e-002 - 4.900000e-001 -8.906677e-002 - 5.000000e-001 -1.282715e-001 - 5.100000e-001 -1.845218e-001 - 5.200000e-001 -2.513573e-001 - 5.300000e-001 -3.220347e-001 - 5.400000e-001 -3.899722e-001 - 5.500000e-001 -4.491698e-001 - 5.600000e-001 -4.945797e-001 - 5.700000e-001 -5.224065e-001 - 5.800000e-001 -5.303183e-001 - 5.900000e-001 -5.175603e-001 - 6.000000e-001 -4.849629e-001 - 6.100000e-001 -4.348489e-001 - 6.200000e-001 -3.708459e-001 - 6.300000e-001 -2.976187e-001 - 6.400000e-001 -2.205402e-001 - 6.500000e-001 -1.453223e-001 - 6.600000e-001 -7.763208e-002 - 6.700000e-001 -2.271702e-002 - 6.800000e-001 1.493620e-002 - 6.900000e-001 3.188834e-002 - 7.000000e-001 2.596220e-002 - 7.100000e-001 -3.627668e-003 - 7.200000e-001 -5.623694e-002 - 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5.999000e+001 5.424471e-002 diff --git a/docs/examples/srfit_ex/data/ni.cif b/docs/examples/srfit_ex/data/ni.cif deleted file mode 100644 index c455635..0000000 --- a/docs/examples/srfit_ex/data/ni.cif +++ /dev/null @@ -1,236 +0,0 @@ -#------------------------------------------------------------------------------ -#$Date: 2008-03-10 08:25:41 +0000 (Mon, 10 Mar 2008) $ -#$Revision: 255 $ -#$URL: svn://cod.ibt.lt/cod/cif/9/9008476.cif $ -#------------------------------------------------------------------------------ -# -# This file is available in the Crystallography Open Database (COD), -# http://www.crystallography.net/ -# -# All data on this site have been placed in the public domain by the -# contributors. -# -data_9008476 -loop_ -_publ_author_name -'Wyckoff R W G' -_publ_section_title -; - Second edition. 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876b2c8..0000000 --- a/docs/examples/srfit_ex/data/pb.cif +++ /dev/null @@ -1,240 +0,0 @@ -#------------------------------------------------------------------------------ -#$Date: 2010-01-30 13:59:17 +0000 (Sat, 30 Jan 2010) $ -#$Revision: 966 $ -#$URL: svn://cod.ibt.lt/cod/cif/9/9008477.cif $ -#------------------------------------------------------------------------------ -# -# This file is available in the Crystallography Open Database (COD), -# http://www.crystallography.net/ -# -# All data on this site have been placed in the public domain by the -# contributors. -# -data_9008477 -_space_group_IT_number 225 -_symmetry_space_group_name_Hall '-F 4 2 3' -_symmetry_space_group_name_H-M 'F m -3 m' -_[local]_cod_cif_authors_sg_H-M 'F m 3 m' -loop_ -_publ_author_name -'Wyckoff R W G' -_publ_section_title -; - Second edition. Interscience Publishers, New York, New York - Cubic closest packed, ccp, structure -; -_journal_name_full 'Crystal Structures' -_journal_page_first 7 -_journal_page_last 83 -_journal_volume 1 -_journal_year 1963 -_chemical_formula_sum Pb -_chemical_name_mineral Lead -_cell_angle_alpha 90 -_cell_angle_beta 90 -_cell_angle_gamma 90 -_cell_length_a 4.9505 -_cell_length_b 4.9505 -_cell_length_c 4.9505 -_cell_volume 121.324 -loop_ -_symmetry_equiv_pos_as_xyz -x,y,z -x,1/2+y,1/2+z -1/2+x,y,1/2+z -1/2+x,1/2+y,z -z,-x,y -z,1/2-x,1/2+y -1/2+z,-x,1/2+y -1/2+z,1/2-x,y --y,z,-x --y,1/2+z,1/2-x -1/2-y,z,1/2-x -1/2-y,1/2+z,-x -x,-y,z -x,1/2-y,1/2+z -1/2+x,-y,1/2+z -1/2+x,1/2-y,z --z,x,-y --z,1/2+x,1/2-y -1/2-z,x,1/2-y -1/2-z,1/2+x,-y -y,-z,x -y,1/2-z,1/2+x -1/2+y,-z,1/2+x -1/2+y,1/2-z,x --x,y,-z --x,1/2+y,1/2-z -1/2-x,y,1/2-z -1/2-x,1/2+y,-z -x,-z,-y -x,1/2-z,1/2-y -1/2+x,-z,1/2-y -1/2+x,1/2-z,-y --z,y,x --z,1/2+y,1/2+x -1/2-z,y,1/2+x -1/2-z,1/2+y,x -y,-x,-z -y,1/2-x,1/2-z -1/2+y,-x,1/2-z 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+0,0 @@ -History written: Mon Apr 21 20:48:28 2008 -Produced by -####### Get_XPDF ####### - -##### General_Setting -title=X-ray PDF -workingdirectory=e:\Ahmad\MUCAT0804\standards\pdfgetx2 -sourcedir=C:\Program Files\PDFgetX2\ -logfile=.pdfgetx2.log -quiet=0 debug=0 autosave_isa=1 savefilenamebase=si325_mesh_300k_nor_4-8 -iqfilesurfix=.iq sqfilesurfix=.sq fqfilesurfix=.fq grfilesurfix=.gr - -##### DataFileFormat -datatype=1 (0:SPEC, 1:CHI, 2:nxm column, 3:unknown) -num_skiplines=3 comment_id=# delimiter= -### SPEC Format scan_id=#S scan_delimiter= -columnname_id=#L columnname_delimiter= -data_id= data_delimiter= -### CHI Format -### nxm column Format -### End of file format - -##### Data&Background -samfile=si325_mesh_300k_nor_4-8.chi num_sams=1 -sambkgfile=kapton_bgrd_300k_nor_2-3.chi num_sambkgs=1 -confile= num_cons=1 -conbkgfile= num_conbkgs=1 -det# used xcol detcol deterrcol xmin xmax add_det mul_det add_bkg mul_bkg add_con mul_con add_conbkg mul_conbkg - 0 1 0 1 3 0.600000 32.0000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 - -##### Experiment_Setup -title=PDF analysis -user=me -facility=In house -temperature=300.000 containermut=0.000500000 filtermut=0.0200000 -## X-Ray radiationtype=3 - (0: Ag K_alpha, 1:Cu K_alpha, 2:Mo K_alpha, 3:Customize) -lambda=0.142773 energy=86.8406 polartype=0 polardegree=1.00000 -## MonoChromator crystaltype=0 (0:Perfect, 1:Mosaic, 2:None) -position=0 (0:Primary beam, 1:Diffracted beam) -dspacetype=0 (0:Si{111}, 1:Ge{111}, 2:Customize) dspacing=3.13200 - -##### Sample_Setup information num_atoms=1 -#L symbol valence fractions z user_f1 user_f2 user_macoef - Si 0.00 1.000000 14 0.000000 0.000000 0.001000 -geometry=2 mut=0.50000000 numberdensity=0.00600000 -thickness=2.00000 packingFraction=0.500000 theory_mut=0.00579218 - -##### GetIQ_Setup -xformat=1 -smoothcorr_isa=0 selfnormalize_isa=0 -#L par_name sample sample_bkg container container_bkg -smooth_degree 2 2 2 2 -smooth_width 6 6 6 6 -selfnormalize 0 0 0 0 -filtercorr_isa=0 samfiltercorr_isa=0 sambkgfiltercorr_isa=0 -confiltercorr_isa=0 conbkgfiltercorr_isa=0 -scatveffcorr_isa=1 samconveffcorr_isa=1 sambkgveffcorr_isa=0 -conbkgveffcorr_isa=0 -nonegative_isa=1 negativevalue=-1.00000 - -##### Calibration_Data -## Detection efficiency energy dependence detedepxaxis=0 -detedepfunctype=0 detedep_elastic=1.00000 detedep_fluores=1.80000 -detedep_quadra=0.000000 detedep_spline=0.000000 detedep_file= -## Detector transmission energy dependence dettcoefxaxis=0 -dettcoeffunctype=0 dettcoef_elastic=0.950000 dettcoef_fluores=0.600000 -dettcoef_quadra=0.000000 dettcoef_spline=0.000000 dettcoef_file= - -##### IQ_Simulation -### Elastic used_isa=1 mymethod=1 -do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 -do_polarization=1 do_oblincident=0 do_energydep=0 -do_breitdirac=0 breitdiracexpo=2.00000 -do_rulandwin=0 rulandwinwidth=0.00100000 -do_useredit=0 add_user=0.000000 mul_user=1.00000 -### Compton used_isa=1 mymethod=1 -do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 -do_polarization=1 do_oblincident=0 do_energydep=0 -do_breitdirac=0 breitdiracexpo=2.00000 -do_rulandwin=0 rulandwinwidth=0.00100000 -do_useredit=0 add_user=0.000000 mul_user=1.00000 -### Fluores used_isa=1 mymethod=1 -do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 -do_polarization=1 do_oblincident=0 do_energydep=0 -do_breitdirac=0 breitdiracexpo=2.00000 -do_rulandwin=0 rulandwinwidth=0.00100000 -do_useredit=0 add_user=0.000000 mul_user=1.00000 - -##### Correction_Setup corrmethod=0 -oblincident_isa=1 dettranscoef=0.980000 samfluore_isa=1 -samfluoretype=0 samfluorescale=15.000000 -multiscat_isa=1 xraypolar_isa=1 samabsorp_isa=1 -highqscale_isa=1 highqratio=0.600000 scaleconst=0.039181914 -scaleconst_theory=0.039181914 -comptonscat_isa=1 rulandwin_isa=0 rulandintewidth=0.0100000 -comptonmethod=0 breitdirac_isa=1 breitdiracexponent=3 -detefficiency_isa=1 detefficiencytype=2 (0-1: linear, 2-3: quadratic) -detefficiency_a=-0.054826792 detefficiency_b=0.028062565 -lauediffuse_isa=1 -weight_isa=1 weighttype=0 (0: ^2, 1: , 2: Data Smoothed) -weightsmoothrmin=3.00000 weightsmoothwidth=100 weightsmoothcycles=600 -editsq_isa=0 editsqtype=0 add_sq=0.000000 mul_sq=1.00000 -editsqsmoothrmin=3.00000 editsqsmoothwidth=100 editsqsmoothcycles=600 -smoothdata_isa=0 smoothfunctype=0 smoothqmin=12.0000 smoothboxwidth=9 -interpolateqmin_isa=0 qmininterpolationtype=0 -dampfq_isa=0 dampfqtype=0 dampfqwidth=23.0000 - -##### SqGr_Optimization Setup -ftmethod=0 -## S(q) qmin=0.010000 qmax=27.000000 qgrid=0.000000 -## G(r) rmin=0.010000 rmax=60.000000 rgrid=0.010000 -## SqOptimization sqoptfunction=1 -optqmin=15.0000 optqmax=40.0000 optqgrid=0.000000 -optrmin=0.000000 optrmax=2.20000 optrgrid=0.0200000 -maxiter=20 relstep=0.000000 weighttype=0 weightfunc=0 -fitbkgmult_isa=0 fitsampmut_isa=1 fitpolariz_isa=1 -fitoblique_isa=0 fitfluores_isa=0 -fitrulandw_isa=0 fitenergya_isa=1 fitenergyb_isa=1 -fitsimurulandw_isa=1 fitDetEdepfluores_isa=0 fitDetEdepquadra_isa=0 -fitDetEdepspline_isa=0 fitDetTCoefElastic_isa=0 fitDetTCoefFluores_isa=0 -fitDetTcoefquadra_isa=0 fitDetTcoefspline_isa=0 - -##### Save&Plot Settings -datatype=GrData iqcorrtype=Int iqsimutype=SimuIq -sqcorrtype=Oblin sqtofqtype=DampFq -gropttype=OptFq miscdatatype=AtomASF -##### start data -#F si325_mesh_300k_nor_4-8.gr -#D Mon Apr 21 21:17:23 2008 -#C -#S 1 G(r) -#D -#L r(A) G(r) d_r d_Gr - 1.000000e-002 1.105784e-001 -7.539822e-004 1.802192e-003 - 2.000000e-002 2.199684e-001 -1.507964e-003 3.521449e-003 - 3.000000e-002 3.270088e-001 -2.261947e-003 5.079115e-003 - 4.000000e-002 4.305913e-001 -3.015929e-003 6.404892e-003 - 5.000000e-002 5.296853e-001 -3.769911e-003 7.440527e-003 - 6.000000e-002 6.233606e-001 -4.523893e-003 8.142955e-003 - 7.000000e-002 7.108060e-001 -5.277876e-003 8.486813e-003 - 8.000000e-002 7.913456e-001 -6.031858e-003 8.466340e-003 - 9.000000e-002 8.644501e-001 -6.785840e-003 8.096858e-003 - 1.000000e-001 9.297440e-001 -7.539822e-003 7.416456e-003 - 1.100000e-001 9.870074e-001 -8.293804e-003 6.489448e-003 - 1.200000e-001 1.036173e+000 -9.047787e-003 5.415684e-003 - 1.300000e-001 1.077320e+000 -9.801769e-003 4.355248e-003 - 1.400000e-001 1.110658e+000 -1.055575e-002 3.575199e-003 - 1.500000e-001 1.136512e+000 -1.130973e-002 3.413945e-003 - 1.600000e-001 1.155303e+000 -1.206372e-002 3.933423e-003 - 1.700000e-001 1.167523e+000 -1.281770e-002 4.815308e-003 - 1.800000e-001 1.173706e+000 -1.357168e-002 5.750912e-003 - 1.900000e-001 1.174409e+000 -1.432566e-002 6.564132e-003 - 2.000000e-001 1.170178e+000 -1.507964e-002 7.161793e-003 - 2.100000e-001 1.161530e+000 -1.583363e-002 7.497930e-003 - 2.200000e-001 1.148926e+000 -1.658761e-002 7.559422e-003 - 2.300000e-001 1.132758e+000 -1.734159e-002 7.360973e-003 - 2.400000e-001 1.113332e+000 -1.809557e-002 6.944106e-003 - 2.500000e-001 1.090867e+000 -1.884956e-002 6.378589e-003 - 2.600000e-001 1.065491e+000 -1.960354e-002 5.765230e-003 - 2.700000e-001 1.037248e+000 -2.035752e-002 5.235051e-003 - 2.800000e-001 1.006114e+000 -2.111150e-002 4.928301e-003 - 2.900000e-001 9.720130e-001 -2.186548e-002 4.934465e-003 - 3.000000e-001 9.348463e-001 -2.261947e-002 5.230497e-003 - 3.100000e-001 8.945173e-001 -2.337345e-002 5.699069e-003 - 3.200000e-001 8.509643e-001 -2.412743e-002 6.203244e-003 - 3.300000e-001 8.041928e-001 -2.488141e-002 6.634315e-003 - 3.400000e-001 7.543052e-001 -2.563540e-002 6.921889e-003 - 3.500000e-001 7.015281e-001 -2.638938e-002 7.030258e-003 - 3.600000e-001 6.462341e-001 -2.714336e-002 6.953808e-003 - 3.700000e-001 5.889563e-001 -2.789734e-002 6.714182e-003 - 3.800000e-001 5.303932e-001 -2.865132e-002 6.358755e-003 - 3.900000e-001 4.714050e-001 -2.940531e-002 5.958818e-003 - 4.000000e-001 4.129979e-001 -3.015929e-002 5.603599e-003 - 4.100000e-001 3.562986e-001 -3.091327e-002 5.383204e-003 - 4.200000e-001 3.025178e-001 -3.166725e-002 5.357170e-003 - 4.300000e-001 2.529049e-001 -3.242124e-002 5.525004e-003 - 4.400000e-001 2.086951e-001 -3.317522e-002 5.827505e-003 - 4.500000e-001 1.710513e-001 -3.392920e-002 6.178212e-003 - 4.600000e-001 1.410036e-001 -3.468318e-002 6.495339e-003 - 4.700000e-001 1.193896e-001 -3.543716e-002 6.718036e-003 - 4.800000e-001 1.067979e-001 -3.619115e-002 6.810827e-003 - 4.900000e-001 1.035199e-001 -3.694513e-002 6.763386e-003 - 5.000000e-001 1.095111e-001 -3.769911e-002 6.589230e-003 - 5.100000e-001 1.243654e-001 -3.845309e-002 6.324106e-003 - 5.200000e-001 1.473058e-001 -3.920708e-002 6.023134e-003 - 5.300000e-001 1.771912e-001 -3.996106e-002 5.754161e-003 - 5.400000e-001 2.125414e-001 -4.071504e-002 5.583831e-003 - 5.500000e-001 2.515800e-001 -4.146902e-002 5.556275e-003 - 5.600000e-001 2.922938e-001 -4.222300e-002 5.674577e-003 - 5.700000e-001 3.325075e-001 -4.297699e-002 5.900045e-003 - 5.800000e-001 3.699698e-001 -4.373097e-002 6.170277e-003 - 5.900000e-001 4.024484e-001 -4.448495e-002 6.421243e-003 - 6.000000e-001 4.278290e-001 -4.523893e-002 6.601852e-003 - 6.100000e-001 4.442137e-001 -4.599292e-002 6.680300e-003 - 6.200000e-001 4.500142e-001 -4.674690e-002 6.645748e-003 - 6.300000e-001 4.440342e-001 -4.750088e-002 6.508004e-003 - 6.400000e-001 4.255377e-001 -4.825486e-002 6.296085e-003 - 6.500000e-001 3.942979e-001 -4.900884e-002 6.055106e-003 - 6.600000e-001 3.506241e-001 -4.976283e-002 5.839825e-003 - 6.700000e-001 2.953646e-001 -5.051681e-002 5.702920e-003 - 6.800000e-001 2.298832e-001 -5.127079e-002 5.679014e-003 - 6.900000e-001 1.560117e-001 -5.202477e-002 5.771555e-003 - 7.000000e-001 7.597746e-002 -5.277876e-002 5.951898e-003 - 7.100000e-001 -7.689663e-003 -5.353274e-002 6.171453e-003 - 7.200000e-001 -9.226787e-002 -5.428672e-002 6.378052e-003 - 7.300000e-001 -1.749662e-001 -5.504070e-002 6.528334e-003 - 7.400000e-001 -2.530538e-001 -5.579468e-002 6.594295e-003 - 7.500000e-001 -3.239902e-001 -5.654867e-002 6.565757e-003 - 7.600000e-001 -3.855483e-001 -5.730265e-002 6.450587e-003 - 7.700000e-001 -4.359263e-001 -5.805663e-002 6.273433e-003 - 7.800000e-001 -4.738401e-001 -5.881061e-002 6.072606e-003 - 7.900000e-001 -4.985928e-001 -5.956460e-002 5.893988e-003 - 8.000000e-001 -5.101162e-001 -6.031858e-002 5.780941e-003 - 8.100000e-001 -5.089818e-001 -6.107256e-002 5.761594e-003 - 8.200000e-001 -4.963805e-001 -6.182654e-002 5.838919e-003 - 8.300000e-001 -4.740701e-001 -6.258052e-002 5.989978e-003 - 8.400000e-001 -4.442934e-001 -6.333451e-002 6.174951e-003 - 8.500000e-001 -4.096707e-001 -6.408849e-002 6.349969e-003 - 8.600000e-001 -3.730710e-001 -6.484247e-002 6.477655e-003 - 8.700000e-001 -3.374671e-001 -6.559645e-002 6.533361e-003 - 8.800000e-001 -3.057848e-001 -6.635044e-002 6.507902e-003 - 8.900000e-001 -2.807502e-001 -6.710442e-002 6.408064e-003 - 9.000000e-001 -2.647453e-001 -6.785840e-002 6.255446e-003 - 9.100000e-001 -2.596788e-001 -6.861238e-002 6.083424e-003 - 9.200000e-001 -2.668793e-001 -6.936636e-002 5.931448e-003 - 9.300000e-001 -2.870165e-001 -7.012035e-002 5.836197e-003 - 9.400000e-001 -3.200559e-001 -7.087433e-002 5.821081e-003 - 9.500000e-001 -3.652491e-001 -7.162831e-002 5.888409e-003 - 9.600000e-001 -4.211612e-001 -7.238229e-002 6.018856e-003 - 9.700000e-001 -4.857356e-001 -7.313628e-002 6.178633e-003 - 9.800000e-001 -5.563918e-001 -7.389026e-002 6.329966e-003 - 9.900000e-001 -6.301529e-001 -7.464424e-002 6.440191e-003 - 1.000000e+000 -7.037970e-001 -7.539822e-002 6.487525e-003 - 1.010000e+000 -7.740236e-001 -7.615220e-002 6.463841e-003 - 1.020000e+000 -8.376278e-001 -7.690619e-002 6.375286e-003 - 1.030000e+000 -8.916727e-001 -7.766017e-002 6.241211e-003 - 1.040000e+000 -9.336516e-001 -7.841415e-002 6.091214e-003 - 1.050000e+000 -9.616294e-001 -7.916813e-002 5.959806e-003 - 1.060000e+000 -9.743579e-001 -7.992212e-002 5.878559e-003 - 1.070000e+000 -9.713566e-001 -8.067610e-002 5.867219e-003 - 1.080000e+000 -9.529540e-001 -8.143008e-002 5.927372e-003 - 1.090000e+000 -9.202882e-001 -8.218406e-002 6.042140e-003 - 1.100000e+000 -8.752634e-001 -8.293804e-002 6.182140e-003 - 1.110000e+000 -8.204662e-001 -8.369203e-002 6.314303e-003 - 1.120000e+000 -7.590436e-001 -8.444601e-002 6.409810e-003 - 1.130000e+000 -6.945489e-001 -8.519999e-002 6.449393e-003 - 1.140000e+000 -6.307639e-001 -8.595397e-002 6.426019e-003 - 1.150000e+000 -5.715048e-001 -8.670796e-002 6.345560e-003 - 1.160000e+000 -5.204225e-001 -8.746194e-002 6.225748e-003 - 1.170000e+000 -4.808080e-001 -8.821592e-002 6.093310e-003 - 1.180000e+000 -4.554131e-001 -8.896990e-002 5.978935e-003 - 1.190000e+000 -4.462949e-001 -8.972388e-002 5.910177e-003 - 1.200000e+000 -4.546953e-001 -9.047787e-002 5.903784e-003 - 1.210000e+000 -4.809597e-001 -9.123185e-002 5.960464e-003 - 1.220000e+000 -5.245015e-001 -9.198583e-002 6.064856e-003 - 1.230000e+000 -5.838154e-001 -9.273981e-002 6.190699e-003 - 1.240000e+000 -6.565378e-001 -9.349380e-002 6.308476e-003 - 1.250000e+000 -7.395547e-001 -9.424778e-002 6.392427e-003 - 1.260000e+000 -8.291489e-001 -9.500176e-002 6.425383e-003 - 1.270000e+000 -9.211832e-001 -9.575574e-002 6.401314e-003 - 1.280000e+000 -1.011307e+000 -9.650973e-002 6.325974e-003 - 1.290000e+000 -1.095180e+000 -9.726371e-002 6.215888e-003 - 1.300000e+000 -1.168696e+000 -9.801769e-002 6.095581e-003 - 1.310000e+000 -1.228198e+000 -9.877167e-002 5.992836e-003 - 1.320000e+000 -1.270680e+000 -9.952565e-002 5.932217e-003 - 1.330000e+000 -1.293949e+000 -1.002796e-001 5.928311e-003 - 1.340000e+000 -1.296753e+000 -1.010336e-001 5.981279e-003 - 1.350000e+000 -1.278861e+000 -1.017876e-001 6.076977e-003 - 1.360000e+000 -1.241088e+000 -1.025416e-001 6.191562e-003 - 1.370000e+000 -1.185270e+000 -1.032956e-001 6.298272e-003 - 1.380000e+000 -1.114183e+000 -1.040495e-001 6.373738e-003 - 1.390000e+000 -1.031413e+000 -1.048035e-001 6.402445e-003 - 1.400000e+000 -9.411808e-001 -1.055575e-001 6.379124e-003 - 1.410000e+000 -8.481324e-001 -1.063115e-001 6.309362e-003 - 1.420000e+000 -7.571032e-001 -1.070655e-001 6.208593e-003 - 1.430000e+000 -6.728701e-001 -1.078195e-001 6.099410e-003 - 1.440000e+000 -5.999032e-001 -1.085734e-001 6.007094e-003 - 1.450000e+000 -5.421301e-001 -1.093274e-001 5.953678e-003 - 1.460000e+000 -5.027256e-001 -1.100814e-001 5.951944e-003 - 1.470000e+000 -4.839381e-001 -1.108354e-001 6.001616e-003 - 1.480000e+000 -4.869629e-001 -1.115894e-001 6.089599e-003 - 1.490000e+000 -5.118681e-001 -1.123434e-001 6.194121e-003 - 1.500000e+000 -5.575799e-001 -1.130973e-001 6.290802e-003 - 1.510000e+000 -6.219268e-001 -1.138513e-001 6.358379e-003 - 1.520000e+000 -7.017428e-001 -1.146053e-001 6.382824e-003 - 1.530000e+000 -7.930236e-001 -1.153593e-001 6.359590e-003 - 1.540000e+000 -8.911297e-001 -1.161133e-001 6.294168e-003 - 1.550000e+000 -9.910247e-001 -1.168672e-001 6.201089e-003 - 1.560000e+000 -1.087538e+000 -1.176212e-001 6.101313e-003 - 1.570000e+000 -1.175640e+000 -1.183752e-001 6.017986e-003 - 1.580000e+000 -1.250708e+000 -1.191292e-001 5.970977e-003 - 1.590000e+000 -1.308781e+000 -1.198832e-001 5.971498e-003 - 1.600000e+000 -1.346777e+000 -1.206372e-001 6.018826e-003 - 1.610000e+000 -1.362671e+000 -1.213911e-001 6.100655e-003 - 1.620000e+000 -1.355618e+000 -1.221451e-001 6.196887e-003 - 1.630000e+000 -1.326016e+000 -1.228991e-001 6.285131e-003 - 1.640000e+000 -1.275498e+000 -1.236531e-001 6.345933e-003 - 1.650000e+000 -1.206870e+000 -1.244071e-001 6.366574e-003 - 1.660000e+000 -1.123978e+000 -1.251610e-001 6.343177e-003 - 1.670000e+000 -1.031516e+000 -1.259150e-001 6.281203e-003 - 1.680000e+000 -9.347922e-001 -1.266690e-001 6.194445e-003 - 1.690000e+000 -8.394571e-001 -1.274230e-001 6.102498e-003 - 1.700000e+000 -7.512059e-001 -1.281770e-001 6.026720e-003 - 1.710000e+000 -6.754769e-001 -1.289310e-001 5.985162e-003 - 1.720000e+000 -6.171570e-001 -1.296849e-001 5.987713e-003 - 1.730000e+000 -5.803118e-001 -1.304389e-001 6.033256e-003 - 1.740000e+000 -5.679542e-001 -1.311929e-001 6.110105e-003 - 1.750000e+000 -5.818638e-001 -1.319469e-001 6.199534e-003 - 1.760000e+000 -6.224687e-001 -1.327009e-001 6.280808e-003 - 1.770000e+000 -6.887963e-001 -1.334549e-001 6.335992e-003 - 1.780000e+000 -7.784959e-001 -1.342088e-001 6.353482e-003 - 1.790000e+000 -8.879351e-001 -1.349628e-001 6.329965e-003 - 1.800000e+000 -1.012364e+000 -1.357168e-001 6.270855e-003 - 1.810000e+000 -1.146144e+000 -1.364708e-001 6.189290e-003 - 1.820000e+000 -1.283020e+000 -1.372248e-001 6.103669e-003 - 1.830000e+000 -1.416443e+000 -1.379787e-001 6.033819e-003 - 1.840000e+000 -1.539898e+000 -1.387327e-001 5.996275e-003 - 1.850000e+000 -1.647254e+000 -1.394867e-001 5.999867e-003 - 1.860000e+000 -1.733083e+000 -1.402407e-001 6.043224e-003 - 1.870000e+000 -1.792967e+000 -1.409947e-001 6.115280e-003 - 1.880000e+000 -1.823741e+000 -1.417487e-001 6.198552e-003 - 1.890000e+000 -1.823692e+000 -1.425026e-001 6.273785e-003 - 1.900000e+000 -1.792673e+000 -1.432566e-001 6.324403e-003 - 1.910000e+000 -1.732148e+000 -1.440106e-001 6.339796e-003 - 1.920000e+000 -1.645147e+000 -1.447646e-001 6.317144e-003 - 1.930000e+000 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6.048045e-003 - 2.100000e+000 -1.529484e+000 -1.583363e-001 6.019170e-003 - 2.110000e+000 -1.652962e+000 -1.590902e-001 6.026293e-003 - 2.120000e+000 -1.746122e+000 -1.598442e-001 6.067328e-003 - 2.130000e+000 -1.798339e+000 -1.605982e-001 6.131987e-003 - 2.140000e+000 -1.799929e+000 -1.613522e-001 6.204715e-003 - 2.150000e+000 -1.742611e+000 -1.621062e-001 6.268712e-003 - 2.160000e+000 -1.619919e+000 -1.628602e-001 6.309771e-003 - 2.170000e+000 -1.427555e+000 -1.636141e-001 6.319129e-003 - 2.180000e+000 -1.163652e+000 -1.643681e-001 6.295027e-003 - 2.190000e+000 -8.289467e-001 -1.651221e-001 6.242954e-003 - 2.200000e+000 -4.268475e-001 -1.658761e-001 6.174596e-003 - 2.210000e+000 3.660895e-002 -1.666301e-001 6.105538e-003 - 2.220000e+000 5.529041e-001 -1.673841e-001 6.051890e-003 - 2.230000e+000 1.111288e+000 -1.681380e-001 6.026395e-003 - 2.240000e+000 1.699122e+000 -1.688920e-001 6.035072e-003 - 2.250000e+000 2.302301e+000 -1.696460e-001 6.075557e-003 - 2.260000e+000 2.905732e+000 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3.317497e+000 -1.832177e-001 6.303804e-003 - 2.440000e+000 2.768292e+000 -1.839717e-001 6.279921e-003 - 2.450000e+000 2.216027e+000 -1.847256e-001 6.231642e-003 - 2.460000e+000 1.673492e+000 -1.854796e-001 6.169863e-003 - 2.470000e+000 1.152381e+000 -1.862336e-001 6.108720e-003 - 2.480000e+000 6.629607e-001 -1.869876e-001 6.062477e-003 - 2.490000e+000 2.138015e-001 -1.877416e-001 6.042074e-003 - 2.500000e+000 -1.884112e-001 -1.884956e-001 6.052262e-003 - 2.510000e+000 -5.389853e-001 -1.892495e-001 6.090326e-003 - 2.520000e+000 -8.352506e-001 -1.900035e-001 6.146899e-003 - 2.530000e+000 -1.076508e+000 -1.907575e-001 6.208532e-003 - 2.540000e+000 -1.263910e+000 -1.915115e-001 6.261071e-003 - 2.550000e+000 -1.400272e+000 -1.922655e-001 6.292855e-003 - 2.560000e+000 -1.489839e+000 -1.930195e-001 6.297077e-003 - 2.570000e+000 -1.538008e+000 -1.937734e-001 6.273027e-003 - 2.580000e+000 -1.551027e+000 -1.945274e-001 6.226174e-003 - 2.590000e+000 -1.535680e+000 -1.952814e-001 6.167088e-003 - 2.600000e+000 -1.498977e+000 -1.960354e-001 6.109283e-003 - 2.610000e+000 -1.447860e+000 -1.967894e-001 6.066226e-003 - 2.620000e+000 -1.388926e+000 -1.975433e-001 6.048068e-003 - 2.630000e+000 -1.328199e+000 -1.982973e-001 6.058997e-003 - 2.640000e+000 -1.270938e+000 -1.990513e-001 6.096127e-003 - 2.650000e+000 -1.221494e+000 -1.998053e-001 6.150344e-003 - 2.660000e+000 -1.183216e+000 -2.005593e-001 6.208784e-003 - 2.670000e+000 -1.158418e+000 -2.013133e-001 6.258037e-003 - 2.680000e+000 -1.148379e+000 -2.020672e-001 6.287168e-003 - 2.690000e+000 -1.153406e+000 -2.028212e-001 6.289939e-003 - 2.700000e+000 -1.172919e+000 -2.035752e-001 6.265957e-003 - 2.710000e+000 -1.205579e+000 -2.043292e-001 6.220702e-003 - 2.720000e+000 -1.249439e+000 -2.050832e-001 6.164438e-003 - 2.730000e+000 -1.302100e+000 -2.058371e-001 6.110095e-003 - 2.740000e+000 -1.360883e+000 -2.065911e-001 6.070384e-003 - 2.750000e+000 -1.422997e+000 -2.073451e-001 6.054705e-003 - 2.760000e+000 -1.485693e+000 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2.930000e+000 -1.671284e+000 -2.209168e-001 6.253740e-003 - 2.940000e+000 -1.662691e+000 -2.216708e-001 6.278387e-003 - 2.950000e+000 -1.657923e+000 -2.224248e-001 6.278710e-003 - 2.960000e+000 -1.657092e+000 -2.231787e-001 6.254857e-003 - 2.970000e+000 -1.660054e+000 -2.239327e-001 6.212308e-003 - 2.980000e+000 -1.666438e+000 -2.246867e-001 6.160768e-003 - 2.990000e+000 -1.675686e+000 -2.254407e-001 6.112127e-003 - 3.000000e+000 -1.687101e+000 -2.261947e-001 6.077779e-003 - 3.010000e+000 -1.699901e+000 -2.269487e-001 6.065836e-003 - 3.020000e+000 -1.713270e+000 -2.277026e-001 6.079035e-003 - 3.030000e+000 -1.726413e+000 -2.284566e-001 6.114026e-003 - 3.040000e+000 -1.738604e+000 -2.292106e-001 6.162317e-003 - 3.050000e+000 -1.749228e+000 -2.299646e-001 6.212515e-003 - 3.060000e+000 -1.757815e+000 -2.307186e-001 6.253107e-003 - 3.070000e+000 -1.764064e+000 -2.314725e-001 6.275032e-003 - 3.080000e+000 -1.767855e+000 -2.322265e-001 6.273536e-003 - 3.090000e+000 -1.769253e+000 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3.260000e+000 -1.870596e+000 -2.457982e-001 6.079886e-003 - 3.270000e+000 -1.890796e+000 -2.465522e-001 6.071061e-003 - 3.280000e+000 -1.909271e+000 -2.473062e-001 6.085618e-003 - 3.290000e+000 -1.924961e+000 -2.480602e-001 6.119949e-003 - 3.300000e+000 -1.936846e+000 -2.488141e-001 6.165839e-003 - 3.310000e+000 -1.944001e+000 -2.495681e-001 6.212596e-003 - 3.320000e+000 -1.945645e+000 -2.503221e-001 6.249629e-003 - 3.330000e+000 -1.941185e+000 -2.510761e-001 6.268791e-003 - 3.340000e+000 -1.930261e+000 -2.518301e-001 6.266038e-003 - 3.350000e+000 -1.912772e+000 -2.525840e-001 6.242194e-003 - 3.360000e+000 -1.888895e+000 -2.533380e-001 6.202747e-003 - 3.370000e+000 -1.859097e+000 -2.540920e-001 6.156722e-003 - 3.380000e+000 -1.824120e+000 -2.548460e-001 6.114748e-003 - 3.390000e+000 -1.784964e+000 -2.556000e-001 6.086627e-003 - 3.400000e+000 -1.742850e+000 -2.563540e-001 6.078938e-003 - 3.410000e+000 -1.699161e+000 -2.571079e-001 6.093356e-003 - 3.420000e+000 -1.655384e+000 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3.590000e+000 -1.170037e+000 -2.706796e-001 6.263290e-003 - 3.600000e+000 -1.041710e+000 -2.714336e-001 6.257888e-003 - 3.610000e+000 -8.771255e-001 -2.721876e-001 6.233267e-003 - 3.620000e+000 -6.724891e-001 -2.729416e-001 6.194997e-003 - 3.630000e+000 -4.247576e-001 -2.736955e-001 6.151776e-003 - 3.640000e+000 -1.318216e-001 -2.744495e-001 6.113550e-003 - 3.650000e+000 2.073298e-001 -2.752035e-001 6.089223e-003 - 3.660000e+000 5.924716e-001 -2.759575e-001 6.084477e-003 - 3.670000e+000 1.022039e+000 -2.767115e-001 6.100320e-003 - 3.680000e+000 1.493063e+000 -2.774655e-001 6.132843e-003 - 3.690000e+000 2.001153e+000 -2.782194e-001 6.174266e-003 - 3.700000e+000 2.540524e+000 -2.789734e-001 6.214918e-003 - 3.710000e+000 3.104075e+000 -2.797274e-001 6.245530e-003 - 3.720000e+000 3.683516e+000 -2.804814e-001 6.259278e-003 - 3.730000e+000 4.269547e+000 -2.812354e-001 6.253185e-003 - 3.740000e+000 4.852071e+000 -2.819894e-001 6.228691e-003 - 3.750000e+000 5.420449e+000 -2.827433e-001 6.191344e-003 - 3.760000e+000 5.963786e+000 -2.834973e-001 6.149650e-003 - 3.770000e+000 6.471236e+000 -2.842513e-001 6.113221e-003 - 3.780000e+000 6.932311e+000 -2.850053e-001 6.090561e-003 - 3.790000e+000 7.337199e+000 -2.857593e-001 6.086983e-003 - 3.800000e+000 7.677062e+000 -2.865132e-001 6.103248e-003 - 3.810000e+000 7.944315e+000 -2.872672e-001 6.135398e-003 - 3.820000e+000 8.132870e+000 -2.880212e-001 6.175801e-003 - 3.830000e+000 8.238336e+000 -2.887752e-001 6.215086e-003 - 3.840000e+000 8.258170e+000 -2.895292e-001 6.244352e-003 - 3.850000e+000 8.191770e+000 -2.902832e-001 6.257127e-003 - 3.860000e+000 8.040505e+000 -2.910371e-001 6.250694e-003 - 3.870000e+000 7.807685e+000 -2.917911e-001 6.226607e-003 - 3.880000e+000 7.498465e+000 -2.925451e-001 6.190355e-003 - 3.890000e+000 7.119692e+000 -2.932991e-001 6.150213e-003 - 3.900000e+000 6.679695e+000 -2.940531e-001 6.115433e-003 - 3.910000e+000 6.188032e+000 -2.948071e-001 6.094103e-003 - 3.920000e+000 5.655192e+000 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6.238956e-003 - 4.260000e+000 -1.018967e+000 -3.211964e-001 6.214976e-003 - 4.270000e+000 -9.082017e-001 -3.219504e-001 6.181238e-003 - 4.280000e+000 -7.672686e-001 -3.227044e-001 6.145515e-003 - 4.290000e+000 -5.938690e-001 -3.234584e-001 6.116136e-003 - 4.300000e+000 -3.865776e-001 -3.242124e-001 6.100020e-003 - 4.310000e+000 -1.449573e-001 -3.249663e-001 6.100979e-003 - 4.320000e+000 1.303658e-001 -3.257203e-001 6.118748e-003 - 4.330000e+000 4.376674e-001 -3.264743e-001 6.149068e-003 - 4.340000e+000 7.741317e-001 -3.272283e-001 6.184790e-003 - 4.350000e+000 1.135899e+000 -3.279823e-001 6.217639e-003 - 4.360000e+000 1.518149e+000 -3.287363e-001 6.240143e-003 - 4.370000e+000 1.915223e+000 -3.294902e-001 6.247268e-003 - 4.380000e+000 2.320771e+000 -3.302442e-001 6.237458e-003 - 4.390000e+000 2.727923e+000 -3.309982e-001 6.212943e-003 - 4.400000e+000 3.129478e+000 -3.317522e-001 6.179268e-003 - 4.410000e+000 3.518103e+000 -3.325062e-001 6.144118e-003 - 4.420000e+000 3.886536e+000 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3.332860e+000 -3.460778e-001 6.152111e-003 - 4.600000e+000 2.941264e+000 -3.468318e-001 6.185903e-003 - 4.610000e+000 2.538432e+000 -3.475858e-001 6.216376e-003 - 4.620000e+000 2.130434e+000 -3.483398e-001 6.236605e-003 - 4.630000e+000 1.723080e+000 -3.490938e-001 6.242081e-003 - 4.640000e+000 1.321805e+000 -3.498478e-001 6.231646e-003 - 4.650000e+000 9.315629e-001 -3.506017e-001 6.207713e-003 - 4.660000e+000 5.567417e-001 -3.513557e-001 6.175751e-003 - 4.670000e+000 2.010969e-001 -3.521097e-001 6.143110e-003 - 4.680000e+000 -1.322974e-001 -3.528637e-001 6.117374e-003 - 4.690000e+000 -4.410765e-001 -3.536177e-001 6.104572e-003 - 4.700000e+000 -7.235930e-001 -3.543716e-001 6.107692e-003 - 4.710000e+000 -9.789064e-001 -3.551256e-001 6.125930e-003 - 4.720000e+000 -1.206754e+000 -3.558796e-001 6.154912e-003 - 4.730000e+000 -1.407504e+000 -3.566336e-001 6.187809e-003 - 4.740000e+000 -1.582099e+000 -3.573876e-001 6.217007e-003 - 4.750000e+000 -1.731979e+000 -3.581416e-001 6.235859e-003 - 4.760000e+000 -1.859002e+000 -3.588955e-001 6.240144e-003 - 4.770000e+000 -1.965353e+000 -3.596495e-001 6.228933e-003 - 4.780000e+000 -2.053453e+000 -3.604035e-001 6.204774e-003 - 4.790000e+000 -2.125863e+000 -3.611575e-001 6.173156e-003 - 4.800000e+000 -2.185191e+000 -3.619115e-001 6.141323e-003 - 4.810000e+000 -2.234004e+000 -3.626655e-001 6.116657e-003 - 4.820000e+000 -2.274749e+000 -3.634194e-001 6.104934e-003 - 4.830000e+000 -2.309685e+000 -3.641734e-001 6.108901e-003 - 4.840000e+000 -2.340817e+000 -3.649274e-001 6.127591e-003 - 4.850000e+000 -2.369859e+000 -3.656814e-001 6.156582e-003 - 4.860000e+000 -2.398197e+000 -3.664354e-001 6.189119e-003 - 4.870000e+000 -2.426877e+000 -3.671893e-001 6.217754e-003 - 4.880000e+000 -2.456603e+000 -3.679433e-001 6.236052e-003 - 4.890000e+000 -2.487749e+000 -3.686973e-001 6.239990e-003 - 4.900000e+000 -2.520384e+000 -3.694513e-001 6.228780e-003 - 4.910000e+000 -2.554314e+000 -3.702053e-001 6.205015e-003 - 4.920000e+000 -2.589123e+000 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5.090000e+000 -2.826813e+000 -3.837770e-001 6.115191e-003 - 5.100000e+000 -2.815985e+000 -3.845309e-001 6.134136e-003 - 5.110000e+000 -2.803671e+000 -3.852849e-001 6.162036e-003 - 5.120000e+000 -2.789681e+000 -3.860389e-001 6.192381e-003 - 5.130000e+000 -2.773614e+000 -3.867929e-001 6.218186e-003 - 5.140000e+000 -2.754854e+000 -3.875469e-001 6.233598e-003 - 5.150000e+000 -2.732588e+000 -3.883008e-001 6.235168e-003 - 5.160000e+000 -2.705823e+000 -3.890548e-001 6.222566e-003 - 5.170000e+000 -2.673433e+000 -3.898088e-001 6.198652e-003 - 5.180000e+000 -2.634201e+000 -3.905628e-001 6.168863e-003 - 5.190000e+000 -2.586888e+000 -3.913168e-001 6.140036e-003 - 5.200000e+000 -2.530290e+000 -3.920708e-001 6.118863e-003 - 5.210000e+000 -2.463318e+000 -3.928247e-001 6.110299e-003 - 5.220000e+000 -2.385061e+000 -3.935787e-001 6.116346e-003 - 5.230000e+000 -2.294863e+000 -3.943327e-001 6.135549e-003 - 5.240000e+000 -2.192374e+000 -3.950867e-001 6.163378e-003 - 5.250000e+000 -2.077610e+000 -3.958407e-001 6.193358e-003 - 5.260000e+000 -1.950987e+000 -3.965947e-001 6.218627e-003 - 5.270000e+000 -1.813344e+000 -3.973486e-001 6.233490e-003 - 5.280000e+000 -1.665952e+000 -3.981026e-001 6.234658e-003 - 5.290000e+000 -1.510499e+000 -3.988566e-001 6.221922e-003 - 5.300000e+000 -1.349061e+000 -3.996106e-001 6.198189e-003 - 5.310000e+000 -1.184058e+000 -4.003646e-001 6.168856e-003 - 5.320000e+000 -1.018189e+000 -4.011185e-001 6.140642e-003 - 5.330000e+000 -8.543563e-001 -4.018725e-001 6.120061e-003 - 5.340000e+000 -6.955838e-001 -4.026265e-001 6.111879e-003 - 5.350000e+000 -5.449206e-001 -4.033805e-001 6.117946e-003 - 5.360000e+000 -4.053484e-001 -4.041345e-001 6.136743e-003 - 5.370000e+000 -2.796867e-001 -4.048885e-001 6.163776e-003 - 5.380000e+000 -1.705042e-001 -4.056424e-001 6.192709e-003 - 5.390000e+000 -8.003744e-002 -4.063964e-001 6.216879e-003 - 5.400000e+000 -1.012246e-002 -4.071504e-001 6.230815e-003 - 5.410000e+000 3.786032e-002 -4.079044e-001 6.231423e-003 - 5.420000e+000 6.302458e-002 -4.086584e-001 6.218623e-003 - 5.430000e+000 6.499957e-002 -4.094123e-001 6.195355e-003 - 5.440000e+000 4.393390e-002 -4.101663e-001 6.166945e-003 - 5.450000e+000 4.825130e-004 -4.109203e-001 6.139937e-003 - 5.460000e+000 -6.422218e-002 -4.116743e-001 6.120603e-003 - 5.470000e+000 -1.486127e-001 -4.124283e-001 6.113451e-003 - 5.480000e+000 -2.507403e-001 -4.131823e-001 6.120118e-003 - 5.490000e+000 -3.683363e-001 -4.139362e-001 6.138969e-003 - 5.500000e+000 -4.988795e-001 -4.146902e-001 6.165522e-003 - 5.510000e+000 -6.396640e-001 -4.154442e-001 6.193571e-003 - 5.520000e+000 -7.878669e-001 -4.161982e-001 6.216669e-003 - 5.530000e+000 -9.406112e-001 -4.169522e-001 6.229593e-003 - 5.540000e+000 -1.095022e+000 -4.177062e-001 6.229482e-003 - 5.550000e+000 -1.248274e+000 -4.184601e-001 6.216427e-003 - 5.560000e+000 -1.397634e+000 -4.192141e-001 6.193437e-003 - 5.570000e+000 -1.540483e+000 -4.199681e-001 6.165795e-003 - 5.580000e+000 -1.674344e+000 -4.207221e-001 6.139890e-003 - 5.590000e+000 -1.796886e+000 -4.214761e-001 6.121758e-003 - 5.600000e+000 -1.905934e+000 -4.222300e-001 6.115638e-003 - 5.610000e+000 -1.999463e+000 -4.229840e-001 6.122931e-003 - 5.620000e+000 -2.075599e+000 -4.237380e-001 6.141856e-003 - 5.630000e+000 -2.132613e+000 -4.244920e-001 6.167907e-003 - 5.640000e+000 -2.168920e+000 -4.252460e-001 6.194974e-003 - 5.650000e+000 -2.183082e+000 -4.260000e-001 6.216801e-003 - 5.660000e+000 -2.173820e+000 -4.267539e-001 6.228409e-003 - 5.670000e+000 -2.140026e+000 -4.275079e-001 6.227177e-003 - 5.680000e+000 -2.080793e+000 -4.282619e-001 6.213389e-003 - 5.690000e+000 -1.995444e+000 -4.290159e-001 6.190169e-003 - 5.700000e+000 -1.883575e+000 -4.297699e-001 6.162812e-003 - 5.710000e+000 -1.745098e+000 -4.305239e-001 6.137618e-003 - 5.720000e+000 -1.580294e+000 -4.312778e-001 6.120448e-003 - 5.730000e+000 -1.389856e+000 -4.320318e-001 6.115325e-003 - 5.740000e+000 -1.174941e+000 -4.327858e-001 6.123444e-003 - 5.750000e+000 -9.372060e-001 -4.335398e-001 6.142874e-003 - 5.760000e+000 -6.788413e-001 -4.342938e-001 6.169053e-003 - 5.770000e+000 -4.025839e-001 -4.350477e-001 6.195914e-003 - 5.780000e+000 -1.117195e-001 -4.358017e-001 6.217323e-003 - 5.790000e+000 1.899369e-001 -4.365557e-001 6.228462e-003 - 5.800000e+000 4.980797e-001 -4.373097e-001 6.226875e-003 - 5.810000e+000 8.079733e-001 -4.380637e-001 6.212974e-003 - 5.820000e+000 1.114533e+000 -4.388177e-001 6.189942e-003 - 5.830000e+000 1.412428e+000 -4.395716e-001 6.163056e-003 - 5.840000e+000 1.696194e+000 -4.403256e-001 6.138516e-003 - 5.850000e+000 1.960375e+000 -4.410796e-001 6.122029e-003 - 5.860000e+000 2.199656e+000 -4.418336e-001 6.117445e-003 - 5.870000e+000 2.409017e+000 -4.425876e-001 6.125813e-003 - 5.880000e+000 2.583876e+000 -4.433415e-001 6.145128e-003 - 5.890000e+000 2.720232e+000 -4.440955e-001 6.170839e-003 - 5.900000e+000 2.814793e+000 -4.448495e-001 6.196972e-003 - 5.910000e+000 2.865088e+000 -4.456035e-001 6.217547e-003 - 5.920000e+000 2.869557e+000 -4.463575e-001 6.227920e-003 - 5.930000e+000 2.827616e+000 -4.471115e-001 6.225791e-003 - 5.940000e+000 2.739689e+000 -4.478654e-001 6.211677e-003 - 5.950000e+000 2.607214e+000 -4.486194e-001 6.188794e-003 - 5.960000e+000 2.432609e+000 -4.493734e-001 6.162362e-003 - 5.970000e+000 2.219216e+000 -4.501274e-001 6.138453e-003 - 5.980000e+000 1.971206e+000 -4.508814e-001 6.122596e-003 - 5.990000e+000 1.693462e+000 -4.516354e-001 6.118458e-003 - 6.000000e+000 1.391438e+000 -4.523893e-001 6.126947e-003 - 6.010000e+000 1.070997e+000 -4.531433e-001 6.145994e-003 - 6.020000e+000 7.382436e-001 -4.538973e-001 6.171081e-003 - 6.030000e+000 3.993431e-001 -4.546513e-001 6.196356e-003 - 6.040000e+000 6.034626e-002 -4.554053e-001 6.216016e-003 - 6.050000e+000 -2.729810e-001 -4.561592e-001 6.225612e-003 - 6.060000e+000 -5.953141e-001 -4.569132e-001 6.223015e-003 - 6.070000e+000 -9.019075e-001 -4.576672e-001 6.208852e-003 - 6.080000e+000 -1.188710e+000 -4.584212e-001 6.186368e-003 - 6.090000e+000 -1.452451e+000 -4.591752e-001 6.160719e-003 - 6.100000e+000 -1.690700e+000 -4.599292e-001 6.137827e-003 - 6.110000e+000 -1.901892e+000 -4.606831e-001 6.123020e-003 - 6.120000e+000 -2.085324e+000 -4.614371e-001 6.119755e-003 - 6.130000e+000 -2.241119e+000 -4.621911e-001 6.128771e-003 - 6.140000e+000 -2.370165e+000 -4.629451e-001 6.147917e-003 - 6.150000e+000 -2.474029e+000 -4.636991e-001 6.172696e-003 - 6.160000e+000 -2.554846e+000 -4.644531e-001 6.197368e-003 - 6.170000e+000 -2.615197e+000 -4.652070e-001 6.216307e-003 - 6.180000e+000 -2.657978e+000 -4.659610e-001 6.225263e-003 - 6.190000e+000 -2.686256e+000 -4.667150e-001 6.222282e-003 - 6.200000e+000 -2.703130e+000 -4.674690e-001 6.208104e-003 - 6.210000e+000 -2.711598e+000 -4.682230e-001 6.186001e-003 - 6.220000e+000 -2.714430e+000 -4.689769e-001 6.161060e-003 - 6.230000e+000 -2.714060e+000 -4.697309e-001 6.139050e-003 - 6.240000e+000 -2.712485e+000 -4.704849e-001 6.125086e-003 - 6.250000e+000 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6.175761e-003 - 6.420000e+000 -1.682966e+000 -4.840566e-001 6.198906e-003 - 6.430000e+000 -1.421877e+000 -4.848106e-001 6.215985e-003 - 6.440000e+000 -1.125507e+000 -4.855646e-001 6.223154e-003 - 6.450000e+000 -7.941368e-001 -4.863185e-001 6.218838e-003 - 6.460000e+000 -4.288090e-001 -4.870725e-001 6.204061e-003 - 6.470000e+000 -3.135871e-002 -4.878265e-001 6.182215e-003 - 6.480000e+000 3.955719e-001 -4.885805e-001 6.158325e-003 - 6.490000e+000 8.485353e-001 -4.893345e-001 6.137921e-003 - 6.500000e+000 1.323299e+000 -4.900884e-001 6.125756e-003 - 6.510000e+000 1.814882e+000 -4.908424e-001 6.124663e-003 - 6.520000e+000 2.317618e+000 -4.915964e-001 6.134864e-003 - 6.530000e+000 2.825229e+000 -4.923504e-001 6.153919e-003 - 6.540000e+000 3.330925e+000 -4.931044e-001 6.177338e-003 - 6.550000e+000 3.827525e+000 -4.938584e-001 6.199676e-003 - 6.560000e+000 4.307586e+000 -4.946123e-001 6.215800e-003 - 6.570000e+000 4.763562e+000 -4.953663e-001 6.222047e-003 - 6.580000e+000 5.187964e+000 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3.874085e+000 -5.089380e-001 6.137702e-003 - 6.760000e+000 3.404116e+000 -5.096920e-001 6.127148e-003 - 6.770000e+000 2.937399e+000 -5.104460e-001 6.127374e-003 - 6.780000e+000 2.483977e+000 -5.111999e-001 6.138296e-003 - 6.790000e+000 2.053449e+000 -5.119539e-001 6.157309e-003 - 6.800000e+000 1.654701e+000 -5.127079e-001 6.179933e-003 - 6.810000e+000 1.295673e+000 -5.134619e-001 6.200894e-003 - 6.820000e+000 9.831380e-001 -5.142159e-001 6.215358e-003 - 6.830000e+000 7.225244e-001 -5.149699e-001 6.220010e-003 - 6.840000e+000 5.177757e-001 -5.157238e-001 6.213772e-003 - 6.850000e+000 3.712560e-001 -5.164778e-001 6.198035e-003 - 6.860000e+000 2.837033e-001 -5.172318e-001 6.176355e-003 - 6.870000e+000 2.542334e-001 -5.179858e-001 6.153680e-003 - 6.880000e+000 2.803929e-001 -5.187398e-001 6.135238e-003 - 6.890000e+000 3.582598e-001 -5.194938e-001 6.125319e-003 - 6.900000e+000 4.825872e-001 -5.202477e-001 6.126244e-003 - 6.910000e+000 6.469854e-001 -5.210017e-001 6.137794e-003 - 6.920000e+000 8.441353e-001 -5.217557e-001 6.157273e-003 - 6.930000e+000 1.066025e+000 -5.225097e-001 6.180171e-003 - 6.940000e+000 1.304203e+000 -5.232637e-001 6.201252e-003 - 6.950000e+000 1.550036e+000 -5.240176e-001 6.215760e-003 - 6.960000e+000 1.794962e+000 -5.247716e-001 6.220480e-003 - 6.970000e+000 2.030740e+000 -5.255256e-001 6.214424e-003 - 6.980000e+000 2.249670e+000 -5.262796e-001 6.199033e-003 - 6.990000e+000 2.444795e+000 -5.270336e-001 6.177862e-003 - 7.000000e+000 2.610065e+000 -5.277876e-001 6.155797e-003 - 7.010000e+000 2.740471e+000 -5.285415e-001 6.137953e-003 - 7.020000e+000 2.832135e+000 -5.292955e-001 6.128485e-003 - 7.030000e+000 2.882361e+000 -5.300495e-001 6.129587e-003 - 7.040000e+000 2.889643e+000 -5.308035e-001 6.140960e-003 - 7.050000e+000 2.853643e+000 -5.315575e-001 6.159896e-003 - 7.060000e+000 2.775125e+000 -5.323115e-001 6.181949e-003 - 7.070000e+000 2.655861e+000 -5.330654e-001 6.202006e-003 - 7.080000e+000 2.498514e+000 -5.338194e-001 6.215475e-003 - 7.090000e+000 2.306495e+000 -5.345734e-001 6.219305e-003 - 7.100000e+000 2.083819e+000 -5.353274e-001 6.212644e-003 - 7.110000e+000 1.834935e+000 -5.360814e-001 6.197013e-003 - 7.120000e+000 1.564575e+000 -5.368353e-001 6.175974e-003 - 7.130000e+000 1.277594e+000 -5.375893e-001 6.154345e-003 - 7.140000e+000 9.788285e-001 -5.383433e-001 6.137111e-003 - 7.150000e+000 6.729621e-001 -5.390973e-001 6.128256e-003 - 7.160000e+000 3.644169e-001 -5.398513e-001 6.129810e-003 - 7.170000e+000 5.725944e-002 -5.406053e-001 6.141353e-003 - 7.180000e+000 -2.448687e-001 -5.413592e-001 6.160127e-003 - 7.190000e+000 -5.387993e-001 -5.421132e-001 6.181719e-003 - 7.200000e+000 -8.218641e-001 -5.428672e-001 6.201126e-003 - 7.210000e+000 -1.091901e+000 -5.436212e-001 6.213909e-003 - 7.220000e+000 -1.347241e+000 -5.443752e-001 6.217184e-003 - 7.230000e+000 -1.586684e+000 -5.451291e-001 6.210243e-003 - 7.240000e+000 -1.809453e+000 -5.458831e-001 6.194700e-003 - 7.250000e+000 -2.015147e+000 -5.466371e-001 6.174133e-003 - 7.260000e+000 -2.203686e+000 -5.473911e-001 6.153296e-003 - 7.270000e+000 -2.375247e+000 -5.481451e-001 6.137035e-003 - 7.280000e+000 -2.530203e+000 -5.488991e-001 6.129155e-003 - 7.290000e+000 -2.669065e+000 -5.496530e-001 6.131498e-003 - 7.300000e+000 -2.792425e+000 -5.504070e-001 6.143495e-003 - 7.310000e+000 -2.900902e+000 -5.511610e-001 6.162309e-003 - 7.320000e+000 -2.995103e+000 -5.519150e-001 6.183535e-003 - 7.330000e+000 -3.075580e+000 -5.526690e-001 6.202258e-003 - 7.340000e+000 -3.142801e+000 -5.534230e-001 6.214181e-003 - 7.350000e+000 -3.197130e+000 -5.541769e-001 6.216590e-003 - 7.360000e+000 -3.238812e+000 -5.549309e-001 6.208934e-003 - 7.370000e+000 -3.267962e+000 -5.556849e-001 6.192946e-003 - 7.380000e+000 -3.284570e+000 -5.564389e-001 6.172262e-003 - 7.390000e+000 -3.288507e+000 -5.571929e-001 6.151623e-003 - 7.400000e+000 -3.279534e+000 -5.579468e-001 6.135801e-003 - 7.410000e+000 -3.257326e+000 -5.587008e-001 6.128477e-003 - 7.420000e+000 -3.221494e+000 -5.594548e-001 6.131357e-003 - 7.430000e+000 -3.171615e+000 -5.602088e-001 6.143757e-003 - 7.440000e+000 -3.107264e+000 -5.609628e-001 6.162773e-003 - 7.450000e+000 -3.028055e+000 -5.617168e-001 6.183998e-003 - 7.460000e+000 -2.933678e+000 -5.624707e-001 6.202569e-003 - 7.470000e+000 -2.823945e+000 -5.632247e-001 6.214286e-003 - 7.480000e+000 -2.698833e+000 -5.639787e-001 6.216542e-003 - 7.490000e+000 -2.558527e+000 -5.647327e-001 6.208881e-003 - 7.500000e+000 -2.403466e+000 -5.654867e-001 6.193090e-003 - 7.510000e+000 -2.234373e+000 -5.662407e-001 6.172806e-003 - 7.520000e+000 -2.052296e+000 -5.669946e-001 6.152709e-003 - 7.530000e+000 -1.858629e+000 -5.677486e-001 6.137463e-003 - 7.540000e+000 -1.655127e+000 -5.685026e-001 6.130616e-003 - 7.550000e+000 -1.443910e+000 -5.692566e-001 6.133750e-003 - 7.560000e+000 -1.227451e+000 -5.700106e-001 6.146095e-003 - 7.570000e+000 -1.008550e+000 -5.707645e-001 6.164726e-003 - 7.580000e+000 -7.902942e-001 -5.715185e-001 6.185282e-003 - 7.590000e+000 -5.759941e-001 -5.722725e-001 6.203004e-003 - 7.600000e+000 -3.691133e-001 -5.730265e-001 6.213832e-003 - 7.610000e+000 -1.731754e-001 -5.737805e-001 6.215300e-003 - 7.620000e+000 8.339132e-003 -5.745345e-001 6.207073e-003 - 7.630000e+000 1.721064e-001 -5.752884e-001 6.191009e-003 - 7.640000e+000 3.150803e-001 -5.760424e-001 6.170755e-003 - 7.650000e+000 4.346155e-001 -5.767964e-001 6.150941e-003 - 7.660000e+000 5.285883e-001 -5.775504e-001 6.136125e-003 - 7.670000e+000 5.955096e-001 -5.783044e-001 6.129724e-003 - 7.680000e+000 6.346248e-001 -5.790584e-001 6.133194e-003 - 7.690000e+000 6.459958e-001 -5.798123e-001 6.145680e-003 - 7.700000e+000 6.305582e-001 -5.805663e-001 6.164230e-003 - 7.710000e+000 5.901524e-001 -5.813203e-001 6.184524e-003 - 7.720000e+000 5.275215e-001 -5.820743e-001 6.201902e-003 - 7.730000e+000 4.462768e-001 -5.828283e-001 6.212428e-003 - 7.740000e+000 3.508278e-001 -5.835822e-001 6.213768e-003 - 7.750000e+000 2.462770e-001 -5.843362e-001 6.205683e-003 - 7.760000e+000 1.382830e-001 -5.850902e-001 6.190076e-003 - 7.770000e+000 3.289347e-002 -5.858442e-001 6.170570e-003 - 7.780000e+000 -6.364660e-002 -5.865982e-001 6.151694e-003 - 7.790000e+000 -1.451046e-001 -5.873522e-001 6.137856e-003 - 7.800000e+000 -2.054812e-001 -5.881061e-001 6.132292e-003 - 7.810000e+000 -2.392345e-001 -5.888601e-001 6.136296e-003 - 7.820000e+000 -2.414980e-001 -5.896141e-001 6.148896e-003 - 7.830000e+000 -2.082837e-001 -5.903681e-001 6.167108e-003 - 7.840000e+000 -1.366624e-001 -5.911221e-001 6.186664e-003 - 7.850000e+000 -2.491182e-002 -5.918760e-001 6.203025e-003 - 7.860000e+000 1.273730e-001 -5.926300e-001 6.212427e-003 - 7.870000e+000 3.192146e-001 -5.933840e-001 6.212717e-003 - 7.880000e+000 5.482349e-001 -5.941380e-001 6.203822e-003 - 7.890000e+000 8.106889e-001 -5.948920e-001 6.187758e-003 - 7.900000e+000 1.101548e+000 -5.956460e-001 6.168193e-003 - 7.910000e+000 1.414631e+000 -5.963999e-001 6.149632e-003 - 7.920000e+000 1.742785e+000 -5.971539e-001 6.136386e-003 - 7.930000e+000 2.078094e+000 -5.979079e-001 6.131553e-003 - 7.940000e+000 2.412130e+000 -5.986619e-001 6.136273e-003 - 7.950000e+000 2.736223e+000 -5.994159e-001 6.149448e-003 - 7.960000e+000 3.041732e+000 -6.001699e-001 6.168015e-003 - 7.970000e+000 3.320335e+000 -6.009238e-001 6.187689e-003 - 7.980000e+000 3.564293e+000 -6.016778e-001 6.203978e-003 - 7.990000e+000 3.766702e+000 -6.024318e-001 6.213203e-003 - 8.000000e+000 3.921712e+000 -6.031858e-001 6.213311e-003 - 8.010000e+000 4.024710e+000 -6.039398e-001 6.204315e-003 - 8.020000e+000 4.072449e+000 -6.046937e-001 6.188283e-003 - 8.030000e+000 4.063140e+000 -6.054477e-001 6.168888e-003 - 8.040000e+000 3.996477e+000 -6.062017e-001 6.150584e-003 - 8.050000e+000 3.873618e+000 -6.069557e-001 6.137593e-003 - 8.060000e+000 3.697112e+000 -6.077097e-001 6.132906e-003 - 8.070000e+000 3.470771e+000 -6.084637e-001 6.137570e-003 - 8.080000e+000 3.199516e+000 -6.092176e-001 6.150433e-003 - 8.090000e+000 2.889169e+000 -6.099716e-001 6.168438e-003 - 8.100000e+000 2.546242e+000 -6.107256e-001 6.187369e-003 - 8.110000e+000 2.177692e+000 -6.114796e-001 6.202848e-003 - 8.120000e+000 1.790687e+000 -6.122336e-001 6.211339e-003 - 8.130000e+000 1.392368e+000 -6.129876e-001 6.210927e-003 - 8.140000e+000 9.896326e-001 -6.137415e-001 6.201734e-003 - 8.150000e+000 5.889436e-001 -6.144955e-001 6.185883e-003 - 8.160000e+000 1.961669e-001 -6.152495e-001 6.167034e-003 - 8.170000e+000 -1.835499e-001 -6.160035e-001 6.149557e-003 - 8.180000e+000 -5.458586e-001 -6.167575e-001 6.137535e-003 - 8.190000e+000 -8.872482e-001 -6.175114e-001 6.133789e-003 - 8.200000e+000 -1.205040e+000 -6.182654e-001 6.139201e-003 - 8.210000e+000 -1.497346e+000 -6.190194e-001 6.152497e-003 - 8.220000e+000 -1.762988e+000 -6.197734e-001 6.170562e-003 - 8.230000e+000 -2.001392e+000 -6.205274e-001 6.189198e-003 - 8.240000e+000 -2.212464e+000 -6.212814e-001 6.204108e-003 - 8.250000e+000 -2.396448e+000 -6.220353e-001 6.211880e-003 - 8.260000e+000 -2.553791e+000 -6.227893e-001 6.210740e-003 - 8.270000e+000 -2.684999e+000 -6.235433e-001 6.200933e-003 - 8.280000e+000 -2.790526e+000 -6.242973e-001 6.184673e-003 - 8.290000e+000 -2.870670e+000 -6.250513e-001 6.165651e-003 - 8.300000e+000 -2.925501e+000 -6.258052e-001 6.148219e-003 - 8.310000e+000 -2.954827e+000 -6.265592e-001 6.136391e-003 - 8.320000e+000 -2.958183e+000 -6.273132e-001 6.132893e-003 - 8.330000e+000 -2.934865e+000 -6.280672e-001 6.138511e-003 - 8.340000e+000 -2.883990e+000 -6.288212e-001 6.151904e-003 - 8.350000e+000 -2.804586e+000 -6.295752e-001 6.169937e-003 - 8.360000e+000 -2.695707e+000 -6.303291e-001 6.188439e-003 - 8.370000e+000 -2.556564e+000 -6.310831e-001 6.203189e-003 - 8.380000e+000 -2.386664e+000 -6.318371e-001 6.210868e-003 - 8.390000e+000 -2.185949e+000 -6.325911e-001 6.209796e-003 - 8.400000e+000 -1.954925e+000 -6.333451e-001 6.200284e-003 - 8.410000e+000 -1.694774e+000 -6.340991e-001 6.184564e-003 - 8.420000e+000 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8.590000e+000 2.880114e+000 -6.476707e-001 6.141718e-003 - 8.600000e+000 2.817884e+000 -6.484247e-001 6.155378e-003 - 8.610000e+000 2.711768e+000 -6.491787e-001 6.173078e-003 - 8.620000e+000 2.565926e+000 -6.499327e-001 6.190724e-003 - 8.630000e+000 2.385483e+000 -6.506867e-001 6.204274e-003 - 8.640000e+000 2.176343e+000 -6.514406e-001 6.210659e-003 - 8.650000e+000 1.944980e+000 -6.521946e-001 6.208452e-003 - 8.660000e+000 1.698204e+000 -6.529486e-001 6.198175e-003 - 8.670000e+000 1.442921e+000 -6.537026e-001 6.182184e-003 - 8.680000e+000 1.185896e+000 -6.544566e-001 6.164142e-003 - 8.690000e+000 9.335277e-001 -6.552106e-001 6.148200e-003 - 8.700000e+000 6.916384e-001 -6.559645e-001 6.138036e-003 - 8.710000e+000 4.652952e-001 -6.567185e-001 6.135987e-003 - 8.720000e+000 2.586653e-001 -6.574725e-001 6.142483e-003 - 8.730000e+000 7.490966e-002 -6.582265e-001 6.155953e-003 - 8.740000e+000 -8.388014e-002 -6.589805e-001 6.173210e-003 - 8.750000e+000 -2.167023e-001 -6.597344e-001 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6.147447e-003 - 9.090000e+000 -3.479029e+000 -6.853698e-001 6.139037e-003 - 9.100000e+000 -3.589997e+000 -6.861238e-001 6.138562e-003 - 9.110000e+000 -3.687562e+000 -6.868778e-001 6.146125e-003 - 9.120000e+000 -3.770974e+000 -6.876318e-001 6.159942e-003 - 9.130000e+000 -3.839580e+000 -6.883858e-001 6.176780e-003 - 9.140000e+000 -3.892832e+000 -6.891398e-001 6.192733e-003 - 9.150000e+000 -3.930299e+000 -6.898937e-001 6.204132e-003 - 9.160000e+000 -3.951688e+000 -6.906477e-001 6.208375e-003 - 9.170000e+000 -3.956866e+000 -6.914017e-001 6.204501e-003 - 9.180000e+000 -3.945884e+000 -6.921557e-001 6.193399e-003 - 9.190000e+000 -3.919007e+000 -6.929097e-001 6.177608e-003 - 9.200000e+000 -3.876730e+000 -6.936636e-001 6.160758e-003 - 9.210000e+000 -3.819805e+000 -6.944176e-001 6.146748e-003 - 9.220000e+000 -3.749242e+000 -6.951716e-001 6.138838e-003 - 9.230000e+000 -3.666317e+000 -6.959256e-001 6.138876e-003 - 9.240000e+000 -3.572553e+000 -6.966796e-001 6.146852e-003 - 9.250000e+000 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6.203467e-003 - 9.420000e+000 -1.979918e+000 -7.102513e-001 6.206918e-003 - 9.430000e+000 -1.931595e+000 -7.110052e-001 6.202497e-003 - 9.440000e+000 -1.878758e+000 -7.117592e-001 6.191230e-003 - 9.450000e+000 -1.818784e+000 -7.125132e-001 6.175711e-003 - 9.460000e+000 -1.749153e+000 -7.132672e-001 6.159517e-003 - 9.470000e+000 -1.667559e+000 -7.140212e-001 6.146401e-003 - 9.480000e+000 -1.572012e+000 -7.147752e-001 6.139411e-003 - 9.490000e+000 -1.460935e+000 -7.155291e-001 6.140167e-003 - 9.500000e+000 -1.333246e+000 -7.162831e-001 6.148471e-003 - 9.510000e+000 -1.188424e+000 -7.170371e-001 6.162357e-003 - 9.520000e+000 -1.026555e+000 -7.177911e-001 6.178572e-003 - 9.530000e+000 -8.483554e-001 -7.185451e-001 6.193352e-003 - 9.540000e+000 -6.551817e-001 -7.192990e-001 6.203298e-003 - 9.550000e+000 -4.490082e-001 -7.200530e-001 6.206139e-003 - 9.560000e+000 -2.323906e-001 -7.208070e-001 6.201238e-003 - 9.570000e+000 -8.407650e-003 -7.215610e-001 6.189724e-003 - 9.580000e+000 2.194138e-001 -7.223150e-001 6.174248e-003 - 9.590000e+000 4.471888e-001 -7.230690e-001 6.158389e-003 - 9.600000e+000 6.707751e-001 -7.238229e-001 6.145841e-003 - 9.610000e+000 8.858821e-001 -7.245769e-001 6.139552e-003 - 9.620000e+000 1.088185e+000 -7.253309e-001 6.141016e-003 - 9.630000e+000 1.273437e+000 -7.260849e-001 6.149915e-003 - 9.640000e+000 1.437586e+000 -7.268389e-001 6.164194e-003 - 9.650000e+000 1.576877e+000 -7.275928e-001 6.180560e-003 - 9.660000e+000 1.687955e+000 -7.283468e-001 6.195263e-003 - 9.670000e+000 1.767951e+000 -7.291008e-001 6.204957e-003 - 9.680000e+000 1.814562e+000 -7.298548e-001 6.207453e-003 - 9.690000e+000 1.826117e+000 -7.306088e-001 6.202201e-003 - 9.700000e+000 1.801624e+000 -7.313628e-001 6.190402e-003 - 9.710000e+000 1.740813e+000 -7.321167e-001 6.174747e-003 - 9.720000e+000 1.644153e+000 -7.328707e-001 6.158819e-003 - 9.730000e+000 1.512866e+000 -7.336247e-001 6.146277e-003 - 9.740000e+000 1.348919e+000 -7.343787e-001 6.140008e-003 - 9.750000e+000 1.155011e+000 -7.351327e-001 6.141440e-003 - 9.760000e+000 9.345374e-001 -7.358867e-001 6.150201e-003 - 9.770000e+000 6.915529e-001 -7.366406e-001 6.164215e-003 - 9.780000e+000 4.307146e-001 -7.373946e-001 6.180207e-003 - 9.790000e+000 1.572181e-001 -7.381486e-001 6.194476e-003 - 9.800000e+000 -1.232785e-001 -7.389026e-001 6.203757e-003 - 9.810000e+000 -4.047403e-001 -7.396566e-001 6.205946e-003 - 9.820000e+000 -6.808524e-001 -7.404105e-001 6.200562e-003 - 9.830000e+000 -9.451244e-001 -7.411645e-001 6.188847e-003 - 9.840000e+000 -1.191005e+000 -7.419185e-001 6.173488e-003 - 9.850000e+000 -1.412003e+000 -7.426725e-001 6.158015e-003 - 9.860000e+000 -1.601815e+000 -7.434265e-001 6.145998e-003 - 9.870000e+000 -1.754455e+000 -7.441805e-001 6.140212e-003 - 9.880000e+000 -1.864389e+000 -7.449344e-001 6.141976e-003 - 9.890000e+000 -1.926667e+000 -7.456884e-001 6.150839e-003 - 9.900000e+000 -1.937052e+000 -7.464424e-001 6.164696e-003 - 9.910000e+000 -1.892140e+000 -7.471964e-001 6.180300e-003 - 9.920000e+000 -1.789469e+000 -7.479504e-001 6.194033e-003 - 9.930000e+000 -1.627616e+000 -7.487044e-001 6.202745e-003 - 9.940000e+000 -1.406270e+000 -7.494583e-001 6.204461e-003 - 9.950000e+000 -1.126289e+000 -7.502123e-001 6.198817e-003 - 9.960000e+000 -7.897233e-001 -7.509663e-001 6.187134e-003 - 9.970000e+000 -3.998180e-001 -7.517203e-001 6.172125e-003 - 9.980000e+000 3.902139e-002 -7.524743e-001 6.157288e-003 - 9.990000e+000 5.212914e-001 -7.532282e-001 6.146098e-003 - 1.000000e+001 1.040487e+000 -7.539822e-001 6.141200e-003 - 1.001000e+001 1.589226e+000 -7.547362e-001 6.143768e-003 - 1.002000e+001 2.159410e+000 -7.554902e-001 6.153223e-003 - 1.003000e+001 2.742399e+000 -7.562442e-001 6.167375e-003 - 1.004000e+001 3.329218e+000 -7.569982e-001 6.182947e-003 - 1.005000e+001 3.910773e+000 -7.577521e-001 6.196355e-003 - 1.006000e+001 4.478077e+000 -7.585061e-001 6.204526e-003 - 1.007000e+001 5.022484e+000 -7.592601e-001 6.205590e-003 - 1.008000e+001 5.535905e+000 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6.180025e-003 - 3.107000e+001 -1.060538e+000 -2.342623e+000 6.175490e-003 - 3.108000e+001 -9.824705e-001 -2.343377e+000 6.170406e-003 - 3.109000e+001 -8.954551e-001 -2.344131e+000 6.165946e-003 - 3.110000e+001 -7.988646e-001 -2.344885e+000 6.163139e-003 - 3.111000e+001 -6.921999e-001 -2.345639e+000 6.162633e-003 - 3.112000e+001 -5.751129e-001 -2.346393e+000 6.164544e-003 - 3.113000e+001 -4.474270e-001 -2.347147e+000 6.168426e-003 - 3.114000e+001 -3.091515e-001 -2.347901e+000 6.173379e-003 - 3.115000e+001 -1.604920e-001 -2.348655e+000 6.178257e-003 - 3.116000e+001 -1.854315e-003 -2.349409e+000 6.181938e-003 - 3.117000e+001 1.661561e-001 -2.350163e+000 6.183576e-003 - 3.118000e+001 3.427416e-001 -2.350917e+000 6.182799e-003 - 3.119000e+001 5.269238e-001 -2.351671e+000 6.179787e-003 - 3.120000e+001 7.175604e-001 -2.352425e+000 6.175237e-003 - 3.121000e+001 9.133652e-001 -2.353179e+000 6.170198e-003 - 3.122000e+001 1.112932e+000 -2.353933e+000 6.165835e-003 - 3.123000e+001 1.314758e+000 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3.641716e+000 -2.367504e+000 6.173991e-003 - 3.141000e+001 3.647655e+000 -2.368258e+000 6.178716e-003 - 3.142000e+001 3.635098e+000 -2.369012e+000 6.182142e-003 - 3.143000e+001 3.604095e+000 -2.369766e+000 6.183478e-003 - 3.144000e+001 3.554856e+000 -2.370520e+000 6.182419e-003 - 3.145000e+001 3.487764e+000 -2.371274e+000 6.179208e-003 - 3.146000e+001 3.403375e+000 -2.372028e+000 6.174586e-003 - 3.147000e+001 3.302426e+000 -2.372782e+000 6.169618e-003 - 3.148000e+001 3.185834e+000 -2.373536e+000 6.165454e-003 - 3.149000e+001 3.054691e+000 -2.374290e+000 6.163057e-003 - 3.150000e+001 2.910260e+000 -2.375044e+000 6.162983e-003 - 3.151000e+001 2.753957e+000 -2.375798e+000 6.165248e-003 - 3.152000e+001 2.587341e+000 -2.376552e+000 6.169327e-003 - 3.153000e+001 2.412086e+000 -2.377306e+000 6.174274e-003 - 3.154000e+001 2.229957e+000 -2.378060e+000 6.178945e-003 - 3.155000e+001 2.042779e+000 -2.378814e+000 6.182263e-003 - 3.156000e+001 1.852405e+000 -2.379568e+000 6.183465e-003 - 3.157000e+001 1.660675e+000 -2.380322e+000 6.182274e-003 - 3.158000e+001 1.469384e+000 -2.381076e+000 6.178964e-003 - 3.159000e+001 1.280247e+000 -2.381830e+000 6.174300e-003 - 3.160000e+001 1.094857e+000 -2.382584e+000 6.169356e-003 - 3.161000e+001 9.146610e-001 -2.383338e+000 6.165275e-003 - 3.162000e+001 7.409304e-001 -2.384092e+000 6.163004e-003 - 3.163000e+001 5.747406e-001 -2.384846e+000 6.163069e-003 - 3.164000e+001 4.169564e-001 -2.385600e+000 6.165454e-003 - 3.165000e+001 2.682257e-001 -2.386354e+000 6.169607e-003 - 3.166000e+001 1.289803e-001 -2.387108e+000 6.174566e-003 - 3.167000e+001 -5.562476e-004 -2.387862e+000 6.179184e-003 - 3.168000e+001 -1.203527e-001 -2.388616e+000 6.182397e-003 - 3.169000e+001 -2.305479e-001 -2.389370e+000 6.183465e-003 - 3.170000e+001 -3.314239e-001 -2.390124e+000 6.182143e-003 - 3.171000e+001 -4.233739e-001 -2.390878e+000 6.178733e-003 - 3.172000e+001 -5.068687e-001 -2.391632e+000 6.174020e-003 - 3.173000e+001 -5.824220e-001 -2.392386e+000 6.169092e-003 - 3.174000e+001 -6.505563e-001 -2.393140e+000 6.165086e-003 - 3.175000e+001 -7.117720e-001 -2.393894e+000 6.162931e-003 - 3.176000e+001 -7.665204e-001 -2.394648e+000 6.163126e-003 - 3.177000e+001 -8.151819e-001 -2.395402e+000 6.165628e-003 - 3.178000e+001 -8.580513e-001 -2.396156e+000 6.169857e-003 - 3.179000e+001 -8.953301e-001 -2.396909e+000 6.174836e-003 - 3.180000e+001 -9.271258e-001 -2.397663e+000 6.179415e-003 - 3.181000e+001 -9.534597e-001 -2.398417e+000 6.182541e-003 - 3.182000e+001 -9.742802e-001 -2.399171e+000 6.183494e-003 - 3.183000e+001 -9.894834e-001 -2.399925e+000 6.182055e-003 - 3.184000e+001 -9.989374e-001 -2.400679e+000 6.178555e-003 - 3.185000e+001 -1.002510e+000 -2.401433e+000 6.173796e-003 - 3.186000e+001 -1.000100e+000 -2.402187e+000 6.168876e-003 - 3.187000e+001 -9.916621e-001 -2.402941e+000 6.164928e-003 - 3.188000e+001 -9.772384e-001 -2.403695e+000 6.162864e-003 - 3.189000e+001 -9.569787e-001 -2.404449e+000 6.163163e-003 - 3.190000e+001 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3.273000e+001 2.172171e+000 -2.467784e+000 6.182958e-003 - 3.274000e+001 2.243754e+000 -2.468538e+000 6.180781e-003 - 3.275000e+001 2.299849e+000 -2.469292e+000 6.176835e-003 - 3.276000e+001 2.339903e+000 -2.470046e+000 6.172027e-003 - 3.277000e+001 2.363495e+000 -2.470800e+000 6.167466e-003 - 3.278000e+001 2.370350e+000 -2.471554e+000 6.164203e-003 - 3.279000e+001 2.360355e+000 -2.472308e+000 6.162993e-003 - 3.280000e+001 2.333571e+000 -2.473062e+000 6.164112e-003 - 3.281000e+001 2.290248e+000 -2.473816e+000 6.167302e-003 - 3.282000e+001 2.230830e+000 -2.474570e+000 6.171823e-003 - 3.283000e+001 2.155964e+000 -2.475324e+000 6.176630e-003 - 3.284000e+001 2.066499e+000 -2.476078e+000 6.180616e-003 - 3.285000e+001 1.963477e+000 -2.476832e+000 6.182867e-003 - 3.286000e+001 1.848127e+000 -2.477586e+000 6.182866e-003 - 3.287000e+001 1.721846e+000 -2.478340e+000 6.180618e-003 - 3.288000e+001 1.586174e+000 -2.479094e+000 6.176641e-003 - 3.289000e+001 1.442771e+000 -2.479848e+000 6.171851e-003 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6.164514e-003 - 3.307000e+001 -7.125322e-001 -2.493419e+000 6.167817e-003 - 3.308000e+001 -7.522224e-001 -2.494173e+000 6.172338e-003 - 3.309000e+001 -7.825569e-001 -2.494927e+000 6.177028e-003 - 3.310000e+001 -8.038789e-001 -2.495681e+000 6.180806e-003 - 3.311000e+001 -8.165437e-001 -2.496435e+000 6.182800e-003 - 3.312000e+001 -8.209069e-001 -2.497189e+000 6.182554e-003 - 3.313000e+001 -8.173180e-001 -2.497943e+000 6.180125e-003 - 3.314000e+001 -8.061169e-001 -2.498697e+000 6.176075e-003 - 3.315000e+001 -7.876356e-001 -2.499451e+000 6.171338e-003 - 3.316000e+001 -7.622032e-001 -2.500205e+000 6.167009e-003 - 3.317000e+001 -7.301537e-001 -2.500959e+000 6.164090e-003 - 3.318000e+001 -6.918357e-001 -2.501713e+000 6.163258e-003 - 3.319000e+001 -6.476232e-001 -2.502467e+000 6.164703e-003 - 3.320000e+001 -5.979264e-001 -2.503221e+000 6.168091e-003 - 3.321000e+001 -5.432007e-001 -2.503975e+000 6.172635e-003 - 3.322000e+001 -4.839542e-001 -2.504729e+000 6.177284e-003 - 3.323000e+001 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3.340000e+001 6.148457e-001 -2.518301e+000 6.175566e-003 - 3.341000e+001 6.476530e-001 -2.519055e+000 6.170850e-003 - 3.342000e+001 6.772041e-001 -2.519809e+000 6.166657e-003 - 3.343000e+001 7.038472e-001 -2.520563e+000 6.163956e-003 - 3.344000e+001 7.279240e-001 -2.521317e+000 6.163372e-003 - 3.345000e+001 7.497409e-001 -2.522071e+000 6.165040e-003 - 3.346000e+001 7.695410e-001 -2.522825e+000 6.168571e-003 - 3.347000e+001 7.874792e-001 -2.523579e+000 6.173146e-003 - 3.348000e+001 8.036014e-001 -2.524332e+000 6.177708e-003 - 3.349000e+001 8.178288e-001 -2.525086e+000 6.181202e-003 - 3.350000e+001 8.299483e-001 -2.525840e+000 6.182827e-003 - 3.351000e+001 8.396101e-001 -2.526594e+000 6.182208e-003 - 3.352000e+001 8.463323e-001 -2.527348e+000 6.179490e-003 - 3.353000e+001 8.495126e-001 -2.528102e+000 6.175299e-003 - 3.354000e+001 8.484466e-001 -2.528856e+000 6.170603e-003 - 3.355000e+001 8.423533e-001 -2.529610e+000 6.166487e-003 - 3.356000e+001 8.304039e-001 -2.530364e+000 6.163902e-003 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1.121360e-001 -2.605763e+000 6.177722e-003 - 3.457000e+001 2.345479e-001 -2.606517e+000 6.173299e-003 - 3.458000e+001 3.592975e-001 -2.607271e+000 6.168828e-003 - 3.459000e+001 4.852106e-001 -2.608025e+000 6.165342e-003 - 3.460000e+001 6.110773e-001 -2.608779e+000 6.163647e-003 - 3.461000e+001 7.356798e-001 -2.609532e+000 6.164137e-003 - 3.462000e+001 8.578219e-001 -2.610286e+000 6.166696e-003 - 3.463000e+001 9.763556e-001 -2.611040e+000 6.170733e-003 - 3.464000e+001 1.090208e+000 -2.611794e+000 6.175313e-003 - 3.465000e+001 1.198403e+000 -2.612548e+000 6.179378e-003 - 3.466000e+001 1.300081e+000 -2.613302e+000 6.181994e-003 - 3.467000e+001 1.394513e+000 -2.614056e+000 6.182559e-003 - 3.468000e+001 1.481107e+000 -2.614810e+000 6.180944e-003 - 3.469000e+001 1.559416e+000 -2.615564e+000 6.177521e-003 - 3.470000e+001 1.629131e+000 -2.616318e+000 6.173079e-003 - 3.471000e+001 1.690081e+000 -2.617072e+000 6.168641e-003 - 3.472000e+001 1.742214e+000 -2.617826e+000 6.165234e-003 - 3.473000e+001 1.785590e+000 -2.618580e+000 6.163643e-003 - 3.474000e+001 1.820357e+000 -2.619334e+000 6.164238e-003 - 3.475000e+001 1.846739e+000 -2.620088e+000 6.166879e-003 - 3.476000e+001 1.865012e+000 -2.620842e+000 6.170953e-003 - 3.477000e+001 1.875484e+000 -2.621596e+000 6.175518e-003 - 3.478000e+001 1.878485e+000 -2.622350e+000 6.179521e-003 - 3.479000e+001 1.874346e+000 -2.623104e+000 6.182040e-003 - 3.480000e+001 1.863389e+000 -2.623858e+000 6.182498e-003 - 3.481000e+001 1.845922e+000 -2.624612e+000 6.180790e-003 - 3.482000e+001 1.822231e+000 -2.625366e+000 6.177311e-003 - 3.483000e+001 1.792584e+000 -2.626120e+000 6.172863e-003 - 3.484000e+001 1.757235e+000 -2.626874e+000 6.168472e-003 - 3.485000e+001 1.716426e+000 -2.627628e+000 6.165154e-003 - 3.486000e+001 1.670403e+000 -2.628382e+000 6.163674e-003 - 3.487000e+001 1.619423e+000 -2.629136e+000 6.164375e-003 - 3.488000e+001 1.563769e+000 -2.629890e+000 6.167094e-003 - 3.489000e+001 1.503760e+000 -2.630644e+000 6.171198e-003 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6.182335e-003 - 3.507000e+001 3.385649e-001 -2.644216e+000 6.180427e-003 - 3.508000e+001 3.105544e-001 -2.644970e+000 6.176830e-003 - 3.509000e+001 2.891445e-001 -2.645724e+000 6.172374e-003 - 3.510000e+001 2.742375e-001 -2.646478e+000 6.168086e-003 - 3.511000e+001 2.656308e-001 -2.647232e+000 6.164960e-003 - 3.512000e+001 2.630263e-001 -2.647986e+000 6.163718e-003 - 3.513000e+001 2.660425e-001 -2.648740e+000 6.164647e-003 - 3.514000e+001 2.742263e-001 -2.649494e+000 6.167533e-003 - 3.515000e+001 2.870665e-001 -2.650248e+000 6.171706e-003 - 3.516000e+001 3.040062e-001 -2.651002e+000 6.176201e-003 - 3.517000e+001 3.244540e-001 -2.651755e+000 6.179981e-003 - 3.518000e+001 3.477946e-001 -2.652509e+000 6.182174e-003 - 3.519000e+001 3.733970e-001 -2.653263e+000 6.182278e-003 - 3.520000e+001 4.006202e-001 -2.654017e+000 6.180269e-003 - 3.521000e+001 4.288183e-001 -2.654771e+000 6.176608e-003 - 3.522000e+001 4.573428e-001 -2.655525e+000 6.172140e-003 - 3.523000e+001 4.855439e-001 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3.392688e-001 -2.669097e+000 6.167908e-003 - 3.541000e+001 2.736594e-001 -2.669851e+000 6.172131e-003 - 3.542000e+001 2.028108e-001 -2.670605e+000 6.176573e-003 - 3.543000e+001 1.276698e-001 -2.671359e+000 6.180210e-003 - 3.544000e+001 4.933699e-002 -2.672113e+000 6.182205e-003 - 3.545000e+001 -3.095373e-002 -2.672867e+000 6.182100e-003 - 3.546000e+001 -1.118623e-001 -2.673621e+000 6.179922e-003 - 3.547000e+001 -1.919747e-001 -2.674375e+000 6.176173e-003 - 3.548000e+001 -2.698404e-001 -2.675129e+000 6.171718e-003 - 3.549000e+001 -3.440116e-001 -2.675883e+000 6.167585e-003 - 3.550000e+001 -4.130860e-001 -2.676637e+000 6.164729e-003 - 3.551000e+001 -4.757480e-001 -2.677391e+000 6.163811e-003 - 3.552000e+001 -5.308094e-001 -2.678145e+000 6.165042e-003 - 3.553000e+001 -5.772463e-001 -2.678899e+000 6.168136e-003 - 3.554000e+001 -6.142312e-001 -2.679653e+000 6.172374e-003 - 3.555000e+001 -6.411590e-001 -2.680407e+000 6.176778e-003 - 3.556000e+001 -6.576649e-001 -2.681161e+000 6.180330e-003 - 3.557000e+001 -6.636349e-001 -2.681915e+000 6.182213e-003 - 3.558000e+001 -6.592065e-001 -2.682669e+000 6.181997e-003 - 3.559000e+001 -6.447612e-001 -2.683423e+000 6.179730e-003 - 3.560000e+001 -6.209079e-001 -2.684177e+000 6.175937e-003 - 3.561000e+001 -5.884587e-001 -2.684931e+000 6.171491e-003 - 3.562000e+001 -5.483976e-001 -2.685685e+000 6.167420e-003 - 3.563000e+001 -5.018437e-001 -2.686439e+000 6.164662e-003 - 3.564000e+001 -4.500110e-001 -2.687193e+000 6.163857e-003 - 3.565000e+001 -3.941651e-001 -2.687947e+000 6.165189e-003 - 3.566000e+001 -3.355814e-001 -2.688701e+000 6.168347e-003 - 3.567000e+001 -2.755033e-001 -2.689455e+000 6.172599e-003 - 3.568000e+001 -2.151047e-001 -2.690209e+000 6.176962e-003 - 3.569000e+001 -1.554579e-001 -2.690963e+000 6.180428e-003 - 3.570000e+001 -9.750696e-002 -2.691717e+000 6.182201e-003 - 3.571000e+001 -4.204920e-002 -2.692471e+000 6.181873e-003 - 3.572000e+001 1.027577e-002 -2.693225e+000 6.179522e-003 - 3.573000e+001 5.898878e-002 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3.025267e-001 -2.706796e+000 6.163971e-003 - 3.591000e+001 2.814729e-001 -2.707550e+000 6.165508e-003 - 3.592000e+001 2.552154e-001 -2.708304e+000 6.168797e-003 - 3.593000e+001 2.235418e-001 -2.709058e+000 6.173076e-003 - 3.594000e+001 1.863286e-001 -2.709812e+000 6.177356e-003 - 3.595000e+001 1.435629e-001 -2.710566e+000 6.180649e-003 - 3.596000e+001 9.535886e-002 -2.711320e+000 6.182199e-003 - 3.597000e+001 4.196891e-002 -2.712074e+000 6.181649e-003 - 3.598000e+001 -1.621201e-002 -2.712828e+000 6.179128e-003 - 3.599000e+001 -7.864935e-002 -2.713582e+000 6.175218e-003 - 3.600000e+001 -1.446788e-001 -2.714336e+000 6.170820e-003 - 3.601000e+001 -2.135229e-001 -2.715090e+000 6.166950e-003 - 3.602000e+001 -2.843140e-001 -2.715844e+000 6.164505e-003 - 3.603000e+001 -3.561216e-001 -2.716598e+000 6.164049e-003 - 3.604000e+001 -4.279838e-001 -2.717352e+000 6.165688e-003 - 3.605000e+001 -4.989401e-001 -2.718106e+000 6.169040e-003 - 3.606000e+001 -5.680656e-001 -2.718860e+000 6.173329e-003 - 3.607000e+001 -6.345023e-001 -2.719614e+000 6.177563e-003 - 3.608000e+001 -6.974889e-001 -2.720368e+000 6.180765e-003 - 3.609000e+001 -7.563850e-001 -2.721122e+000 6.182200e-003 - 3.610000e+001 -8.106899e-001 -2.721876e+000 6.181536e-003 - 3.611000e+001 -8.600544e-001 -2.722630e+000 6.178928e-003 - 3.612000e+001 -9.042857e-001 -2.723384e+000 6.174978e-003 - 3.613000e+001 -9.433442e-001 -2.724138e+000 6.170594e-003 - 3.614000e+001 -9.773332e-001 -2.724892e+000 6.166791e-003 - 3.615000e+001 -1.006481e+000 -2.725646e+000 6.164448e-003 - 3.616000e+001 -1.031120e+000 -2.726400e+000 6.164105e-003 - 3.617000e+001 -1.051655e+000 -2.727154e+000 6.165843e-003 - 3.618000e+001 -1.068537e+000 -2.727908e+000 6.169256e-003 - 3.619000e+001 -1.082228e+000 -2.728662e+000 6.173555e-003 - 3.620000e+001 -1.093167e+000 -2.729416e+000 6.177745e-003 - 3.621000e+001 -1.101748e+000 -2.730170e+000 6.180860e-003 - 3.622000e+001 -1.108282e+000 -2.730924e+000 6.182184e-003 - 3.623000e+001 -1.112985e+000 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6.166352e-003 - 3.657000e+001 4.856127e-001 -2.757313e+000 6.169924e-003 - 3.658000e+001 5.249871e-001 -2.758067e+000 6.174227e-003 - 3.659000e+001 5.604943e-001 -2.758821e+000 6.178267e-003 - 3.660000e+001 5.924936e-001 -2.759575e+000 6.181113e-003 - 3.661000e+001 6.213544e-001 -2.760329e+000 6.182110e-003 - 3.662000e+001 6.474313e-001 -2.761083e+000 6.181030e-003 - 3.663000e+001 6.710415e-001 -2.761837e+000 6.178123e-003 - 3.664000e+001 6.924455e-001 -2.762591e+000 6.174060e-003 - 3.665000e+001 7.118334e-001 -2.763345e+000 6.169777e-003 - 3.666000e+001 7.293153e-001 -2.764099e+000 6.166266e-003 - 3.667000e+001 7.449177e-001 -2.764853e+000 6.164337e-003 - 3.668000e+001 7.585856e-001 -2.765607e+000 6.164437e-003 - 3.669000e+001 7.701903e-001 -2.766361e+000 6.166543e-003 - 3.670000e+001 7.795408e-001 -2.767115e+000 6.170165e-003 - 3.671000e+001 7.864011e-001 -2.767869e+000 6.174465e-003 - 3.672000e+001 7.905090e-001 -2.768623e+000 6.178449e-003 - 3.673000e+001 7.915976e-001 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3.877760e-001 -2.782194e+000 6.173609e-003 - 3.691000e+001 3.621796e-001 -2.782948e+000 6.169390e-003 - 3.692000e+001 3.398047e-001 -2.783702e+000 6.166032e-003 - 3.693000e+001 3.209547e-001 -2.784456e+000 6.164311e-003 - 3.694000e+001 3.058202e-001 -2.785210e+000 6.164624e-003 - 3.695000e+001 2.944745e-001 -2.785964e+000 6.166899e-003 - 3.696000e+001 2.868728e-001 -2.786718e+000 6.170606e-003 - 3.697000e+001 2.828559e-001 -2.787472e+000 6.174886e-003 - 3.698000e+001 2.821570e-001 -2.788226e+000 6.178752e-003 - 3.699000e+001 2.844117e-001 -2.788980e+000 6.181312e-003 - 3.700000e+001 2.891705e-001 -2.789734e+000 6.181977e-003 - 3.701000e+001 2.959130e-001 -2.790488e+000 6.180596e-003 - 3.702000e+001 3.040637e-001 -2.791242e+000 6.177487e-003 - 3.703000e+001 3.130076e-001 -2.791996e+000 6.173368e-003 - 3.704000e+001 3.221062e-001 -2.792750e+000 6.169190e-003 - 3.705000e+001 3.307126e-001 -2.793504e+000 6.165917e-003 - 3.706000e+001 3.381855e-001 -2.794258e+000 6.164308e-003 - 3.707000e+001 3.439016e-001 -2.795012e+000 6.164735e-003 - 3.708000e+001 3.472669e-001 -2.795766e+000 6.167097e-003 - 3.709000e+001 3.477249e-001 -2.796520e+000 6.170847e-003 - 3.710000e+001 3.447646e-001 -2.797274e+000 6.175116e-003 - 3.711000e+001 3.379253e-001 -2.798028e+000 6.178919e-003 - 3.712000e+001 3.268011e-001 -2.798782e+000 6.181378e-003 - 3.713000e+001 3.110431e-001 -2.799536e+000 6.181929e-003 - 3.714000e+001 2.903611e-001 -2.800290e+000 6.180445e-003 - 3.715000e+001 2.645247e-001 -2.801044e+000 6.177269e-003 - 3.716000e+001 2.333631e-001 -2.801798e+000 6.173132e-003 - 3.717000e+001 1.967656e-001 -2.802552e+000 6.168988e-003 - 3.718000e+001 1.546814e-001 -2.803306e+000 6.165796e-003 - 3.719000e+001 1.071193e-001 -2.804060e+000 6.164293e-003 - 3.720000e+001 5.414833e-002 -2.804814e+000 6.164826e-003 - 3.721000e+001 -4.102545e-003 -2.805568e+000 6.167272e-003 - 3.722000e+001 -6.744406e-002 -2.806322e+000 6.171062e-003 - 3.723000e+001 -1.356265e-001 -2.807076e+000 6.175320e-003 - 3.724000e+001 -2.083400e-001 -2.807830e+000 6.179062e-003 - 3.725000e+001 -2.852147e-001 -2.808584e+000 6.181426e-003 - 3.726000e+001 -3.658220e-001 -2.809338e+000 6.181870e-003 - 3.727000e+001 -4.496764e-001 -2.810092e+000 6.180292e-003 - 3.728000e+001 -5.362380e-001 -2.810846e+000 6.177056e-003 - 3.729000e+001 -6.249158e-001 -2.811600e+000 6.172909e-003 - 3.730000e+001 -7.150724e-001 -2.812354e+000 6.168808e-003 - 3.731000e+001 -8.060294e-001 -2.813108e+000 6.165700e-003 - 3.732000e+001 -8.970738e-001 -2.813862e+000 6.164305e-003 - 3.733000e+001 -9.874647e-001 -2.814616e+000 6.164944e-003 - 3.734000e+001 -1.076441e+000 -2.815370e+000 6.167469e-003 - 3.735000e+001 -1.163232e+000 -2.816124e+000 6.171294e-003 - 3.736000e+001 -1.247059e+000 -2.816878e+000 6.175534e-003 - 3.737000e+001 -1.327152e+000 -2.817632e+000 6.179208e-003 - 3.738000e+001 -1.402753e+000 -2.818386e+000 6.181471e-003 - 3.739000e+001 -1.473123e+000 -2.819140e+000 6.181803e-003 - 3.740000e+001 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6.168437e-003 - 3.757000e+001 -1.280507e+000 -2.832711e+000 6.165500e-003 - 3.758000e+001 -1.179017e+000 -2.833465e+000 6.164320e-003 - 3.759000e+001 -1.069780e+000 -2.834219e+000 6.165170e-003 - 3.760000e+001 -9.535464e-001 -2.834973e+000 6.167853e-003 - 3.761000e+001 -8.311558e-001 -2.835727e+000 6.171746e-003 - 3.762000e+001 -7.035261e-001 -2.836481e+000 6.175949e-003 - 3.763000e+001 -5.716463e-001 -2.837235e+000 6.179492e-003 - 3.764000e+001 -4.365635e-001 -2.837989e+000 6.181559e-003 - 3.765000e+001 -2.993699e-001 -2.838743e+000 6.181675e-003 - 3.766000e+001 -1.611861e-001 -2.839497e+000 6.179814e-003 - 3.767000e+001 -2.314449e-002 -2.840251e+000 6.176406e-003 - 3.768000e+001 1.136289e-001 -2.841005e+000 6.172235e-003 - 3.769000e+001 2.480332e-001 -2.841759e+000 6.168266e-003 - 3.770000e+001 3.790102e-001 -2.842513e+000 6.165414e-003 - 3.771000e+001 5.055625e-001 -2.843267e+000 6.164341e-003 - 3.772000e+001 6.267682e-001 -2.844021e+000 6.165293e-003 - 3.773000e+001 7.417951e-001 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1.423374e+000 -2.857593e+000 6.181626e-003 - 3.791000e+001 1.389085e+000 -2.858347e+000 6.181536e-003 - 3.792000e+001 1.347501e+000 -2.859101e+000 6.179503e-003 - 3.793000e+001 1.298811e+000 -2.859855e+000 6.175995e-003 - 3.794000e+001 1.243228e+000 -2.860609e+000 6.171822e-003 - 3.795000e+001 1.181008e+000 -2.861363e+000 6.167945e-003 - 3.796000e+001 1.112463e+000 -2.862117e+000 6.165260e-003 - 3.797000e+001 1.037974e+000 -2.862871e+000 6.164388e-003 - 3.798000e+001 9.580063e-001 -2.863624e+000 6.165529e-003 - 3.799000e+001 8.731202e-001 -2.864378e+000 6.168417e-003 - 3.800000e+001 7.839792e-001 -2.865132e+000 6.172383e-003 - 3.801000e+001 6.913529e-001 -2.865886e+000 6.176510e-003 - 3.802000e+001 5.961166e-001 -2.866640e+000 6.179846e-003 - 3.803000e+001 4.992442e-001 -2.867394e+000 6.181624e-003 - 3.804000e+001 4.017972e-001 -2.868148e+000 6.181436e-003 - 3.805000e+001 3.049073e-001 -2.868902e+000 6.179329e-003 - 3.806000e+001 2.097548e-001 -2.869656e+000 6.175789e-003 - 3.807000e+001 1.175425e-001 -2.870410e+000 6.171632e-003 - 3.808000e+001 2.946598e-002 -2.871164e+000 6.167820e-003 - 3.809000e+001 -5.331750e-002 -2.871918e+000 6.165233e-003 - 3.810000e+001 -1.297221e-001 -2.872672e+000 6.164471e-003 - 3.811000e+001 -1.987653e-001 -2.873426e+000 6.165708e-003 - 3.812000e+001 -2.595986e-001 -2.874180e+000 6.168656e-003 - 3.813000e+001 -3.115348e-001 -2.874934e+000 6.172631e-003 - 3.814000e+001 -3.540710e-001 -2.875688e+000 6.176714e-003 - 3.815000e+001 -3.869060e-001 -2.876442e+000 6.179961e-003 - 3.816000e+001 -4.099515e-001 -2.877196e+000 6.181624e-003 - 3.817000e+001 -4.233369e-001 -2.877950e+000 6.181321e-003 - 3.818000e+001 -4.274055e-001 -2.878704e+000 6.179123e-003 - 3.819000e+001 -4.227052e-001 -2.879458e+000 6.175535e-003 - 3.820000e+001 -4.099711e-001 -2.880212e+000 6.171386e-003 - 3.821000e+001 -3.901025e-001 -2.880966e+000 6.167634e-003 - 3.822000e+001 -3.641342e-001 -2.881720e+000 6.165147e-003 - 3.823000e+001 -3.332042e-001 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5.108841e-004 -2.895292e+000 6.177083e-003 - 3.841000e+001 -1.531753e-002 -2.896046e+000 6.180184e-003 - 3.842000e+001 -3.401321e-002 -2.896800e+000 6.181650e-003 - 3.843000e+001 -5.506728e-002 -2.897554e+000 6.181147e-003 - 3.844000e+001 -7.797163e-002 -2.898308e+000 6.178791e-003 - 3.845000e+001 -1.022289e-001 -2.899062e+000 6.175126e-003 - 3.846000e+001 -1.273587e-001 -2.899816e+000 6.170997e-003 - 3.847000e+001 -1.529008e-001 -2.900570e+000 6.167359e-003 - 3.848000e+001 -1.784143e-001 -2.901324e+000 6.165051e-003 - 3.849000e+001 -2.034753e-001 -2.902078e+000 6.164608e-003 - 3.850000e+001 -2.276714e-001 -2.902832e+000 6.166130e-003 - 3.851000e+001 -2.505959e-001 -2.903586e+000 6.169263e-003 - 3.852000e+001 -2.718414e-001 -2.904340e+000 6.173281e-003 - 3.853000e+001 -2.909942e-001 -2.905094e+000 6.177255e-003 - 3.854000e+001 -3.076300e-001 -2.905848e+000 6.180266e-003 - 3.855000e+001 -3.213117e-001 -2.906601e+000 6.181623e-003 - 3.856000e+001 -3.315904e-001 -2.907355e+000 6.181014e-003 - 3.857000e+001 -3.380088e-001 -2.908109e+000 6.178579e-003 - 3.858000e+001 -3.401085e-001 -2.908863e+000 6.174882e-003 - 3.859000e+001 -3.374397e-001 -2.909617e+000 6.170775e-003 - 3.860000e+001 -3.295745e-001 -2.910371e+000 6.167207e-003 - 3.861000e+001 -3.161220e-001 -2.911125e+000 6.165004e-003 - 3.862000e+001 -2.967444e-001 -2.911879e+000 6.164676e-003 - 3.863000e+001 -2.711748e-001 -2.912633e+000 6.166299e-003 - 3.864000e+001 -2.392335e-001 -2.913387e+000 6.169495e-003 - 3.865000e+001 -2.008438e-001 -2.914141e+000 6.173525e-003 - 3.866000e+001 -1.560445e-001 -2.914895e+000 6.177456e-003 - 3.867000e+001 -1.049999e-001 -2.915649e+000 6.180382e-003 - 3.868000e+001 -4.800529e-002 -2.916403e+000 6.181628e-003 - 3.869000e+001 1.451207e-002 -2.917157e+000 6.180908e-003 - 3.870000e+001 8.199707e-002 -2.917911e+000 6.178388e-003 - 3.871000e+001 1.537757e-001 -2.918665e+000 6.174647e-003 - 3.872000e+001 2.290689e-001 -2.919419e+000 6.170550e-003 - 3.873000e+001 3.070110e-001 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1.245677e+000 -2.932991e+000 6.169875e-003 - 3.891000e+001 1.253403e+000 -2.933745e+000 6.173918e-003 - 3.892000e+001 1.255756e+000 -2.934499e+000 6.177767e-003 - 3.893000e+001 1.252892e+000 -2.935253e+000 6.180534e-003 - 3.894000e+001 1.244931e+000 -2.936007e+000 6.181583e-003 - 3.895000e+001 1.231944e+000 -2.936761e+000 6.180674e-003 - 3.896000e+001 1.213951e+000 -2.937515e+000 6.178018e-003 - 3.897000e+001 1.190919e+000 -2.938269e+000 6.174227e-003 - 3.898000e+001 1.162768e+000 -2.939023e+000 6.170176e-003 - 3.899000e+001 1.129382e+000 -2.939777e+000 6.166803e-003 - 3.900000e+001 1.090622e+000 -2.940531e+000 6.164888e-003 - 3.901000e+001 1.046349e+000 -2.941285e+000 6.164874e-003 - 3.902000e+001 9.964394e-001 -2.942039e+000 6.166764e-003 - 3.903000e+001 9.408133e-001 -2.942793e+000 6.170119e-003 - 3.904000e+001 8.794523e-001 -2.943547e+000 6.174162e-003 - 3.905000e+001 8.124233e-001 -2.944301e+000 6.177959e-003 - 3.906000e+001 7.398965e-001 -2.945055e+000 6.180633e-003 - 3.907000e+001 6.621597e-001 -2.945809e+000 6.181569e-003 - 3.908000e+001 5.796289e-001 -2.946563e+000 6.180550e-003 - 3.909000e+001 4.928524e-001 -2.947317e+000 6.177813e-003 - 3.910000e+001 4.025090e-001 -2.948071e+000 6.173986e-003 - 3.911000e+001 3.094005e-001 -2.948824e+000 6.169952e-003 - 3.912000e+001 2.144376e-001 -2.949578e+000 6.166643e-003 - 3.913000e+001 1.186206e-001 -2.950332e+000 6.164825e-003 - 3.914000e+001 2.301487e-002 -2.951086e+000 6.164919e-003 - 3.915000e+001 -7.127652e-002 -2.951840e+000 6.166903e-003 - 3.916000e+001 -1.631439e-001 -2.952594e+000 6.170317e-003 - 3.917000e+001 -2.515027e-001 -2.953348e+000 6.174372e-003 - 3.918000e+001 -3.353246e-001 -2.954102e+000 6.178133e-003 - 3.919000e+001 -4.136680e-001 -2.954856e+000 6.180733e-003 - 3.920000e+001 -4.857048e-001 -2.955610e+000 6.181574e-003 - 3.921000e+001 -5.507429e-001 -2.956364e+000 6.180464e-003 - 3.922000e+001 -6.082447e-001 -2.957118e+000 6.177659e-003 - 3.923000e+001 -6.578384e-001 -2.957872e+000 6.173804e-003 - 3.924000e+001 -6.993240e-001 -2.958626e+000 6.169789e-003 - 3.925000e+001 -7.326725e-001 -2.959380e+000 6.166541e-003 - 3.926000e+001 -7.580194e-001 -2.960134e+000 6.164809e-003 - 3.927000e+001 -7.756517e-001 -2.960888e+000 6.164994e-003 - 3.928000e+001 -7.859910e-001 -2.961642e+000 6.167052e-003 - 3.929000e+001 -7.895718e-001 -2.962396e+000 6.170506e-003 - 3.930000e+001 -7.870174e-001 -2.963150e+000 6.174556e-003 - 3.931000e+001 -7.790141e-001 -2.963904e+000 6.178266e-003 - 3.932000e+001 -7.662853e-001 -2.964658e+000 6.180782e-003 - 3.933000e+001 -7.495659e-001 -2.965412e+000 6.181526e-003 - 3.934000e+001 -7.295795e-001 -2.966166e+000 6.180326e-003 - 3.935000e+001 -7.070183e-001 -2.966920e+000 6.177461e-003 - 3.936000e+001 -6.825262e-001 -2.967674e+000 6.173590e-003 - 3.937000e+001 -6.566873e-001 -2.968428e+000 6.169606e-003 - 3.938000e+001 -6.300181e-001 -2.969182e+000 6.166429e-003 - 3.939000e+001 -6.029642e-001 -2.969936e+000 6.164795e-003 - 3.940000e+001 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6.174928e-003 - 3.957000e+001 -3.048669e-001 -2.983508e+000 6.178536e-003 - 3.958000e+001 -3.078284e-001 -2.984262e+000 6.180888e-003 - 3.959000e+001 -3.131681e-001 -2.985016e+000 6.181444e-003 - 3.960000e+001 -3.206758e-001 -2.985770e+000 6.180079e-003 - 3.961000e+001 -3.300596e-001 -2.986524e+000 6.177108e-003 - 3.962000e+001 -3.409480e-001 -2.987278e+000 6.173216e-003 - 3.963000e+001 -3.528960e-001 -2.988032e+000 6.169302e-003 - 3.964000e+001 -3.653948e-001 -2.988786e+000 6.166270e-003 - 3.965000e+001 -3.778859e-001 -2.989540e+000 6.164819e-003 - 3.966000e+001 -3.897782e-001 -2.990294e+000 6.165285e-003 - 3.967000e+001 -4.004676e-001 -2.991047e+000 6.167556e-003 - 3.968000e+001 -4.093589e-001 -2.991801e+000 6.171106e-003 - 3.969000e+001 -4.158873e-001 -2.992555e+000 6.175111e-003 - 3.970000e+001 -4.195408e-001 -2.993309e+000 6.178647e-003 - 3.971000e+001 -4.198802e-001 -2.994063e+000 6.180899e-003 - 3.972000e+001 -4.165576e-001 -2.994817e+000 6.181350e-003 - 3.973000e+001 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6.168939e-003 - 3.990000e+001 5.284572e-002 -3.008389e+000 6.166084e-003 - 3.991000e+001 7.129775e-002 -3.009143e+000 6.164854e-003 - 3.992000e+001 8.627448e-002 -3.009897e+000 6.165534e-003 - 3.993000e+001 9.771673e-002 -3.010651e+000 6.167966e-003 - 3.994000e+001 1.056316e-001 -3.011405e+000 6.171587e-003 - 3.995000e+001 1.100813e-001 -3.012159e+000 6.175558e-003 - 3.996000e+001 1.111718e-001 -3.012913e+000 6.178962e-003 - 3.997000e+001 1.090396e-001 -3.013667e+000 6.181016e-003 - 3.998000e+001 1.038406e-001 -3.014421e+000 6.181246e-003 - 3.999000e+001 9.573941e-002 -3.015175e+000 6.179600e-003 - 4.000000e+001 8.490034e-002 -3.015929e+000 6.176458e-003 - 4.001000e+001 7.148108e-002 -3.016683e+000 6.172543e-003 - 4.002000e+001 5.562870e-002 -3.017437e+000 6.168759e-003 - 4.003000e+001 3.747831e-002 -3.018191e+000 6.165980e-003 - 4.004000e+001 1.715421e-002 -3.018945e+000 6.164850e-003 - 4.005000e+001 -5.226693e-003 -3.019699e+000 6.165628e-003 - 4.006000e+001 -2.954972e-002 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4.023000e+001 -5.411390e-001 -3.033270e+000 6.181084e-003 - 4.024000e+001 -5.603836e-001 -3.034024e+000 6.181116e-003 - 4.025000e+001 -5.767759e-001 -3.034778e+000 6.179301e-003 - 4.026000e+001 -5.902337e-001 -3.035532e+000 6.176058e-003 - 4.027000e+001 -6.007200e-001 -3.036286e+000 6.172135e-003 - 4.028000e+001 -6.082361e-001 -3.037040e+000 6.168437e-003 - 4.029000e+001 -6.128122e-001 -3.037794e+000 6.165819e-003 - 4.030000e+001 -6.144969e-001 -3.038548e+000 6.164887e-003 - 4.031000e+001 -6.133442e-001 -3.039302e+000 6.165855e-003 - 4.032000e+001 -6.094023e-001 -3.040056e+000 6.168498e-003 - 4.033000e+001 -6.027016e-001 -3.040810e+000 6.172204e-003 - 4.034000e+001 -5.932453e-001 -3.041564e+000 6.176115e-003 - 4.035000e+001 -5.810020e-001 -3.042318e+000 6.179328e-003 - 4.036000e+001 -5.659018e-001 -3.043072e+000 6.181104e-003 - 4.037000e+001 -5.478366e-001 -3.043826e+000 6.181034e-003 - 4.038000e+001 -5.266641e-001 -3.044580e+000 6.179135e-003 - 4.039000e+001 -5.022163e-001 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3.520750e-001 -3.058152e+000 6.164927e-003 - 4.057000e+001 3.953040e-001 -3.058906e+000 6.166076e-003 - 4.058000e+001 4.311528e-001 -3.059660e+000 6.168845e-003 - 4.059000e+001 4.585898e-001 -3.060414e+000 6.172593e-003 - 4.060000e+001 4.767462e-001 -3.061168e+000 6.176453e-003 - 4.061000e+001 4.849539e-001 -3.061922e+000 6.179536e-003 - 4.062000e+001 4.827789e-001 -3.062676e+000 6.181132e-003 - 4.063000e+001 4.700465e-001 -3.063430e+000 6.180876e-003 - 4.064000e+001 4.468585e-001 -3.064184e+000 6.178827e-003 - 4.065000e+001 4.136001e-001 -3.064938e+000 6.175459e-003 - 4.066000e+001 3.709371e-001 -3.065692e+000 6.171550e-003 - 4.067000e+001 3.198022e-001 -3.066446e+000 6.168001e-003 - 4.068000e+001 2.613713e-001 -3.067200e+000 6.165633e-003 - 4.069000e+001 1.970308e-001 -3.067954e+000 6.164994e-003 - 4.070000e+001 1.283359e-001 -3.068708e+000 6.166231e-003 - 4.071000e+001 5.696289e-002 -3.069462e+000 6.169055e-003 - 4.072000e+001 -1.534324e-002 -3.070216e+000 6.172812e-003 - 4.073000e+001 -8.682463e-002 -3.070970e+000 6.176632e-003 - 4.074000e+001 -1.557660e-001 -3.071724e+000 6.179635e-003 - 4.075000e+001 -2.205490e-001 -3.072478e+000 6.181129e-003 - 4.076000e+001 -2.797019e-001 -3.073232e+000 6.180770e-003 - 4.077000e+001 -3.319440e-001 -3.073986e+000 6.178642e-003 - 4.078000e+001 -3.762220e-001 -3.074740e+000 6.175236e-003 - 4.079000e+001 -4.117371e-001 -3.075494e+000 6.171338e-003 - 4.080000e+001 -4.379623e-001 -3.076247e+000 6.167848e-003 - 4.081000e+001 -4.546494e-001 -3.077001e+000 6.165573e-003 - 4.082000e+001 -4.618245e-001 -3.077755e+000 6.165040e-003 - 4.083000e+001 -4.597736e-001 -3.078509e+000 6.166372e-003 - 4.084000e+001 -4.490195e-001 -3.079263e+000 6.169260e-003 - 4.085000e+001 -4.302893e-001 -3.080017e+000 6.173035e-003 - 4.086000e+001 -4.044764e-001 -3.080771e+000 6.176823e-003 - 4.087000e+001 -3.725971e-001 -3.081525e+000 6.179752e-003 - 4.088000e+001 -3.357448e-001 -3.082279e+000 6.181146e-003 - 4.089000e+001 -2.950432e-001 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3.589764e-001 -3.095851e+000 6.167584e-003 - 4.107000e+001 3.922804e-001 -3.096605e+000 6.165471e-003 - 4.108000e+001 4.265005e-001 -3.097359e+000 6.165121e-003 - 4.109000e+001 4.616842e-001 -3.098113e+000 6.166615e-003 - 4.110000e+001 4.977755e-001 -3.098867e+000 6.169604e-003 - 4.111000e+001 5.346173e-001 -3.099621e+000 6.173397e-003 - 4.112000e+001 5.719583e-001 -3.100375e+000 6.177116e-003 - 4.113000e+001 6.094655e-001 -3.101129e+000 6.179905e-003 - 4.114000e+001 6.467401e-001 -3.101883e+000 6.181122e-003 - 4.115000e+001 6.833362e-001 -3.102637e+000 6.180490e-003 - 4.116000e+001 7.187813e-001 -3.103391e+000 6.178155e-003 - 4.117000e+001 7.525972e-001 -3.104145e+000 6.174657e-003 - 4.118000e+001 7.843209e-001 -3.104899e+000 6.170803e-003 - 4.119000e+001 8.135224e-001 -3.105653e+000 6.167483e-003 - 4.120000e+001 8.398221e-001 -3.106407e+000 6.165465e-003 - 4.121000e+001 8.629032e-001 -3.107161e+000 6.165214e-003 - 4.122000e+001 8.825216e-001 -3.107915e+000 6.166786e-003 - 4.123000e+001 8.985114e-001 -3.108669e+000 6.169817e-003 - 4.124000e+001 9.107872e-001 -3.109423e+000 6.173604e-003 - 4.125000e+001 9.193413e-001 -3.110177e+000 6.177270e-003 - 4.126000e+001 9.242399e-001 -3.110931e+000 6.179972e-003 - 4.127000e+001 9.256142e-001 -3.111685e+000 6.181087e-003 - 4.128000e+001 9.236514e-001 -3.112439e+000 6.180361e-003 - 4.129000e+001 9.185830e-001 -3.113193e+000 6.177962e-003 - 4.130000e+001 9.106739e-001 -3.113947e+000 6.174446e-003 - 4.131000e+001 9.002100e-001 -3.114701e+000 6.170624e-003 - 4.132000e+001 8.874883e-001 -3.115455e+000 6.167379e-003 - 4.133000e+001 8.728072e-001 -3.116209e+000 6.165462e-003 - 4.134000e+001 8.564590e-001 -3.116963e+000 6.165316e-003 - 4.135000e+001 8.387240e-001 -3.117717e+000 6.166972e-003 - 4.136000e+001 8.198670e-001 -3.118470e+000 6.170044e-003 - 4.137000e+001 8.001350e-001 -3.119224e+000 6.173820e-003 - 4.138000e+001 7.797577e-001 -3.119978e+000 6.177425e-003 - 4.139000e+001 7.589478e-001 -3.120732e+000 6.180028e-003 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6.173936e-003 - 4.157000e+001 4.605935e-001 -3.134304e+000 6.170158e-003 - 4.158000e+001 4.469357e-001 -3.135058e+000 6.167059e-003 - 4.159000e+001 4.317043e-001 -3.135812e+000 6.165358e-003 - 4.160000e+001 4.143299e-001 -3.136566e+000 6.165449e-003 - 4.161000e+001 3.942235e-001 -3.137320e+000 6.167312e-003 - 4.162000e+001 3.707964e-001 -3.138074e+000 6.170516e-003 - 4.163000e+001 3.434810e-001 -3.138828e+000 6.174320e-003 - 4.164000e+001 3.117534e-001 -3.139582e+000 6.177846e-003 - 4.165000e+001 2.751560e-001 -3.140336e+000 6.180278e-003 - 4.166000e+001 2.333193e-001 -3.141090e+000 6.181057e-003 - 4.167000e+001 1.859816e-001 -3.141844e+000 6.180003e-003 - 4.168000e+001 1.330067e-001 -3.142598e+000 6.177356e-003 - 4.169000e+001 7.439711e-002 -3.143352e+000 6.173726e-003 - 4.170000e+001 1.030366e-002 -3.144106e+000 6.169948e-003 - 4.171000e+001 -5.897006e-002 -3.144860e+000 6.166896e-003 - 4.172000e+001 -1.329685e-001 -3.145614e+000 6.165276e-003 - 4.173000e+001 -2.110899e-001 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4.190000e+001 -1.281863e+000 -3.159186e+000 6.178090e-003 - 4.191000e+001 -1.287611e+000 -3.159940e+000 6.180405e-003 - 4.192000e+001 -1.285703e+000 -3.160693e+000 6.181036e-003 - 4.193000e+001 -1.276548e+000 -3.161447e+000 6.179840e-003 - 4.194000e+001 -1.260632e+000 -3.162201e+000 6.177094e-003 - 4.195000e+001 -1.238501e+000 -3.162955e+000 6.173430e-003 - 4.196000e+001 -1.210741e+000 -3.163709e+000 6.169693e-003 - 4.197000e+001 -1.177957e+000 -3.164463e+000 6.166745e-003 - 4.198000e+001 -1.140757e+000 -3.165217e+000 6.165266e-003 - 4.199000e+001 -1.099736e+000 -3.165971e+000 6.165596e-003 - 4.200000e+001 -1.055460e+000 -3.166725e+000 6.167657e-003 - 4.201000e+001 -1.008458e+000 -3.167479e+000 6.170969e-003 - 4.202000e+001 -9.592126e-001 -3.168233e+000 6.174767e-003 - 4.203000e+001 -9.081542e-001 -3.168987e+000 6.178173e-003 - 4.204000e+001 -8.556595e-001 -3.169741e+000 6.180405e-003 - 4.205000e+001 -8.020505e-001 -3.170495e+000 6.180950e-003 - 4.206000e+001 -7.475974e-001 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4.223000e+001 1.840231e-001 -3.184067e+000 6.166595e-003 - 4.224000e+001 2.332969e-001 -3.184821e+000 6.165336e-003 - 4.225000e+001 2.809487e-001 -3.185575e+000 6.165874e-003 - 4.226000e+001 3.267318e-001 -3.186329e+000 6.168083e-003 - 4.227000e+001 3.703849e-001 -3.187083e+000 6.171452e-003 - 4.228000e+001 4.116359e-001 -3.187837e+000 6.175198e-003 - 4.229000e+001 4.502059e-001 -3.188591e+000 6.178457e-003 - 4.230000e+001 4.858141e-001 -3.189345e+000 6.180477e-003 - 4.231000e+001 5.181846e-001 -3.190099e+000 6.180791e-003 - 4.232000e+001 5.470529e-001 -3.190853e+000 6.179329e-003 - 4.233000e+001 5.721741e-001 -3.191607e+000 6.176429e-003 - 4.234000e+001 5.933316e-001 -3.192361e+000 6.172759e-003 - 4.235000e+001 6.103459e-001 -3.193115e+000 6.169168e-003 - 4.236000e+001 6.230842e-001 -3.193869e+000 6.166488e-003 - 4.237000e+001 6.314690e-001 -3.194623e+000 6.165341e-003 - 4.238000e+001 6.354864e-001 -3.195377e+000 6.165993e-003 - 4.239000e+001 6.351933e-001 -3.196131e+000 6.168293e-003 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6.176191e-003 - 4.307000e+001 -8.085271e-002 -3.247401e+000 6.179085e-003 - 4.308000e+001 -5.163804e-002 -3.248155e+000 6.180591e-003 - 4.309000e+001 -2.350437e-002 -3.248909e+000 6.180363e-003 - 4.310000e+001 3.329866e-003 -3.249663e+000 6.178456e-003 - 4.311000e+001 2.866583e-002 -3.250417e+000 6.175311e-003 - 4.312000e+001 5.232185e-002 -3.251171e+000 6.171656e-003 - 4.313000e+001 7.413186e-002 -3.251925e+000 6.168337e-003 - 4.314000e+001 9.394513e-002 -3.252679e+000 6.166124e-003 - 4.315000e+001 1.116270e-001 -3.253433e+000 6.165530e-003 - 4.316000e+001 1.270607e-001 -3.254187e+000 6.166694e-003 - 4.317000e+001 1.401503e-001 -3.254941e+000 6.169345e-003 - 4.318000e+001 1.508233e-001 -3.255695e+000 6.172870e-003 - 4.319000e+001 1.590349e-001 -3.256449e+000 6.176451e-003 - 4.320000e+001 1.647700e-001 -3.257203e+000 6.179262e-003 - 4.321000e+001 1.680467e-001 -3.257957e+000 6.180653e-003 - 4.322000e+001 1.689167e-001 -3.258711e+000 6.180303e-003 - 4.323000e+001 1.674661e-001 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6.169833e-003 - 4.357000e+001 -5.149409e-001 -3.285101e+000 6.173430e-003 - 4.358000e+001 -5.265946e-001 -3.285855e+000 6.176948e-003 - 4.359000e+001 -5.336825e-001 -3.286609e+000 6.179575e-003 - 4.360000e+001 -5.360194e-001 -3.287363e+000 6.180707e-003 - 4.361000e+001 -5.335634e-001 -3.288116e+000 6.180085e-003 - 4.362000e+001 -5.264264e-001 -3.288870e+000 6.177852e-003 - 4.363000e+001 -5.148778e-001 -3.289624e+000 6.174523e-003 - 4.364000e+001 -4.993419e-001 -3.290378e+000 6.170866e-003 - 4.365000e+001 -4.803887e-001 -3.291132e+000 6.167725e-003 - 4.366000e+001 -4.587176e-001 -3.291886e+000 6.165828e-003 - 4.367000e+001 -4.351356e-001 -3.292640e+000 6.165613e-003 - 4.368000e+001 -4.105293e-001 -3.293394e+000 6.167130e-003 - 4.369000e+001 -3.858335e-001 -3.294148e+000 6.170027e-003 - 4.370000e+001 -3.619961e-001 -3.294902e+000 6.173634e-003 - 4.371000e+001 -3.399417e-001 -3.295656e+000 6.177119e-003 - 4.372000e+001 -3.205355e-001 -3.296410e+000 6.179677e-003 - 4.373000e+001 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6.174144e-003 - 4.390000e+001 -5.367319e-001 -3.309982e+000 6.170513e-003 - 4.391000e+001 -5.435755e-001 -3.310736e+000 6.167478e-003 - 4.392000e+001 -5.450203e-001 -3.311490e+000 6.165742e-003 - 4.393000e+001 -5.408382e-001 -3.312244e+000 6.165704e-003 - 4.394000e+001 -5.309719e-001 -3.312998e+000 6.167374e-003 - 4.395000e+001 -5.155297e-001 -3.313752e+000 6.170366e-003 - 4.396000e+001 -4.947723e-001 -3.314506e+000 6.173986e-003 - 4.397000e+001 -4.690954e-001 -3.315260e+000 6.177401e-003 - 4.398000e+001 -4.390069e-001 -3.316014e+000 6.179824e-003 - 4.399000e+001 -4.051001e-001 -3.316768e+000 6.180698e-003 - 4.400000e+001 -3.680258e-001 -3.317522e+000 6.179824e-003 - 4.401000e+001 -3.284632e-001 -3.318276e+000 6.177404e-003 - 4.402000e+001 -2.870913e-001 -3.319030e+000 6.173996e-003 - 4.403000e+001 -2.445626e-001 -3.319784e+000 6.170385e-003 - 4.404000e+001 -2.014801e-001 -3.320538e+000 6.167407e-003 - 4.405000e+001 -1.583776e-001 -3.321292e+000 6.165747e-003 - 4.406000e+001 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4.423000e+001 4.550592e-001 -3.334863e+000 6.177684e-003 - 4.424000e+001 4.802864e-001 -3.335617e+000 6.179945e-003 - 4.425000e+001 5.038013e-001 -3.336371e+000 6.180629e-003 - 4.426000e+001 5.252802e-001 -3.337125e+000 6.179579e-003 - 4.427000e+001 5.443934e-001 -3.337879e+000 6.177038e-003 - 4.428000e+001 5.608210e-001 -3.338633e+000 6.173590e-003 - 4.429000e+001 5.742682e-001 -3.339387e+000 6.170032e-003 - 4.430000e+001 5.844792e-001 -3.340141e+000 6.167184e-003 - 4.431000e+001 5.912502e-001 -3.340895e+000 6.165707e-003 - 4.432000e+001 5.944393e-001 -3.341649e+000 6.165940e-003 - 4.433000e+001 5.939744e-001 -3.342403e+000 6.167830e-003 - 4.434000e+001 5.898576e-001 -3.343157e+000 6.170938e-003 - 4.435000e+001 5.821668e-001 -3.343911e+000 6.174545e-003 - 4.436000e+001 5.710541e-001 -3.344665e+000 6.177818e-003 - 4.437000e+001 5.567418e-001 -3.345419e+000 6.180003e-003 - 4.438000e+001 5.395155e-001 -3.346173e+000 6.180597e-003 - 4.439000e+001 5.197154e-001 -3.346927e+000 6.179463e-003 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6.167010e-003 - 4.457000e+001 1.782433e-001 -3.360499e+000 6.165697e-003 - 4.458000e+001 1.787989e-001 -3.361253e+000 6.166098e-003 - 4.459000e+001 1.821639e-001 -3.362007e+000 6.168118e-003 - 4.460000e+001 1.882410e-001 -3.362761e+000 6.171289e-003 - 4.461000e+001 1.968886e-001 -3.363515e+000 6.174877e-003 - 4.462000e+001 2.079201e-001 -3.364269e+000 6.178053e-003 - 4.463000e+001 2.211039e-001 -3.365023e+000 6.180086e-003 - 4.464000e+001 2.361639e-001 -3.365777e+000 6.180508e-003 - 4.465000e+001 2.527817e-001 -3.366531e+000 6.179223e-003 - 4.466000e+001 2.706004e-001 -3.367285e+000 6.176528e-003 - 4.467000e+001 2.892294e-001 -3.368039e+000 6.173045e-003 - 4.468000e+001 3.082521e-001 -3.368793e+000 6.169576e-003 - 4.469000e+001 3.272343e-001 -3.369547e+000 6.166924e-003 - 4.470000e+001 3.457349e-001 -3.370301e+000 6.165701e-003 - 4.471000e+001 3.633175e-001 -3.371055e+000 6.166189e-003 - 4.472000e+001 3.795639e-001 -3.371809e+000 6.168274e-003 - 4.473000e+001 3.940867e-001 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3.238720e-001 -3.385380e+000 6.180374e-003 - 4.491000e+001 3.155738e-001 -3.386134e+000 6.178923e-003 - 4.492000e+001 3.089583e-001 -3.386888e+000 6.176128e-003 - 4.493000e+001 3.041252e-001 -3.387642e+000 6.172634e-003 - 4.494000e+001 3.010769e-001 -3.388396e+000 6.169248e-003 - 4.495000e+001 2.997181e-001 -3.389150e+000 6.166753e-003 - 4.496000e+001 2.998609e-001 -3.389904e+000 6.165725e-003 - 4.497000e+001 3.012341e-001 -3.390658e+000 6.166404e-003 - 4.498000e+001 3.034961e-001 -3.391412e+000 6.168632e-003 - 4.499000e+001 3.062520e-001 -3.392166e+000 6.171893e-003 - 4.500000e+001 3.090720e-001 -3.392920e+000 6.175433e-003 - 4.501000e+001 3.115131e-001 -3.393674e+000 6.178435e-003 - 4.502000e+001 3.131403e-001 -3.394428e+000 6.180208e-003 - 4.503000e+001 3.135477e-001 -3.395182e+000 6.180343e-003 - 4.504000e+001 3.123785e-001 -3.395936e+000 6.178810e-003 - 4.505000e+001 3.093418e-001 -3.396690e+000 6.175962e-003 - 4.506000e+001 3.042268e-001 -3.397444e+000 6.172456e-003 - 4.507000e+001 2.969125e-001 -3.398198e+000 6.169100e-003 - 4.508000e+001 2.873729e-001 -3.398952e+000 6.166670e-003 - 4.509000e+001 2.756772e-001 -3.399706e+000 6.165727e-003 - 4.510000e+001 2.619855e-001 -3.400460e+000 6.166489e-003 - 4.511000e+001 2.465396e-001 -3.401214e+000 6.168779e-003 - 4.512000e+001 2.296492e-001 -3.401968e+000 6.172065e-003 - 4.513000e+001 2.116753e-001 -3.402722e+000 6.175589e-003 - 4.514000e+001 1.930102e-001 -3.403476e+000 6.178536e-003 - 4.515000e+001 1.740562e-001 -3.404230e+000 6.180227e-003 - 4.516000e+001 1.552037e-001 -3.404984e+000 6.180275e-003 - 4.517000e+001 1.368101e-001 -3.405738e+000 6.178668e-003 - 4.518000e+001 1.191792e-001 -3.406492e+000 6.175778e-003 - 4.519000e+001 1.025452e-001 -3.407246e+000 6.172271e-003 - 4.520000e+001 8.705856e-002 -3.408000e+000 6.168957e-003 - 4.521000e+001 7.277724e-002 -3.408754e+000 6.166601e-003 - 4.522000e+001 5.966219e-002 -3.409508e+000 6.165748e-003 - 4.523000e+001 4.757824e-002 -3.410262e+000 6.166595e-003 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4.557000e+001 -6.037523e-001 -3.435897e+000 6.175227e-003 - 4.558000e+001 -5.916441e-001 -3.436651e+000 6.171715e-003 - 4.559000e+001 -5.776279e-001 -3.437405e+000 6.168525e-003 - 4.560000e+001 -5.621674e-001 -3.438159e+000 6.166394e-003 - 4.561000e+001 -5.457126e-001 -3.438913e+000 6.165814e-003 - 4.562000e+001 -5.286850e-001 -3.439667e+000 6.166919e-003 - 4.563000e+001 -5.114661e-001 -3.440421e+000 6.169451e-003 - 4.564000e+001 -4.943876e-001 -3.441175e+000 6.172824e-003 - 4.565000e+001 -4.777249e-001 -3.441929e+000 6.176258e-003 - 4.566000e+001 -4.616939e-001 -3.442683e+000 6.178961e-003 - 4.567000e+001 -4.464496e-001 -3.443437e+000 6.180310e-003 - 4.568000e+001 -4.320885e-001 -3.444191e+000 6.179996e-003 - 4.569000e+001 -4.186523e-001 -3.444945e+000 6.178092e-003 - 4.570000e+001 -4.061335e-001 -3.445699e+000 6.175037e-003 - 4.571000e+001 -3.944832e-001 -3.446453e+000 6.171538e-003 - 4.572000e+001 -3.836184e-001 -3.447207e+000 6.168402e-003 - 4.573000e+001 -3.734307e-001 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4.590000e+001 -1.952766e-001 -3.460778e+000 6.173242e-003 - 4.591000e+001 -1.812361e-001 -3.461532e+000 6.176637e-003 - 4.592000e+001 -1.668964e-001 -3.462286e+000 6.179221e-003 - 4.593000e+001 -1.523572e-001 -3.463040e+000 6.180399e-003 - 4.594000e+001 -1.377383e-001 -3.463794e+000 6.179901e-003 - 4.595000e+001 -1.231801e-001 -3.464548e+000 6.177841e-003 - 4.596000e+001 -1.088420e-001 -3.465302e+000 6.174691e-003 - 4.597000e+001 -9.490039e-002 -3.466056e+000 6.171178e-003 - 4.598000e+001 -8.154544e-002 -3.466810e+000 6.168109e-003 - 4.599000e+001 -6.897597e-002 -3.467564e+000 6.166192e-003 - 4.600000e+001 -5.739357e-002 -3.468318e+000 6.165869e-003 - 4.601000e+001 -4.699531e-002 -3.469072e+000 6.167213e-003 - 4.602000e+001 -3.796563e-002 -3.469826e+000 6.169913e-003 - 4.603000e+001 -3.046753e-002 -3.470580e+000 6.173342e-003 - 4.604000e+001 -2.463358e-002 -3.471334e+000 6.176711e-003 - 4.605000e+001 -2.055720e-002 -3.472088e+000 6.179243e-003 - 4.606000e+001 -1.828457e-002 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4.623000e+001 -5.048803e-002 -3.485660e+000 6.170839e-003 - 4.624000e+001 -3.806233e-002 -3.486414e+000 6.167898e-003 - 4.625000e+001 -2.284810e-002 -3.487168e+000 6.166159e-003 - 4.626000e+001 -5.015648e-003 -3.487922e+000 6.166025e-003 - 4.627000e+001 1.518054e-002 -3.488676e+000 6.167528e-003 - 4.628000e+001 3.741087e-002 -3.489430e+000 6.170319e-003 - 4.629000e+001 6.128292e-002 -3.490184e+000 6.173755e-003 - 4.630000e+001 8.635628e-002 -3.490938e+000 6.177040e-003 - 4.631000e+001 1.121595e-001 -3.491692e+000 6.179419e-003 - 4.632000e+001 1.382079e-001 -3.492446e+000 6.180344e-003 - 4.633000e+001 1.640227e-001 -3.493200e+000 6.179601e-003 - 4.634000e+001 1.891484e-001 -3.493954e+000 6.177363e-003 - 4.635000e+001 2.131700e-001 -3.494708e+000 6.174144e-003 - 4.636000e+001 2.357281e-001 -3.495462e+000 6.170687e-003 - 4.637000e+001 2.565306e-001 -3.496216e+000 6.167789e-003 - 4.638000e+001 2.753620e-001 -3.496970e+000 6.166120e-003 - 4.639000e+001 2.920889e-001 -3.497724e+000 6.166065e-003 - 4.640000e+001 3.066613e-001 -3.498478e+000 6.167635e-003 - 4.641000e+001 3.191107e-001 -3.499232e+000 6.170467e-003 - 4.642000e+001 3.295439e-001 -3.499985e+000 6.173905e-003 - 4.643000e+001 3.381342e-001 -3.500739e+000 6.177154e-003 - 4.644000e+001 3.451089e-001 -3.501493e+000 6.179466e-003 - 4.645000e+001 3.507353e-001 -3.502247e+000 6.180309e-003 - 4.646000e+001 3.553046e-001 -3.503001e+000 6.179489e-003 - 4.647000e+001 3.591159e-001 -3.503755e+000 6.177196e-003 - 4.648000e+001 3.624590e-001 -3.504509e+000 6.173960e-003 - 4.649000e+001 3.655994e-001 -3.505263e+000 6.170526e-003 - 4.650000e+001 3.687640e-001 -3.506017e+000 6.167689e-003 - 4.651000e+001 3.721294e-001 -3.506771e+000 6.166105e-003 - 4.652000e+001 3.758127e-001 -3.507525e+000 6.166142e-003 - 4.653000e+001 3.798656e-001 -3.508279e+000 6.167789e-003 - 4.654000e+001 3.842720e-001 -3.509033e+000 6.170667e-003 - 4.655000e+001 3.889483e-001 -3.509787e+000 6.174108e-003 - 4.656000e+001 3.937475e-001 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2.547406e-001 -3.523359e+000 6.176913e-003 - 4.674000e+001 2.260188e-001 -3.524113e+000 6.173638e-003 - 4.675000e+001 1.955864e-001 -3.524867e+000 6.170244e-003 - 4.676000e+001 1.637260e-001 -3.525621e+000 6.167515e-003 - 4.677000e+001 1.307325e-001 -3.526375e+000 6.166082e-003 - 4.678000e+001 9.690576e-002 -3.527129e+000 6.166276e-003 - 4.679000e+001 6.254485e-002 -3.527883e+000 6.168050e-003 - 4.680000e+001 2.794282e-002 -3.528637e+000 6.170993e-003 - 4.681000e+001 -6.616838e-003 -3.529391e+000 6.174422e-003 - 4.682000e+001 -4.086276e-002 -3.530145e+000 6.177546e-003 - 4.683000e+001 -7.453713e-002 -3.530899e+000 6.179642e-003 - 4.684000e+001 -1.073962e-001 -3.531653e+000 6.180229e-003 - 4.685000e+001 -1.392099e-001 -3.532407e+000 6.179170e-003 - 4.686000e+001 -1.697614e-001 -3.533161e+000 6.176710e-003 - 4.687000e+001 -1.988463e-001 -3.533915e+000 6.173414e-003 - 4.688000e+001 -2.262717e-001 -3.534669e+000 6.170044e-003 - 4.689000e+001 -2.518560e-001 -3.535423e+000 6.167376e-003 - 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4.629303e-001 -3.636456e+000 6.172846e-003 - 4.824000e+001 4.263485e-001 -3.637210e+000 6.176088e-003 - 4.825000e+001 3.869685e-001 -3.637964e+000 6.178627e-003 - 4.826000e+001 3.452289e-001 -3.638718e+000 6.179878e-003 - 4.827000e+001 3.016052e-001 -3.639472e+000 6.179556e-003 - 4.828000e+001 2.565958e-001 -3.640226e+000 6.177738e-003 - 4.829000e+001 2.107075e-001 -3.640980e+000 6.174847e-003 - 4.830000e+001 1.644411e-001 -3.641734e+000 6.171555e-003 - 4.831000e+001 1.182788e-001 -3.642488e+000 6.168625e-003 - 4.832000e+001 7.267232e-002 -3.643242e+000 6.166738e-003 - 4.833000e+001 2.803435e-002 -3.643996e+000 6.166334e-003 - 4.834000e+001 -1.526894e-002 -3.644750e+000 6.167506e-003 - 4.835000e+001 -5.692212e-002 -3.645504e+000 6.169983e-003 - 4.836000e+001 -9.666246e-002 -3.646258e+000 6.173191e-003 - 4.837000e+001 -1.342795e-001 -3.647012e+000 6.176386e-003 - 4.838000e+001 -1.696123e-001 -3.647766e+000 6.178828e-003 - 4.839000e+001 -2.025453e-001 -3.648520e+000 6.179951e-003 - 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5.123000e+001 3.985785e-002 -3.862651e+000 6.179201e-003 - 5.124000e+001 4.447710e-002 -3.863405e+000 6.180009e-003 - 5.125000e+001 4.922202e-002 -3.864159e+000 6.179255e-003 - 5.126000e+001 5.376615e-002 -3.864913e+000 6.177103e-003 - 5.127000e+001 5.779058e-002 -3.865667e+000 6.174038e-003 - 5.128000e+001 6.099670e-002 -3.866421e+000 6.170753e-003 - 5.129000e+001 6.311825e-002 -3.867175e+000 6.167994e-003 - 5.130000e+001 6.393230e-002 -3.867929e+000 6.166390e-003 - 5.131000e+001 6.326840e-002 -3.868683e+000 6.166305e-003 - 5.132000e+001 6.101590e-002 -3.869437e+000 6.167758e-003 - 5.133000e+001 5.712889e-002 -3.870191e+000 6.170417e-003 - 5.134000e+001 5.162861e-002 -3.870945e+000 6.173674e-003 - 5.135000e+001 4.460325e-002 -3.871699e+000 6.176790e-003 - 5.136000e+001 3.620517e-002 -3.872453e+000 6.179059e-003 - 5.137000e+001 2.664554e-002 -3.873207e+000 6.179972e-003 - 5.138000e+001 1.618666e-002 -3.873961e+000 6.179328e-003 - 5.139000e+001 5.132286e-003 -3.874715e+000 6.177282e-003 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3.033326e-002 -3.900350e+000 6.174523e-003 - 5.174000e+001 2.289168e-002 -3.901104e+000 6.177231e-003 - 5.175000e+001 1.515385e-002 -3.901858e+000 6.178996e-003 - 5.176000e+001 7.284882e-003 -3.902612e+000 6.179400e-003 - 5.177000e+001 -5.835245e-004 -3.903366e+000 6.178339e-003 - 5.178000e+001 -8.359625e-003 -3.904120e+000 6.176049e-003 - 5.179000e+001 -1.599598e-002 -3.904874e+000 6.173051e-003 - 5.180000e+001 -2.349146e-002 -3.905628e+000 6.170035e-003 - 5.181000e+001 -3.089070e-002 -3.906382e+000 6.167702e-003 - 5.182000e+001 -3.828115e-002 -3.907136e+000 6.166597e-003 - 5.183000e+001 -4.578765e-002 -3.907890e+000 6.166987e-003 - 5.184000e+001 -5.356492e-002 -3.908644e+000 6.168791e-003 - 5.185000e+001 -6.178815e-002 -3.909398e+000 6.171604e-003 - 5.186000e+001 -7.064226e-002 -3.910152e+000 6.174784e-003 - 5.187000e+001 -8.031009e-002 -3.910906e+000 6.177603e-003 - 5.188000e+001 -9.096034e-002 -3.911660e+000 6.179413e-003 - 5.189000e+001 -1.027356e-001 -3.912414e+000 6.179794e-003 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5.223000e+001 -7.702926e-002 -3.938049e+000 6.168948e-003 - 5.224000e+001 -5.565382e-002 -3.938803e+000 6.171615e-003 - 5.225000e+001 -3.561519e-002 -3.939557e+000 6.174612e-003 - 5.226000e+001 -1.693325e-002 -3.940311e+000 6.177241e-003 - 5.227000e+001 4.409769e-004 -3.941065e+000 6.178891e-003 - 5.228000e+001 1.661809e-002 -3.941819e+000 6.179184e-003 - 5.229000e+001 3.176052e-002 -3.942573e+000 6.178056e-003 - 5.230000e+001 4.607051e-002 -3.943327e+000 6.175774e-003 - 5.231000e+001 5.977649e-002 -3.944081e+000 6.172872e-003 - 5.232000e+001 7.311862e-002 -3.944835e+000 6.170030e-003 - 5.233000e+001 8.633404e-002 -3.945589e+000 6.167913e-003 - 5.234000e+001 9.964269e-002 -3.946343e+000 6.167015e-003 - 5.235000e+001 1.132343e-001 -3.947097e+000 6.167547e-003 - 5.236000e+001 1.272571e-001 -3.947851e+000 6.169385e-003 - 5.237000e+001 1.418092e-001 -3.948605e+000 6.172099e-003 - 5.238000e+001 1.569321e-001 -3.949359e+000 6.175056e-003 - 5.239000e+001 1.726076e-001 -3.950113e+000 6.177566e-003 - 5.240000e+001 1.887579e-001 -3.950867e+000 6.179041e-003 - 5.241000e+001 2.052486e-001 -3.951621e+000 6.179135e-003 - 5.242000e+001 2.218941e-001 -3.952375e+000 6.177822e-003 - 5.243000e+001 2.384666e-001 -3.953129e+000 6.175402e-003 - 5.244000e+001 2.547059e-001 -3.953883e+000 6.172435e-003 - 5.245000e+001 2.703316e-001 -3.954637e+000 6.169609e-003 - 5.246000e+001 2.850557e-001 -3.955391e+000 6.167583e-003 - 5.247000e+001 2.985956e-001 -3.956145e+000 6.166832e-003 - 5.248000e+001 3.106863e-001 -3.956899e+000 6.167537e-003 - 5.249000e+001 3.210918e-001 -3.957653e+000 6.169540e-003 - 5.250000e+001 3.296145e-001 -3.958407e+000 6.172381e-003 - 5.251000e+001 3.361027e-001 -3.959161e+000 6.175405e-003 - 5.252000e+001 3.404554e-001 -3.959915e+000 6.177913e-003 - 5.253000e+001 3.426243e-001 -3.960669e+000 6.179322e-003 - 5.254000e+001 3.426130e-001 -3.961423e+000 6.179304e-003 - 5.255000e+001 3.404739e-001 -3.962177e+000 6.177855e-003 - 5.256000e+001 3.363021e-001 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7.558024e-002 -3.975748e+000 6.166581e-003 - 5.274000e+001 5.136103e-002 -3.976502e+000 6.167372e-003 - 5.275000e+001 2.604273e-002 -3.977256e+000 6.169477e-003 - 5.276000e+001 -2.957647e-004 -3.978010e+000 6.172409e-003 - 5.277000e+001 -2.751994e-002 -3.978764e+000 6.175492e-003 - 5.278000e+001 -5.543663e-002 -3.979518e+000 6.178020e-003 - 5.279000e+001 -8.379412e-002 -3.980272e+000 6.179413e-003 - 5.280000e+001 -1.122856e-001 -3.981026e+000 6.179355e-003 - 5.281000e+001 -1.405556e-001 -3.981780e+000 6.177863e-003 - 5.282000e+001 -1.682100e-001 -3.982534e+000 6.175281e-003 - 5.283000e+001 -1.948284e-001 -3.983288e+000 6.172206e-003 - 5.284000e+001 -2.199784e-001 -3.984042e+000 6.169346e-003 - 5.285000e+001 -2.432319e-001 -3.984796e+000 6.167360e-003 - 5.286000e+001 -2.641817e-001 -3.985550e+000 6.166704e-003 - 5.287000e+001 -2.824582e-001 -3.986304e+000 6.167526e-003 - 5.288000e+001 -2.977451e-001 -3.987058e+000 6.169634e-003 - 5.289000e+001 -3.097935e-001 -3.987812e+000 6.172536e-003 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6.172973e-003 - 5.957000e+001 -1.111968e-002 -4.491472e+000 6.170277e-003 - 5.958000e+001 1.166256e-003 -4.492226e+000 6.168231e-003 - 5.959000e+001 1.389713e-002 -4.492980e+000 6.167308e-003 - 5.960000e+001 2.678053e-002 -4.493734e+000 6.167722e-003 - 5.961000e+001 3.951701e-002 -4.494488e+000 6.169376e-003 - 5.962000e+001 5.181002e-002 -4.495242e+000 6.171890e-003 - 5.963000e+001 6.337555e-002 -4.495996e+000 6.174683e-003 - 5.964000e+001 7.395111e-002 -4.496750e+000 6.177112e-003 - 5.965000e+001 8.330383e-002 -4.497504e+000 6.178618e-003 - 5.966000e+001 9.123736e-002 -4.498258e+000 6.178856e-003 - 5.967000e+001 9.759731e-002 -4.499012e+000 6.177772e-003 - 5.968000e+001 1.022753e-001 -4.499766e+000 6.175616e-003 - 5.969000e+001 1.052112e-001 -4.500520e+000 6.172885e-003 - 5.970000e+001 1.063939e-001 -4.501274e+000 6.170208e-003 - 5.971000e+001 1.058607e-001 -4.502028e+000 6.168202e-003 - 5.972000e+001 1.036942e-001 -4.502782e+000 6.167329e-003 - 5.973000e+001 1.000195e-001 -4.503536e+000 6.167790e-003 - 5.974000e+001 9.499849e-002 -4.504290e+000 6.169476e-003 - 5.975000e+001 8.882436e-002 -4.505044e+000 6.171997e-003 - 5.976000e+001 8.171473e-002 -4.505798e+000 6.174768e-003 - 5.977000e+001 7.390446e-002 -4.506552e+000 6.177152e-003 - 5.978000e+001 6.563822e-002 -4.507306e+000 6.178598e-003 - 5.979000e+001 5.716297e-002 -4.508060e+000 6.178775e-003 - 5.980000e+001 4.872061e-002 -4.508814e+000 6.177644e-003 - 5.981000e+001 4.054111e-002 -4.509568e+000 6.175466e-003 - 5.982000e+001 3.283626e-002 -4.510322e+000 6.172746e-003 - 5.983000e+001 2.579408e-002 -4.511076e+000 6.170112e-003 - 5.984000e+001 1.957425e-002 -4.511830e+000 6.168173e-003 - 5.985000e+001 1.430452e-002 -4.512584e+000 6.167377e-003 - 5.986000e+001 1.007820e-002 -4.513338e+000 6.167909e-003 - 5.987000e+001 6.952773e-003 -4.514092e+000 6.169643e-003 - 5.988000e+001 4.949644e-003 -4.514846e+000 6.172179e-003 - 5.989000e+001 4.055025e-003 -4.515600e+000 6.174928e-003 - 5.990000e+001 4.221840e-003 -4.516354e+000 6.177257e-003 - 5.991000e+001 5.372618e-003 -4.517108e+000 6.178626e-003 - 5.992000e+001 7.403240e-003 -4.517862e+000 6.178721e-003 - 5.993000e+001 1.018741e-002 -4.518615e+000 6.177519e-003 - 5.994000e+001 1.358172e-002 -4.519369e+000 6.175297e-003 - 5.995000e+001 1.743107e-002 -4.520123e+000 6.172568e-003 - 5.996000e+001 2.157437e-002 -4.520877e+000 6.169963e-003 - 5.997000e+001 2.585021e-002 -4.521631e+000 6.168083e-003 - 5.998000e+001 3.010246e-002 -4.522385e+000 6.167364e-003 - 5.999000e+001 3.418543e-002 -4.523139e+000 6.167972e-003 diff --git a/docs/examples/srfit_ex/data/si.cif b/docs/examples/srfit_ex/data/si.cif deleted file mode 100644 index ddcf81b..0000000 --- a/docs/examples/srfit_ex/data/si.cif +++ /dev/null @@ -1,224 +0,0 @@ -data_9008565 -_chemical_name 'Silicon' -loop_ -_publ_author_name -'Wyckoff R W G' -_journal_name_full "Crystal Structures" -_journal_volume 1 -_journal_year 1963 -_journal_page_first 7 -_journal_page_last 83 -_publ_section_title -; - Second edition. Interscience Publishers, New York, New York - Sample at T = 300 K -; -_chemical_formula_sum 'Si' -_cell_length_a 5.43070 -_cell_length_b 5.43070 -_cell_length_c 5.43070 -_cell_angle_alpha 90 -_cell_angle_beta 90 -_cell_angle_gamma 90 -_cell_volume 160.165 -_symmetry_space_group_name_H-M 'F d 3 m' -loop_ -_symmetry_equiv_pos_as_xyz - 'x,y,z' - 'x,1/2+y,1/2+z' - '1/2+x,y,1/2+z' - '1/2+x,1/2+y,z' - '3/4+z,3/4-x,1/4+y' - '3/4+z,1/4-x,3/4+y' - '1/4+z,3/4-x,3/4+y' - '1/4+z,1/4-x,1/4+y' - '-y,1/2+z,1/2-x' - '-y,+z,-x' - '1/2-y,1/2+z,-x' - '1/2-y,+z,1/2-x' - '3/4+x,3/4-y,1/4+z' - '3/4+x,1/4-y,3/4+z' - '1/4+x,3/4-y,3/4+z' - '1/4+x,1/4-y,1/4+z' - '-z,1/2+x,1/2-y' - '-z,+x,-y' - '1/2-z,1/2+x,-y' - '1/2-z,+x,1/2-y' - '3/4+y,3/4-z,1/4+x' - '3/4+y,1/4-z,3/4+x' - '1/4+y,3/4-z,3/4+x' - '1/4+y,1/4-z,1/4+x' - '-x,1/2+y,1/2-z' - '-x,+y,-z' - '1/2-x,1/2+y,-z' - '1/2-x,+y,1/2-z' - '1/2+x,-z,1/2-y' - '1/2+x,1/2-z,-y' - '+x,-z,-y' - '+x,1/2-z,1/2-y' - '3/4-z,3/4+y,1/4+x' - '3/4-z,1/4+y,3/4+x' - '1/4-z,3/4+y,3/4+x' - '1/4-z,1/4+y,1/4+x' - '1/2+y,-x,1/2-z' - '1/2+y,1/2-x,-z' - '+y,-x,-z' - '+y,1/2-x,1/2-z' - '3/4-x,3/4+z,1/4+y' - '3/4-x,1/4+z,3/4+y' - '1/4-x,3/4+z,3/4+y' - '1/4-x,1/4+z,1/4+y' - '1/2+z,-y,1/2-x' - '1/2+z,1/2-y,-x' - '+z,-y,-x' - '+z,1/2-y,1/2-x' - '3/4-y,3/4+x,1/4+z' - '3/4-y,1/4+x,3/4+z' - '1/4-y,3/4+x,3/4+z' - '1/4-y,1/4+x,1/4+z' - 'x,1/2+z,1/2+y' - 'x,+z,+y' - '1/2+x,1/2+z,+y' - '1/2+x,+z,1/2+y' - '1/4-z,3/4-y,3/4-x' - '1/4-z,1/4-y,1/4-x' - '3/4-z,3/4-y,1/4-x' - '3/4-z,1/4-y,3/4-x' - 'y,1/2+x,1/2+z' - 'y,+x,+z' - '1/2+y,1/2+x,+z' - '1/2+y,+x,1/2+z' - '1/4-x,3/4-z,3/4-y' - '1/4-x,1/4-z,1/4-y' - '3/4-x,3/4-z,1/4-y' - '3/4-x,1/4-z,3/4-y' - 'z,1/2+y,1/2+x' - 'z,+y,+x' - '1/2+z,1/2+y,+x' - '1/2+z,+y,1/2+x' - '1/4-y,3/4-x,3/4-z' - '1/4-y,1/4-x,1/4-z' - '3/4-y,3/4-x,1/4-z' - '3/4-y,1/4-x,3/4-z' - '3/4+z,1/4+x,3/4-y' - '3/4+z,3/4+x,1/4-y' - '1/4+z,1/4+x,1/4-y' - '1/4+z,3/4+x,3/4-y' - '-y,1/2-z,1/2+x' - '-y,-z,+x' - '1/2-y,1/2-z,+x' - '1/2-y,-z,1/2+x' - '3/4+x,1/4+y,3/4-z' - '3/4+x,3/4+y,1/4-z' - '1/4+x,1/4+y,1/4-z' - '1/4+x,3/4+y,3/4-z' - '-z,1/2-x,1/2+y' - '-z,-x,+y' - '1/2-z,1/2-x,+y' - '1/2-z,-x,1/2+y' - '3/4+y,1/4+z,3/4-x' - '3/4+y,3/4+z,1/4-x' - '1/4+y,1/4+z,1/4-x' - '1/4+y,3/4+z,3/4-x' - '-x,1/2-y,1/2+z' - '-x,-y,+z' - '1/2-x,1/2-y,+z' - '1/2-x,-y,1/2+z' - '1/4-z,3/4+x,3/4+y' - '1/4-z,1/4+x,1/4+y' - '3/4-z,3/4+x,1/4+y' - '3/4-z,1/4+x,3/4+y' - 'y,-z,-x' - 'y,1/2-z,1/2-x' - '1/2+y,-z,1/2-x' - '1/2+y,1/2-z,-x' - '1/4-x,3/4+y,3/4+z' - '1/4-x,1/4+y,1/4+z' - '3/4-x,3/4+y,1/4+z' - '3/4-x,1/4+y,3/4+z' - 'z,-x,-y' - 'z,1/2-x,1/2-y' - '1/2+z,-x,1/2-y' - '1/2+z,1/2-x,-y' - '1/4-y,3/4+z,3/4+x' - '1/4-y,1/4+z,1/4+x' - '3/4-y,3/4+z,1/4+x' - '3/4-y,1/4+z,3/4+x' - 'x,-y,-z' - 'x,1/2-y,1/2-z' - '1/2+x,-y,1/2-z' - '1/2+x,1/2-y,-z' - '1/2-x,1/2+z,-y' - '1/2-x,+z,1/2-y' - '-x,1/2+z,1/2-y' - '-x,+z,-y' - '1/4+z,3/4-y,3/4+x' - '1/4+z,1/4-y,1/4+x' - '3/4+z,3/4-y,1/4+x' - '3/4+z,1/4-y,3/4+x' - '1/2-y,1/2+x,-z' - '1/2-y,+x,1/2-z' - '-y,1/2+x,1/2-z' - '-y,+x,-z' - '1/4+x,3/4-z,3/4+y' - '1/4+x,1/4-z,1/4+y' - '3/4+x,3/4-z,1/4+y' - '3/4+x,1/4-z,3/4+y' - '1/2-z,1/2+y,-x' - '1/2-z,+y,1/2-x' - '-z,1/2+y,1/2-x' - '-z,+y,-x' - '1/4+y,3/4-x,3/4+z' - '1/4+y,1/4-x,1/4+z' - '3/4+y,3/4-x,1/4+z' - '3/4+y,1/4-x,3/4+z' - '-x,-z,y' - '-x,1/2-z,1/2+y' - '1/2-x,-z,1/2+y' - '1/2-x,1/2-z,y' - '3/4+z,3/4+y,1/4-x' - '3/4+z,1/4+y,3/4-x' - '1/4+z,3/4+y,3/4-x' - '1/4+z,1/4+y,1/4-x' - '-y,-x,z' - '-y,1/2-x,1/2+z' - '1/2-y,-x,1/2+z' - '1/2-y,1/2-x,z' - '3/4+x,3/4+z,1/4-y' - '3/4+x,1/4+z,3/4-y' - '1/4+x,3/4+z,3/4-y' - '1/4+x,1/4+z,1/4-y' - '-z,-y,x' - '-z,1/2-y,1/2+x' - '1/2-z,-y,1/2+x' - '1/2-z,1/2-y,x' - '3/4+y,3/4+x,1/4-z' - '3/4+y,1/4+x,3/4-z' - '1/4+y,3/4+x,3/4-z' - '1/4+y,1/4+x,1/4-z' - '1/4-z,1/4-x,1/4-y' - '1/4-z,3/4-x,3/4-y' - '3/4-z,1/4-x,3/4-y' - '3/4-z,3/4-x,1/4-y' - 'y,z,x' - 'y,1/2+z,1/2+x' - '1/2+y,z,1/2+x' - '1/2+y,1/2+z,x' - '1/4-x,1/4-y,1/4-z' - '1/4-x,3/4-y,3/4-z' - '3/4-x,1/4-y,3/4-z' - '3/4-x,3/4-y,1/4-z' - 'z,x,y' - 'z,1/2+x,1/2+y' - '1/2+z,x,1/2+y' - '1/2+z,1/2+x,y' - '1/4-y,1/4-z,1/4-x' - '1/4-y,3/4-z,3/4-x' - '3/4-y,1/4-z,3/4-x' - '3/4-y,3/4-z,1/4-x' -loop_ -_atom_site_label -_atom_site_fract_x -_atom_site_fract_y -_atom_site_fract_z -Si 0.00000 0.00000 0.00000 diff --git a/docs/examples/srfit_ex/data/si90ni10-q27r60-xray.gr b/docs/examples/srfit_ex/data/si90ni10-q27r60-xray.gr deleted file mode 100644 index 02ea8a1..0000000 --- a/docs/examples/srfit_ex/data/si90ni10-q27r60-xray.gr +++ /dev/null @@ -1,6134 +0,0 @@ -History written: Mon Apr 21 20:48:28 2008 -Produced by -####### Get_XPDF ####### - -##### General_Setting -title=X-ray PDF -workingdirectory=e:\Ahmad\MUCAT0804\standards\pdfgetx2 -sourcedir=C:\Program Files\PDFgetX2\ -logfile=.pdfgetx2.log -quiet=0 debug=0 autosave_isa=1 savefilenamebase=si90ni10_300k_nor_1-6 -iqfilesurfix=.iq sqfilesurfix=.sq fqfilesurfix=.fq grfilesurfix=.gr - -##### DataFileFormat -datatype=1 (0:SPEC, 1:CHI, 2:nxm column, 3:unknown) -num_skiplines=3 comment_id=# delimiter= -### SPEC Format scan_id=#S scan_delimiter= -columnname_id=#L columnname_delimiter= -data_id= data_delimiter= -### CHI Format -### nxm column Format -### End of file format - -##### Data&Background -samfile=si90ni10_300k_nor_1-6.chi num_sams=1 -sambkgfile=kapton_bgrd_300k_nor_2-3.chi num_sambkgs=1 -confile= num_cons=1 -conbkgfile= num_conbkgs=1 -det# used xcol detcol deterrcol xmin xmax add_det mul_det add_bkg mul_bkg add_con mul_con add_conbkg mul_conbkg - 0 1 0 1 3 0.600000 32.0000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 0.000000 1.00000 - -##### Experiment_Setup -title=PDF analysis -user=me -facility=In house -temperature=300.000 containermut=0.000500000 filtermut=0.0200000 -## X-Ray radiationtype=3 - (0: Ag K_alpha, 1:Cu K_alpha, 2:Mo K_alpha, 3:Customize) -lambda=0.142773 energy=86.8406 polartype=0 polardegree=1.00000 -## MonoChromator crystaltype=0 (0:Perfect, 1:Mosaic, 2:None) -position=0 (0:Primary beam, 1:Diffracted beam) -dspacetype=0 (0:Si{111}, 1:Ge{111}, 2:Customize) dspacing=3.13200 - -##### Sample_Setup information num_atoms=2 -#L symbol valence fractions z user_f1 user_f2 user_macoef - Si 0.00 0.900000 14 0.000000 0.000000 0.001000 - Ni 0.00 0.100000 28 0.000000 0.000000 0.001000 -geometry=2 mut=0.50000000 numberdensity=0.00600000 -thickness=2.00000 packingFraction=0.500000 theory_mut=0.00871359 - -##### GetIQ_Setup -xformat=1 -smoothcorr_isa=0 selfnormalize_isa=0 -#L par_name sample sample_bkg container container_bkg -smooth_degree 2 2 2 2 -smooth_width 6 6 6 6 -selfnormalize 0 0 0 0 -filtercorr_isa=0 samfiltercorr_isa=0 sambkgfiltercorr_isa=0 -confiltercorr_isa=0 conbkgfiltercorr_isa=0 -scatveffcorr_isa=1 samconveffcorr_isa=1 sambkgveffcorr_isa=0 -conbkgveffcorr_isa=0 -nonegative_isa=1 negativevalue=-1.00000 - -##### Calibration_Data -## Detection efficiency energy dependence detedepxaxis=0 -detedepfunctype=0 detedep_elastic=1.00000 detedep_fluores=1.80000 -detedep_quadra=0.000000 detedep_spline=0.000000 detedep_file= -## Detector transmission energy dependence dettcoefxaxis=0 -dettcoeffunctype=0 dettcoef_elastic=0.950000 dettcoef_fluores=0.600000 -dettcoef_quadra=0.000000 dettcoef_spline=0.000000 dettcoef_file= - -##### IQ_Simulation -### Elastic used_isa=1 mymethod=1 -do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 -do_polarization=1 do_oblincident=0 do_energydep=0 -do_breitdirac=0 breitdiracexpo=2.00000 -do_rulandwin=0 rulandwinwidth=0.00100000 -do_useredit=0 add_user=0.000000 mul_user=1.00000 -### Compton used_isa=1 mymethod=1 -do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 -do_polarization=1 do_oblincident=0 do_energydep=0 -do_breitdirac=0 breitdiracexpo=2.00000 -do_rulandwin=0 rulandwinwidth=0.00100000 -do_useredit=0 add_user=0.000000 mul_user=1.00000 -### Fluores used_isa=1 mymethod=1 -do_samabsorp=1 do_multscat=1 do_conabsorp=0 do_airabsorp=0 -do_polarization=1 do_oblincident=0 do_energydep=0 -do_breitdirac=0 breitdiracexpo=2.00000 -do_rulandwin=0 rulandwinwidth=0.00100000 -do_useredit=0 add_user=0.000000 mul_user=1.00000 - -##### Correction_Setup corrmethod=0 -oblincident_isa=1 dettranscoef=0.980000 samfluore_isa=1 -samfluoretype=0 samfluorescale=15.000000 -multiscat_isa=1 xraypolar_isa=1 samabsorp_isa=1 -highqscale_isa=1 highqratio=0.600000 scaleconst=0.021144960 -scaleconst_theory=0.021144960 -comptonscat_isa=1 rulandwin_isa=0 rulandintewidth=0.0100000 -comptonmethod=0 breitdirac_isa=1 breitdiracexponent=3 -detefficiency_isa=1 detefficiencytype=2 (0-1: linear, 2-3: quadratic) -detefficiency_a=-0.022312320 detefficiency_b=0.029174900 -lauediffuse_isa=1 -weight_isa=1 weighttype=0 (0: ^2, 1: , 2: Data Smoothed) -weightsmoothrmin=3.00000 weightsmoothwidth=100 weightsmoothcycles=600 -editsq_isa=0 editsqtype=0 add_sq=0.000000 mul_sq=1.00000 -editsqsmoothrmin=3.00000 editsqsmoothwidth=100 editsqsmoothcycles=600 -smoothdata_isa=0 smoothfunctype=0 smoothqmin=12.0000 smoothboxwidth=9 -interpolateqmin_isa=0 qmininterpolationtype=0 -dampfq_isa=0 dampfqtype=0 dampfqwidth=23.0000 - -##### SqGr_Optimization Setup -ftmethod=0 -## S(q) qmin=0.010000 qmax=27.000000 qgrid=0.000000 -## G(r) rmin=0.010000 rmax=60.000000 rgrid=0.010000 -## SqOptimization sqoptfunction=1 -optqmin=17.0000 optqmax=40.0000 optqgrid=0.000000 -optrmin=0.000000 optrmax=2.20000 optrgrid=0.0200000 -maxiter=20 relstep=0.000000 weighttype=0 weightfunc=0 -fitbkgmult_isa=0 fitsampmut_isa=1 fitpolariz_isa=1 -fitoblique_isa=0 fitfluores_isa=0 -fitrulandw_isa=0 fitenergya_isa=1 fitenergyb_isa=1 -fitsimurulandw_isa=1 fitDetEdepfluores_isa=0 fitDetEdepquadra_isa=0 -fitDetEdepspline_isa=0 fitDetTCoefElastic_isa=0 fitDetTCoefFluores_isa=0 -fitDetTcoefquadra_isa=0 fitDetTcoefspline_isa=0 - -##### Save&Plot Settings -datatype=GrData iqcorrtype=Int iqsimutype=SimuIq -sqcorrtype=Oblin sqtofqtype=DampFq -gropttype=OptFq miscdatatype=AtomASF -##### start data -#F si90ni10_300k_nor_1-6.gr -#D Mon Apr 21 23:17:50 2008 -#C -#S 1 G(r) -#D -#L r(A) G(r) d_r d_Gr - 1.000000e-002 -5.044565e-002 -7.539822e-004 8.698774e-004 - 2.000000e-002 -9.975593e-002 -1.507964e-003 1.699714e-003 - 3.000000e-002 -1.468212e-001 -2.261947e-003 2.451544e-003 - 4.000000e-002 -1.905826e-001 -3.015929e-003 3.091455e-003 - 5.000000e-002 -2.300554e-001 -3.769911e-003 3.591375e-003 - 6.000000e-002 -2.643508e-001 -4.523893e-003 3.930603e-003 - 7.000000e-002 -2.926941e-001 -5.277876e-003 4.097027e-003 - 8.000000e-002 -3.144414e-001 -6.031858e-003 4.088065e-003 - 9.000000e-002 -3.290915e-001 -6.785840e-003 3.911398e-003 - 1.000000e-001 -3.362954e-001 -7.539822e-003 3.585829e-003 - 1.100000e-001 -3.358625e-001 -8.293804e-003 3.143032e-003 - 1.200000e-001 -3.277631e-001 -9.047787e-003 2.632135e-003 - 1.300000e-001 -3.121288e-001 -9.801769e-003 2.131402e-003 - 1.400000e-001 -2.892501e-001 -1.055575e-002 1.768437e-003 - 1.500000e-001 -2.595712e-001 -1.130973e-002 1.697932e-003 - 1.600000e-001 -2.236838e-001 -1.206372e-002 1.943846e-003 - 1.700000e-001 -1.823186e-001 -1.281770e-002 2.359542e-003 - 1.800000e-001 -1.363355e-001 -1.357168e-002 2.801063e-003 - 1.900000e-001 -8.671203e-002 -1.432566e-002 3.184323e-003 - 2.000000e-001 -3.453073e-002 -1.507964e-002 3.464293e-003 - 2.100000e-001 1.903589e-002 -1.583363e-002 3.618747e-003 - 2.200000e-001 7.274187e-002 -1.658761e-002 3.641492e-003 - 2.300000e-001 1.252868e-001 -1.734159e-002 3.539953e-003 - 2.400000e-001 1.753373e-001 -1.809557e-002 3.334713e-003 - 2.500000e-001 2.215516e-001 -1.884956e-002 3.060243e-003 - 2.600000e-001 2.626065e-001 -1.960354e-002 2.766252e-003 - 2.700000e-001 2.972279e-001 -2.035752e-002 2.516951e-003 - 2.800000e-001 3.242235e-001 -2.111150e-002 2.379756e-003 - 2.900000e-001 3.425179e-001 -2.186548e-002 2.395030e-003 - 3.000000e-001 3.511888e-001 -2.261947e-002 2.547701e-003 - 3.100000e-001 3.495040e-001 -2.337345e-002 2.779142e-003 - 3.200000e-001 3.369570e-001 -2.412743e-002 3.023468e-003 - 3.300000e-001 3.133000e-001 -2.488141e-002 3.229175e-003 - 3.400000e-001 2.785729e-001 -2.563540e-002 3.363238e-003 - 3.500000e-001 2.331258e-001 -2.638938e-002 3.409233e-003 - 3.600000e-001 1.776343e-001 -2.714336e-002 3.365204e-003 - 3.700000e-001 1.131041e-001 -2.789734e-002 3.242384e-003 - 3.800000e-001 4.086570e-002 -2.865132e-002 3.064547e-003 - 3.900000e-001 -3.744403e-002 -2.940531e-002 2.867181e-003 - 4.000000e-001 -1.199123e-001 -3.015929e-002 2.694489e-003 - 4.100000e-001 -2.043945e-001 -3.091327e-002 2.590671e-003 - 4.200000e-001 -2.885701e-001 -3.166725e-002 2.583957e-003 - 4.300000e-001 -3.700100e-001 -3.242124e-002 2.672256e-003 - 4.400000e-001 -4.462540e-001 -3.317522e-002 2.824850e-003 - 4.500000e-001 -5.148942e-001 -3.392920e-002 2.998648e-003 - 4.600000e-001 -5.736632e-001 -3.468318e-002 3.153724e-003 - 4.700000e-001 -6.205229e-001 -3.543716e-002 3.260817e-003 - 4.800000e-001 -6.537497e-001 -3.619115e-002 3.303184e-003 - 4.900000e-001 -6.720131e-001 -3.694513e-002 3.276371e-003 - 5.000000e-001 -6.744430e-001 -3.769911e-002 3.187556e-003 - 5.100000e-001 -6.606829e-001 -3.845309e-002 3.054780e-003 - 5.200000e-001 -6.309253e-001 -3.920708e-002 2.905572e-003 - 5.300000e-001 -5.859261e-001 -3.996106e-002 2.773644e-003 - 5.400000e-001 -5.269983e-001 -4.071504e-002 2.691872e-003 - 5.500000e-001 -4.559815e-001 -4.146902e-002 2.681546e-003 - 5.600000e-001 -3.751895e-001 -4.222300e-002 2.743243e-003 - 5.700000e-001 -2.873363e-001 -4.297699e-002 2.856911e-003 - 5.800000e-001 -1.954426e-001 -4.373097e-002 2.991248e-003 - 5.900000e-001 -1.027272e-001 -4.448495e-002 3.114673e-003 - 6.000000e-001 -1.248604e-002 -4.523893e-002 3.202312e-003 - 6.100000e-001 7.203493e-002 -4.599292e-002 3.238916e-003 - 6.200000e-001 1.477682e-001 -4.674690e-002 3.219569e-003 - 6.300000e-001 2.119487e-001 -4.750088e-002 3.149489e-003 - 6.400000e-001 2.622280e-001 -4.825486e-002 3.043322e-003 - 6.500000e-001 2.967721e-001 -4.900884e-002 2.923613e-003 - 6.600000e-001 3.143398e-001 -4.976283e-002 2.817604e-003 - 6.700000e-001 3.143362e-001 -5.051681e-002 2.751345e-003 - 6.800000e-001 2.968387e-001 -5.127079e-002 2.741663e-003 - 6.900000e-001 2.625945e-001 -5.202477e-002 2.789674e-003 - 7.000000e-001 2.129879e-001 -5.277876e-002 2.880568e-003 - 7.100000e-001 1.499799e-001 -5.353274e-002 2.989921e-003 - 7.200000e-001 7.602137e-002 -5.428672e-002 3.091881e-003 - 7.300000e-001 -6.056242e-003 -5.504070e-002 3.165205e-003 - 7.400000e-001 -9.316715e-002 -5.579468e-002 3.196352e-003 - 7.500000e-001 -1.821096e-001 -5.654867e-002 3.180609e-003 - 7.600000e-001 -2.697092e-001 -5.730265e-002 3.122152e-003 - 7.700000e-001 -3.529609e-001 -5.805663e-002 3.033414e-003 - 7.800000e-001 -4.291625e-001 -5.881061e-002 2.933549e-003 - 7.900000e-001 -4.960329e-001 -5.956460e-002 2.845396e-003 - 8.000000e-001 -5.518109e-001 -6.031858e-002 2.790432e-003 - 8.100000e-001 -5.953266e-001 -6.107256e-002 2.782383e-003 - 8.200000e-001 -6.260458e-001 -6.182654e-002 2.822309e-003 - 8.300000e-001 -6.440813e-001 -6.258052e-002 2.898392e-003 - 8.400000e-001 -6.501732e-001 -6.333451e-002 2.990600e-003 - 8.500000e-001 -6.456381e-001 -6.408849e-002 3.077144e-003 - 8.600000e-001 -6.322900e-001 -6.484247e-002 3.139641e-003 - 8.700000e-001 -6.123362e-001 -6.559645e-002 3.166113e-003 - 8.800000e-001 -5.882546e-001 -6.635044e-002 3.152260e-003 - 8.900000e-001 -5.626588e-001 -6.710442e-002 3.101669e-003 - 9.000000e-001 -5.381559e-001 -6.785840e-002 3.025230e-003 - 9.100000e-001 -5.172073e-001 -6.861238e-002 2.939634e-003 - 9.200000e-001 -5.019977e-001 -6.936636e-002 2.864531e-003 - 9.300000e-001 -4.943193e-001 -7.012035e-002 2.818103e-003 - 9.400000e-001 -4.954790e-001 -7.087433e-002 2.811800e-003 - 9.500000e-001 -5.062309e-001 -7.162831e-002 2.846453e-003 - 9.600000e-001 -5.267398e-001 -7.238229e-002 2.912127e-003 - 9.700000e-001 -5.565767e-001 -7.313628e-002 2.991821e-003 - 9.800000e-001 -5.947469e-001 -7.389026e-002 3.066741e-003 - 9.900000e-001 -6.397483e-001 -7.464424e-002 3.120781e-003 - 1.000000e+000 -6.896588e-001 -7.539822e-002 3.143323e-003 - 1.010000e+000 -7.422459e-001 -7.615220e-002 3.130538e-003 - 1.020000e+000 -7.950938e-001 -7.690619e-002 3.085668e-003 - 1.030000e+000 -8.457412e-001 -7.766017e-002 3.018473e-003 - 1.040000e+000 -8.918217e-001 -7.841415e-002 2.943770e-003 - 1.050000e+000 -9.311997e-001 -7.916813e-002 2.878771e-003 - 1.060000e+000 -9.620942e-001 -7.992212e-002 2.839145e-003 - 1.070000e+000 -9.831828e-001 -8.067610e-002 2.834565e-003 - 1.080000e+000 -9.936822e-001 -8.143008e-002 2.865558e-003 - 1.090000e+000 -9.933978e-001 -8.218406e-002 2.923446e-003 - 1.100000e+000 -9.827418e-001 -8.293804e-002 2.993419e-003 - 1.110000e+000 -9.627174e-001 -8.369203e-002 3.058985e-003 - 1.120000e+000 -9.348699e-001 -8.444601e-002 3.105891e-003 - 1.130000e+000 -9.012074e-001 -8.519999e-002 3.124704e-003 - 1.140000e+000 -8.640945e-001 -8.595397e-002 3.112094e-003 - 1.150000e+000 -8.261255e-001 -8.670796e-002 3.071135e-003 - 1.160000e+000 -7.899833e-001 -8.746194e-002 3.010779e-003 - 1.170000e+000 -7.582916e-001 -8.821592e-002 2.944439e-003 - 1.180000e+000 -7.334687e-001 -8.896990e-002 2.887472e-003 - 1.190000e+000 -7.175904e-001 -8.972388e-002 2.853628e-003 - 1.200000e+000 -7.122707e-001 -9.047787e-002 2.851179e-003 - 1.210000e+000 -7.185653e-001 -9.123185e-002 2.880313e-003 - 1.220000e+000 -7.369055e-001 -9.198583e-002 2.933161e-003 - 1.230000e+000 -7.670642e-001 -9.273981e-002 2.996474e-003 - 1.240000e+000 -8.081582e-001 -9.349380e-002 3.055481e-003 - 1.250000e+000 -8.586856e-001 -9.424778e-002 3.097375e-003 - 1.260000e+000 -9.165977e-001 -9.500176e-002 3.113685e-003 - 1.270000e+000 -9.794010e-001 -9.575574e-002 3.101494e-003 - 1.280000e+000 -1.044285e+000 -9.650973e-002 3.063738e-003 - 1.290000e+000 -1.108267e+000 -9.726371e-002 3.008695e-003 - 1.300000e+000 -1.168352e+000 -9.801769e-002 2.948611e-003 - 1.310000e+000 -1.221690e+000 -9.877167e-002 2.897348e-003 - 1.320000e+000 -1.265731e+000 -9.952565e-002 2.867155e-003 - 1.330000e+000 -1.298364e+000 -1.002796e-001 2.865273e-003 - 1.340000e+000 -1.318033e+000 -1.010336e-001 2.891720e-003 - 1.350000e+000 -1.323831e+000 -1.017876e-001 2.939370e-003 - 1.360000e+000 -1.315549e+000 -1.025416e-001 2.996293e-003 - 1.370000e+000 -1.293700e+000 -1.032956e-001 3.049166e-003 - 1.380000e+000 -1.259497e+000 -1.040495e-001 3.086405e-003 - 1.390000e+000 -1.214797e+000 -1.048035e-001 3.100364e-003 - 1.400000e+000 -1.162007e+000 -1.055575e-001 3.088497e-003 - 1.410000e+000 -1.103968e+000 -1.063115e-001 3.053636e-003 - 1.420000e+000 -1.043803e+000 -1.070655e-001 3.003493e-003 - 1.430000e+000 -9.847594e-001 -1.078195e-001 2.949322e-003 - 1.440000e+000 -9.300397e-001 -1.085734e-001 2.903692e-003 - 1.450000e+000 -8.826311e-001 -1.093274e-001 2.877534e-003 - 1.460000e+000 -8.451497e-001 -1.100814e-001 2.877135e-003 - 1.470000e+000 -8.197008e-001 -1.108354e-001 2.902254e-003 - 1.480000e+000 -8.077662e-001 -1.115894e-001 2.946268e-003 - 1.490000e+000 -8.101246e-001 -1.123434e-001 2.998282e-003 - 1.500000e+000 -8.268082e-001 -1.130973e-001 3.046170e-003 - 1.510000e+000 -8.570995e-001 -1.138513e-001 3.079416e-003 - 1.520000e+000 -8.995676e-001 -1.146053e-001 3.091129e-003 - 1.530000e+000 -9.521429e-001 -1.153593e-001 3.079139e-003 - 1.540000e+000 -1.012227e+000 -1.161133e-001 3.046251e-003 - 1.550000e+000 -1.076829e+000 -1.168672e-001 2.999750e-003 - 1.560000e+000 -1.142730e+000 -1.176212e-001 2.950096e-003 - 1.570000e+000 -1.206648e+000 -1.183752e-001 2.908818e-003 - 1.580000e+000 -1.265425e+000 -1.191292e-001 2.885781e-003 - 1.590000e+000 -1.316189e+000 -1.198832e-001 2.886496e-003 - 1.600000e+000 -1.356517e+000 -1.206372e-001 2.910495e-003 - 1.610000e+000 -1.384570e+000 -1.213911e-001 2.951539e-003 - 1.620000e+000 -1.399189e+000 -1.221451e-001 2.999549e-003 - 1.630000e+000 -1.399970e+000 -1.228991e-001 3.043366e-003 - 1.640000e+000 -1.387288e+000 -1.236531e-001 3.073347e-003 - 1.650000e+000 -1.362281e+000 -1.244071e-001 3.083233e-003 - 1.660000e+000 -1.326798e+000 -1.251610e-001 3.071174e-003 - 1.670000e+000 -1.283301e+000 -1.259150e-001 3.039955e-003 - 1.680000e+000 -1.234741e+000 -1.266690e-001 2.996498e-003 - 1.690000e+000 -1.184396e+000 -1.274230e-001 2.950597e-003 - 1.700000e+000 -1.135706e+000 -1.281770e-001 2.912914e-003 - 1.710000e+000 -1.092080e+000 -1.289310e-001 2.892433e-003 - 1.720000e+000 -1.056714e+000 -1.296849e-001 2.894039e-003 - 1.730000e+000 -1.032420e+000 -1.304389e-001 2.917093e-003 - 1.740000e+000 -1.021462e+000 -1.311929e-001 2.955680e-003 - 1.750000e+000 -1.025431e+000 -1.319469e-001 3.000405e-003 - 1.760000e+000 -1.045150e+000 -1.327009e-001 3.040917e-003 - 1.770000e+000 -1.080617e+000 -1.334549e-001 3.068305e-003 - 1.780000e+000 -1.130994e+000 -1.342088e-001 3.076836e-003 - 1.790000e+000 -1.194636e+000 -1.349628e-001 3.064912e-003 - 1.800000e+000 -1.269165e+000 -1.357168e-001 3.035269e-003 - 1.810000e+000 -1.351582e+000 -1.364708e-001 2.994481e-003 - 1.820000e+000 -1.438414e+000 -1.372248e-001 2.951734e-003 - 1.830000e+000 -1.525884e+000 -1.379787e-001 2.916918e-003 - 1.840000e+000 -1.610102e+000 -1.387327e-001 2.898271e-003 - 1.850000e+000 -1.687259e+000 -1.394867e-001 2.900170e-003 - 1.860000e+000 -1.753824e+000 -1.402407e-001 2.921884e-003 - 1.870000e+000 -1.806725e+000 -1.409947e-001 2.957848e-003 - 1.880000e+000 -1.843504e+000 -1.417487e-001 2.999317e-003 - 1.890000e+000 -1.862455e+000 -1.425026e-001 3.036698e-003 - 1.900000e+000 -1.862709e+000 -1.432566e-001 3.061768e-003 - 1.910000e+000 -1.844285e+000 -1.440106e-001 3.069289e-003 - 1.920000e+000 -1.808097e+000 -1.447646e-001 3.057906e-003 - 1.930000e+000 -1.755909e+000 -1.455186e-001 3.030315e-003 - 1.940000e+000 -1.690252e+000 -1.462726e-001 2.992762e-003 - 1.950000e+000 -1.614298e+000 -1.470265e-001 2.953839e-003 - 1.960000e+000 -1.531699e+000 -1.477805e-001 2.922671e-003 - 1.970000e+000 -1.446399e+000 -1.485345e-001 2.906718e-003 - 1.980000e+000 -1.362433e+000 -1.492885e-001 2.909780e-003 - 1.990000e+000 -1.283712e+000 -1.500425e-001 2.930931e-003 - 2.000000e+000 -1.213812e+000 -1.507964e-001 2.964828e-003 - 2.010000e+000 -1.155780e+000 -1.515504e-001 3.003267e-003 - 2.020000e+000 -1.111958e+000 -1.523044e-001 3.037337e-003 - 2.030000e+000 -1.083838e+000 -1.530584e-001 3.059464e-003 - 2.040000e+000 -1.071956e+000 -1.538124e-001 3.064915e-003 - 2.050000e+000 -1.075830e+000 -1.545664e-001 3.052625e-003 - 2.060000e+000 -1.093943e+000 -1.553203e-001 3.025343e-003 - 2.070000e+000 -1.123771e+000 -1.560743e-001 2.989120e-003 - 2.080000e+000 -1.161862e+000 -1.568283e-001 2.952143e-003 - 2.090000e+000 -1.203955e+000 -1.575823e-001 2.922985e-003 - 2.100000e+000 -1.245137e+000 -1.583363e-001 2.908542e-003 - 2.110000e+000 -1.280029e+000 -1.590902e-001 2.912198e-003 - 2.120000e+000 -1.302995e+000 -1.598442e-001 2.932880e-003 - 2.130000e+000 -1.308369e+000 -1.605982e-001 2.965409e-003 - 2.140000e+000 -1.290679e+000 -1.613522e-001 3.001981e-003 - 2.150000e+000 -1.244868e+000 -1.621062e-001 3.034190e-003 - 2.160000e+000 -1.166500e+000 -1.628602e-001 3.054942e-003 - 2.170000e+000 -1.051944e+000 -1.636141e-001 3.059867e-003 - 2.180000e+000 -8.985252e-001 -1.643681e-001 3.048085e-003 - 2.190000e+000 -7.046397e-001 -1.651221e-001 3.022321e-003 - 2.200000e+000 -4.698345e-001 -1.658761e-001 2.988384e-003 - 2.210000e+000 -1.948401e-001 -1.666301e-001 2.954027e-003 - 2.220000e+000 1.184366e-001 -1.673841e-001 2.927273e-003 - 2.230000e+000 4.669595e-001 -1.681380e-001 2.914482e-003 - 2.240000e+000 8.466488e-001 -1.688920e-001 2.918663e-003 - 2.250000e+000 1.252499e+000 -1.696460e-001 2.938649e-003 - 2.260000e+000 1.678721e+000 -1.704000e-001 2.969470e-003 - 2.270000e+000 2.118912e+000 -1.711540e-001 3.003752e-003 - 2.280000e+000 2.566229e+000 -1.719079e-001 3.033614e-003 - 2.290000e+000 3.013574e+000 -1.726619e-001 3.052455e-003 - 2.300000e+000 3.453782e+000 -1.734159e-001 3.056281e-003 - 2.310000e+000 3.879793e+000 -1.741699e-001 3.044406e-003 - 2.320000e+000 4.284817e+000 -1.749239e-001 3.019552e-003 - 2.330000e+000 4.662485e+000 -1.756779e-001 2.987313e-003 - 2.340000e+000 5.006971e+000 -1.764318e-001 2.955048e-003 - 2.350000e+000 5.313101e+000 -1.771858e-001 2.930272e-003 - 2.360000e+000 5.576425e+000 -1.779398e-001 2.918841e-003 - 2.370000e+000 5.793282e+000 -1.786938e-001 2.923404e-003 - 2.380000e+000 5.960827e+000 -1.794478e-001 2.942684e-003 - 2.390000e+000 6.077044e+000 -1.802018e-001 2.971873e-003 - 2.400000e+000 6.140744e+000 -1.809557e-001 3.003972e-003 - 2.410000e+000 6.151537e+000 -1.817097e-001 3.031570e-003 - 2.420000e+000 6.109802e+000 -1.824637e-001 3.048523e-003 - 2.430000e+000 6.016643e+000 -1.832177e-001 3.051196e-003 - 2.440000e+000 5.873834e+000 -1.839717e-001 3.039113e-003 - 2.450000e+000 5.683772e+000 -1.847256e-001 3.015022e-003 - 2.460000e+000 5.449415e+000 -1.854796e-001 2.984357e-003 - 2.470000e+000 5.174225e+000 -1.862336e-001 2.954146e-003 - 2.480000e+000 4.862112e+000 -1.869876e-001 2.931458e-003 - 2.490000e+000 4.517377e+000 -1.877416e-001 2.921688e-003 - 2.500000e+000 4.144649e+000 -1.884956e-001 2.927134e-003 - 2.510000e+000 3.748834e+000 -1.892495e-001 2.946371e-003 - 2.520000e+000 3.335049e+000 -1.900035e-001 2.974683e-003 - 2.530000e+000 2.908563e+000 -1.907575e-001 3.005351e-003 - 2.540000e+000 2.474728e+000 -1.915115e-001 3.031344e-003 - 2.550000e+000 2.038910e+000 -1.922655e-001 3.046904e-003 - 2.560000e+000 1.606415e+000 -1.930195e-001 3.048698e-003 - 2.570000e+000 1.182408e+000 -1.937734e-001 3.036433e-003 - 2.580000e+000 7.718332e-001 -1.945274e-001 3.012883e-003 - 2.590000e+000 3.793285e-001 -1.952814e-001 2.983344e-003 - 2.600000e+000 9.141401e-003 -1.960354e-001 2.954564e-003 - 2.610000e+000 -3.349529e-001 -1.967894e-001 2.933245e-003 - 2.620000e+000 -6.497285e-001 -1.975433e-001 2.924415e-003 - 2.630000e+000 -9.325782e-001 -1.982973e-001 2.930106e-003 - 2.640000e+000 -1.181571e+000 -1.990513e-001 2.948814e-003 - 2.650000e+000 -1.395495e+000 -1.998053e-001 2.975940e-003 - 2.660000e+000 -1.573888e+000 -2.005593e-001 3.005037e-003 - 2.670000e+000 -1.717041e+000 -2.013133e-001 3.029423e-003 - 2.680000e+000 -1.825988e+000 -2.020672e-001 3.043678e-003 - 2.690000e+000 -1.902471e+000 -2.028212e-001 3.044739e-003 - 2.700000e+000 -1.948890e+000 -2.035752e-001 3.032463e-003 - 2.710000e+000 -1.968219e+000 -2.043292e-001 3.009631e-003 - 2.720000e+000 -1.963920e+000 -2.050832e-001 2.981403e-003 - 2.730000e+000 -1.939831e+000 -2.058371e-001 2.954257e-003 - 2.740000e+000 -1.900045e+000 -2.065911e-001 2.934548e-003 - 2.750000e+000 -1.848783e+000 -2.073451e-001 2.926957e-003 - 2.760000e+000 -1.790258e+000 -2.080991e-001 2.933263e-003 - 2.770000e+000 -1.728552e+000 -2.088531e-001 2.951873e-003 - 2.780000e+000 -1.667486e+000 -2.096071e-001 2.978281e-003 - 2.790000e+000 -1.610513e+000 -2.103610e-001 3.006276e-003 - 2.800000e+000 -1.560620e+000 -2.111150e-001 3.029478e-003 - 2.810000e+000 -1.520251e+000 -2.118690e-001 3.042762e-003 - 2.820000e+000 -1.491252e+000 -2.126230e-001 3.043289e-003 - 2.830000e+000 -1.474841e+000 -2.133770e-001 3.031030e-003 - 2.840000e+000 -1.471599e+000 -2.141310e-001 3.008751e-003 - 2.850000e+000 -1.481491e+000 -2.148849e-001 2.981462e-003 - 2.860000e+000 -1.503905e+000 -2.156389e-001 2.955387e-003 - 2.870000e+000 -1.537714e+000 -2.163929e-001 2.936569e-003 - 2.880000e+000 -1.581352e+000 -2.171469e-001 2.929404e-003 - 2.890000e+000 -1.632913e+000 -2.179009e-001 2.935499e-003 - 2.900000e+000 -1.690246e+000 -2.186548e-001 2.953253e-003 - 2.910000e+000 -1.751065e+000 -2.194088e-001 2.978317e-003 - 2.920000e+000 -1.813057e+000 -2.201628e-001 3.004763e-003 - 2.930000e+000 -1.873980e+000 -2.209168e-001 3.026537e-003 - 2.940000e+000 -1.931759e+000 -2.216708e-001 3.038820e-003 - 2.950000e+000 -1.984568e+000 -2.224248e-001 3.038998e-003 - 2.960000e+000 -2.030892e+000 -2.231787e-001 3.027150e-003 - 2.970000e+000 -2.069580e+000 -2.239327e-001 3.006006e-003 - 2.980000e+000 -2.099873e+000 -2.246867e-001 2.980399e-003 - 2.990000e+000 -2.121415e+000 -2.254407e-001 2.956248e-003 - 3.000000e+000 -2.134249e+000 -2.261947e-001 2.939226e-003 - 3.010000e+000 -2.138790e+000 -2.269487e-001 2.933366e-003 - 3.020000e+000 -2.135792e+000 -2.277026e-001 2.940016e-003 - 3.030000e+000 -2.126295e+000 -2.284566e-001 2.957493e-003 - 3.040000e+000 -2.111565e+000 -2.292106e-001 2.981554e-003 - 3.050000e+000 -2.093031e+000 -2.299646e-001 3.006523e-003 - 3.060000e+000 -2.072217e+000 -2.307186e-001 3.026677e-003 - 3.070000e+000 -2.050675e+000 -2.314725e-001 3.037529e-003 - 3.080000e+000 -2.029920e+000 -2.322265e-001 3.036736e-003 - 3.090000e+000 -2.011372e+000 -2.329805e-001 3.024546e-003 - 3.100000e+000 -1.996302e+000 -2.337345e-001 3.003730e-003 - 3.110000e+000 -1.985797e+000 -2.344885e-001 2.979025e-003 - 3.120000e+000 -1.980721e+000 -2.352425e-001 2.956131e-003 - 3.130000e+000 -1.981692e+000 -2.359964e-001 2.940416e-003 - 3.140000e+000 -1.989076e+000 -2.367504e-001 2.935595e-003 - 3.150000e+000 -2.002975e+000 -2.375044e-001 2.942767e-003 - 3.160000e+000 -2.023239e+000 -2.382584e-001 2.960124e-003 - 3.170000e+000 -2.049471e+000 -2.390124e-001 2.983455e-003 - 3.180000e+000 -2.081050e+000 -2.397663e-001 3.007243e-003 - 3.190000e+000 -2.117149e+000 -2.405203e-001 3.026006e-003 - 3.200000e+000 -2.156763e+000 -2.412743e-001 3.035513e-003 - 3.210000e+000 -2.198734e+000 -2.420283e-001 3.033647e-003 - 3.220000e+000 -2.241784e+000 -2.427823e-001 3.020811e-003 - 3.230000e+000 -2.284544e+000 -2.435363e-001 2.999842e-003 - 3.240000e+000 -2.325582e+000 -2.442902e-001 2.975447e-003 - 3.250000e+000 -2.363441e+000 -2.450442e-001 2.953208e-003 - 3.260000e+000 -2.396664e+000 -2.457982e-001 2.938315e-003 - 3.270000e+000 -2.423836e+000 -2.465522e-001 2.934299e-003 - 3.280000e+000 -2.443608e+000 -2.473062e-001 2.942109e-003 - 3.290000e+000 -2.454742e+000 -2.480602e-001 2.959876e-003 - 3.300000e+000 -2.456136e+000 -2.488141e-001 2.983419e-003 - 3.310000e+000 -2.446869e+000 -2.495681e-001 3.007333e-003 - 3.320000e+000 -2.426228e+000 -2.503221e-001 3.026279e-003 - 3.330000e+000 -2.393748e+000 -2.510761e-001 3.036161e-003 - 3.340000e+000 -2.349235e+000 -2.518301e-001 3.034949e-003 - 3.350000e+000 -2.292798e+000 -2.525840e-001 3.023051e-003 - 3.360000e+000 -2.224866e+000 -2.533380e-001 3.003219e-003 - 3.370000e+000 -2.146197e+000 -2.540920e-001 2.979977e-003 - 3.380000e+000 -2.057884e+000 -2.548460e-001 2.958668e-003 - 3.390000e+000 -1.961336e+000 -2.556000e-001 2.944230e-003 - 3.400000e+000 -1.858262e+000 -2.563540e-001 2.939998e-003 - 3.410000e+000 -1.750626e+000 -2.571079e-001 2.946849e-003 - 3.420000e+000 -1.640597e+000 -2.578619e-001 2.962986e-003 - 3.430000e+000 -1.530482e+000 -2.586159e-001 2.984443e-003 - 3.440000e+000 -1.422642e+000 -2.593699e-001 3.006112e-003 - 3.450000e+000 -1.319404e+000 -2.601239e-001 3.022980e-003 - 3.460000e+000 -1.222959e+000 -2.608779e-001 3.031245e-003 - 3.470000e+000 -1.135258e+000 -2.616318e-001 3.029093e-003 - 3.480000e+000 -1.057905e+000 -2.623858e-001 3.017051e-003 - 3.490000e+000 -9.920558e-001 -2.631398e-001 2.997862e-003 - 3.500000e+000 -9.383276e-001 -2.638938e-001 2.975924e-003 - 3.510000e+000 -8.967178e-001 -2.646478e-001 2.956340e-003 - 3.520000e+000 -8.665455e-001 -2.654017e-001 2.943743e-003 - 3.530000e+000 -8.464158e-001 -2.661557e-001 2.941154e-003 - 3.540000e+000 -8.342101e-001 -2.669097e-001 2.949198e-003 - 3.550000e+000 -8.271074e-001 -2.676637e-001 2.965950e-003 - 3.560000e+000 -8.216367e-001 -2.684177e-001 2.987448e-003 - 3.570000e+000 -8.137612e-001 -2.691717e-001 3.008711e-003 - 3.580000e+000 -7.989935e-001 -2.699256e-001 3.024920e-003 - 3.590000e+000 -7.725385e-001 -2.706796e-001 3.032482e-003 - 3.600000e+000 -7.294605e-001 -2.714336e-001 3.029764e-003 - 3.610000e+000 -6.648694e-001 -2.721876e-001 3.017401e-003 - 3.620000e+000 -5.741182e-001 -2.729416e-001 2.998163e-003 - 3.630000e+000 -4.530057e-001 -2.736955e-001 2.976388e-003 - 3.640000e+000 -2.979757e-001 -2.744495e-001 2.957049e-003 - 3.650000e+000 -1.063044e-001 -2.752035e-001 2.944613e-003 - 3.660000e+000 1.237328e-001 -2.759575e-001 2.941950e-003 - 3.670000e+000 3.927215e-001 -2.767115e-001 2.949600e-003 - 3.680000e+000 7.000045e-001 -2.774655e-001 2.965644e-003 - 3.690000e+000 1.043618e+000 -2.782194e-001 2.986222e-003 - 3.700000e+000 1.420272e+000 -2.789734e-001 3.006522e-003 - 3.710000e+000 1.825381e+000 -2.797274e-001 3.021925e-003 - 3.720000e+000 2.253139e+000 -2.804814e-001 3.029021e-003 - 3.730000e+000 2.696645e+000 -2.812354e-001 3.026304e-003 - 3.740000e+000 3.148069e+000 -2.819894e-001 3.014462e-003 - 3.750000e+000 3.598859e+000 -2.827433e-001 2.996220e-003 - 3.760000e+000 4.039976e+000 -2.834973e-001 2.975775e-003 - 3.770000e+000 4.462159e+000 -2.842513e-001 2.957879e-003 - 3.780000e+000 4.856194e+000 -2.850053e-001 2.946741e-003 - 3.790000e+000 5.213195e+000 -2.857593e-001 2.944991e-003 - 3.800000e+000 5.524877e+000 -2.865132e-001 2.953008e-003 - 3.810000e+000 5.783809e+000 -2.872672e-001 2.968831e-003 - 3.820000e+000 5.983643e+000 -2.880212e-001 2.988680e-003 - 3.830000e+000 6.119312e+000 -2.887752e-001 3.007920e-003 - 3.840000e+000 6.187177e+000 -2.895292e-001 3.022157e-003 - 3.850000e+000 6.185143e+000 -2.902832e-001 3.028204e-003 - 3.860000e+000 6.112705e+000 -2.910371e-001 3.024738e-003 - 3.870000e+000 5.970962e+000 -2.917911e-001 3.012556e-003 - 3.880000e+000 5.762561e+000 -2.925451e-001 2.994403e-003 - 3.890000e+000 5.491614e+000 -2.932991e-001 2.974407e-003 - 3.900000e+000 5.163552e+000 -2.940531e-001 2.957172e-003 - 3.910000e+000 4.784953e+000 -2.948071e-001 2.946715e-003 - 3.920000e+000 4.363337e+000 -2.955610e-001 2.945481e-003 - 3.930000e+000 3.906943e+000 -2.963150e-001 2.953713e-003 - 3.940000e+000 3.424487e+000 -2.970690e-001 2.969407e-003 - 3.950000e+000 2.924927e+000 -2.978230e-001 2.988836e-003 - 3.960000e+000 2.417224e+000 -2.985770e-001 3.007495e-003 - 3.970000e+000 1.910125e+000 -2.993309e-001 3.021158e-003 - 3.980000e+000 1.411962e+000 -3.000849e-001 3.026807e-003 - 3.990000e+000 9.304826e-001 -3.008389e-001 3.023250e-003 - 4.000000e+000 4.727113e-001 -3.015929e-001 3.011347e-003 - 4.010000e+000 4.484123e-002 -3.023469e-001 2.993826e-003 - 4.020000e+000 -3.478339e-001 -3.031009e-001 2.974712e-003 - 4.030000e+000 -7.009562e-001 -3.038548e-001 2.958438e-003 - 4.040000e+000 -1.011107e+000 -3.046088e-001 2.948821e-003 - 4.050000e+000 -1.275781e+000 -3.053628e-001 2.948117e-003 - 4.060000e+000 -1.493338e+000 -3.061168e-001 2.956452e-003 - 4.070000e+000 -1.662933e+000 -3.068708e-001 2.971799e-003 - 4.080000e+000 -1.784440e+000 -3.076247e-001 2.990514e-003 - 4.090000e+000 -1.858355e+000 -3.083787e-001 3.008248e-003 - 4.100000e+000 -1.885717e+000 -3.091327e-001 3.020972e-003 - 4.110000e+000 -1.868015e+000 -3.098867e-001 3.025859e-003 - 4.120000e+000 -1.807113e+000 -3.106407e-001 3.021864e-003 - 4.130000e+000 -1.705180e+000 -3.113947e-001 3.009925e-003 - 4.140000e+000 -1.564638e+000 -3.121486e-001 2.992765e-003 - 4.150000e+000 -1.388122e+000 -3.129026e-001 2.974307e-003 - 4.160000e+000 -1.178448e+000 -3.136566e-001 2.958819e-003 - 4.170000e+000 -9.386033e-001 -3.144106e-001 2.949905e-003 - 4.180000e+000 -6.717341e-001 -3.151646e-001 2.949626e-003 - 4.190000e+000 -3.811497e-001 -3.159186e-001 2.957972e-003 - 4.200000e+000 -7.032301e-002 -3.166725e-001 2.972875e-003 - 4.210000e+000 2.571078e-001 -3.174265e-001 2.990757e-003 - 4.220000e+000 5.973425e-001 -3.181805e-001 3.007420e-003 - 4.230000e+000 9.464304e-001 -3.189345e-001 3.019036e-003 - 4.240000e+000 1.300293e+000 -3.196885e-001 3.022984e-003 - 4.250000e+000 1.654756e+000 -3.204424e-001 3.018403e-003 - 4.260000e+000 2.005602e+000 -3.211964e-001 3.006352e-003 - 4.270000e+000 2.348625e+000 -3.219504e-001 2.989595e-003 - 4.280000e+000 2.679707e+000 -3.227044e-001 2.972011e-003 - 4.290000e+000 2.994897e+000 -3.234584e-001 2.957730e-003 - 4.300000e+000 3.290500e+000 -3.242124e-001 2.950165e-003 - 4.310000e+000 3.563159e+000 -3.249663e-001 2.951157e-003 - 4.320000e+000 3.809951e+000 -3.257203e-001 2.960503e-003 - 4.330000e+000 4.028455e+000 -3.264743e-001 2.976011e-003 - 4.340000e+000 4.216823e+000 -3.272283e-001 2.994064e-003 - 4.350000e+000 4.373827e+000 -3.279823e-001 3.010505e-003 - 4.360000e+000 4.498888e+000 -3.287363e-001 3.021602e-003 - 4.370000e+000 4.592081e+000 -3.294902e-001 3.024862e-003 - 4.380000e+000 4.654116e+000 -3.302442e-001 3.019541e-003 - 4.390000e+000 4.686294e+000 -3.309982e-001 3.006798e-003 - 4.400000e+000 4.690438e+000 -3.317522e-001 2.989452e-003 - 4.410000e+000 4.668807e+000 -3.325062e-001 2.971398e-003 - 4.420000e+000 4.623981e+000 -3.332601e-001 2.956751e-003 - 4.430000e+000 4.558748e+000 -3.340141e-001 2.948883e-003 - 4.440000e+000 4.475966e+000 -3.347681e-001 2.949600e-003 - 4.450000e+000 4.378439e+000 -3.355221e-001 2.958688e-003 - 4.460000e+000 4.268789e+000 -3.362761e-001 2.973974e-003 - 4.470000e+000 4.149335e+000 -3.370301e-001 2.991890e-003 - 4.480000e+000 4.022004e+000 -3.377840e-001 3.008351e-003 - 4.490000e+000 3.888244e+000 -3.385380e-001 3.019695e-003 - 4.500000e+000 3.748985e+000 -3.392920e-001 3.023475e-003 - 4.510000e+000 3.604609e+000 -3.400460e-001 3.018953e-003 - 4.520000e+000 3.454969e+000 -3.408000e-001 3.007237e-003 - 4.530000e+000 3.299426e+000 -3.415539e-001 2.991037e-003 - 4.540000e+000 3.136920e+000 -3.423079e-001 2.974086e-003 - 4.550000e+000 2.966071e+000 -3.430619e-001 2.960311e-003 - 4.560000e+000 2.785292e+000 -3.438159e-001 2.952910e-003 - 4.570000e+000 2.592930e+000 -3.445699e-001 2.953570e-003 - 4.580000e+000 2.387405e+000 -3.453239e-001 2.962048e-003 - 4.590000e+000 2.167356e+000 -3.460778e-001 2.976246e-003 - 4.600000e+000 1.931781e+000 -3.468318e-001 2.992761e-003 - 4.610000e+000 1.680165e+000 -3.475858e-001 3.007722e-003 - 4.620000e+000 1.412580e+000 -3.483398e-001 3.017699e-003 - 4.630000e+000 1.129769e+000 -3.490938e-001 3.020446e-003 - 4.640000e+000 8.331946e-001 -3.498478e-001 3.015372e-003 - 4.650000e+000 5.250509e-001 -3.506017e-001 3.003650e-003 - 4.660000e+000 2.082425e-001 -3.513557e-001 2.987964e-003 - 4.670000e+000 -1.136736e-001 -3.521097e-001 2.971934e-003 - 4.680000e+000 -4.365805e-001 -3.528637e-001 2.959294e-003 - 4.690000e+000 -7.559245e-001 -3.536177e-001 2.953014e-003 - 4.700000e+000 -1.066864e+000 -3.543716e-001 2.954563e-003 - 4.710000e+000 -1.364438e+000 -3.551256e-001 2.963535e-003 - 4.720000e+000 -1.643748e+000 -3.558796e-001 2.977762e-003 - 4.730000e+000 -1.900139e+000 -3.566336e-001 2.993870e-003 - 4.740000e+000 -2.129386e+000 -3.573876e-001 3.008106e-003 - 4.750000e+000 -2.327854e+000 -3.581416e-001 3.017205e-003 - 4.760000e+000 -2.492657e+000 -3.588955e-001 3.019106e-003 - 4.770000e+000 -2.621771e+000 -3.596495e-001 3.013383e-003 - 4.780000e+000 -2.714126e+000 -3.604035e-001 3.001330e-003 - 4.790000e+000 -2.769661e+000 -3.611575e-001 2.985687e-003 - 4.800000e+000 -2.789336e+000 -3.619115e-001 2.970059e-003 - 4.810000e+000 -2.775109e+000 -3.626655e-001 2.958098e-003 - 4.820000e+000 -2.729868e+000 -3.634194e-001 2.952644e-003 - 4.830000e+000 -2.657334e+000 -3.641734e-001 2.955016e-003 - 4.840000e+000 -2.561928e+000 -3.649274e-001 2.964682e-003 - 4.850000e+000 -2.448616e+000 -3.656814e-001 2.979391e-003 - 4.860000e+000 -2.322730e+000 -3.664354e-001 2.995748e-003 - 4.870000e+000 -2.189778e+000 -3.671893e-001 3.010031e-003 - 4.880000e+000 -2.055259e+000 -3.679433e-001 3.019046e-003 - 4.890000e+000 -1.924468e+000 -3.686973e-001 3.020810e-003 - 4.900000e+000 -1.802325e+000 -3.694513e-001 3.014966e-003 - 4.910000e+000 -1.693215e+000 -3.702053e-001 3.002842e-003 - 4.920000e+000 -1.600858e+000 -3.709593e-001 2.987177e-003 - 4.930000e+000 -1.528206e+000 -3.717132e-001 2.971532e-003 - 4.940000e+000 -1.477372e+000 -3.724672e-001 2.959487e-003 - 4.950000e+000 -1.449595e+000 -3.732212e-001 2.953807e-003 - 4.960000e+000 -1.445237e+000 -3.739752e-001 2.955755e-003 - 4.970000e+000 -1.463823e+000 -3.747292e-001 2.964785e-003 - 4.980000e+000 -1.504095e+000 -3.754831e-001 2.978686e-003 - 4.990000e+000 -1.564111e+000 -3.762371e-001 2.994152e-003 - 5.000000e+000 -1.641350e+000 -3.769911e-001 3.007581e-003 - 5.010000e+000 -1.732848e+000 -3.777451e-001 3.015906e-003 - 5.020000e+000 -1.835327e+000 -3.784991e-001 3.017259e-003 - 5.030000e+000 -1.945346e+000 -3.792531e-001 3.011362e-003 - 5.040000e+000 -2.059433e+000 -3.800070e-001 2.999572e-003 - 5.050000e+000 -2.174217e+000 -3.807610e-001 2.984595e-003 - 5.060000e+000 -2.286545e+000 -3.815150e-001 2.969898e-003 - 5.070000e+000 -2.393582e+000 -3.822690e-001 2.958928e-003 - 5.080000e+000 -2.492884e+000 -3.830230e-001 2.954286e-003 - 5.090000e+000 -2.582455e+000 -3.837770e-001 2.957091e-003 - 5.100000e+000 -2.660775e+000 -3.845309e-001 2.966692e-003 - 5.110000e+000 -2.726809e+000 -3.852849e-001 2.980842e-003 - 5.120000e+000 -2.779985e+000 -3.860389e-001 2.996264e-003 - 5.130000e+000 -2.820161e+000 -3.867929e-001 3.009437e-003 - 5.140000e+000 -2.847570e+000 -3.875469e-001 3.017405e-003 - 5.150000e+000 -2.862752e+000 -3.883008e-001 3.018411e-003 - 5.160000e+000 -2.866479e+000 -3.890548e-001 3.012265e-003 - 5.170000e+000 -2.859677e+000 -3.898088e-001 3.000374e-003 - 5.180000e+000 -2.843337e+000 -3.905628e-001 2.985447e-003 - 5.190000e+000 -2.818448e+000 -3.913168e-001 2.970910e-003 - 5.200000e+000 -2.785922e+000 -3.920708e-001 2.960131e-003 - 5.210000e+000 -2.746536e+000 -3.928247e-001 2.955627e-003 - 5.220000e+000 -2.700888e+000 -3.935787e-001 2.958441e-003 - 5.230000e+000 -2.649366e+000 -3.943327e-001 2.967887e-003 - 5.240000e+000 -2.592135e+000 -3.950867e-001 2.981728e-003 - 5.250000e+000 -2.529135e+000 -3.958407e-001 2.996740e-003 - 5.260000e+000 -2.460099e+000 -3.965947e-001 3.009487e-003 - 5.270000e+000 -2.384586e+000 -3.973486e-001 3.017103e-003 - 5.280000e+000 -2.302018e+000 -3.981026e-001 3.017907e-003 - 5.290000e+000 -2.211737e+000 -3.988566e-001 3.011750e-003 - 5.300000e+000 -2.113059e+000 -3.996106e-001 3.000038e-003 - 5.310000e+000 -2.005338e+000 -4.003646e-001 2.985429e-003 - 5.320000e+000 -1.888032e+000 -4.011185e-001 2.971254e-003 - 5.330000e+000 -1.760759e+000 -4.018725e-001 2.960770e-003 - 5.340000e+000 -1.623358e+000 -4.026265e-001 2.956381e-003 - 5.350000e+000 -1.475936e+000 -4.033805e-001 2.959060e-003 - 5.360000e+000 -1.318908e+000 -4.041345e-001 2.968102e-003 - 5.370000e+000 -1.153028e+000 -4.048885e-001 2.981322e-003 - 5.380000e+000 -9.794056e-001 -4.056424e-001 2.995599e-003 - 5.390000e+000 -7.995084e-001 -4.063964e-001 3.007638e-003 - 5.400000e+000 -6.151555e-001 -4.071504e-001 3.014712e-003 - 5.410000e+000 -4.284942e-001 -4.079044e-001 3.015263e-003 - 5.420000e+000 -2.419655e-001 -4.086584e-001 3.009215e-003 - 5.430000e+000 -5.825803e-002 -4.094123e-001 2.997983e-003 - 5.440000e+000 1.197489e-001 -4.101663e-001 2.984169e-003 - 5.450000e+000 2.890513e-001 -4.109203e-001 2.970982e-003 - 5.460000e+000 4.465933e-001 -4.116743e-001 2.961514e-003 - 5.470000e+000 5.893466e-001 -4.124283e-001 2.957993e-003 - 5.480000e+000 7.143919e-001 -4.131823e-001 2.961239e-003 - 5.490000e+000 8.190034e-001 -4.139362e-001 2.970464e-003 - 5.500000e+000 9.007309e-001 -4.146902e-001 2.983472e-003 - 5.510000e+000 9.574803e-001 -4.154442e-001 2.997215e-003 - 5.520000e+000 9.875879e-001 -4.161982e-001 3.008521e-003 - 5.530000e+000 9.898877e-001 -4.169522e-001 3.014823e-003 - 5.540000e+000 9.637695e-001 -4.177062e-001 3.014711e-003 - 5.550000e+000 9.092252e-001 -4.184601e-001 3.008227e-003 - 5.560000e+000 8.268815e-001 -4.192141e-001 2.996856e-003 - 5.570000e+000 7.180188e-001 -4.199681e-001 2.983197e-003 - 5.580000e+000 5.845721e-001 -4.207221e-001 2.970401e-003 - 5.590000e+000 4.291169e-001 -4.214761e-001 2.961440e-003 - 5.600000e+000 2.548347e-001 -4.222300e-001 2.958404e-003 - 5.610000e+000 6.546269e-002 -4.229840e-001 2.961979e-003 - 5.620000e+000 -1.347755e-001 -4.237380e-001 2.971282e-003 - 5.630000e+000 -3.412559e-001 -4.244920e-001 2.984086e-003 - 5.640000e+000 -5.490551e-001 -4.252460e-001 2.997377e-003 - 5.650000e+000 -7.530650e-001 -4.260000e-001 3.008071e-003 - 5.660000e+000 -9.481184e-001 -4.267539e-001 3.013722e-003 - 5.670000e+000 -1.129122e+000 -4.275079e-001 3.013045e-003 - 5.680000e+000 -1.291195e+000 -4.282619e-001 3.006195e-003 - 5.690000e+000 -1.429804e+000 -4.290159e-001 2.994723e-003 - 5.700000e+000 -1.540899e+000 -4.297699e-001 2.981251e-003 - 5.710000e+000 -1.621042e+000 -4.305239e-001 2.968892e-003 - 5.720000e+000 -1.667511e+000 -4.312778e-001 2.960535e-003 - 5.730000e+000 -1.678406e+000 -4.320318e-001 2.958155e-003 - 5.740000e+000 -1.652719e+000 -4.327858e-001 2.962322e-003 - 5.750000e+000 -1.590388e+000 -4.335398e-001 2.972060e-003 - 5.760000e+000 -1.492323e+000 -4.342938e-001 2.985094e-003 - 5.770000e+000 -1.360402e+000 -4.350477e-001 2.998413e-003 - 5.780000e+000 -1.197440e+000 -4.358017e-001 3.008982e-003 - 5.790000e+000 -1.007130e+000 -4.365557e-001 3.014428e-003 - 5.800000e+000 -7.939509e-001 -4.373097e-001 3.013548e-003 - 5.810000e+000 -5.630545e-001 -4.380637e-001 3.006565e-003 - 5.820000e+000 -3.201287e-001 -4.388177e-001 2.995073e-003 - 5.830000e+000 -7.124029e-002 -4.395716e-001 2.981698e-003 - 5.840000e+000 1.773348e-001 -4.403256e-001 2.969520e-003 - 5.850000e+000 4.192902e-001 -4.410796e-001 2.961366e-003 - 5.860000e+000 6.484703e-001 -4.418336e-001 2.959138e-003 - 5.870000e+000 8.590480e-001 -4.425876e-001 2.963341e-003 - 5.880000e+000 1.045693e+000 -4.433415e-001 2.972964e-003 - 5.890000e+000 1.203724e+000 -4.440955e-001 2.985734e-003 - 5.900000e+000 1.329244e+000 -4.448495e-001 2.998682e-003 - 5.910000e+000 1.419240e+000 -4.456035e-001 3.008839e-003 - 5.920000e+000 1.471671e+000 -4.463575e-001 3.013911e-003 - 5.930000e+000 1.485502e+000 -4.471115e-001 3.012771e-003 - 5.940000e+000 1.460727e+000 -4.478654e-001 3.005690e-003 - 5.950000e+000 1.398340e+000 -4.486194e-001 2.994280e-003 - 5.960000e+000 1.300285e+000 -4.493734e-001 2.981144e-003 - 5.970000e+000 1.169369e+000 -4.501274e-001 2.969305e-003 - 5.980000e+000 1.009149e+000 -4.508814e-001 2.961507e-003 - 5.990000e+000 8.237964e-001 -4.516354e-001 2.959565e-003 - 6.000000e+000 6.179453e-001 -4.523893e-001 2.963915e-003 - 6.010000e+000 3.965231e-001 -4.531433e-001 2.973509e-003 - 6.020000e+000 1.645796e-001 -4.538973e-001 2.986085e-003 - 6.030000e+000 -7.288521e-002 -4.546513e-001 2.998721e-003 - 6.040000e+000 -3.110869e-001 -4.554053e-001 3.008524e-003 - 6.050000e+000 -5.456095e-001 -4.561592e-001 3.013282e-003 - 6.060000e+000 -7.725408e-001 -4.569132e-001 3.011940e-003 - 6.070000e+000 -9.885843e-001 -4.576672e-001 3.004815e-003 - 6.080000e+000 -1.191145e+000 -4.584212e-001 2.993525e-003 - 6.090000e+000 -1.378386e+000 -4.591752e-001 2.980642e-003 - 6.100000e+000 -1.549252e+000 -4.599292e-001 2.969119e-003 - 6.110000e+000 -1.703467e+000 -4.606831e-001 2.961614e-003 - 6.120000e+000 -1.841493e+000 -4.614371e-001 2.959856e-003 - 6.130000e+000 -1.964464e+000 -4.621911e-001 2.964221e-003 - 6.140000e+000 -2.074096e+000 -4.629451e-001 2.973646e-003 - 6.150000e+000 -2.172571e+000 -4.636991e-001 2.985898e-003 - 6.160000e+000 -2.262399e+000 -4.644531e-001 2.998132e-003 - 6.170000e+000 -2.346280e+000 -4.652070e-001 3.007554e-003 - 6.180000e+000 -2.426943e+000 -4.659610e-001 3.012057e-003 - 6.190000e+000 -2.506991e+000 -4.667150e-001 3.010672e-003 - 6.200000e+000 -2.588752e+000 -4.674690e-001 3.003766e-003 - 6.210000e+000 -2.674135e+000 -4.682230e-001 2.992960e-003 - 6.220000e+000 -2.764499e+000 -4.689769e-001 2.980772e-003 - 6.230000e+000 -2.860549e+000 -4.697309e-001 2.970055e-003 - 6.240000e+000 -2.962243e+000 -4.704849e-001 2.963334e-003 - 6.250000e+000 -3.068737e+000 -4.712389e-001 2.962200e-003 - 6.260000e+000 -3.178354e+000 -4.719929e-001 2.966917e-003 - 6.270000e+000 -3.288579e+000 -4.727469e-001 2.976361e-003 - 6.280000e+000 -3.396093e+000 -4.735008e-001 2.988299e-003 - 6.290000e+000 -3.496830e+000 -4.742548e-001 2.999942e-003 - 6.300000e+000 -3.586070e+000 -4.750088e-001 3.008599e-003 - 6.310000e+000 -3.658551e+000 -4.757628e-001 3.012284e-003 - 6.320000e+000 -3.708616e+000 -4.765168e-001 3.010143e-003 - 6.330000e+000 -3.730369e+000 -4.772707e-001 3.002641e-003 - 6.340000e+000 -3.717855e+000 -4.780247e-001 2.991452e-003 - 6.350000e+000 -3.665251e+000 -4.787787e-001 2.979108e-003 - 6.360000e+000 -3.567061e+000 -4.795327e-001 2.968427e-003 - 6.370000e+000 -3.418311e+000 -4.802867e-001 2.961871e-003 - 6.380000e+000 -3.214744e+000 -4.810407e-001 2.960949e-003 - 6.390000e+000 -2.953000e+000 -4.817946e-001 2.965851e-003 - 6.400000e+000 -2.630781e+000 -4.825486e-001 2.975402e-003 - 6.410000e+000 -2.246998e+000 -4.833026e-001 2.987365e-003 - 6.420000e+000 -1.801885e+000 -4.840566e-001 2.998977e-003 - 6.430000e+000 -1.297088e+000 -4.848106e-001 3.007606e-003 - 6.440000e+000 -7.357172e-001 -4.855646e-001 3.011332e-003 - 6.450000e+000 -1.223623e-001 -4.863185e-001 3.009364e-003 - 6.460000e+000 5.369346e-001 -4.870725e-001 3.002201e-003 - 6.470000e+000 1.234743e+000 -4.878265e-001 2.991518e-003 - 6.480000e+000 1.962352e+000 -4.885805e-001 2.979798e-003 - 6.490000e+000 2.709915e+000 -4.893345e-001 2.969780e-003 - 6.500000e+000 3.466635e+000 -4.900884e-001 2.963816e-003 - 6.510000e+000 4.220980e+000 -4.908424e-001 2.963308e-003 - 6.520000e+000 4.960929e+000 -4.915964e-001 2.968363e-003 - 6.530000e+000 5.674244e+000 -4.923504e-001 2.977770e-003 - 6.540000e+000 6.348753e+000 -4.931044e-001 2.989306e-003 - 6.550000e+000 6.972645e+000 -4.938584e-001 3.000274e-003 - 6.560000e+000 7.534766e+000 -4.946123e-001 3.008142e-003 - 6.570000e+000 8.024908e+000 -4.953663e-001 3.011104e-003 - 6.580000e+000 8.434078e+000 -4.961203e-001 3.008477e-003 - 6.590000e+000 8.754748e+000 -4.968743e-001 3.000841e-003 - 6.600000e+000 8.981067e+000 -4.976283e-001 2.989917e-003 - 6.610000e+000 9.109035e+000 -4.983823e-001 2.978187e-003 - 6.620000e+000 9.136635e+000 -4.991362e-001 2.968347e-003 - 6.630000e+000 9.063907e+000 -4.998902e-001 2.962671e-003 - 6.640000e+000 8.892969e+000 -5.006442e-001 2.962474e-003 - 6.650000e+000 8.627989e+000 -5.013982e-001 2.967782e-003 - 6.660000e+000 8.275089e+000 -5.021522e-001 2.977333e-003 - 6.670000e+000 7.842207e+000 -5.029061e-001 2.988894e-003 - 6.680000e+000 7.338896e+000 -5.036601e-001 2.999799e-003 - 6.690000e+000 6.776084e+000 -5.044141e-001 3.007574e-003 - 6.700000e+000 6.165798e+000 -5.051681e-001 3.010491e-003 - 6.710000e+000 5.520853e+000 -5.059221e-001 3.007933e-003 - 6.720000e+000 4.854520e+000 -5.066761e-001 3.000527e-003 - 6.730000e+000 4.180190e+000 -5.074300e-001 2.990002e-003 - 6.740000e+000 3.511029e+000 -5.081840e-001 2.978808e-003 - 6.750000e+000 2.859650e+000 -5.089380e-001 2.969563e-003 - 6.760000e+000 2.237808e+000 -5.096920e-001 2.964442e-003 - 6.770000e+000 1.656117e+000 -5.104460e-001 2.964646e-003 - 6.780000e+000 1.123814e+000 -5.111999e-001 2.970113e-003 - 6.790000e+000 6.485660e-001 -5.119539e-001 2.979526e-003 - 6.800000e+000 2.363277e-001 -5.127079e-001 2.990649e-003 - 6.810000e+000 -1.087473e-001 -5.134619e-001 3.000863e-003 - 6.820000e+000 -3.843375e-001 -5.142159e-001 3.007779e-003 - 6.830000e+000 -5.899307e-001 -5.149699e-001 3.009773e-003 - 6.840000e+000 -7.267488e-001 -5.157238e-001 3.006343e-003 - 6.850000e+000 -7.976252e-001 -5.164778e-001 2.998214e-003 - 6.860000e+000 -8.068400e-001 -5.172318e-001 2.987188e-003 - 6.870000e+000 -7.599214e-001 -5.179858e-001 2.975756e-003 - 6.880000e+000 -6.634217e-001 -5.187398e-001 2.966539e-003 - 6.890000e+000 -5.246759e-001 -5.194938e-001 2.961683e-003 - 6.900000e+000 -3.515543e-001 -5.202477e-001 2.962336e-003 - 6.910000e+000 -1.522155e-001 -5.210017e-001 2.968370e-003 - 6.920000e+000 6.512917e-002 -5.217557e-001 2.978415e-003 - 6.930000e+000 2.924340e-001 -5.225097e-001 2.990190e-003 - 6.940000e+000 5.220125e-001 -5.232637e-001 3.001057e-003 - 6.950000e+000 7.467014e-001 -5.240176e-001 3.008622e-003 - 6.960000e+000 9.599931e-001 -5.247716e-001 3.011260e-003 - 6.970000e+000 1.156132e+000 -5.255256e-001 3.008463e-003 - 6.980000e+000 1.330179e+000 -5.262796e-001 3.000938e-003 - 6.990000e+000 1.478040e+000 -5.270336e-001 2.990447e-003 - 7.000000e+000 1.596467e+000 -5.277876e-001 2.979421e-003 - 7.010000e+000 1.683032e+000 -5.285415e-001 2.970412e-003 - 7.020000e+000 1.736083e+000 -5.292955e-001 2.965502e-003 - 7.030000e+000 1.754680e+000 -5.300495e-001 2.965801e-003 - 7.040000e+000 1.738524e+000 -5.308035e-001 2.971181e-003 - 7.050000e+000 1.687883e+000 -5.315575e-001 2.980317e-003 - 7.060000e+000 1.603521e+000 -5.323115e-001 2.991018e-003 - 7.070000e+000 1.486627e+000 -5.330654e-001 3.000763e-003 - 7.080000e+000 1.338756e+000 -5.338194e-001 3.007283e-003 - 7.090000e+000 1.161785e+000 -5.345734e-001 3.009073e-003 - 7.100000e+000 9.578777e-001 -5.353274e-001 3.005719e-003 - 7.110000e+000 7.294620e-001 -5.360814e-001 2.997978e-003 - 7.120000e+000 4.792193e-001 -5.368353e-001 2.987616e-003 - 7.130000e+000 2.100826e-001 -5.375893e-001 2.977018e-003 - 7.140000e+000 -7.476029e-002 -5.383433e-001 2.968647e-003 - 7.150000e+000 -3.718621e-001 -5.390973e-001 2.964462e-003 - 7.160000e+000 -6.775146e-001 -5.398513e-001 2.965448e-003 - 7.170000e+000 -9.877533e-001 -5.406053e-001 2.971374e-003 - 7.180000e+000 -1.298374e+000 -5.413592e-001 2.980848e-003 - 7.190000e+000 -1.604961e+000 -5.421132e-001 2.991663e-003 - 7.200000e+000 -1.902938e+000 -5.428672e-001 3.001329e-003 - 7.210000e+000 -2.187629e+000 -5.436212e-001 3.007643e-003 - 7.220000e+000 -2.454341e+000 -5.443752e-001 3.009184e-003 - 7.230000e+000 -2.698465e+000 -5.451291e-001 3.005616e-003 - 7.240000e+000 -2.915590e+000 -5.458831e-001 2.997757e-003 - 7.250000e+000 -3.101623e+000 -5.466371e-001 2.987401e-003 - 7.260000e+000 -3.252924e+000 -5.473911e-001 2.976927e-003 - 7.270000e+000 -3.366429e+000 -5.481451e-001 2.968752e-003 - 7.280000e+000 -3.439778e+000 -5.488991e-001 2.964775e-003 - 7.290000e+000 -3.471421e+000 -5.496530e-001 2.965908e-003 - 7.300000e+000 -3.460712e+000 -5.504070e-001 2.971863e-003 - 7.310000e+000 -3.407973e+000 -5.511610e-001 2.981222e-003 - 7.320000e+000 -3.314533e+000 -5.519150e-001 2.991786e-003 - 7.330000e+000 -3.182726e+000 -5.526690e-001 3.001106e-003 - 7.340000e+000 -3.015863e+000 -5.534230e-001 3.007046e-003 - 7.350000e+000 -2.818161e+000 -5.541769e-001 3.008259e-003 - 7.360000e+000 -2.594637e+000 -5.549309e-001 3.004476e-003 - 7.370000e+000 -2.350972e+000 -5.556849e-001 2.996563e-003 - 7.380000e+000 -2.093342e+000 -5.564389e-001 2.986330e-003 - 7.390000e+000 -1.828233e+000 -5.571929e-001 2.976134e-003 - 7.400000e+000 -1.562237e+000 -5.579468e-001 2.968342e-003 - 7.410000e+000 -1.301836e+000 -5.587008e-001 2.964776e-003 - 7.420000e+000 -1.053197e+000 -5.594548e-001 2.966271e-003 - 7.430000e+000 -8.219703e-001 -5.602088e-001 2.972473e-003 - 7.440000e+000 -6.131060e-001 -5.609628e-001 2.981924e-003 - 7.450000e+000 -4.307007e-001 -5.617168e-001 2.992425e-003 - 7.460000e+000 -2.778735e-001 -5.624707e-001 3.001557e-003 - 7.470000e+000 -1.566815e-001 -5.632247e-001 3.007242e-003 - 7.480000e+000 -6.807630e-002 -5.639787e-001 3.008198e-003 - 7.490000e+000 -1.190424e-002 -5.647327e-001 3.004218e-003 - 7.500000e+000 1.305115e-002 -5.654867e-001 2.996215e-003 - 7.510000e+000 8.985683e-003 -5.662407e-001 2.986019e-003 - 7.520000e+000 -2.104513e-002 -5.669946e-001 2.975978e-003 - 7.530000e+000 -7.327634e-002 -5.677486e-001 2.968422e-003 - 7.540000e+000 -1.434071e-001 -5.685026e-001 2.965119e-003 - 7.550000e+000 -2.267895e-001 -5.692566e-001 2.966847e-003 - 7.560000e+000 -3.186236e-001 -5.700106e-001 2.973203e-003 - 7.570000e+000 -4.141495e-001 -5.707645e-001 2.982704e-003 - 7.580000e+000 -5.088290e-001 -5.715185e-001 2.993153e-003 - 7.590000e+000 -5.985064e-001 -5.722725e-001 3.002156e-003 - 7.600000e+000 -6.795445e-001 -5.730265e-001 3.007672e-003 - 7.610000e+000 -7.489282e-001 -5.737805e-001 3.008464e-003 - 7.620000e+000 -8.043327e-001 -5.745345e-001 3.004358e-003 - 7.630000e+000 -8.441551e-001 -5.752884e-001 2.996283e-003 - 7.640000e+000 -8.675080e-001 -5.760424e-001 2.986062e-003 - 7.650000e+000 -8.741795e-001 -5.767964e-001 2.976015e-003 - 7.660000e+000 -8.645604e-001 -5.775504e-001 2.968432e-003 - 7.670000e+000 -8.395469e-001 -5.783044e-001 2.965035e-003 - 7.680000e+000 -8.004234e-001 -5.790584e-001 2.966571e-003 - 7.690000e+000 -7.487343e-001 -5.798123e-001 2.972632e-003 - 7.700000e+000 -6.861512e-001 -5.805663e-001 2.981760e-003 - 7.710000e+000 -6.143454e-001 -5.813203e-001 2.991809e-003 - 7.720000e+000 -5.348711e-001 -5.820743e-001 3.000462e-003 - 7.730000e+000 -4.490681e-001 -5.828283e-001 3.005755e-003 - 7.740000e+000 -3.579878e-001 -5.835822e-001 3.006519e-003 - 7.750000e+000 -2.623472e-001 -5.843362e-001 3.002625e-003 - 7.760000e+000 -1.625133e-001 -5.850902e-001 2.995008e-003 - 7.770000e+000 -5.851793e-002 -5.858442e-001 2.985455e-003 - 7.780000e+000 4.989818e-002 -5.865982e-001 2.976208e-003 - 7.790000e+000 1.632154e-001 -5.873522e-001 2.969446e-003 - 7.800000e+000 2.820441e-001 -5.881061e-001 2.966770e-003 - 7.810000e+000 4.070179e-001 -5.888601e-001 2.968814e-003 - 7.820000e+000 5.386798e-001 -5.896141e-001 2.975091e-003 - 7.830000e+000 6.773665e-001 -5.903681e-001 2.984117e-003 - 7.840000e+000 8.231013e-001 -5.911221e-001 2.993771e-003 - 7.850000e+000 9.754998e-001 -5.918760e-001 3.001804e-003 - 7.860000e+000 1.133698e+000 -5.926300e-001 3.006357e-003 - 7.870000e+000 1.296308e+000 -5.933840e-001 3.006372e-003 - 7.880000e+000 1.461401e+000 -5.941380e-001 3.001825e-003 - 7.890000e+000 1.626524e+000 -5.948920e-001 2.993734e-003 - 7.900000e+000 1.788756e+000 -5.956460e-001 2.983933e-003 - 7.910000e+000 1.944784e+000 -5.963999e-001 2.974671e-003 - 7.920000e+000 2.091021e+000 -5.971539e-001 2.968096e-003 - 7.930000e+000 2.223737e+000 -5.979079e-001 2.965749e-003 - 7.940000e+000 2.339210e+000 -5.986619e-001 2.968189e-003 - 7.950000e+000 2.433888e+000 -5.994159e-001 2.974859e-003 - 7.960000e+000 2.504553e+000 -6.001699e-001 2.984222e-003 - 7.970000e+000 2.548471e+000 -6.009238e-001 2.994133e-003 - 7.980000e+000 2.563535e+000 -6.016778e-001 3.002343e-003 - 7.990000e+000 2.548372e+000 -6.024318e-001 3.007015e-003 - 8.000000e+000 2.502435e+000 -6.031858e-001 3.007120e-003 - 8.010000e+000 2.426044e+000 -6.039398e-001 3.002660e-003 - 8.020000e+000 2.320401e+000 -6.046937e-001 2.994663e-003 - 8.030000e+000 2.187554e+000 -6.054477e-001 2.984955e-003 - 8.040000e+000 2.030327e+000 -6.062017e-001 2.975755e-003 - 8.050000e+000 1.852210e+000 -6.069557e-001 2.969169e-003 - 8.060000e+000 1.657223e+000 -6.077097e-001 2.966697e-003 - 8.070000e+000 1.449742e+000 -6.084637e-001 2.968870e-003 - 8.080000e+000 1.234319e+000 -6.092176e-001 2.975127e-003 - 8.090000e+000 1.015487e+000 -6.099716e-001 2.983961e-003 - 8.100000e+000 7.975658e-001 -6.107256e-001 2.993288e-003 - 8.110000e+000 5.844806e-001 -6.114796e-001 3.000943e-003 - 8.120000e+000 3.795972e-001 -6.122336e-001 3.005177e-003 - 8.130000e+000 1.855883e-001 -6.129876e-001 3.005045e-003 - 8.140000e+000 4.333462e-003 -6.137415e-001 3.000607e-003 - 8.150000e+000 -1.631397e-001 -6.144955e-001 2.992915e-003 - 8.160000e+000 -3.166697e-001 -6.152495e-001 2.983775e-003 - 8.170000e+000 -4.569303e-001 -6.160035e-001 2.975339e-003 - 8.180000e+000 -5.853545e-001 -6.167575e-001 2.969611e-003 - 8.190000e+000 -7.040176e-001 -6.175114e-001 2.967965e-003 - 8.200000e+000 -8.154842e-001 -6.182654e-001 2.970809e-003 - 8.210000e+000 -9.226269e-001 -6.190194e-001 2.977486e-003 - 8.220000e+000 -1.028425e+000 -6.197734e-001 2.986431e-003 - 8.230000e+000 -1.135754e+000 -6.205274e-001 2.995554e-003 - 8.240000e+000 -1.247174e+000 -6.212814e-001 3.002729e-003 - 8.250000e+000 -1.364736e+000 -6.220353e-001 3.006284e-003 - 8.260000e+000 -1.489798e+000 -6.227893e-001 3.005369e-003 - 8.270000e+000 -1.622888e+000 -6.235433e-001 3.000144e-003 - 8.280000e+000 -1.763595e+000 -6.242973e-001 2.991750e-003 - 8.290000e+000 -1.910509e+000 -6.250513e-001 2.982060e-003 - 8.300000e+000 -2.061214e+000 -6.258052e-001 2.973269e-003 - 8.310000e+000 -2.212327e+000 -6.265592e-001 2.967390e-003 - 8.320000e+000 -2.359595e+000 -6.273132e-001 2.965781e-003 - 8.330000e+000 -2.498037e+000 -6.280672e-001 2.968818e-003 - 8.340000e+000 -2.622125e+000 -6.288212e-001 2.975802e-003 - 8.350000e+000 -2.726010e+000 -6.295752e-001 2.985134e-003 - 8.360000e+000 -2.803761e+000 -6.303291e-001 2.994695e-003 - 8.370000e+000 -2.849638e+000 -6.310831e-001 3.002346e-003 - 8.380000e+000 -2.858350e+000 -6.318371e-001 3.006405e-003 - 8.390000e+000 -2.825318e+000 -6.325911e-001 3.006014e-003 - 8.400000e+000 -2.746919e+000 -6.333451e-001 3.001320e-003 - 8.410000e+000 -2.620693e+000 -6.340991e-001 2.993434e-003 - 8.420000e+000 -2.445518e+000 -6.348530e-001 2.984187e-003 - 8.430000e+000 -2.221734e+000 -6.356070e-001 2.975721e-003 - 8.440000e+000 -1.951212e+000 -6.363610e-001 2.969992e-003 - 8.450000e+000 -1.637371e+000 -6.371150e-001 2.968317e-003 - 8.460000e+000 -1.285129e+000 -6.378690e-001 2.971052e-003 - 8.470000e+000 -9.007988e-001 -6.386229e-001 2.977516e-003 - 8.480000e+000 -4.919303e-001 -6.393769e-001 2.986161e-003 - 8.490000e+000 -6.710052e-002 -6.401309e-001 2.994948e-003 - 8.500000e+000 3.643376e-001 -6.408849e-001 3.001837e-003 - 8.510000e+000 7.925392e-001 -6.416389e-001 3.005243e-003 - 8.520000e+000 1.207474e+000 -6.423929e-001 3.004395e-003 - 8.530000e+000 1.599245e+000 -6.431468e-001 2.999495e-003 - 8.540000e+000 1.958406e+000 -6.439008e-001 2.991675e-003 - 8.550000e+000 2.276266e+000 -6.446548e-001 2.982744e-003 - 8.560000e+000 2.545175e+000 -6.454088e-001 2.974778e-003 - 8.570000e+000 2.758770e+000 -6.461628e-001 2.969642e-003 - 8.580000e+000 2.912189e+000 -6.469168e-001 2.968543e-003 - 8.590000e+000 3.002225e+000 -6.476707e-001 2.971738e-003 - 8.600000e+000 3.027437e+000 -6.484247e-001 2.978473e-003 - 8.610000e+000 2.988196e+000 -6.491787e-001 2.987165e-003 - 8.620000e+000 2.886676e+000 -6.499327e-001 2.995789e-003 - 8.630000e+000 2.726790e+000 -6.506867e-001 3.002350e-003 - 8.640000e+000 2.514068e+000 -6.514406e-001 3.005339e-003 - 8.650000e+000 2.255487e+000 -6.521946e-001 3.004064e-003 - 8.660000e+000 1.959257e+000 -6.529486e-001 2.998804e-003 - 8.670000e+000 1.634575e+000 -6.537026e-001 2.990745e-003 - 8.680000e+000 1.291345e+000 -6.544566e-001 2.981719e-003 - 8.690000e+000 9.398853e-001 -6.552106e-001 2.973797e-003 - 8.700000e+000 5.906239e-001 -6.559645e-001 2.968807e-003 - 8.710000e+000 2.537975e-001 -6.567185e-001 2.967904e-003 - 8.720000e+000 -6.084253e-002 -6.574725e-001 2.971285e-003 - 8.730000e+000 -3.443049e-001 -6.582265e-001 2.978150e-003 - 8.740000e+000 -5.886072e-001 -6.589805e-001 2.986890e-003 - 8.750000e+000 -7.869924e-001 -6.597344e-001 2.995482e-003 - 8.760000e+000 -9.341074e-001 -6.604884e-001 3.001957e-003 - 8.770000e+000 -1.026139e+000 -6.612424e-001 3.004847e-003 - 8.780000e+000 -1.060908e+000 -6.619964e-001 3.003508e-003 - 8.790000e+000 -1.037911e+000 -6.627504e-001 2.998260e-003 - 8.800000e+000 -9.583200e-001 -6.635044e-001 2.990310e-003 - 8.810000e+000 -8.249393e-001 -6.642583e-001 2.981495e-003 - 8.820000e+000 -6.421106e-001 -6.650123e-001 2.973860e-003 - 8.830000e+000 -4.155860e-001 -6.657663e-001 2.969192e-003 - 8.840000e+000 -1.523607e-001 -6.665203e-001 2.968591e-003 - 8.850000e+000 1.395230e-001 -6.672743e-001 2.972208e-003 - 8.860000e+000 4.511986e-001 -6.680283e-001 2.979204e-003 - 8.870000e+000 7.732164e-001 -6.687822e-001 2.987961e-003 - 8.880000e+000 1.095798e+000 -6.695362e-001 2.996465e-003 - 8.890000e+000 1.409098e+000 -6.702902e-001 3.002780e-003 - 8.900000e+000 1.703464e+000 -6.710442e-001 3.005478e-003 - 8.910000e+000 1.969688e+000 -6.717982e-001 3.003958e-003 - 8.920000e+000 2.199252e+000 -6.725521e-001 2.998570e-003 - 8.930000e+000 2.384545e+000 -6.733061e-001 2.990536e-003 - 8.940000e+000 2.519062e+000 -6.740601e-001 2.981686e-003 - 8.950000e+000 2.597568e+000 -6.748141e-001 2.974041e-003 - 8.960000e+000 2.616236e+000 -6.755681e-001 2.969352e-003 - 8.970000e+000 2.572736e+000 -6.763221e-001 2.968684e-003 - 8.980000e+000 2.466297e+000 -6.770760e-001 2.972162e-003 - 8.990000e+000 2.297714e+000 -6.778300e-001 2.978944e-003 - 9.000000e+000 2.069328e+000 -6.785840e-001 2.987431e-003 - 9.010000e+000 1.784946e+000 -6.793380e-001 2.995655e-003 - 9.020000e+000 1.449740e+000 -6.800920e-001 3.001731e-003 - 9.030000e+000 1.070094e+000 -6.808460e-001 3.004293e-003 - 9.040000e+000 6.534261e-001 -6.815999e-001 3.002784e-003 - 9.050000e+000 2.079806e-001 -6.823539e-001 2.997578e-003 - 9.060000e+000 -2.574063e-001 -6.831079e-001 2.989893e-003 - 9.070000e+000 -7.335514e-001 -6.838619e-001 2.981518e-003 - 9.080000e+000 -1.211182e+000 -6.846159e-001 2.974405e-003 - 9.090000e+000 -1.681191e+000 -6.853698e-001 2.970217e-003 - 9.100000e+000 -2.134891e+000 -6.861238e-001 2.969931e-003 - 9.110000e+000 -2.564247e+000 -6.868778e-001 2.973598e-003 - 9.120000e+000 -2.962093e+000 -6.876318e-001 2.980340e-003 - 9.130000e+000 -3.322317e+000 -6.883858e-001 2.988560e-003 - 9.140000e+000 -3.640012e+000 -6.891398e-001 2.996330e-003 - 9.150000e+000 -3.911588e+000 -6.898937e-001 3.001844e-003 - 9.160000e+000 -4.134840e+000 -6.906477e-001 3.003826e-003 - 9.170000e+000 -4.308973e+000 -6.914017e-001 3.001814e-003 - 9.180000e+000 -4.434575e+000 -6.921557e-001 2.996263e-003 - 9.190000e+000 -4.513552e+000 -6.929097e-001 2.988444e-003 - 9.200000e+000 -4.549014e+000 -6.936636e-001 2.980162e-003 - 9.210000e+000 -4.545125e+000 -6.944176e-001 2.973352e-003 - 9.220000e+000 -4.506920e+000 -6.951716e-001 2.969621e-003 - 9.230000e+000 -4.440092e+000 -6.959256e-001 2.969870e-003 - 9.240000e+000 -4.350763e+000 -6.966796e-001 2.974068e-003 - 9.250000e+000 -4.245242e+000 -6.974336e-001 2.981262e-003 - 9.260000e+000 -4.129784e+000 -6.981875e-001 2.989805e-003 - 9.270000e+000 -4.010350e+000 -6.989415e-001 2.997747e-003 - 9.280000e+000 -3.892387e+000 -6.996955e-001 3.003286e-003 - 9.290000e+000 -3.780631e+000 -7.004495e-001 3.005173e-003 - 9.300000e+000 -3.678940e+000 -7.012035e-001 3.002980e-003 - 9.310000e+000 -3.590164e+000 -7.019575e-001 2.997199e-003 - 9.320000e+000 -3.516052e+000 -7.027114e-001 2.989128e-003 - 9.330000e+000 -3.457214e+000 -7.034654e-001 2.980590e-003 - 9.340000e+000 -3.413116e+000 -7.042194e-001 2.973520e-003 - 9.350000e+000 -3.382128e+000 -7.049734e-001 2.969522e-003 - 9.360000e+000 -3.361616e+000 -7.057274e-001 2.969484e-003 - 9.370000e+000 -3.348066e+000 -7.064813e-001 2.973375e-003 - 9.380000e+000 -3.337249e+000 -7.072353e-001 2.980250e-003 - 9.390000e+000 -3.324414e+000 -7.079893e-001 2.988483e-003 - 9.400000e+000 -3.304494e+000 -7.087433e-001 2.996161e-003 - 9.410000e+000 -3.272331e+000 -7.094973e-001 3.001523e-003 - 9.420000e+000 -3.222901e+000 -7.102513e-001 3.003357e-003 - 9.430000e+000 -3.151538e+000 -7.110052e-001 3.001266e-003 - 9.440000e+000 -3.054134e+000 -7.117592e-001 2.995747e-003 - 9.450000e+000 -2.927333e+000 -7.125132e-001 2.988083e-003 - 9.460000e+000 -2.768686e+000 -7.132672e-001 2.980049e-003 - 9.470000e+000 -2.576772e+000 -7.140212e-001 2.973516e-003 - 9.480000e+000 -2.351293e+000 -7.147752e-001 2.970008e-003 - 9.490000e+000 -2.093111e+000 -7.155291e-001 2.970342e-003 - 9.500000e+000 -1.804261e+000 -7.162831e-001 2.974428e-003 - 9.510000e+000 -1.487908e+000 -7.170371e-001 2.981299e-003 - 9.520000e+000 -1.148273e+000 -7.177911e-001 2.989341e-003 - 9.530000e+000 -7.905207e-001 -7.185451e-001 2.996685e-003 - 9.540000e+000 -4.206136e-001 -7.192990e-001 3.001640e-003 - 9.550000e+000 -4.514111e-002 -7.200530e-001 3.003071e-003 - 9.560000e+000 3.288707e-001 -7.208070e-001 3.000656e-003 - 9.570000e+000 6.941640e-001 -7.215610e-001 2.994950e-003 - 9.580000e+000 1.043459e+000 -7.223150e-001 2.987264e-003 - 9.590000e+000 1.369663e+000 -7.230690e-001 2.979375e-003 - 9.600000e+000 1.666073e+000 -7.238229e-001 2.973118e-003 - 9.610000e+000 1.926560e+000 -7.245769e-001 2.969963e-003 - 9.620000e+000 2.145739e+000 -7.253309e-001 2.970659e-003 - 9.630000e+000 2.319110e+000 -7.260849e-001 2.975054e-003 - 9.640000e+000 2.443174e+000 -7.268389e-001 2.982136e-003 - 9.650000e+000 2.515517e+000 -7.275928e-001 2.990273e-003 - 9.660000e+000 2.534860e+000 -7.283468e-001 2.997607e-003 - 9.670000e+000 2.501080e+000 -7.291008e-001 3.002475e-003 - 9.680000e+000 2.415196e+000 -7.298548e-001 3.003790e-003 - 9.690000e+000 2.279327e+000 -7.306088e-001 3.001272e-003 - 9.700000e+000 2.096624e+000 -7.313628e-001 2.995512e-003 - 9.710000e+000 1.871171e+000 -7.321167e-001 2.987836e-003 - 9.720000e+000 1.607874e+000 -7.328707e-001 2.980014e-003 - 9.730000e+000 1.312330e+000 -7.336247e-001 2.973851e-003 - 9.740000e+000 9.906842e-001 -7.343787e-001 2.970775e-003 - 9.750000e+000 6.494827e-001 -7.351327e-001 2.971487e-003 - 9.760000e+000 2.955193e-001 -7.358867e-001 2.975799e-003 - 9.770000e+000 -6.431231e-002 -7.366406e-001 2.982682e-003 - 9.780000e+000 -4.231628e-001 -7.373946e-001 2.990513e-003 - 9.790000e+000 -7.743615e-001 -7.381486e-001 2.997465e-003 - 9.800000e+000 -1.111539e+000 -7.389026e-001 3.001926e-003 - 9.810000e+000 -1.428734e+000 -7.396566e-001 3.002866e-003 - 9.820000e+000 -1.720489e+000 -7.404105e-001 3.000060e-003 - 9.830000e+000 -1.981919e+000 -7.411645e-001 2.994138e-003 - 9.840000e+000 -2.208774e+000 -7.419185e-001 2.986444e-003 - 9.850000e+000 -2.397476e+000 -7.426725e-001 2.978738e-003 - 9.860000e+000 -2.545143e+000 -7.434265e-001 2.972796e-003 - 9.870000e+000 -2.649592e+000 -7.441805e-001 2.969992e-003 - 9.880000e+000 -2.709334e+000 -7.449344e-001 2.970973e-003 - 9.890000e+000 -2.723552e+000 -7.456884e-001 2.975503e-003 - 9.900000e+000 -2.692069e+000 -7.464424e-001 2.982521e-003 - 9.910000e+000 -2.615306e+000 -7.471964e-001 2.990399e-003 - 9.920000e+000 -2.494234e+000 -7.479504e-001 2.997330e-003 - 9.930000e+000 -2.330323e+000 -7.487044e-001 3.001741e-003 - 9.940000e+000 -2.125485e+000 -7.494583e-001 3.002649e-003 - 9.950000e+000 -1.882019e+000 -7.502123e-001 2.999875e-003 - 9.960000e+000 -1.602555e+000 -7.509663e-001 2.994077e-003 - 9.970000e+000 -1.290005e+000 -7.517203e-001 2.986611e-003 - 9.980000e+000 -9.475079e-001 -7.524743e-001 2.979221e-003 - 9.990000e+000 -5.783919e-001 -7.532282e-001 2.973639e-003 - 1.000000e+001 -1.861297e-001 -7.539822e-001 2.971185e-003 - 1.001000e+001 2.256937e-001 -7.547362e-001 2.972442e-003 - 1.002000e+001 6.534111e-001 -7.554902e-001 2.977123e-003 - 1.003000e+001 1.093298e+000 -7.562442e-001 2.984134e-003 - 1.004000e+001 1.541594e+000 -7.569982e-001 2.991844e-003 - 1.005000e+001 1.994522e+000 -7.577521e-001 2.998467e-003 - 1.006000e+001 2.448303e+000 -7.585061e-001 3.002473e-003 - 1.007000e+001 2.899177e+000 -7.592601e-001 3.002936e-003 - 1.008000e+001 3.343415e+000 -7.600141e-001 2.999732e-003 - 1.009000e+001 3.777342e+000 -7.607681e-001 2.993570e-003 - 1.010000e+001 4.197358e+000 -7.615220e-001 2.985835e-003 - 1.011000e+001 4.599963e+000 -7.622760e-001 2.978284e-003 - 1.012000e+001 4.981791e+000 -7.630300e-001 2.972643e-003 - 1.013000e+001 5.339642e+000 -7.637840e-001 2.970207e-003 - 1.014000e+001 5.670522e+000 -7.645380e-001 2.971530e-003 - 1.015000e+001 5.971689e+000 -7.652920e-001 2.976295e-003 - 1.016000e+001 6.240697e+000 -7.660459e-001 2.983391e-003 - 1.017000e+001 6.475444e+000 -7.667999e-001 2.991184e-003 - 1.018000e+001 6.674222e+000 -7.675539e-001 2.997896e-003 - 1.019000e+001 6.835757e+000 -7.683079e-001 3.002020e-003 - 1.020000e+001 6.959256e+000 -7.690619e-001 3.002650e-003 - 1.021000e+001 7.044434e+000 -7.698159e-001 2.999678e-003 - 1.022000e+001 7.091539e+000 -7.705698e-001 2.993813e-003 - 1.023000e+001 7.101366e+000 -7.713238e-001 2.986423e-003 - 1.024000e+001 7.075254e+000 -7.720778e-001 2.979229e-003 - 1.025000e+001 7.015063e+000 -7.728318e-001 2.973904e-003 - 1.026000e+001 6.923148e+000 -7.735858e-001 2.971690e-003 - 1.027000e+001 6.802303e+000 -7.743397e-001 2.973093e-003 - 1.028000e+001 6.655693e+000 -7.750937e-001 2.977769e-003 - 1.029000e+001 6.486772e+000 -7.758477e-001 2.984608e-003 - 1.030000e+001 6.299191e+000 -7.766017e-001 2.992003e-003 - 1.031000e+001 6.096684e+000 -7.773557e-001 2.998232e-003 - 1.032000e+001 5.882957e+000 -7.781097e-001 3.001855e-003 - 1.033000e+001 5.661575e+000 -7.788636e-001 3.002036e-003 - 1.034000e+001 5.435839e+000 -7.796176e-001 2.998730e-003 - 1.035000e+001 5.208680e+000 -7.803716e-001 2.992688e-003 - 1.036000e+001 4.982562e+000 -7.811256e-001 2.985295e-003 - 1.037000e+001 4.759394e+000 -7.818796e-001 2.978254e-003 - 1.038000e+001 4.540474e+000 -7.826336e-001 2.973201e-003 - 1.039000e+001 4.326445e+000 -7.833875e-001 2.971317e-003 - 1.040000e+001 4.117283e+000 -7.841415e-001 2.973044e-003 - 1.041000e+001 3.912317e+000 -7.848955e-001 2.977981e-003 - 1.042000e+001 3.710272e+000 -7.856495e-001 2.984981e-003 - 1.043000e+001 3.509345e+000 -7.864035e-001 2.992423e-003 - 1.044000e+001 3.307304e+000 -7.871574e-001 2.998599e-003 - 1.045000e+001 3.101615e+000 -7.879114e-001 3.002098e-003 - 1.046000e+001 2.889587e+000 -7.886654e-001 3.002126e-003 - 1.047000e+001 2.668528e+000 -7.894194e-001 2.998676e-003 - 1.048000e+001 2.435910e+000 -7.901734e-001 2.992527e-003 - 1.049000e+001 2.189536e+000 -7.909274e-001 2.985076e-003 - 1.050000e+001 1.927696e+000 -7.916813e-001 2.978020e-003 - 1.051000e+001 1.649309e+000 -7.924353e-001 2.972970e-003 - 1.052000e+001 1.354049e+000 -7.931893e-001 2.971072e-003 - 1.053000e+001 1.042432e+000 -7.939433e-001 2.972737e-003 - 1.054000e+001 7.158755e-001 -7.946973e-001 2.977541e-003 - 1.055000e+001 3.767233e-001 -7.954512e-001 2.984335e-003 - 1.056000e+001 2.822107e-002 -7.962052e-001 2.991516e-003 - 1.057000e+001 -3.255432e-001 -7.969592e-001 2.997411e-003 - 1.058000e+001 -6.797422e-001 -7.977132e-001 3.000661e-003 - 1.059000e+001 -1.028949e+000 -7.984672e-001 3.000519e-003 - 1.060000e+001 -1.367312e+000 -7.992212e-001 2.997021e-003 - 1.061000e+001 -1.688754e+000 -7.999751e-001 2.990973e-003 - 1.062000e+001 -1.987194e+000 -8.007291e-001 2.983771e-003 - 1.063000e+001 -2.256777e+000 -8.014831e-001 2.977088e-003 - 1.064000e+001 -2.492105e+000 -8.022371e-001 2.972490e-003 - 1.065000e+001 -2.688465e+000 -8.029911e-001 2.971063e-003 - 1.066000e+001 -2.842028e+000 -8.037451e-001 2.973159e-003 - 1.067000e+001 -2.950028e+000 -8.044990e-001 2.978305e-003 - 1.068000e+001 -3.010904e+000 -8.052530e-001 2.985322e-003 - 1.069000e+001 -3.024397e+000 -8.060070e-001 2.992607e-003 - 1.070000e+001 -2.991596e+000 -8.067610e-001 2.998510e-003 - 1.071000e+001 -2.914942e+000 -8.075150e-001 3.001706e-003 - 1.072000e+001 -2.798166e+000 -8.082689e-001 3.001495e-003 - 1.073000e+001 -2.646187e+000 -8.090229e-001 2.997953e-003 - 1.074000e+001 -2.464958e+000 -8.097769e-001 2.991911e-003 - 1.075000e+001 -2.261268e+000 -8.105309e-001 2.984772e-003 - 1.076000e+001 -2.042510e+000 -8.112849e-001 2.978194e-003 - 1.077000e+001 -1.816427e+000 -8.120389e-001 2.973709e-003 - 1.078000e+001 -1.590839e+000 -8.127928e-001 2.972361e-003 - 1.079000e+001 -1.373368e+000 -8.135468e-001 2.974460e-003 - 1.080000e+001 -1.171169e+000 -8.143008e-001 2.979505e-003 - 1.081000e+001 -9.906805e-001 -8.150548e-001 2.986309e-003 - 1.082000e+001 -8.374074e-001 -8.158088e-001 2.993282e-003 - 1.083000e+001 -7.157362e-001 -8.165628e-001 2.998809e-003 - 1.084000e+001 -6.288009e-001 -8.173167e-001 3.001613e-003 - 1.085000e+001 -5.783991e-001 -8.180707e-001 3.001048e-003 - 1.086000e+001 -5.649630e-001 -8.188247e-001 2.997231e-003 - 1.087000e+001 -5.875859e-001 -8.195787e-001 2.991024e-003 - 1.088000e+001 -6.441036e-001 -8.203327e-001 2.983837e-003 - 1.089000e+001 -7.312256e-001 -8.210866e-001 2.977315e-003 - 1.090000e+001 -8.447100e-001 -8.218406e-001 2.972954e-003 - 1.091000e+001 -9.795743e-001 -8.225946e-001 2.971756e-003 - 1.092000e+001 -1.130333e+000 -8.233486e-001 2.973982e-003 - 1.093000e+001 -1.291248e+000 -8.241026e-001 2.979097e-003 - 1.094000e+001 -1.456587e+000 -8.248566e-001 2.985899e-003 - 1.095000e+001 -1.620868e+000 -8.256105e-001 2.992807e-003 - 1.096000e+001 -1.779093e+000 -8.263645e-001 2.998230e-003 - 1.097000e+001 -1.926944e+000 -8.271185e-001 3.000935e-003 - 1.098000e+001 -2.060945e+000 -8.278725e-001 3.000316e-003 - 1.099000e+001 -2.178585e+000 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1.116000e+001 -2.929746e+000 -8.414442e-001 2.972935e-003 - 1.117000e+001 -3.013661e+000 -8.421981e-001 2.972088e-003 - 1.118000e+001 -3.098978e+000 -8.429521e-001 2.974584e-003 - 1.119000e+001 -3.181509e+000 -8.437061e-001 2.979823e-003 - 1.120000e+001 -3.256651e+000 -8.444601e-001 2.986576e-003 - 1.121000e+001 -3.319593e+000 -8.452141e-001 2.993275e-003 - 1.122000e+001 -3.365528e+000 -8.459681e-001 2.998383e-003 - 1.123000e+001 -3.389863e+000 -8.467220e-001 3.000741e-003 - 1.124000e+001 -3.388428e+000 -8.474760e-001 2.999827e-003 - 1.125000e+001 -3.357667e+000 -8.482300e-001 2.995866e-003 - 1.126000e+001 -3.294795e+000 -8.489840e-001 2.989782e-003 - 1.127000e+001 -3.197933e+000 -8.497380e-001 2.982988e-003 - 1.128000e+001 -3.066197e+000 -8.504920e-001 2.977067e-003 - 1.129000e+001 -2.899750e+000 -8.512459e-001 2.973402e-003 - 1.130000e+001 -2.699809e+000 -8.519999e-001 2.972854e-003 - 1.131000e+001 -2.468609e+000 -8.527539e-001 2.975553e-003 - 1.132000e+001 -2.209326e+000 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1.946480e+000 -8.663256e-001 3.000829e-003 - 1.150000e+001 1.994846e+000 -8.670796e-001 2.999498e-003 - 1.151000e+001 2.020671e+000 -8.678335e-001 2.995241e-003 - 1.152000e+001 2.026469e+000 -8.685875e-001 2.989026e-003 - 1.153000e+001 2.014881e+000 -8.693415e-001 2.982275e-003 - 1.154000e+001 1.988567e+000 -8.700955e-001 2.976535e-003 - 1.155000e+001 1.950091e+000 -8.708495e-001 2.973125e-003 - 1.156000e+001 1.901834e+000 -8.716035e-001 2.972821e-003 - 1.157000e+001 1.845925e+000 -8.723574e-001 2.975673e-003 - 1.158000e+001 1.784180e+000 -8.731114e-001 2.980994e-003 - 1.159000e+001 1.718074e+000 -8.738654e-001 2.987531e-003 - 1.160000e+001 1.648723e+000 -8.746194e-001 2.993757e-003 - 1.161000e+001 1.576893e+000 -8.753734e-001 2.998237e-003 - 1.162000e+001 1.503018e+000 -8.761273e-001 2.999945e-003 - 1.163000e+001 1.427238e+000 -8.768813e-001 2.998498e-003 - 1.164000e+001 1.349447e+000 -8.776353e-001 2.994240e-003 - 1.165000e+001 1.269343e+000 -8.783893e-001 2.988160e-003 - 1.166000e+001 1.186492e+000 -8.791433e-001 2.981676e-003 - 1.167000e+001 1.100381e+000 -8.798973e-001 2.976309e-003 - 1.168000e+001 1.010485e+000 -8.806512e-001 2.973326e-003 - 1.169000e+001 9.163097e-001 -8.814052e-001 2.973447e-003 - 1.170000e+001 8.174441e-001 -8.821592e-001 2.976664e-003 - 1.171000e+001 7.135961e-001 -8.829132e-001 2.982247e-003 - 1.172000e+001 6.046211e-001 -8.836672e-001 2.988917e-003 - 1.173000e+001 4.905411e-001 -8.844212e-001 2.995152e-003 - 1.174000e+001 3.715540e-001 -8.851751e-001 2.999537e-003 - 1.175000e+001 2.480344e-001 -8.859291e-001 3.001085e-003 - 1.176000e+001 1.205265e-001 -8.866831e-001 2.999456e-003 - 1.177000e+001 -1.027013e-002 -8.874371e-001 2.995031e-003 - 1.178000e+001 -1.435189e-001 -8.881911e-001 2.988827e-003 - 1.179000e+001 -2.782692e-001 -8.889450e-001 2.982270e-003 - 1.180000e+001 -4.134818e-001 -8.896990e-001 2.976871e-003 - 1.181000e+001 -5.480547e-001 -8.904530e-001 2.973876e-003 - 1.182000e+001 -6.808498e-001 -8.912070e-001 2.973970e-003 - 1.183000e+001 -8.107187e-001 -8.919610e-001 2.977116e-003 - 1.184000e+001 -9.365267e-001 -8.927150e-001 2.982564e-003 - 1.185000e+001 -1.057176e+000 -8.934689e-001 2.989030e-003 - 1.186000e+001 -1.171627e+000 -8.942229e-001 2.995008e-003 - 1.187000e+001 -1.278916e+000 -8.949769e-001 2.999110e-003 - 1.188000e+001 -1.378175e+000 -8.957309e-001 3.000388e-003 - 1.189000e+001 -1.468644e+000 -8.964849e-001 2.998542e-003 - 1.190000e+001 -1.549688e+000 -8.972388e-001 2.993984e-003 - 1.191000e+001 -1.620810e+000 -8.979928e-001 2.987750e-003 - 1.192000e+001 -1.681657e+000 -8.987468e-001 2.981264e-003 - 1.193000e+001 -1.732034e+000 -8.995008e-001 2.976019e-003 - 1.194000e+001 -1.771907e+000 -9.002548e-001 2.973226e-003 - 1.195000e+001 -1.801406e+000 -9.010088e-001 2.973531e-003 - 1.196000e+001 -1.820827e+000 -9.017627e-001 2.976858e-003 - 1.197000e+001 -1.830621e+000 -9.025167e-001 2.982432e-003 - 1.198000e+001 -1.831391e+000 -9.032707e-001 2.988962e-003 - 1.199000e+001 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2.997873e-003 - 1.216000e+001 -1.105146e+000 -9.168424e-001 2.993089e-003 - 1.217000e+001 -1.024915e+000 -9.175964e-001 2.986803e-003 - 1.218000e+001 -9.335094e-001 -9.183504e-001 2.980442e-003 - 1.219000e+001 -8.293374e-001 -9.191043e-001 2.975463e-003 - 1.220000e+001 -7.110059e-001 -9.198583e-001 2.973010e-003 - 1.221000e+001 -5.774186e-001 -9.206123e-001 2.973648e-003 - 1.222000e+001 -4.278691e-001 -9.213663e-001 2.977224e-003 - 1.223000e+001 -2.621266e-001 -9.221203e-001 2.982909e-003 - 1.224000e+001 -8.050752e-002 -9.228742e-001 2.989390e-003 - 1.225000e+001 1.160692e-001 -9.236282e-001 2.995186e-003 - 1.226000e+001 3.260487e-001 -9.243822e-001 2.998985e-003 - 1.227000e+001 5.472307e-001 -9.251362e-001 2.999938e-003 - 1.228000e+001 7.767851e-001 -9.258902e-001 2.997848e-003 - 1.229000e+001 1.011296e+000 -9.266442e-001 2.993210e-003 - 1.230000e+001 1.246829e+000 -9.273981e-001 2.987097e-003 - 1.231000e+001 1.479031e+000 -9.281521e-001 2.980924e-003 - 1.232000e+001 1.703241e+000 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1.119556e+000 -9.417238e-001 2.983642e-003 - 1.250000e+001 8.343383e-001 -9.424778e-001 2.989821e-003 - 1.251000e+001 5.450218e-001 -9.432318e-001 2.995185e-003 - 1.252000e+001 2.572317e-001 -9.439857e-001 2.998503e-003 - 1.253000e+001 -2.363413e-002 -9.447397e-001 2.999015e-003 - 1.254000e+001 -2.925463e-001 -9.454937e-001 2.996610e-003 - 1.255000e+001 -5.449645e-001 -9.462477e-001 2.991843e-003 - 1.256000e+001 -7.769342e-001 -9.470017e-001 2.985817e-003 - 1.257000e+001 -9.851568e-001 -9.477557e-001 2.979931e-003 - 1.258000e+001 -1.167032e+000 -9.485096e-001 2.975560e-003 - 1.259000e+001 -1.320669e+000 -9.492636e-001 2.973735e-003 - 1.260000e+001 -1.444877e+000 -9.500176e-001 2.974899e-003 - 1.261000e+001 -1.539122e+000 -9.507716e-001 2.978796e-003 - 1.262000e+001 -1.603472e+000 -9.515256e-001 2.984540e-003 - 1.263000e+001 -1.638518e+000 -9.522796e-001 2.990819e-003 - 1.264000e+001 -1.645290e+000 -9.530335e-001 2.996206e-003 - 1.265000e+001 -1.625160e+000 -9.537875e-001 2.999490e-003 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2.985089e-003 - 1.283000e+001 1.293607e+000 -9.673592e-001 2.979451e-003 - 1.284000e+001 1.473622e+000 -9.681132e-001 2.975429e-003 - 1.285000e+001 1.638500e+000 -9.688672e-001 2.973972e-003 - 1.286000e+001 1.784966e+000 -9.696211e-001 2.975439e-003 - 1.287000e+001 1.909803e+000 -9.703751e-001 2.979505e-003 - 1.288000e+001 2.009963e+000 -9.711291e-001 2.985244e-003 - 1.289000e+001 2.082674e+000 -9.718831e-001 2.991347e-003 - 1.290000e+001 2.125557e+000 -9.726371e-001 2.996428e-003 - 1.291000e+001 2.136734e+000 -9.733911e-001 2.999342e-003 - 1.292000e+001 2.114930e+000 -9.741450e-001 2.999442e-003 - 1.293000e+001 2.059556e+000 -9.748990e-001 2.996721e-003 - 1.294000e+001 1.970771e+000 -9.756530e-001 2.991811e-003 - 1.295000e+001 1.849522e+000 -9.764070e-001 2.985843e-003 - 1.296000e+001 1.697556e+000 -9.771610e-001 2.980189e-003 - 1.297000e+001 1.517395e+000 -9.779149e-001 2.976153e-003 - 1.298000e+001 1.312291e+000 -9.786689e-001 2.974657e-003 - 1.299000e+001 1.086149e+000 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1.366000e+001 -1.195423e+000 -1.029940e+000 2.986645e-003 - 1.367000e+001 -8.744382e-001 -1.030694e+000 2.992151e-003 - 1.368000e+001 -4.990416e-001 -1.031448e+000 2.996349e-003 - 1.369000e+001 -7.298061e-002 -1.032202e+000 2.998277e-003 - 1.370000e+001 3.987225e-001 -1.032956e+000 2.997493e-003 - 1.371000e+001 9.098780e-001 -1.033710e+000 2.994181e-003 - 1.372000e+001 1.453268e+000 -1.034464e+000 2.989102e-003 - 1.373000e+001 2.020815e+000 -1.035218e+000 2.983426e-003 - 1.374000e+001 2.603771e+000 -1.035972e+000 2.978464e-003 - 1.375000e+001 3.192920e+000 -1.036726e+000 2.975368e-003 - 1.376000e+001 3.778798e+000 -1.037480e+000 2.974858e-003 - 1.377000e+001 4.351904e+000 -1.038234e+000 2.977051e-003 - 1.378000e+001 4.902919e+000 -1.038988e+000 2.981433e-003 - 1.379000e+001 5.422903e+000 -1.039741e+000 2.986986e-003 - 1.380000e+001 5.903492e+000 -1.040495e+000 2.992428e-003 - 1.381000e+001 6.337059e+000 -1.041249e+000 2.996511e-003 - 1.382000e+001 6.716869e+000 -1.042003e+000 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2.993675e-003 - 1.433000e+001 -2.508109e+000 -1.080457e+000 2.997116e-003 - 1.434000e+001 -2.533164e+000 -1.081211e+000 2.998201e-003 - 1.435000e+001 -2.560428e+000 -1.081964e+000 2.996671e-003 - 1.436000e+001 -2.588578e+000 -1.082718e+000 2.992866e-003 - 1.437000e+001 -2.616271e+000 -1.083472e+000 2.987645e-003 - 1.438000e+001 -2.642211e+000 -1.084226e+000 2.982197e-003 - 1.439000e+001 -2.665217e+000 -1.084980e+000 2.977766e-003 - 1.440000e+001 -2.684273e+000 -1.085734e+000 2.975369e-003 - 1.441000e+001 -2.698569e+000 -1.086488e+000 2.975552e-003 - 1.442000e+001 -2.707529e+000 -1.087242e+000 2.978262e-003 - 1.443000e+001 -2.710821e+000 -1.087996e+000 2.982862e-003 - 1.444000e+001 -2.708357e+000 -1.088750e+000 2.988282e-003 - 1.445000e+001 -2.700272e+000 -1.089504e+000 2.993271e-003 - 1.446000e+001 -2.686900e+000 -1.090258e+000 2.996688e-003 - 1.447000e+001 -2.668728e+000 -1.091012e+000 2.997759e-003 - 1.448000e+001 -2.646351e+000 -1.091766e+000 2.996249e-003 - 1.449000e+001 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2.977936e-003 - 1.466000e+001 -1.720444e+000 -1.105338e+000 2.975861e-003 - 1.467000e+001 -1.608503e+000 -1.106092e+000 2.976329e-003 - 1.468000e+001 -1.486481e+000 -1.106846e+000 2.979231e-003 - 1.469000e+001 -1.354832e+000 -1.107600e+000 2.983891e-003 - 1.470000e+001 -1.214355e+000 -1.108354e+000 2.989232e-003 - 1.471000e+001 -1.066191e+000 -1.109108e+000 2.994025e-003 - 1.472000e+001 -9.117984e-001 -1.109862e+000 2.997179e-003 - 1.473000e+001 -7.529154e-001 -1.110616e+000 2.997979e-003 - 1.474000e+001 -5.915111e-001 -1.111370e+000 2.996255e-003 - 1.475000e+001 -4.297226e-001 -1.112124e+000 2.992409e-003 - 1.476000e+001 -2.697855e-001 -1.112878e+000 2.987333e-003 - 1.477000e+001 -1.139573e-001 -1.113632e+000 2.982200e-003 - 1.478000e+001 3.556067e-002 -1.114386e+000 2.978199e-003 - 1.479000e+001 1.767002e-001 -1.115140e+000 2.976257e-003 - 1.480000e+001 3.075991e-001 -1.115894e+000 2.976819e-003 - 1.481000e+001 4.266666e-001 -1.116648e+000 2.979746e-003 - 1.482000e+001 5.326372e-001 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1.747527e-001 -1.985235e+000 2.981936e-003 - 2.634000e+001 6.832796e-002 -1.985989e+000 2.984288e-003 - 2.635000e+001 -4.522690e-002 -1.986743e+000 2.987220e-003 - 2.636000e+001 -1.643025e-001 -1.987497e+000 2.990055e-003 - 2.637000e+001 -2.873075e-001 -1.988251e+000 2.992139e-003 - 2.638000e+001 -4.126856e-001 -1.989005e+000 2.992995e-003 - 2.639000e+001 -5.389276e-001 -1.989759e+000 2.992427e-003 - 2.640000e+001 -6.645780e-001 -1.990513e+000 2.990567e-003 - 2.641000e+001 -7.882377e-001 -1.991267e+000 2.987843e-003 - 2.642000e+001 -9.085631e-001 -1.992021e+000 2.984882e-003 - 2.643000e+001 -1.024263e+000 -1.992775e+000 2.982367e-003 - 2.644000e+001 -1.134094e+000 -1.993529e+000 2.980878e-003 - 2.645000e+001 -1.236855e+000 -1.994283e+000 2.980758e-003 - 2.646000e+001 -1.331386e+000 -1.995037e+000 2.982031e-003 - 2.647000e+001 -1.416563e+000 -1.995791e+000 2.984399e-003 - 2.648000e+001 -1.491299e+000 -1.996545e+000 2.987311e-003 - 2.649000e+001 -1.554551e+000 -1.997299e+000 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-3.343683e-001 -2.249129e+000 2.983166e-003 - 2.984000e+001 -1.746468e-001 -2.249883e+000 2.985543e-003 - 2.985000e+001 -1.565186e-002 -2.250637e+000 2.988194e-003 - 2.986000e+001 1.410634e-001 -2.251391e+000 2.990507e-003 - 2.987000e+001 2.939571e-001 -2.252145e+000 2.991952e-003 - 2.988000e+001 4.415134e-001 -2.252899e+000 2.992199e-003 - 2.989000e+001 5.822577e-001 -2.253653e+000 2.991191e-003 - 2.990000e+001 7.147710e-001 -2.254407e+000 2.989164e-003 - 2.991000e+001 8.377052e-001 -2.255161e+000 2.986583e-003 - 2.992000e+001 9.497977e-001 -2.255915e+000 2.984045e-003 - 2.993000e+001 1.049886e+000 -2.256669e+000 2.982137e-003 - 2.994000e+001 1.136923e+000 -2.257423e+000 2.981300e-003 - 2.995000e+001 1.209989e+000 -2.258177e+000 2.981726e-003 - 2.996000e+001 1.268310e+000 -2.258931e+000 2.983317e-003 - 2.997000e+001 1.311263e+000 -2.259685e+000 2.985702e-003 - 2.998000e+001 1.338398e+000 -2.260439e+000 2.988329e-003 - 2.999000e+001 1.349438e+000 -2.261193e+000 2.990593e-003 - 3.000000e+001 1.344296e+000 -2.261947e+000 2.991971e-003 - 3.001000e+001 1.323080e+000 -2.262701e+000 2.992149e-003 - 3.002000e+001 1.286093e+000 -2.263455e+000 2.991086e-003 - 3.003000e+001 1.233841e+000 -2.264209e+000 2.989028e-003 - 3.004000e+001 1.167030e+000 -2.264963e+000 2.986450e-003 - 3.005000e+001 1.086558e+000 -2.265717e+000 2.983946e-003 - 3.006000e+001 9.935136e-001 -2.266471e+000 2.982096e-003 - 3.007000e+001 8.891584e-001 -2.267225e+000 2.981328e-003 - 3.008000e+001 7.749159e-001 -2.267979e+000 2.981820e-003 - 3.009000e+001 6.523515e-001 -2.268733e+000 2.983456e-003 - 3.010000e+001 5.231505e-001 -2.269487e+000 2.985858e-003 - 3.011000e+001 3.890936e-001 -2.270240e+000 2.988469e-003 - 3.012000e+001 2.520286e-001 -2.270994e+000 2.990688e-003 - 3.013000e+001 1.138410e-001 -2.271748e+000 2.992003e-003 - 3.014000e+001 -2.357784e-002 -2.272502e+000 2.992115e-003 - 3.015000e+001 -1.583634e-001 -2.273256e+000 2.990997e-003 - 3.016000e+001 -2.887107e-001 -2.274010e+000 2.988909e-003 - 3.017000e+001 -4.129065e-001 -2.274764e+000 2.986332e-003 - 3.018000e+001 -5.293612e-001 -2.275518e+000 2.983861e-003 - 3.019000e+001 -6.366374e-001 -2.276272e+000 2.982068e-003 - 3.020000e+001 -7.334768e-001 -2.277026e+000 2.981367e-003 - 3.021000e+001 -8.188236e-001 -2.277780e+000 2.981921e-003 - 3.022000e+001 -8.918432e-001 -2.278534e+000 2.983601e-003 - 3.023000e+001 -9.519372e-001 -2.279288e+000 2.986017e-003 - 3.024000e+001 -9.987532e-001 -2.280042e+000 2.988609e-003 - 3.025000e+001 -1.032189e+000 -2.280796e+000 2.990779e-003 - 3.026000e+001 -1.052393e+000 -2.281550e+000 2.992029e-003 - 3.027000e+001 -1.059755e+000 -2.282304e+000 2.992072e-003 - 3.028000e+001 -1.054898e+000 -2.283058e+000 2.990898e-003 - 3.029000e+001 -1.038659e+000 -2.283812e+000 2.988779e-003 - 3.030000e+001 -1.012069e+000 -2.284566e+000 2.986201e-003 - 3.031000e+001 -9.763284e-001 -2.285320e+000 2.983762e-003 - 3.032000e+001 -9.327743e-001 -2.286074e+000 2.982023e-003 - 3.033000e+001 -8.828527e-001 -2.286828e+000 2.981387e-003 - 3.034000e+001 -8.280823e-001 -2.287582e+000 2.982001e-003 - 3.035000e+001 -7.700204e-001 -2.288336e+000 2.983720e-003 - 3.036000e+001 -7.102272e-001 -2.289090e+000 2.986146e-003 - 3.037000e+001 -6.502315e-001 -2.289844e+000 2.988715e-003 - 3.038000e+001 -5.914972e-001 -2.290598e+000 2.990835e-003 - 3.039000e+001 -5.353927e-001 -2.291352e+000 2.992018e-003 - 3.040000e+001 -4.831634e-001 -2.292106e+000 2.991991e-003 - 3.041000e+001 -4.359076e-001 -2.292860e+000 2.990762e-003 - 3.042000e+001 -3.945573e-001 -2.293614e+000 2.988613e-003 - 3.043000e+001 -3.598632e-001 -2.294368e+000 2.986040e-003 - 3.044000e+001 -3.323861e-001 -2.295122e+000 2.983637e-003 - 3.045000e+001 -3.124917e-001 -2.295876e+000 2.981960e-003 - 3.046000e+001 -3.003527e-001 -2.296630e+000 2.981397e-003 - 3.047000e+001 -2.959545e-001 -2.297384e+000 2.982079e-003 - 3.048000e+001 -2.991067e-001 -2.298138e+000 2.983847e-003 - 3.049000e+001 -3.094586e-001 -2.298892e+000 2.986291e-003 - 3.050000e+001 -3.265186e-001 -2.299646e+000 2.988846e-003 - 3.051000e+001 -3.496763e-001 -2.300400e+000 2.990922e-003 - 3.052000e+001 -3.782279e-001 -2.301154e+000 2.992042e-003 - 3.053000e+001 -4.114017e-001 -2.301908e+000 2.991949e-003 - 3.054000e+001 -4.483856e-001 -2.302662e+000 2.990664e-003 - 3.055000e+001 -4.883530e-001 -2.303416e+000 2.988484e-003 - 3.056000e+001 -5.304883e-001 -2.304170e+000 2.985910e-003 - 3.057000e+001 -5.740100e-001 -2.304924e+000 2.983537e-003 - 3.058000e+001 -6.181915e-001 -2.305678e+000 2.981912e-003 - 3.059000e+001 -6.623781e-001 -2.306432e+000 2.981413e-003 - 3.060000e+001 -7.060003e-001 -2.307186e+000 2.982153e-003 - 3.061000e+001 -7.485832e-001 -2.307940e+000 2.983960e-003 - 3.062000e+001 -7.897512e-001 -2.308694e+000 2.986416e-003 - 3.063000e+001 -8.292289e-001 -2.309448e+000 2.988951e-003 - 3.064000e+001 -8.668372e-001 -2.310202e+000 2.990982e-003 - 3.065000e+001 -9.024867e-001 -2.310956e+000 2.992040e-003 - 3.066000e+001 -9.361666e-001 -2.311710e+000 2.991883e-003 - 3.067000e+001 -9.679318e-001 -2.312463e+000 2.990547e-003 - 3.068000e+001 -9.978876e-001 -2.313217e+000 2.988340e-003 - 3.069000e+001 -1.026174e+000 -2.313971e+000 2.985770e-003 - 3.070000e+001 -1.052947e+000 -2.314725e+000 2.983431e-003 - 3.071000e+001 -1.078367e+000 -2.315479e+000 2.981861e-003 - 3.072000e+001 -1.102578e+000 -2.316233e+000 2.981426e-003 - 3.073000e+001 -1.125698e+000 -2.316987e+000 2.982225e-003 - 3.074000e+001 -1.147809e+000 -2.317741e+000 2.984072e-003 - 3.075000e+001 -1.168947e+000 -2.318495e+000 2.986539e-003 - 3.076000e+001 -1.189098e+000 -2.319249e+000 2.989056e-003 - 3.077000e+001 -1.208200e+000 -2.320003e+000 2.991041e-003 - 3.078000e+001 -1.226140e+000 -2.320757e+000 2.992039e-003 - 3.079000e+001 -1.242765e+000 -2.321511e+000 2.991821e-003 - 3.080000e+001 -1.257884e+000 -2.322265e+000 2.990437e-003 - 3.081000e+001 -1.271284e+000 -2.323019e+000 2.988206e-003 - 3.082000e+001 -1.282736e+000 -2.323773e+000 2.985642e-003 - 3.083000e+001 -1.292013e+000 -2.324527e+000 2.983336e-003 - 3.084000e+001 -1.298894e+000 -2.325281e+000 2.981822e-003 - 3.085000e+001 -1.303186e+000 -2.326035e+000 2.981450e-003 - 3.086000e+001 -1.304722e+000 -2.326789e+000 2.982305e-003 - 3.087000e+001 -1.303379e+000 -2.327543e+000 2.984190e-003 - 3.088000e+001 -1.299076e+000 -2.328297e+000 2.986667e-003 - 3.089000e+001 -1.291775e+000 -2.329051e+000 2.989164e-003 - 3.090000e+001 -1.281483e+000 -2.329805e+000 2.991107e-003 - 3.091000e+001 -1.268244e+000 -2.330559e+000 2.992048e-003 - 3.092000e+001 -1.252130e+000 -2.331313e+000 2.991773e-003 - 3.093000e+001 -1.233231e+000 -2.332067e+000 2.990346e-003 - 3.094000e+001 -1.211636e+000 -2.332821e+000 2.988095e-003 - 3.095000e+001 -1.187424e+000 -2.333575e+000 2.985540e-003 - 3.096000e+001 -1.160642e+000 -2.334329e+000 2.983268e-003 - 3.097000e+001 -1.131294e+000 -2.335083e+000 2.981806e-003 - 3.098000e+001 -1.099321e+000 -2.335837e+000 2.981491e-003 - 3.099000e+001 -1.064591e+000 -2.336591e+000 2.982394e-003 - 3.100000e+001 -1.026890e+000 -2.337345e+000 2.984306e-003 - 3.101000e+001 -9.859161e-001 -2.338099e+000 2.986783e-003 - 3.102000e+001 -9.412778e-001 -2.338853e+000 2.989253e-003 - 3.103000e+001 -8.925004e-001 -2.339607e+000 2.991147e-003 - 3.104000e+001 -8.390350e-001 -2.340361e+000 2.992030e-003 - 3.105000e+001 -7.802740e-001 -2.341115e+000 2.991700e-003 - 3.106000e+001 -7.155716e-001 -2.341869e+000 2.990235e-003 - 3.107000e+001 -6.442693e-001 -2.342623e+000 2.987972e-003 - 3.108000e+001 -5.657243e-001 -2.343377e+000 2.985434e-003 - 3.109000e+001 -4.793410e-001 -2.344131e+000 2.983206e-003 - 3.110000e+001 -3.846046e-001 -2.344885e+000 2.981803e-003 - 3.111000e+001 -2.811137e-001 -2.345639e+000 2.981548e-003 - 3.112000e+001 -1.686125e-001 -2.346393e+000 2.982501e-003 - 3.113000e+001 -4.701975e-002 -2.347147e+000 2.984438e-003 - 3.114000e+001 8.354604e-002 -2.347901e+000 2.986910e-003 - 3.115000e+001 2.227473e-001 -2.348655e+000 2.989346e-003 - 3.116000e+001 3.700140e-001 -2.349409e+000 2.991184e-003 - 3.117000e+001 5.245387e-001 -2.350163e+000 2.992003e-003 - 3.118000e+001 6.852780e-001 -2.350917e+000 2.991615e-003 - 3.119000e+001 8.509639e-001 -2.351671e+000 2.990112e-003 - 3.120000e+001 1.020122e+000 -2.352425e+000 2.987841e-003 - 3.121000e+001 1.191100e+000 -2.353179e+000 2.985325e-003 - 3.122000e+001 1.362097e+000 -2.353933e+000 2.983146e-003 - 3.123000e+001 1.531210e+000 -2.354686e+000 2.981808e-003 - 3.124000e+001 1.696470e+000 -2.355440e+000 2.981619e-003 - 3.125000e+001 1.855900e+000 -2.356194e+000 2.982622e-003 - 3.126000e+001 2.007553e+000 -2.356948e+000 2.984582e-003 - 3.127000e+001 2.149571e+000 -2.357702e+000 2.987043e-003 - 3.128000e+001 2.280227e+000 -2.358456e+000 2.989436e-003 - 3.129000e+001 2.397968e+000 -2.359210e+000 2.991209e-003 - 3.130000e+001 2.501457e+000 -2.359964e+000 2.991953e-003 - 3.131000e+001 2.589601e+000 -2.360718e+000 2.991500e-003 - 3.132000e+001 2.661578e+000 -2.361472e+000 2.989954e-003 - 3.133000e+001 2.716851e+000 -2.362226e+000 2.987673e-003 - 3.134000e+001 2.755174e+000 -2.362980e+000 2.985185e-003 - 3.135000e+001 2.776592e+000 -2.363734e+000 2.983066e-003 - 3.136000e+001 2.781428e+000 -2.364488e+000 2.981807e-003 - 3.137000e+001 2.770266e+000 -2.365242e+000 2.981700e-003 - 3.138000e+001 2.743921e+000 -2.365996e+000 2.982770e-003 - 3.139000e+001 2.703408e+000 -2.366750e+000 2.984767e-003 - 3.140000e+001 2.649909e+000 -2.367504e+000 2.987228e-003 - 3.141000e+001 2.584726e+000 -2.368258e+000 2.989582e-003 - 3.142000e+001 2.509242e+000 -2.369012e+000 2.991286e-003 - 3.143000e+001 2.424883e+000 -2.369766e+000 2.991947e-003 - 3.144000e+001 2.333072e+000 -2.370520e+000 2.991411e-003 - 3.145000e+001 2.235197e+000 -2.371274e+000 2.989802e-003 - 3.146000e+001 2.132577e+000 -2.372028e+000 2.987491e-003 - 3.147000e+001 2.026435e+000 -2.372782e+000 2.985009e-003 - 3.148000e+001 1.917877e+000 -2.373536e+000 2.982932e-003 - 3.149000e+001 1.807880e+000 -2.374290e+000 2.981740e-003 - 3.150000e+001 1.697283e+000 -2.375044e+000 2.981710e-003 - 3.151000e+001 1.586786e+000 -2.375798e+000 2.982849e-003 - 3.152000e+001 1.476956e+000 -2.376552e+000 2.984894e-003 - 3.153000e+001 1.368237e+000 -2.377306e+000 2.987370e-003 - 3.154000e+001 1.260964e+000 -2.378060e+000 2.989706e-003 - 3.155000e+001 1.155382e+000 -2.378814e+000 2.991361e-003 - 3.156000e+001 1.051668e+000 -2.379568e+000 2.991956e-003 - 3.157000e+001 9.499455e-001 -2.380322e+000 2.991352e-003 - 3.158000e+001 8.503126e-001 -2.381076e+000 2.989689e-003 - 3.159000e+001 7.528560e-001 -2.381830e+000 2.987347e-003 - 3.160000e+001 6.576688e-001 -2.382584e+000 2.984867e-003 - 3.161000e+001 5.648639e-001 -2.383338e+000 2.982821e-003 - 3.162000e+001 4.745832e-001 -2.384092e+000 2.981683e-003 - 3.163000e+001 3.870022e-001 -2.384846e+000 2.981717e-003 - 3.164000e+001 3.023314e-001 -2.385600e+000 2.982916e-003 - 3.165000e+001 2.208126e-001 -2.386354e+000 2.985001e-003 - 3.166000e+001 1.427118e-001 -2.387108e+000 2.987491e-003 - 3.167000e+001 6.830856e-002 -2.387862e+000 2.989812e-003 - 3.168000e+001 -2.116127e-003 -2.388616e+000 2.991429e-003 - 3.169000e+001 -6.829486e-002 -2.389370e+000 2.991971e-003 - 3.170000e+001 -1.299886e-001 -2.390124e+000 2.991313e-003 - 3.171000e+001 -1.870017e-001 -2.390878e+000 2.989606e-003 - 3.172000e+001 -2.391950e-001 -2.391632e+000 2.987244e-003 - 3.173000e+001 -2.864981e-001 -2.392386e+000 2.984768e-003 - 3.174000e+001 -3.289173e-001 -2.393140e+000 2.982752e-003 - 3.175000e+001 -3.665420e-001 -2.393894e+000 2.981660e-003 - 3.176000e+001 -3.995457e-001 -2.394648e+000 2.981746e-003 - 3.177000e+001 -4.281844e-001 -2.395402e+000 2.982988e-003 - 3.178000e+001 -4.527907e-001 -2.396156e+000 2.985101e-003 - 3.179000e+001 -4.737641e-001 -2.396909e+000 2.987594e-003 - 3.180000e+001 -4.915587e-001 -2.397663e+000 2.989894e-003 - 3.181000e+001 -5.066676e-001 -2.398417e+000 2.991472e-003 - 3.182000e+001 -5.196061e-001 -2.399171e+000 2.991965e-003 - 3.183000e+001 -5.308933e-001 -2.399925e+000 2.991262e-003 - 3.184000e+001 -5.410337e-001 -2.400679e+000 2.989525e-003 - 3.185000e+001 -5.504990e-001 -2.401433e+000 2.987152e-003 - 3.186000e+001 -5.597122e-001 -2.402187e+000 2.984692e-003 - 3.187000e+001 -5.690326e-001 -2.402941e+000 2.982709e-003 - 3.188000e+001 -5.787446e-001 -2.403695e+000 2.981664e-003 - 3.189000e+001 -5.890493e-001 -2.404449e+000 2.981795e-003 - 3.190000e+001 -6.000595e-001 -2.405203e+000 2.983073e-003 - 3.191000e+001 -6.117992e-001 -2.405957e+000 2.985201e-003 - 3.192000e+001 -6.242060e-001 -2.406711e+000 2.987686e-003 - 3.193000e+001 -6.371373e-001 -2.407465e+000 2.989957e-003 - 3.194000e+001 -6.503803e-001 -2.408219e+000 2.991491e-003 - 3.195000e+001 -6.636642e-001 -2.408973e+000 2.991939e-003 - 3.196000e+001 -6.766745e-001 -2.409727e+000 2.991199e-003 - 3.197000e+001 -6.890698e-001 -2.410481e+000 2.989443e-003 - 3.198000e+001 -7.004980e-001 -2.411235e+000 2.987077e-003 - 3.199000e+001 -7.106141e-001 -2.411989e+000 2.984646e-003 - 3.200000e+001 -7.190966e-001 -2.412743e+000 2.982711e-003 - 3.201000e+001 -7.256630e-001 -2.413497e+000 2.981719e-003 - 3.202000e+001 -7.300836e-001 -2.414251e+000 2.981898e-003 - 3.203000e+001 -7.321926e-001 -2.415005e+000 2.983205e-003 - 3.204000e+001 -7.318974e-001 -2.415759e+000 2.985335e-003 - 3.205000e+001 -7.291848e-001 -2.416513e+000 2.987795e-003 - 3.206000e+001 -7.241232e-001 -2.417267e+000 2.990016e-003 - 3.207000e+001 -7.168635e-001 -2.418021e+000 2.991488e-003 - 3.208000e+001 -7.076361e-001 -2.418775e+000 2.991874e-003 - 3.209000e+001 -6.967449e-001 -2.419529e+000 2.991088e-003 - 3.210000e+001 -6.845599e-001 -2.420283e+000 2.989312e-003 - 3.211000e+001 -6.715068e-001 -2.421037e+000 2.986957e-003 - 3.212000e+001 -6.580556e-001 -2.421791e+000 2.984567e-003 - 3.213000e+001 -6.447072e-001 -2.422545e+000 2.982695e-003 - 3.214000e+001 -6.319801e-001 -2.423299e+000 2.981774e-003 - 3.215000e+001 -6.203957e-001 -2.424053e+000 2.982016e-003 - 3.216000e+001 -6.104641e-001 -2.424807e+000 2.983363e-003 - 3.217000e+001 -6.026704e-001 -2.425561e+000 2.985500e-003 - 3.218000e+001 -5.974612e-001 -2.426315e+000 2.987933e-003 - 3.219000e+001 -5.952319e-001 -2.427069e+000 2.990097e-003 - 3.220000e+001 -5.963159e-001 -2.427823e+000 2.991494e-003 - 3.221000e+001 -6.009746e-001 -2.428577e+000 2.991804e-003 - 3.222000e+001 -6.093885e-001 -2.429331e+000 2.990955e-003 - 3.223000e+001 -6.216507e-001 -2.430085e+000 2.989146e-003 - 3.224000e+001 -6.377617e-001 -2.430839e+000 2.986794e-003 - 3.225000e+001 -6.576255e-001 -2.431593e+000 2.984443e-003 - 3.226000e+001 -6.810481e-001 -2.432347e+000 2.982637e-003 - 3.227000e+001 -7.077373e-001 -2.433101e+000 2.981796e-003 - 3.228000e+001 -7.373043e-001 -2.433855e+000 2.982113e-003 - 3.229000e+001 -7.692673e-001 -2.434609e+000 2.983514e-003 - 3.230000e+001 -8.030565e-001 -2.435363e+000 2.985672e-003 - 3.231000e+001 -8.380210e-001 -2.436117e+000 2.988087e-003 - 3.232000e+001 -8.734374e-001 -2.436871e+000 2.990199e-003 - 3.233000e+001 -9.085197e-001 -2.437625e+000 2.991520e-003 - 3.234000e+001 -9.424307e-001 -2.438379e+000 2.991745e-003 - 3.235000e+001 -9.742953e-001 -2.439133e+000 2.990823e-003 - 3.236000e+001 -1.003214e+000 -2.439886e+000 2.988966e-003 - 3.237000e+001 -1.028280e+000 -2.440640e+000 2.986601e-003 - 3.238000e+001 -1.048590e+000 -2.441394e+000 2.984277e-003 - 3.239000e+001 -1.063267e+000 -2.442148e+000 2.982529e-003 - 3.240000e+001 -1.071472e+000 -2.442902e+000 2.981766e-003 - 3.241000e+001 -1.072423e+000 -2.443656e+000 2.982163e-003 - 3.242000e+001 -1.065409e+000 -2.444410e+000 2.983629e-003 - 3.243000e+001 -1.049807e+000 -2.445164e+000 2.985825e-003 - 3.244000e+001 -1.025093e+000 -2.445918e+000 2.988240e-003 - 3.245000e+001 -9.908577e-001 -2.446672e+000 2.990318e-003 - 3.246000e+001 -9.468134e-001 -2.447426e+000 2.991578e-003 - 3.247000e+001 -8.928051e-001 -2.448180e+000 2.991729e-003 - 3.248000e+001 -8.288151e-001 -2.448934e+000 2.990736e-003 - 3.249000e+001 -7.549665e-001 -2.449688e+000 2.988826e-003 - 3.250000e+001 -6.715245e-001 -2.450442e+000 2.986437e-003 - 3.251000e+001 -5.788942e-001 -2.451196e+000 2.984121e-003 - 3.252000e+001 -4.776168e-001 -2.451950e+000 2.982412e-003 - 3.253000e+001 -3.683626e-001 -2.452704e+000 2.981707e-003 - 3.254000e+001 -2.519224e-001 -2.453458e+000 2.982168e-003 - 3.255000e+001 -1.291964e-001 -2.454212e+000 2.983690e-003 - 3.256000e+001 -1.181694e-003 -2.454966e+000 2.985919e-003 - 3.257000e+001 1.310417e-001 -2.455720e+000 2.988342e-003 - 3.258000e+001 2.663257e-001 -2.456474e+000 2.990400e-003 - 3.259000e+001 4.034702e-001 -2.457228e+000 2.991617e-003 - 3.260000e+001 5.412389e-001 -2.457982e+000 2.991716e-003 - 3.261000e+001 6.783756e-001 -2.458736e+000 2.990672e-003 - 3.262000e+001 8.136203e-001 -2.459490e+000 2.988725e-003 - 3.263000e+001 9.457245e-001 -2.460244e+000 2.986323e-003 - 3.264000e+001 1.073466e+000 -2.460998e+000 2.984018e-003 - 3.265000e+001 1.195665e+000 -2.461752e+000 2.982342e-003 - 3.266000e+001 1.311194e+000 -2.462506e+000 2.981682e-003 - 3.267000e+001 1.418993e+000 -2.463260e+000 2.982191e-003 - 3.268000e+001 1.518079e+000 -2.464014e+000 2.983750e-003 - 3.269000e+001 1.607559e+000 -2.464768e+000 2.985999e-003 - 3.270000e+001 1.686635e+000 -2.465522e+000 2.988418e-003 - 3.271000e+001 1.754619e+000 -2.466276e+000 2.990450e-003 - 3.272000e+001 1.810933e+000 -2.467030e+000 2.991629e-003 - 3.273000e+001 1.855121e+000 -2.467784e+000 2.991686e-003 - 3.274000e+001 1.886851e+000 -2.468538e+000 2.990607e-003 - 3.275000e+001 1.905923e+000 -2.469292e+000 2.988642e-003 - 3.276000e+001 1.912267e+000 -2.470046e+000 2.986243e-003 - 3.277000e+001 1.905947e+000 -2.470800e+000 2.983963e-003 - 3.278000e+001 1.887164e+000 -2.471554e+000 2.982328e-003 - 3.279000e+001 1.856250e+000 -2.472308e+000 2.981714e-003 - 3.280000e+001 1.813667e+000 -2.473062e+000 2.982264e-003 - 3.281000e+001 1.760000e+000 -2.473816e+000 2.983847e-003 - 3.282000e+001 1.695955e+000 -2.474570e+000 2.986097e-003 - 3.283000e+001 1.622344e+000 -2.475324e+000 2.988494e-003 - 3.284000e+001 1.540077e+000 -2.476078e+000 2.990485e-003 - 3.285000e+001 1.450148e+000 -2.476832e+000 2.991613e-003 - 3.286000e+001 1.353622e+000 -2.477586e+000 2.991622e-003 - 3.287000e+001 1.251615e+000 -2.478340e+000 2.990511e-003 - 3.288000e+001 1.145283e+000 -2.479094e+000 2.988538e-003 - 3.289000e+001 1.035794e+000 -2.479848e+000 2.986157e-003 - 3.290000e+001 9.243206e-001 -2.480602e+000 2.983920e-003 - 3.291000e+001 8.120110e-001 -2.481356e+000 2.982343e-003 - 3.292000e+001 6.999773e-001 -2.482109e+000 2.981790e-003 - 3.293000e+001 5.892763e-001 -2.482863e+000 2.982388e-003 - 3.294000e+001 4.808943e-001 -2.483617e+000 2.983996e-003 - 3.295000e+001 3.757338e-001 -2.484371e+000 2.986242e-003 - 3.296000e+001 2.746030e-001 -2.485125e+000 2.988604e-003 - 3.297000e+001 1.782076e-001 -2.485879e+000 2.990537e-003 - 3.298000e+001 8.714605e-002 -2.486633e+000 2.991598e-003 - 3.299000e+001 1.907482e-003 -2.487387e+000 2.991543e-003 - 3.300000e+001 -7.712665e-002 -2.488141e+000 2.990387e-003 - 3.301000e+001 -1.496785e-001 -2.488895e+000 2.988398e-003 - 3.302000e+001 -2.155666e-001 -2.489649e+000 2.986036e-003 - 3.303000e+001 -2.746972e-001 -2.490403e+000 2.983847e-003 - 3.304000e+001 -3.270526e-001 -2.491157e+000 2.982339e-003 - 3.305000e+001 -3.726792e-001 -2.491911e+000 2.981862e-003 - 3.306000e+001 -4.116744e-001 -2.492665e+000 2.982524e-003 - 3.307000e+001 -4.441739e-001 -2.493419e+000 2.984172e-003 - 3.308000e+001 -4.703394e-001 -2.494173e+000 2.986423e-003 - 3.309000e+001 -4.903474e-001 -2.494927e+000 2.988755e-003 - 3.310000e+001 -5.043796e-001 -2.495681e+000 2.990628e-003 - 3.311000e+001 -5.126159e-001 -2.496435e+000 2.991612e-003 - 3.312000e+001 -5.152292e-001 -2.497189e+000 2.991480e-003 - 3.313000e+001 -5.123830e-001 -2.497943e+000 2.990262e-003 - 3.314000e+001 -5.042312e-001 -2.498697e+000 2.988240e-003 - 3.315000e+001 -4.909206e-001 -2.499451e+000 2.985880e-003 - 3.316000e+001 -4.725953e-001 -2.500205e+000 2.983728e-003 - 3.317000e+001 -4.494028e-001 -2.500959e+000 2.982283e-003 - 3.318000e+001 -4.215011e-001 -2.501713e+000 2.981880e-003 - 3.319000e+001 -3.890663e-001 -2.502467e+000 2.982612e-003 - 3.320000e+001 -3.523011e-001 -2.503221e+000 2.984310e-003 - 3.321000e+001 -3.114413e-001 -2.503975e+000 2.986580e-003 - 3.322000e+001 -2.667620e-001 -2.504729e+000 2.988896e-003 - 3.323000e+001 -2.185822e-001 -2.505483e+000 2.990724e-003 - 3.324000e+001 -1.672664e-001 -2.506237e+000 2.991643e-003 - 3.325000e+001 -1.132249e-001 -2.506991e+000 2.991440e-003 - 3.326000e+001 -5.691083e-002 -2.507745e+000 2.990162e-003 - 3.327000e+001 1.185273e-003 -2.508499e+000 2.988103e-003 - 3.328000e+001 6.054283e-002 -2.509253e+000 2.985738e-003 - 3.329000e+001 1.206210e-001 -2.510007e+000 2.983611e-003 - 3.330000e+001 1.808700e-001 -2.510761e+000 2.982216e-003 - 3.331000e+001 2.407432e-001 -2.511515e+000 2.981875e-003 - 3.332000e+001 2.997097e-001 -2.512269e+000 2.982668e-003 - 3.333000e+001 3.572669e-001 -2.513023e+000 2.984410e-003 - 3.334000e+001 4.129511e-001 -2.513777e+000 2.986698e-003 - 3.335000e+001 4.663476e-001 -2.514531e+000 2.989004e-003 - 3.336000e+001 5.170973e-001 -2.515285e+000 2.990795e-003 - 3.337000e+001 5.649015e-001 -2.516039e+000 2.991659e-003 - 3.338000e+001 6.095227e-001 -2.516793e+000 2.991398e-003 - 3.339000e+001 6.507829e-001 -2.517547e+000 2.990071e-003 - 3.340000e+001 6.885576e-001 -2.518301e+000 2.987984e-003 - 3.341000e+001 7.227676e-001 -2.519055e+000 2.985617e-003 - 3.342000e+001 7.533680e-001 -2.519809e+000 2.983516e-003 - 3.343000e+001 7.803340e-001 -2.520563e+000 2.982166e-003 - 3.344000e+001 8.036465e-001 -2.521317e+000 2.981880e-003 - 3.345000e+001 8.232765e-001 -2.522071e+000 2.982723e-003 - 3.346000e+001 8.391695e-001 -2.522825e+000 2.984500e-003 - 3.347000e+001 8.512315e-001 -2.523579e+000 2.986798e-003 - 3.348000e+001 8.593171e-001 -2.524332e+000 2.989087e-003 - 3.349000e+001 8.632199e-001 -2.525086e+000 2.990839e-003 - 3.350000e+001 8.626672e-001 -2.525840e+000 2.991651e-003 - 3.351000e+001 8.573188e-001 -2.526594e+000 2.991337e-003 - 3.352000e+001 8.467699e-001 -2.527348e+000 2.989969e-003 - 3.353000e+001 8.305595e-001 -2.528102e+000 2.987863e-003 - 3.354000e+001 8.081827e-001 -2.528856e+000 2.985503e-003 - 3.355000e+001 7.791080e-001 -2.529610e+000 2.983434e-003 - 3.356000e+001 7.427982e-001 -2.530364e+000 2.982135e-003 - 3.357000e+001 6.987344e-001 -2.531118e+000 2.981906e-003 - 3.358000e+001 6.464423e-001 -2.531872e+000 2.982798e-003 - 3.359000e+001 5.855193e-001 -2.532626e+000 2.984606e-003 - 3.360000e+001 5.156621e-001 -2.533380e+000 2.986909e-003 - 3.361000e+001 4.366929e-001 -2.534134e+000 2.989177e-003 - 3.362000e+001 3.485827e-001 -2.534888e+000 2.990885e-003 - 3.363000e+001 2.514719e-001 -2.535642e+000 2.991643e-003 - 3.364000e+001 1.456859e-001 -2.536396e+000 2.991275e-003 - 3.365000e+001 3.174539e-002 -2.537150e+000 2.989868e-003 - 3.366000e+001 -8.962936e-002 -2.537904e+000 2.987745e-003 - 3.367000e+001 -2.175202e-001 -2.538658e+000 2.985396e-003 - 3.368000e+001 -3.508196e-001 -2.539412e+000 2.983364e-003 - 3.369000e+001 -4.882459e-001 -2.540166e+000 2.982118e-003 - 3.370000e+001 -6.283635e-001 -2.540920e+000 2.981946e-003 - 3.371000e+001 -7.696095e-001 -2.541674e+000 2.982889e-003 - 3.372000e+001 -9.103243e-001 -2.542428e+000 2.984726e-003 - 3.373000e+001 -1.048786e+000 -2.543182e+000 2.987032e-003 - 3.374000e+001 -1.183247e+000 -2.543936e+000 2.989275e-003 - 3.375000e+001 -1.311971e+000 -2.544690e+000 2.990937e-003 - 3.376000e+001 -1.433275e+000 -2.545444e+000 2.991638e-003 - 3.377000e+001 -1.545558e+000 -2.546198e+000 2.991215e-003 - 3.378000e+001 -1.647344e+000 -2.546952e+000 2.989768e-003 - 3.379000e+001 -1.737309e+000 -2.547706e+000 2.987630e-003 - 3.380000e+001 -1.814304e+000 -2.548460e+000 2.985294e-003 - 3.381000e+001 -1.877384e+000 -2.549214e+000 2.983299e-003 - 3.382000e+001 -1.925820e+000 -2.549968e+000 2.982108e-003 - 3.383000e+001 -1.959110e+000 -2.550722e+000 2.981995e-003 - 3.384000e+001 -1.976984e+000 -2.551476e+000 2.982988e-003 - 3.385000e+001 -1.979406e+000 -2.552230e+000 2.984855e-003 - 3.386000e+001 -1.966564e+000 -2.552984e+000 2.987164e-003 - 3.387000e+001 -1.938865e+000 -2.553738e+000 2.989383e-003 - 3.388000e+001 -1.896919e+000 -2.554492e+000 2.991000e-003 - 3.389000e+001 -1.841517e+000 -2.555246e+000 2.991644e-003 - 3.390000e+001 -1.773620e+000 -2.556000e+000 2.991168e-003 - 3.391000e+001 -1.694331e+000 -2.556754e+000 2.989682e-003 - 3.392000e+001 -1.604875e+000 -2.557508e+000 2.987529e-003 - 3.393000e+001 -1.506573e+000 -2.558262e+000 2.985204e-003 - 3.394000e+001 -1.400826e+000 -2.559016e+000 2.983245e-003 - 3.395000e+001 -1.289088e+000 -2.559770e+000 2.982104e-003 - 3.396000e+001 -1.172845e+000 -2.560524e+000 2.982045e-003 - 3.397000e+001 -1.053601e+000 -2.561278e+000 2.983081e-003 - 3.398000e+001 -9.328541e-001 -2.562032e+000 2.984971e-003 - 3.399000e+001 -8.120851e-001 -2.562786e+000 2.987276e-003 - 3.400000e+001 -6.927396e-001 -2.563540e+000 2.989465e-003 - 3.401000e+001 -5.762163e-001 -2.564294e+000 2.991033e-003 - 3.402000e+001 -4.638536e-001 -2.565048e+000 2.991620e-003 - 3.403000e+001 -3.569186e-001 -2.565802e+000 2.991092e-003 - 3.404000e+001 -2.565962e-001 -2.566555e+000 2.989571e-003 - 3.405000e+001 -1.639788e-001 -2.567309e+000 2.987407e-003 - 3.406000e+001 -8.005672e-002 -2.568063e+000 2.985101e-003 - 3.407000e+001 -5.708820e-003 -2.568817e+000 2.983184e-003 - 3.408000e+001 5.830641e-002 -2.569571e+000 2.982100e-003 - 3.409000e+001 1.113591e-001 -2.570325e+000 2.982099e-003 - 3.410000e+001 1.529554e-001 -2.571079e+000 2.983180e-003 - 3.411000e+001 1.827444e-001 -2.571833e+000 2.985093e-003 - 3.412000e+001 2.005231e-001 -2.572587e+000 2.987393e-003 - 3.413000e+001 2.062403e-001 -2.573341e+000 2.989549e-003 - 3.414000e+001 1.999989e-001 -2.574095e+000 2.991064e-003 - 3.415000e+001 1.820549e-001 -2.574849e+000 2.991590e-003 - 3.416000e+001 1.528159e-001 -2.575603e+000 2.991006e-003 - 3.417000e+001 1.128354e-001 -2.576357e+000 2.989448e-003 - 3.418000e+001 6.280566e-002 -2.577111e+000 2.987274e-003 - 3.419000e+001 3.547288e-003 -2.577865e+000 2.984986e-003 - 3.420000e+001 -6.400288e-002 -2.578619e+000 2.983112e-003 - 3.421000e+001 -1.388066e-001 -2.579373e+000 2.982087e-003 - 3.422000e+001 -2.197407e-001 -2.580127e+000 2.982146e-003 - 3.423000e+001 -3.056150e-001 -2.580881e+000 2.983275e-003 - 3.424000e+001 -3.951911e-001 -2.581635e+000 2.985211e-003 - 3.425000e+001 -4.872019e-001 -2.582389e+000 2.987506e-003 - 3.426000e+001 -5.803706e-001 -2.583143e+000 2.989629e-003 - 3.427000e+001 -6.734295e-001 -2.583897e+000 2.991090e-003 - 3.428000e+001 -7.651371e-001 -2.584651e+000 2.991552e-003 - 3.429000e+001 -8.542947e-001 -2.585405e+000 2.990910e-003 - 3.430000e+001 -9.397597e-001 -2.586159e+000 2.989311e-003 - 3.431000e+001 -1.020458e+000 -2.586913e+000 2.987124e-003 - 3.432000e+001 -1.095393e+000 -2.587667e+000 2.984853e-003 - 3.433000e+001 -1.163653e+000 -2.588421e+000 2.983022e-003 - 3.434000e+001 -1.224418e+000 -2.589175e+000 2.982055e-003 - 3.435000e+001 -1.276959e+000 -2.589929e+000 2.982176e-003 - 3.436000e+001 -1.320642e+000 -2.590683e+000 2.983357e-003 - 3.437000e+001 -1.354927e+000 -2.591437e+000 2.985322e-003 - 3.438000e+001 -1.379368e+000 -2.592191e+000 2.987619e-003 - 3.439000e+001 -1.393607e+000 -2.592945e+000 2.989715e-003 - 3.440000e+001 -1.397377e+000 -2.593699e+000 2.991128e-003 - 3.441000e+001 -1.390499e+000 -2.594453e+000 2.991534e-003 - 3.442000e+001 -1.372875e+000 -2.595207e+000 2.990840e-003 - 3.443000e+001 -1.344496e+000 -2.595961e+000 2.989204e-003 - 3.444000e+001 -1.305435e+000 -2.596715e+000 2.987005e-003 - 3.445000e+001 -1.255850e+000 -2.597469e+000 2.984748e-003 - 3.446000e+001 -1.195985e+000 -2.598223e+000 2.982956e-003 - 3.447000e+001 -1.126172e+000 -2.598977e+000 2.982041e-003 - 3.448000e+001 -1.046833e+000 -2.599731e+000 2.982217e-003 - 3.449000e+001 -9.584801e-001 -2.600485e+000 2.983440e-003 - 3.450000e+001 -8.617171e-001 -2.601239e+000 2.985428e-003 - 3.451000e+001 -7.572399e-001 -2.601993e+000 2.987719e-003 - 3.452000e+001 -6.458340e-001 -2.602747e+000 2.989786e-003 - 3.453000e+001 -5.283706e-001 -2.603501e+000 2.991152e-003 - 3.454000e+001 -4.058005e-001 -2.604255e+000 2.991504e-003 - 3.455000e+001 -2.791461e-001 -2.605009e+000 2.990761e-003 - 3.456000e+001 -1.494900e-001 -2.605763e+000 2.989095e-003 - 3.457000e+001 -1.796150e-002 -2.606517e+000 2.986890e-003 - 3.458000e+001 1.142790e-001 -2.607271e+000 2.984655e-003 - 3.459000e+001 2.460580e-001 -2.608025e+000 2.982905e-003 - 3.460000e+001 3.762082e-001 -2.608779e+000 2.982045e-003 - 3.461000e+001 5.035882e-001 -2.609532e+000 2.982275e-003 - 3.462000e+001 6.271036e-001 -2.610286e+000 2.983539e-003 - 3.463000e+001 7.457265e-001 -2.611040e+000 2.985546e-003 - 3.464000e+001 8.585142e-001 -2.611794e+000 2.987829e-003 - 3.465000e+001 9.646262e-001 -2.612548e+000 2.989863e-003 - 3.466000e+001 1.063338e+000 -2.613302e+000 2.991179e-003 - 3.467000e+001 1.154052e+000 -2.614056e+000 2.991476e-003 - 3.468000e+001 1.236306e+000 -2.614810e+000 2.990686e-003 - 3.469000e+001 1.309774e+000 -2.615564e+000 2.988992e-003 - 3.470000e+001 1.374266e+000 -2.616318e+000 2.986785e-003 - 3.471000e+001 1.429727e+000 -2.617072e+000 2.984575e-003 - 3.472000e+001 1.476221e+000 -2.617826e+000 2.982871e-003 - 3.473000e+001 1.513927e+000 -2.618580e+000 2.982069e-003 - 3.474000e+001 1.543115e+000 -2.619334e+000 2.982353e-003 - 3.475000e+001 1.564140e+000 -2.620088e+000 2.983658e-003 - 3.476000e+001 1.577411e+000 -2.620842e+000 2.985680e-003 - 3.477000e+001 1.583385e+000 -2.621596e+000 2.987951e-003 - 3.478000e+001 1.582537e+000 -2.622350e+000 2.989947e-003 - 3.479000e+001 1.575350e+000 -2.623104e+000 2.991209e-003 - 3.480000e+001 1.562298e+000 -2.623858e+000 2.991448e-003 - 3.481000e+001 1.543833e+000 -2.624612e+000 2.990608e-003 - 3.482000e+001 1.520375e+000 -2.625366e+000 2.988886e-003 - 3.483000e+001 1.492307e+000 -2.626120e+000 2.986677e-003 - 3.484000e+001 1.459973e+000 -2.626874e+000 2.984493e-003 - 3.485000e+001 1.423681e+000 -2.627628e+000 2.982838e-003 - 3.486000e+001 1.383703e+000 -2.628382e+000 2.982096e-003 - 3.487000e+001 1.340288e+000 -2.629136e+000 2.982437e-003 - 3.488000e+001 1.293670e+000 -2.629890e+000 2.983782e-003 - 3.489000e+001 1.244081e+000 -2.630644e+000 2.985819e-003 - 3.490000e+001 1.191762e+000 -2.631398e+000 2.988076e-003 - 3.491000e+001 1.136977e+000 -2.632152e+000 2.990033e-003 - 3.492000e+001 1.080025e+000 -2.632906e+000 2.991237e-003 - 3.493000e+001 1.021253e+000 -2.633660e+000 2.991413e-003 - 3.494000e+001 9.610583e-001 -2.634414e+000 2.990521e-003 - 3.495000e+001 8.998982e-001 -2.635168e+000 2.988767e-003 - 3.496000e+001 8.382906e-001 -2.635922e+000 2.986556e-003 - 3.497000e+001 7.768120e-001 -2.636676e+000 2.984398e-003 - 3.498000e+001 7.160917e-001 -2.637430e+000 2.982792e-003 - 3.499000e+001 6.568025e-001 -2.638184e+000 2.982111e-003 - 3.500000e+001 5.996483e-001 -2.638938e+000 2.982511e-003 - 3.501000e+001 5.453482e-001 -2.639692e+000 2.983899e-003 - 3.502000e+001 4.946194e-001 -2.640446e+000 2.985954e-003 - 3.503000e+001 4.481574e-001 -2.641200e+000 2.988199e-003 - 3.504000e+001 4.066164e-001 -2.641954e+000 2.990116e-003 - 3.505000e+001 3.705893e-001 -2.642708e+000 2.991263e-003 - 3.506000e+001 3.405895e-001 -2.643462e+000 2.991376e-003 - 3.507000e+001 3.170332e-001 -2.644216e+000 2.990429e-003 - 3.508000e+001 3.002255e-001 -2.644970e+000 2.988641e-003 - 3.509000e+001 2.903490e-001 -2.645724e+000 2.986423e-003 - 3.510000e+001 2.874557e-001 -2.646478e+000 2.984288e-003 - 3.511000e+001 2.914632e-001 -2.647232e+000 2.982728e-003 - 3.512000e+001 3.021545e-001 -2.647986e+000 2.982105e-003 - 3.513000e+001 3.191816e-001 -2.648740e+000 2.982563e-003 - 3.514000e+001 3.420735e-001 -2.649494e+000 2.983996e-003 - 3.515000e+001 3.702458e-001 -2.650248e+000 2.986071e-003 - 3.516000e+001 4.030151e-001 -2.651002e+000 2.988308e-003 - 3.517000e+001 4.396143e-001 -2.651755e+000 2.990191e-003 - 3.518000e+001 4.792097e-001 -2.652509e+000 2.991287e-003 - 3.519000e+001 5.209196e-001 -2.653263e+000 2.991343e-003 - 3.520000e+001 5.638322e-001 -2.654017e+000 2.990347e-003 - 3.521000e+001 6.070245e-001 -2.654771e+000 2.988528e-003 - 3.522000e+001 6.495793e-001 -2.655525e+000 2.986305e-003 - 3.523000e+001 6.906017e-001 -2.656279e+000 2.984190e-003 - 3.524000e+001 7.292334e-001 -2.657033e+000 2.982672e-003 - 3.525000e+001 7.646659e-001 -2.657787e+000 2.982102e-003 - 3.526000e+001 7.961512e-001 -2.658541e+000 2.982611e-003 - 3.527000e+001 8.230112e-001 -2.659295e+000 2.984081e-003 - 3.528000e+001 8.446450e-001 -2.660049e+000 2.986170e-003 - 3.529000e+001 8.605346e-001 -2.660803e+000 2.988396e-003 - 3.530000e+001 8.702491e-001 -2.661557e+000 2.990246e-003 - 3.531000e+001 8.734482e-001 -2.662311e+000 2.991293e-003 - 3.532000e+001 8.698844e-001 -2.663065e+000 2.991297e-003 - 3.533000e+001 8.594043e-001 -2.663819e+000 2.990259e-003 - 3.534000e+001 8.419498e-001 -2.664573e+000 2.988417e-003 - 3.535000e+001 8.175586e-001 -2.665327e+000 2.986196e-003 - 3.536000e+001 7.863642e-001 -2.666081e+000 2.984109e-003 - 3.537000e+001 7.485954e-001 -2.666835e+000 2.982636e-003 - 3.538000e+001 7.045757e-001 -2.667589e+000 2.982120e-003 - 3.539000e+001 6.547213e-001 -2.668343e+000 2.982677e-003 - 3.540000e+001 5.995385e-001 -2.669097e+000 2.984179e-003 - 3.541000e+001 5.396196e-001 -2.669851e+000 2.986277e-003 - 3.542000e+001 4.756378e-001 -2.670605e+000 2.988485e-003 - 3.543000e+001 4.083401e-001 -2.671359e+000 2.990294e-003 - 3.544000e+001 3.385382e-001 -2.672113e+000 2.991288e-003 - 3.545000e+001 2.670977e-001 -2.672867e+000 2.991238e-003 - 3.546000e+001 1.949255e-001 -2.673621e+000 2.990158e-003 - 3.547000e+001 1.229550e-001 -2.674375e+000 2.988297e-003 - 3.548000e+001 5.212952e-002 -2.675129e+000 2.986083e-003 - 3.549000e+001 -1.661479e-002 -2.675883e+000 2.984028e-003 - 3.550000e+001 -8.236792e-002 -2.676637e+000 2.982607e-003 - 3.551000e+001 -1.442647e-001 -2.677391e+000 2.982148e-003 - 3.552000e+001 -2.015035e-001 -2.678145e+000 2.982758e-003 - 3.553000e+001 -2.533638e-001 -2.678899e+000 2.984294e-003 - 3.554000e+001 -2.992228e-001 -2.679653e+000 2.986400e-003 - 3.555000e+001 -3.385690e-001 -2.680407e+000 2.988588e-003 - 3.556000e+001 -3.710140e-001 -2.681161e+000 2.990354e-003 - 3.557000e+001 -3.963000e-001 -2.681915e+000 2.991291e-003 - 3.558000e+001 -4.143052e-001 -2.682669e+000 2.991185e-003 - 3.559000e+001 -4.250436e-001 -2.683423e+000 2.990060e-003 - 3.560000e+001 -4.286623e-001 -2.684177e+000 2.988177e-003 - 3.561000e+001 -4.254347e-001 -2.684931e+000 2.985970e-003 - 3.562000e+001 -4.157496e-001 -2.685685e+000 2.983948e-003 - 3.563000e+001 -4.000983e-001 -2.686439e+000 2.982580e-003 - 3.564000e+001 -3.790584e-001 -2.687193e+000 2.982181e-003 - 3.565000e+001 -3.532760e-001 -2.687947e+000 2.982844e-003 - 3.566000e+001 -3.234471e-001 -2.688701e+000 2.984414e-003 - 3.567000e+001 -2.902986e-001 -2.689455e+000 2.986526e-003 - 3.568000e+001 -2.545700e-001 -2.690209e+000 2.988692e-003 - 3.569000e+001 -2.169963e-001 -2.690963e+000 2.990411e-003 - 3.570000e+001 -1.782928e-001 -2.691717e+000 2.991288e-003 - 3.571000e+001 -1.391428e-001 -2.692471e+000 2.991120e-003 - 3.572000e+001 -1.001880e-001 -2.693225e+000 2.989947e-003 - 3.573000e+001 -6.202169e-002 -2.693978e+000 2.988040e-003 - 3.574000e+001 -2.518600e-002 -2.694732e+000 2.985838e-003 - 3.575000e+001 9.828834e-003 -2.695486e+000 2.983851e-003 - 3.576000e+001 4.258189e-002 -2.696240e+000 2.982537e-003 - 3.577000e+001 7.267709e-002 -2.696994e+000 2.982203e-003 - 3.578000e+001 9.975705e-002 -2.697748e+000 2.982925e-003 - 3.579000e+001 1.234962e-001 -2.698502e+000 2.984536e-003 - 3.580000e+001 1.435937e-001 -2.699256e+000 2.986662e-003 - 3.581000e+001 1.597671e-001 -2.700010e+000 2.988814e-003 - 3.582000e+001 1.717474e-001 -2.700764e+000 2.990493e-003 - 3.583000e+001 1.792757e-001 -2.701518e+000 2.991314e-003 - 3.584000e+001 1.821029e-001 -2.702272e+000 2.991088e-003 - 3.585000e+001 1.799918e-001 -2.703026e+000 2.989866e-003 - 3.586000e+001 1.727216e-001 -2.703780e+000 2.987931e-003 - 3.587000e+001 1.600958e-001 -2.704534e+000 2.985728e-003 - 3.588000e+001 1.419521e-001 -2.705288e+000 2.983765e-003 - 3.589000e+001 1.181742e-001 -2.706042e+000 2.982496e-003 - 3.590000e+001 8.870467e-002 -2.706796e+000 2.982214e-003 - 3.591000e+001 5.355881e-002 -2.707550e+000 2.982986e-003 - 3.592000e+001 1.283700e-002 -2.708304e+000 2.984630e-003 - 3.593000e+001 -3.326368e-002 -2.709058e+000 2.986767e-003 - 3.594000e+001 -8.444054e-002 -2.709812e+000 2.988903e-003 - 3.595000e+001 -1.402796e-001 -2.710566e+000 2.990546e-003 - 3.596000e+001 -2.002537e-001 -2.711320e+000 2.991317e-003 - 3.597000e+001 -2.637255e-001 -2.712074e+000 2.991041e-003 - 3.598000e+001 -3.299550e-001 -2.712828e+000 2.989782e-003 - 3.599000e+001 -3.981121e-001 -2.713582e+000 2.987828e-003 - 3.600000e+001 -4.672939e-001 -2.714336e+000 2.985632e-003 - 3.601000e+001 -5.365460e-001 -2.715090e+000 2.983700e-003 - 3.602000e+001 -6.048879e-001 -2.715844e+000 2.982478e-003 - 3.603000e+001 -6.713402e-001 -2.716598e+000 2.982250e-003 - 3.604000e+001 -7.349543e-001 -2.717352e+000 2.983067e-003 - 3.605000e+001 -7.948412e-001 -2.718106e+000 2.984739e-003 - 3.606000e+001 -8.502000e-001 -2.718860e+000 2.986880e-003 - 3.607000e+001 -9.003435e-001 -2.719614e+000 2.988994e-003 - 3.608000e+001 -9.447204e-001 -2.720368e+000 2.990594e-003 - 3.609000e+001 -9.829321e-001 -2.721122e+000 2.991313e-003 - 3.610000e+001 -1.014744e+000 -2.721876e+000 2.990985e-003 - 3.611000e+001 -1.040092e+000 -2.722630e+000 2.989687e-003 - 3.612000e+001 -1.059077e+000 -2.723384e+000 2.987717e-003 - 3.613000e+001 -1.071960e+000 -2.724138e+000 2.985531e-003 - 3.614000e+001 -1.079142e+000 -2.724892e+000 2.983632e-003 - 3.615000e+001 -1.081148e+000 -2.725646e+000 2.982459e-003 - 3.616000e+001 -1.078593e+000 -2.726400e+000 2.982284e-003 - 3.617000e+001 -1.072160e+000 -2.727154e+000 2.983146e-003 - 3.618000e+001 -1.062557e+000 -2.727908e+000 2.984845e-003 - 3.619000e+001 -1.050490e+000 -2.728662e+000 2.986986e-003 - 3.620000e+001 -1.036626e+000 -2.729416e+000 2.989075e-003 - 3.621000e+001 -1.021564e+000 -2.730170e+000 2.990629e-003 - 3.622000e+001 -1.005802e+000 -2.730924e+000 2.991293e-003 - 3.623000e+001 -9.897194e-001 -2.731678e+000 2.990912e-003 - 3.624000e+001 -9.735596e-001 -2.732432e+000 2.989576e-003 - 3.625000e+001 -9.574188e-001 -2.733186e+000 2.987593e-003 - 3.626000e+001 -9.412458e-001 -2.733940e+000 2.985419e-003 - 3.627000e+001 -9.248470e-001 -2.734694e+000 2.983558e-003 - 3.628000e+001 -9.079004e-001 -2.735448e+000 2.982439e-003 - 3.629000e+001 -8.899752e-001 -2.736202e+000 2.982320e-003 - 3.630000e+001 -8.705578e-001 -2.736955e+000 2.983230e-003 - 3.631000e+001 -8.490819e-001 -2.737709e+000 2.984956e-003 - 3.632000e+001 -8.249626e-001 -2.738463e+000 2.987099e-003 - 3.633000e+001 -7.976305e-001 -2.739217e+000 2.989163e-003 - 3.634000e+001 -7.665663e-001 -2.739971e+000 2.990672e-003 - 3.635000e+001 -7.313335e-001 -2.740725e+000 2.991280e-003 - 3.636000e+001 -6.916066e-001 -2.741479e+000 2.990847e-003 - 3.637000e+001 -6.471948e-001 -2.742233e+000 2.989474e-003 - 3.638000e+001 -5.980589e-001 -2.742987e+000 2.987476e-003 - 3.639000e+001 -5.443215e-001 -2.743741e+000 2.985315e-003 - 3.640000e+001 -4.862690e-001 -2.744495e+000 2.983490e-003 - 3.641000e+001 -4.243461e-001 -2.745249e+000 2.982423e-003 - 3.642000e+001 -3.591424e-001 -2.746003e+000 2.982361e-003 - 3.643000e+001 -2.913724e-001 -2.746757e+000 2.983317e-003 - 3.644000e+001 -2.218492e-001 -2.747511e+000 2.985069e-003 - 3.645000e+001 -1.514542e-001 -2.748265e+000 2.987211e-003 - 3.646000e+001 -8.110295e-002 -2.749019e+000 2.989249e-003 - 3.647000e+001 -1.170999e-002 -2.749773e+000 2.990713e-003 - 3.648000e+001 5.584602e-002 -2.750527e+000 2.991265e-003 - 3.649000e+001 1.207552e-001 -2.751281e+000 2.990781e-003 - 3.650000e+001 1.823058e-001 -2.752035e+000 2.989372e-003 - 3.651000e+001 2.399083e-001 -2.752789e+000 2.987364e-003 - 3.652000e+001 2.931136e-001 -2.753543e+000 2.985219e-003 - 3.653000e+001 3.416240e-001 -2.754297e+000 2.983434e-003 - 3.654000e+001 3.852967e-001 -2.755051e+000 2.982421e-003 - 3.655000e+001 4.241399e-001 -2.755805e+000 2.982415e-003 - 3.656000e+001 4.583015e-001 -2.756559e+000 2.983417e-003 - 3.657000e+001 4.880517e-001 -2.757313e+000 2.985193e-003 - 3.658000e+001 5.137593e-001 -2.758067e+000 2.987332e-003 - 3.659000e+001 5.358643e-001 -2.758821e+000 2.989340e-003 - 3.660000e+001 5.548480e-001 -2.759575e+000 2.990753e-003 - 3.661000e+001 5.712015e-001 -2.760329e+000 2.991246e-003 - 3.662000e+001 5.853947e-001 -2.761083e+000 2.990706e-003 - 3.663000e+001 5.978481e-001 -2.761837e+000 2.989259e-003 - 3.664000e+001 6.089082e-001 -2.762591e+000 2.987237e-003 - 3.665000e+001 6.188271e-001 -2.763345e+000 2.985108e-003 - 3.666000e+001 6.277491e-001 -2.764099e+000 2.983364e-003 - 3.667000e+001 6.357038e-001 -2.764853e+000 2.982408e-003 - 3.668000e+001 6.426059e-001 -2.765607e+000 2.982462e-003 - 3.669000e+001 6.482626e-001 -2.766361e+000 2.983513e-003 - 3.670000e+001 6.523868e-001 -2.767115e+000 2.985318e-003 - 3.671000e+001 6.546174e-001 -2.767869e+000 2.987458e-003 - 3.672000e+001 6.545434e-001 -2.768623e+000 2.989439e-003 - 3.673000e+001 6.517319e-001 -2.769377e+000 2.990805e-003 - 3.674000e+001 6.457581e-001 -2.770131e+000 2.991241e-003 - 3.675000e+001 6.362359e-001 -2.770885e+000 2.990647e-003 - 3.676000e+001 6.228468e-001 -2.771639e+000 2.989160e-003 - 3.677000e+001 6.053670e-001 -2.772393e+000 2.987122e-003 - 3.678000e+001 5.836890e-001 -2.773147e+000 2.985005e-003 - 3.679000e+001 5.578393e-001 -2.773901e+000 2.983296e-003 - 3.680000e+001 5.279889e-001 -2.774655e+000 2.982391e-003 - 3.681000e+001 4.944572e-001 -2.775409e+000 2.982499e-003 - 3.682000e+001 4.577088e-001 -2.776163e+000 2.983596e-003 - 3.683000e+001 4.183432e-001 -2.776917e+000 2.985426e-003 - 3.684000e+001 3.770781e-001 -2.777671e+000 2.987567e-003 - 3.685000e+001 3.347266e-001 -2.778425e+000 2.989523e-003 - 3.686000e+001 2.921699e-001 -2.779178e+000 2.990845e-003 - 3.687000e+001 2.503264e-001 -2.779932e+000 2.991228e-003 - 3.688000e+001 2.101186e-001 -2.780686e+000 2.990585e-003 - 3.689000e+001 1.724394e-001 -2.781440e+000 2.989064e-003 - 3.690000e+001 1.381201e-001 -2.782194e+000 2.987016e-003 - 3.691000e+001 1.078995e-001 -2.782948e+000 2.984913e-003 - 3.692000e+001 8.239794e-002 -2.783702e+000 2.983240e-003 - 3.693000e+001 6.209536e-002 -2.784456e+000 2.982385e-003 - 3.694000e+001 4.731558e-002 -2.785210e+000 2.982545e-003 - 3.695000e+001 3.821651e-002 -2.785964e+000 2.983683e-003 - 3.696000e+001 3.478700e-002 -2.786718e+000 2.985533e-003 - 3.697000e+001 3.685019e-002 -2.787472e+000 2.987669e-003 - 3.698000e+001 4.407292e-002 -2.788226e+000 2.989596e-003 - 3.699000e+001 5.598066e-002 -2.788980e+000 2.990872e-003 - 3.700000e+001 7.197704e-002 -2.789734e+000 2.991202e-003 - 3.701000e+001 9.136694e-002 -2.790488e+000 2.990513e-003 - 3.702000e+001 1.133821e-001 -2.791242e+000 2.988962e-003 - 3.703000e+001 1.372075e-001 -2.791996e+000 2.986908e-003 - 3.704000e+001 1.620085e-001 -2.792750e+000 2.984825e-003 - 3.705000e+001 1.869555e-001 -2.793504e+000 2.983194e-003 - 3.706000e+001 2.112476e-001 -2.794258e+000 2.982393e-003 - 3.707000e+001 2.341323e-001 -2.795012e+000 2.982606e-003 - 3.708000e+001 2.549217e-001 -2.795766e+000 2.983784e-003 - 3.709000e+001 2.730045e-001 -2.796520e+000 2.985652e-003 - 3.710000e+001 2.878537e-001 -2.797274e+000 2.987779e-003 - 3.711000e+001 2.990297e-001 -2.798028e+000 2.989672e-003 - 3.712000e+001 3.061797e-001 -2.798782e+000 2.990896e-003 - 3.713000e+001 3.090338e-001 -2.799536e+000 2.991169e-003 - 3.714000e+001 3.073977e-001 -2.800290e+000 2.990428e-003 - 3.715000e+001 3.011440e-001 -2.801044e+000 2.988845e-003 - 3.716000e+001 2.902021e-001 -2.801798e+000 2.986784e-003 - 3.717000e+001 2.745474e-001 -2.802552e+000 2.984721e-003 - 3.718000e+001 2.541921e-001 -2.803306e+000 2.983133e-003 - 3.719000e+001 2.291761e-001 -2.804060e+000 2.982388e-003 - 3.720000e+001 1.995604e-001 -2.804814e+000 2.982657e-003 - 3.721000e+001 1.654227e-001 -2.805568e+000 2.983877e-003 - 3.722000e+001 1.268559e-001 -2.806322e+000 2.985767e-003 - 3.723000e+001 8.396824e-002 -2.807076e+000 2.987887e-003 - 3.724000e+001 3.688748e-002 -2.807830e+000 2.989748e-003 - 3.725000e+001 -1.423408e-002 -2.808584e+000 2.990922e-003 - 3.726000e+001 -6.921208e-002 -2.809338e+000 2.991137e-003 - 3.727000e+001 -1.278217e-001 -2.810092e+000 2.990346e-003 - 3.728000e+001 -1.897889e-001 -2.810846e+000 2.988729e-003 - 3.729000e+001 -2.547816e-001 -2.811600e+000 2.986660e-003 - 3.730000e+001 -3.224024e-001 -2.812354e+000 2.984616e-003 - 3.731000e+001 -3.921825e-001 -2.813108e+000 2.983070e-003 - 3.732000e+001 -4.635787e-001 -2.813862e+000 2.982379e-003 - 3.733000e+001 -5.359722e-001 -2.814616e+000 2.982703e-003 - 3.734000e+001 -6.086714e-001 -2.815370e+000 2.983966e-003 - 3.735000e+001 -6.809180e-001 -2.816124e+000 2.985877e-003 - 3.736000e+001 -7.518957e-001 -2.816878e+000 2.987992e-003 - 3.737000e+001 -8.207429e-001 -2.817632e+000 2.989823e-003 - 3.738000e+001 -8.865677e-001 -2.818386e+000 2.990948e-003 - 3.739000e+001 -9.484650e-001 -2.819140e+000 2.991109e-003 - 3.740000e+001 -1.005536e+000 -2.819894e+000 2.990268e-003 - 3.741000e+001 -1.056908e+000 -2.820648e+000 2.988620e-003 - 3.742000e+001 -1.101754e+000 -2.821401e+000 2.986543e-003 - 3.743000e+001 -1.139312e+000 -2.822155e+000 2.984516e-003 - 3.744000e+001 -1.168904e+000 -2.822909e+000 2.983008e-003 - 3.745000e+001 -1.189953e+000 -2.823663e+000 2.982368e-003 - 3.746000e+001 -1.201993e+000 -2.824417e+000 2.982743e-003 - 3.747000e+001 -1.204681e+000 -2.825171e+000 2.984046e-003 - 3.748000e+001 -1.197806e+000 -2.825925e+000 2.985974e-003 - 3.749000e+001 -1.181289e+000 -2.826679e+000 2.988083e-003 - 3.750000e+001 -1.155187e+000 -2.827433e+000 2.989885e-003 - 3.751000e+001 -1.119682e+000 -2.828187e+000 2.990965e-003 - 3.752000e+001 -1.075086e+000 -2.828941e+000 2.991075e-003 - 3.753000e+001 -1.021819e+000 -2.829695e+000 2.990192e-003 - 3.754000e+001 -9.604077e-001 -2.830449e+000 2.988517e-003 - 3.755000e+001 -8.914669e-001 -2.831203e+000 2.986438e-003 - 3.756000e+001 -8.156875e-001 -2.831957e+000 2.984434e-003 - 3.757000e+001 -7.338217e-001 -2.832711e+000 2.982969e-003 - 3.758000e+001 -6.466685e-001 -2.833465e+000 2.982380e-003 - 3.759000e+001 -5.550602e-001 -2.834219e+000 2.982805e-003 - 3.760000e+001 -4.598495e-001 -2.834973e+000 2.984144e-003 - 3.761000e+001 -3.618980e-001 -2.835727e+000 2.986087e-003 - 3.762000e+001 -2.620664e-001 -2.836481e+000 2.988185e-003 - 3.763000e+001 -1.612055e-001 -2.837235e+000 2.989953e-003 - 3.764000e+001 -6.014976e-002 -2.837989e+000 2.990984e-003 - 3.765000e+001 4.028831e-002 -2.838743e+000 2.991043e-003 - 3.766000e+001 1.393228e-001 -2.839497e+000 2.990115e-003 - 3.767000e+001 2.361975e-001 -2.840251e+000 2.988415e-003 - 3.768000e+001 3.301889e-001 -2.841005e+000 2.986336e-003 - 3.769000e+001 4.206084e-001 -2.841759e+000 2.984357e-003 - 3.770000e+001 5.068045e-001 -2.842513e+000 2.982935e-003 - 3.771000e+001 5.881656e-001 -2.843267e+000 2.982400e-003 - 3.772000e+001 6.641225e-001 -2.844021e+000 2.982876e-003 - 3.773000e+001 7.341517e-001 -2.844775e+000 2.984251e-003 - 3.774000e+001 7.977792e-001 -2.845529e+000 2.986207e-003 - 3.775000e+001 8.545846e-001 -2.846283e+000 2.988292e-003 - 3.776000e+001 9.042059e-001 -2.847037e+000 2.990024e-003 - 3.777000e+001 9.463441e-001 -2.847791e+000 2.991005e-003 - 3.778000e+001 9.807680e-001 -2.848545e+000 2.991009e-003 - 3.779000e+001 1.007318e+000 -2.849299e+000 2.990037e-003 - 3.780000e+001 1.025912e+000 -2.850053e+000 2.988311e-003 - 3.781000e+001 1.036545e+000 -2.850807e+000 2.986231e-003 - 3.782000e+001 1.039292e+000 -2.851561e+000 2.984276e-003 - 3.783000e+001 1.034311e+000 -2.852315e+000 2.982898e-003 - 3.784000e+001 1.021838e+000 -2.853069e+000 2.982417e-003 - 3.785000e+001 1.002185e+000 -2.853823e+000 2.982943e-003 - 3.786000e+001 9.757387e-001 -2.854577e+000 2.984354e-003 - 3.787000e+001 9.429499e-001 -2.855331e+000 2.986323e-003 - 3.788000e+001 9.043291e-001 -2.856085e+000 2.988396e-003 - 3.789000e+001 8.604366e-001 -2.856839e+000 2.990092e-003 - 3.790000e+001 8.118735e-001 -2.857593e+000 2.991023e-003 - 3.791000e+001 7.592711e-001 -2.858347e+000 2.990975e-003 - 3.792000e+001 7.032811e-001 -2.859101e+000 2.989958e-003 - 3.793000e+001 6.445647e-001 -2.859855e+000 2.988207e-003 - 3.794000e+001 5.837833e-001 -2.860609e+000 2.986127e-003 - 3.795000e+001 5.215891e-001 -2.861363e+000 2.984197e-003 - 3.796000e+001 4.586169e-001 -2.862117e+000 2.982863e-003 - 3.797000e+001 3.954777e-001 -2.862871e+000 2.982434e-003 - 3.798000e+001 3.327525e-001 -2.863624e+000 2.983009e-003 - 3.799000e+001 2.709879e-001 -2.864378e+000 2.984454e-003 - 3.800000e+001 2.106932e-001 -2.865132e+000 2.986435e-003 - 3.801000e+001 1.523384e-001 -2.865886e+000 2.988493e-003 - 3.802000e+001 9.635281e-002 -2.866640e+000 2.990154e-003 - 3.803000e+001 4.312461e-002 -2.867394e+000 2.991035e-003 - 3.804000e+001 -6.998933e-003 -2.868148e+000 2.990934e-003 - 3.805000e+001 -5.371143e-002 -2.868902e+000 2.989876e-003 - 3.806000e+001 -9.674726e-002 -2.869656e+000 2.988104e-003 - 3.807000e+001 -1.358818e-001 -2.870410e+000 2.986027e-003 - 3.808000e+001 -1.709321e-001 -2.871164e+000 2.984124e-003 - 3.809000e+001 -2.017581e-001 -2.871918e+000 2.982837e-003 - 3.810000e+001 -2.282646e-001 -2.872672e+000 2.982462e-003 - 3.811000e+001 -2.504034e-001 -2.873426e+000 2.983087e-003 - 3.812000e+001 -2.681763e-001 -2.874180e+000 2.984565e-003 - 3.813000e+001 -2.816383e-001 -2.874934e+000 2.986556e-003 - 3.814000e+001 -2.909001e-001 -2.875688e+000 2.988597e-003 - 3.815000e+001 -2.961312e-001 -2.876442e+000 2.990217e-003 - 3.816000e+001 -2.975613e-001 -2.877196e+000 2.991044e-003 - 3.817000e+001 -2.954817e-001 -2.877950e+000 2.990887e-003 - 3.818000e+001 -2.902443e-001 -2.878704e+000 2.989781e-003 - 3.819000e+001 -2.822598e-001 -2.879458e+000 2.987981e-003 - 3.820000e+001 -2.719934e-001 -2.880212e+000 2.985902e-003 - 3.821000e+001 -2.599586e-001 -2.880966e+000 2.984023e-003 - 3.822000e+001 -2.467098e-001 -2.881720e+000 2.982778e-003 - 3.823000e+001 -2.328311e-001 -2.882474e+000 2.982456e-003 - 3.824000e+001 -2.189256e-001 -2.883228e+000 2.983130e-003 - 3.825000e+001 -2.056009e-001 -2.883982e+000 2.984645e-003 - 3.826000e+001 -1.934552e-001 -2.884736e+000 2.986650e-003 - 3.827000e+001 -1.830619e-001 -2.885490e+000 2.988682e-003 - 3.828000e+001 -1.749540e-001 -2.886244e+000 2.990272e-003 - 3.829000e+001 -1.696091e-001 -2.886998e+000 2.991055e-003 - 3.830000e+001 -1.674355e-001 -2.887752e+000 2.990851e-003 - 3.831000e+001 -1.687595e-001 -2.888506e+000 2.989707e-003 - 3.832000e+001 -1.738150e-001 -2.889260e+000 2.987887e-003 - 3.833000e+001 -1.827354e-001 -2.890014e+000 2.985809e-003 - 3.834000e+001 -1.955485e-001 -2.890768e+000 2.983952e-003 - 3.835000e+001 -2.121741e-001 -2.891522e+000 2.982745e-003 - 3.836000e+001 -2.324256e-001 -2.892276e+000 2.982467e-003 - 3.837000e+001 -2.560135e-001 -2.893030e+000 2.983181e-003 - 3.838000e+001 -2.825528e-001 -2.893784e+000 2.984721e-003 - 3.839000e+001 -3.115733e-001 -2.894538e+000 2.986730e-003 - 3.840000e+001 -3.425309e-001 -2.895292e+000 2.988744e-003 - 3.841000e+001 -3.748227e-001 -2.896046e+000 2.990299e-003 - 3.842000e+001 -4.078013e-001 -2.896800e+000 2.991038e-003 - 3.843000e+001 -4.407916e-001 -2.897554e+000 2.990791e-003 - 3.844000e+001 -4.731067e-001 -2.898308e+000 2.989617e-003 - 3.845000e+001 -5.040635e-001 -2.899062e+000 2.987786e-003 - 3.846000e+001 -5.329973e-001 -2.899816e+000 2.985721e-003 - 3.847000e+001 -5.592754e-001 -2.900570e+000 2.983898e-003 - 3.848000e+001 -5.823081e-001 -2.901324e+000 2.982739e-003 - 3.849000e+001 -6.015579e-001 -2.902078e+000 2.982512e-003 - 3.850000e+001 -6.165470e-001 -2.902832e+000 2.983269e-003 - 3.851000e+001 -6.268612e-001 -2.903586e+000 2.984833e-003 - 3.852000e+001 -6.321532e-001 -2.904340e+000 2.986841e-003 - 3.853000e+001 -6.321424e-001 -2.905094e+000 2.988831e-003 - 3.854000e+001 -6.266139e-001 -2.905848e+000 2.990342e-003 - 3.855000e+001 -6.154159e-001 -2.906601e+000 2.991027e-003 - 3.856000e+001 -5.984556e-001 -2.907355e+000 2.990729e-003 - 3.857000e+001 -5.756951e-001 -2.908109e+000 2.989518e-003 - 3.858000e+001 -5.471467e-001 -2.908863e+000 2.987673e-003 - 3.859000e+001 -5.128690e-001 -2.909617e+000 2.985619e-003 - 3.860000e+001 -4.729620e-001 -2.910371e+000 2.983832e-003 - 3.861000e+001 -4.275649e-001 -2.911125e+000 2.982724e-003 - 3.862000e+001 -3.768533e-001 -2.911879e+000 2.982553e-003 - 3.863000e+001 -3.210377e-001 -2.912633e+000 2.983356e-003 - 3.864000e+001 -2.603638e-001 -2.913387e+000 2.984949e-003 - 3.865000e+001 -1.951120e-001 -2.914141e+000 2.986961e-003 - 3.866000e+001 -1.255990e-001 -2.914895e+000 2.988928e-003 - 3.867000e+001 -5.217930e-002 -2.915649e+000 2.990397e-003 - 3.868000e+001 2.475386e-002 -2.916403e+000 2.991029e-003 - 3.869000e+001 1.047668e-001 -2.917157e+000 2.990680e-003 - 3.870000e+001 1.873850e-001 -2.917911e+000 2.989430e-003 - 3.871000e+001 2.720931e-001 -2.918665e+000 2.987568e-003 - 3.872000e+001 3.583368e-001 -2.919419e+000 2.985523e-003 - 3.873000e+001 4.455250e-001 -2.920173e+000 2.983767e-003 - 3.874000e+001 5.330345e-001 -2.920927e+000 2.982706e-003 - 3.875000e+001 6.202150e-001 -2.921681e+000 2.982586e-003 - 3.876000e+001 7.063969e-001 -2.922435e+000 2.983434e-003 - 3.877000e+001 7.908991e-001 -2.923189e+000 2.985053e-003 - 3.878000e+001 8.730386e-001 -2.923943e+000 2.987069e-003 - 3.879000e+001 9.521403e-001 -2.924697e+000 2.989015e-003 - 3.880000e+001 1.027547e+000 -2.925451e+000 2.990443e-003 - 3.881000e+001 1.098631e+000 -2.926205e+000 2.991026e-003 - 3.882000e+001 1.164802e+000 -2.926959e+000 2.990629e-003 - 3.883000e+001 1.225518e+000 -2.927713e+000 2.989346e-003 - 3.884000e+001 1.280290e+000 -2.928467e+000 2.987472e-003 - 3.885000e+001 1.328693e+000 -2.929221e+000 2.985439e-003 - 3.886000e+001 1.370364e+000 -2.929975e+000 2.983717e-003 - 3.887000e+001 1.405012e+000 -2.930729e+000 2.982705e-003 - 3.888000e+001 1.432412e+000 -2.931483e+000 2.982635e-003 - 3.889000e+001 1.452407e+000 -2.932237e+000 2.983523e-003 - 3.890000e+001 1.464907e+000 -2.932991e+000 2.985162e-003 - 3.891000e+001 1.469882e+000 -2.933745e+000 2.987173e-003 - 3.892000e+001 1.467356e+000 -2.934499e+000 2.989089e-003 - 3.893000e+001 1.457406e+000 -2.935253e+000 2.990470e-003 - 3.894000e+001 1.440151e+000 -2.936007e+000 2.990996e-003 - 3.895000e+001 1.415749e+000 -2.936761e+000 2.990548e-003 - 3.896000e+001 1.384392e+000 -2.937515e+000 2.989229e-003 - 3.897000e+001 1.346297e+000 -2.938269e+000 2.987344e-003 - 3.898000e+001 1.301711e+000 -2.939023e+000 2.985326e-003 - 3.899000e+001 1.250900e+000 -2.939777e+000 2.983644e-003 - 3.900000e+001 1.194155e+000 -2.940531e+000 2.982686e-003 - 3.901000e+001 1.131790e+000 -2.941285e+000 2.982674e-003 - 3.902000e+001 1.064146e+000 -2.942039e+000 2.983610e-003 - 3.903000e+001 9.915914e-001 -2.942793e+000 2.985278e-003 - 3.904000e+001 9.145283e-001 -2.943547e+000 2.987289e-003 - 3.905000e+001 8.333953e-001 -2.944301e+000 2.989181e-003 - 3.906000e+001 7.486722e-001 -2.945055e+000 2.990515e-003 - 3.907000e+001 6.608827e-001 -2.945809e+000 2.990985e-003 - 3.908000e+001 5.705968e-001 -2.946563e+000 2.990482e-003 - 3.909000e+001 4.784318e-001 -2.947317e+000 2.989123e-003 - 3.910000e+001 3.850503e-001 -2.948071e+000 2.987220e-003 - 3.911000e+001 2.911577e-001 -2.948824e+000 2.985212e-003 - 3.912000e+001 1.974959e-001 -2.949578e+000 2.983564e-003 - 3.913000e+001 1.048353e-001 -2.950332e+000 2.982655e-003 - 3.914000e+001 1.396491e-002 -2.951086e+000 2.982698e-003 - 3.915000e+001 -7.432078e-002 -2.951840e+000 2.983681e-003 - 3.916000e+001 -1.592353e-001 -2.952594e+000 2.985377e-003 - 3.917000e+001 -2.400157e-001 -2.953348e+000 2.987394e-003 - 3.918000e+001 -3.159388e-001 -2.954102e+000 2.989265e-003 - 3.919000e+001 -3.863368e-001 -2.954856e+000 2.990560e-003 - 3.920000e+001 -4.506134e-001 -2.955610e+000 2.990980e-003 - 3.921000e+001 -5.082575e-001 -2.956364e+000 2.990429e-003 - 3.922000e+001 -5.588563e-001 -2.957118e+000 2.989035e-003 - 3.923000e+001 -6.021046e-001 -2.957872e+000 2.987118e-003 - 3.924000e+001 -6.378129e-001 -2.958626e+000 2.985120e-003 - 3.925000e+001 -6.659107e-001 -2.959380e+000 2.983502e-003 - 3.926000e+001 -6.864473e-001 -2.960134e+000 2.982639e-003 - 3.927000e+001 -6.995892e-001 -2.960888e+000 2.982729e-003 - 3.928000e+001 -7.056134e-001 -2.961642e+000 2.983752e-003 - 3.929000e+001 -7.048984e-001 -2.962396e+000 2.985470e-003 - 3.930000e+001 -6.979120e-001 -2.963150e+000 2.987484e-003 - 3.931000e+001 -6.851966e-001 -2.963904e+000 2.989331e-003 - 3.932000e+001 -6.673538e-001 -2.964658e+000 2.990584e-003 - 3.933000e+001 -6.450268e-001 -2.965412e+000 2.990955e-003 - 3.934000e+001 -6.188834e-001 -2.966166e+000 2.990359e-003 - 3.935000e+001 -5.895991e-001 -2.966920e+000 2.988934e-003 - 3.936000e+001 -5.578412e-001 -2.967674e+000 2.987008e-003 - 3.937000e+001 -5.242546e-001 -2.968428e+000 2.985025e-003 - 3.938000e+001 -4.894496e-001 -2.969182e+000 2.983444e-003 - 3.939000e+001 -4.539924e-001 -2.969936e+000 2.982631e-003 - 3.940000e+001 -4.183985e-001 -2.970690e+000 2.982773e-003 - 3.941000e+001 -3.831279e-001 -2.971444e+000 2.983838e-003 - 3.942000e+001 -3.485844e-001 -2.972198e+000 2.985579e-003 - 3.943000e+001 -3.151164e-001 -2.972952e+000 2.987593e-003 - 3.944000e+001 -2.830205e-001 -2.973706e+000 2.989416e-003 - 3.945000e+001 -2.525463e-001 -2.974460e+000 2.990627e-003 - 3.946000e+001 -2.239028e-001 -2.975214e+000 2.990949e-003 - 3.947000e+001 -1.972657e-001 -2.975968e+000 2.990308e-003 - 3.948000e+001 -1.727840e-001 -2.976722e+000 2.988851e-003 - 3.949000e+001 -1.505871e-001 -2.977476e+000 2.986915e-003 - 3.950000e+001 -1.307902e-001 -2.978230e+000 2.984945e-003 - 3.951000e+001 -1.134989e-001 -2.978984e+000 2.983397e-003 - 3.952000e+001 -9.881137e-002 -2.979738e+000 2.982628e-003 - 3.953000e+001 -8.681926e-002 -2.980492e+000 2.982816e-003 - 3.954000e+001 -7.760651e-002 -2.981246e+000 2.983916e-003 - 3.955000e+001 -7.124608e-002 -2.982000e+000 2.985674e-003 - 3.956000e+001 -6.779514e-002 -2.982754e+000 2.987683e-003 - 3.957000e+001 -6.728889e-002 -2.983508e+000 2.989479e-003 - 3.958000e+001 -6.973348e-002 -2.984262e+000 2.990649e-003 - 3.959000e+001 -7.509852e-002 -2.985016e+000 2.990924e-003 - 3.960000e+001 -8.330971e-002 -2.985770e+000 2.990243e-003 - 3.961000e+001 -9.424225e-002 -2.986524e+000 2.988762e-003 - 3.962000e+001 -1.077155e-001 -2.987278e+000 2.986824e-003 - 3.963000e+001 -1.234893e-001 -2.988032e+000 2.984876e-003 - 3.964000e+001 -1.412629e-001 -2.988786e+000 2.983367e-003 - 3.965000e+001 -1.606759e-001 -2.989540e+000 2.982648e-003 - 3.966000e+001 -1.813122e-001 -2.990294e+000 2.982883e-003 - 3.967000e+001 -2.027067e-001 -2.991047e+000 2.984018e-003 - 3.968000e+001 -2.243546e-001 -2.991801e+000 2.985789e-003 - 3.969000e+001 -2.457233e-001 -2.992555e+000 2.987786e-003 - 3.970000e+001 -2.662659e-001 -2.993309e+000 2.989547e-003 - 3.971000e+001 -2.854370e-001 -2.994063e+000 2.990668e-003 - 3.972000e+001 -3.027088e-001 -2.994817e+000 2.990890e-003 - 3.973000e+001 -3.175878e-001 -2.995571e+000 2.990163e-003 - 3.974000e+001 -3.296313e-001 -2.996325e+000 2.988654e-003 - 3.975000e+001 -3.384625e-001 -2.997079e+000 2.986713e-003 - 3.976000e+001 -3.437838e-001 -2.997833e+000 2.984787e-003 - 3.977000e+001 -3.453884e-001 -2.998587e+000 2.983322e-003 - 3.978000e+001 -3.431684e-001 -2.999341e+000 2.982656e-003 - 3.979000e+001 -3.371199e-001 -3.000095e+000 2.982945e-003 - 3.980000e+001 -3.273447e-001 -3.000849e+000 2.984120e-003 - 3.981000e+001 -3.140482e-001 -3.001603e+000 2.985909e-003 - 3.982000e+001 -2.975344e-001 -3.002357e+000 2.987898e-003 - 3.983000e+001 -2.781963e-001 -3.003111e+000 2.989628e-003 - 3.984000e+001 -2.565052e-001 -3.003865e+000 2.990700e-003 - 3.985000e+001 -2.329957e-001 -3.004619e+000 2.990868e-003 - 3.986000e+001 -2.082496e-001 -3.005373e+000 2.990092e-003 - 3.987000e+001 -1.828789e-001 -3.006127e+000 2.988553e-003 - 3.988000e+001 -1.575075e-001 -3.006881e+000 2.986605e-003 - 3.989000e+001 -1.327533e-001 -3.007635e+000 2.984697e-003 - 3.990000e+001 -1.092108e-001 -3.008389e+000 2.983271e-003 - 3.991000e+001 -8.743594e-002 -3.009143e+000 2.982656e-003 - 3.992000e+001 -6.793213e-002 -3.009897e+000 2.982995e-003 - 3.993000e+001 -5.113876e-002 -3.010651e+000 2.984208e-003 - 3.994000e+001 -3.742284e-002 -3.011405e+000 2.986014e-003 - 3.995000e+001 -2.707329e-002 -3.012159e+000 2.987996e-003 - 3.996000e+001 -2.029834e-002 -3.012913e+000 2.989696e-003 - 3.997000e+001 -1.722582e-002 -3.013667e+000 2.990721e-003 - 3.998000e+001 -1.790621e-002 -3.014421e+000 2.990837e-003 - 3.999000e+001 -2.231806e-002 -3.015175e+000 2.990016e-003 - 4.000000e+001 -3.037549e-002 -3.015929e+000 2.988447e-003 - 4.001000e+001 -4.193715e-002 -3.016683e+000 2.986493e-003 - 4.002000e+001 -5.681619e-002 -3.017437e+000 2.984603e-003 - 4.003000e+001 -7.479077e-002 -3.018191e+000 2.983215e-003 - 4.004000e+001 -9.561441e-002 -3.018945e+000 2.982649e-003 - 4.005000e+001 -1.190258e-001 -3.019699e+000 2.983035e-003 - 4.006000e+001 -1.447576e-001 -3.020453e+000 2.984284e-003 - 4.007000e+001 -1.725438e-001 -3.021207e+000 2.986107e-003 - 4.008000e+001 -2.021257e-001 -3.021961e+000 2.988080e-003 - 4.009000e+001 -2.332553e-001 -3.022715e+000 2.989750e-003 - 4.010000e+001 -2.656977e-001 -3.023469e+000 2.990730e-003 - 4.011000e+001 -2.992313e-001 -3.024223e+000 2.990796e-003 - 4.012000e+001 -3.336456e-001 -3.024977e+000 2.989932e-003 - 4.013000e+001 -3.687383e-001 -3.025731e+000 2.988337e-003 - 4.014000e+001 -4.043111e-001 -3.026485e+000 2.986380e-003 - 4.015000e+001 -4.401639e-001 -3.027239e+000 2.984510e-003 - 4.016000e+001 -4.760896e-001 -3.027993e+000 2.983161e-003 - 4.017000e+001 -5.118675e-001 -3.028747e+000 2.982644e-003 - 4.018000e+001 -5.472586e-001 -3.029501e+000 2.983078e-003 - 4.019000e+001 -5.820003e-001 -3.030255e+000 2.984363e-003 - 4.020000e+001 -6.158029e-001 -3.031009e+000 2.986202e-003 - 4.021000e+001 -6.483475e-001 -3.031763e+000 2.988168e-003 - 4.022000e+001 -6.792850e-001 -3.032517e+000 2.989810e-003 - 4.023000e+001 -7.082379e-001 -3.033270e+000 2.990749e-003 - 4.024000e+001 -7.348028e-001 -3.034024e+000 2.990769e-003 - 4.025000e+001 -7.585554e-001 -3.034778e+000 2.989868e-003 - 4.026000e+001 -7.790576e-001 -3.035532e+000 2.988252e-003 - 4.027000e+001 -7.958655e-001 -3.036286e+000 2.986295e-003 - 4.028000e+001 -8.085390e-001 -3.037040e+000 2.984448e-003 - 4.029000e+001 -8.166530e-001 -3.037794e+000 2.983138e-003 - 4.030000e+001 -8.198087e-001 -3.038548e+000 2.982668e-003 - 4.031000e+001 -8.176453e-001 -3.039302e+000 2.983146e-003 - 4.032000e+001 -8.098527e-001 -3.040056e+000 2.984461e-003 - 4.033000e+001 -7.961821e-001 -3.040810e+000 2.986308e-003 - 4.034000e+001 -7.764575e-001 -3.041564e+000 2.988259e-003 - 4.035000e+001 -7.505846e-001 -3.042318e+000 2.989865e-003 - 4.036000e+001 -7.185594e-001 -3.043072e+000 2.990756e-003 - 4.037000e+001 -6.804744e-001 -3.043826e+000 2.990727e-003 - 4.038000e+001 -6.365226e-001 -3.044580e+000 2.989785e-003 - 4.039000e+001 -5.869994e-001 -3.045334e+000 2.988149e-003 - 4.040000e+001 -5.323030e-001 -3.046088e+000 2.986194e-003 - 4.041000e+001 -4.729308e-001 -3.046842e+000 2.984372e-003 - 4.042000e+001 -4.094746e-001 -3.047596e+000 2.983105e-003 - 4.043000e+001 -3.426133e-001 -3.048350e+000 2.982686e-003 - 4.044000e+001 -2.731026e-001 -3.049104e+000 2.983210e-003 - 4.045000e+001 -2.017638e-001 -3.049858e+000 2.984557e-003 - 4.046000e+001 -1.294700e-001 -3.050612e+000 2.986414e-003 - 4.047000e+001 -5.713095e-002 -3.051366e+000 2.988352e-003 - 4.048000e+001 1.432289e-002 -3.052120e+000 2.989924e-003 - 4.049000e+001 8.395769e-002 -3.052874e+000 2.990767e-003 - 4.050000e+001 1.508535e-001 -3.053628e+000 2.990690e-003 - 4.051000e+001 2.141218e-001 -3.054382e+000 2.989709e-003 - 4.052000e+001 2.729226e-001 -3.055136e+000 2.988051e-003 - 4.053000e+001 3.264804e-001 -3.055890e+000 2.986100e-003 - 4.054000e+001 3.740999e-001 -3.056644e+000 2.984304e-003 - 4.055000e+001 4.151790e-001 -3.057398e+000 2.983079e-003 - 4.056000e+001 4.492205e-001 -3.058152e+000 2.982709e-003 - 4.057000e+001 4.758419e-001 -3.058906e+000 2.983279e-003 - 4.058000e+001 4.947823e-001 -3.059660e+000 2.984655e-003 - 4.059000e+001 5.059067e-001 -3.060414e+000 2.986520e-003 - 4.060000e+001 5.092083e-001 -3.061168e+000 2.988442e-003 - 4.061000e+001 5.048074e-001 -3.061922e+000 2.989977e-003 - 4.062000e+001 4.929481e-001 -3.062676e+000 2.990772e-003 - 4.063000e+001 4.739916e-001 -3.063430e+000 2.990644e-003 - 4.064000e+001 4.484085e-001 -3.064184e+000 2.989624e-003 - 4.065000e+001 4.167679e-001 -3.064938e+000 2.987947e-003 - 4.066000e+001 3.797247e-001 -3.065692e+000 2.986000e-003 - 4.067000e+001 3.380061e-001 -3.066446e+000 2.984231e-003 - 4.068000e+001 2.923960e-001 -3.067200e+000 2.983052e-003 - 4.069000e+001 2.437199e-001 -3.067954e+000 2.982733e-003 - 4.070000e+001 1.928280e-001 -3.068708e+000 2.983349e-003 - 4.071000e+001 1.405799e-001 -3.069462e+000 2.984757e-003 - 4.072000e+001 8.782884e-002 -3.070216e+000 2.986630e-003 - 4.073000e+001 3.540707e-002 -3.070970e+000 2.988535e-003 - 4.074000e+001 -1.588747e-002 -3.071724e+000 2.990033e-003 - 4.075000e+001 -6.530318e-002 -3.072478e+000 2.990779e-003 - 4.076000e+001 -1.121451e-001 -3.073232e+000 2.990600e-003 - 4.077000e+001 -1.557833e-001 -3.073986e+000 2.989540e-003 - 4.078000e+001 -1.956599e-001 -3.074740e+000 2.987841e-003 - 4.079000e+001 -2.312931e-001 -3.075494e+000 2.985896e-003 - 4.080000e+001 -2.622808e-001 -3.076247e+000 2.984153e-003 - 4.081000e+001 -2.883014e-001 -3.077001e+000 2.983017e-003 - 4.082000e+001 -3.091135e-001 -3.077755e+000 2.982748e-003 - 4.083000e+001 -3.245541e-001 -3.078509e+000 2.983410e-003 - 4.084000e+001 -3.345356e-001 -3.079263e+000 2.984849e-003 - 4.085000e+001 -3.390419e-001 -3.080017e+000 2.986732e-003 - 4.086000e+001 -3.381238e-001 -3.080771e+000 2.988623e-003 - 4.087000e+001 -3.318940e-001 -3.081525e+000 2.990086e-003 - 4.088000e+001 -3.205215e-001 -3.082279e+000 2.990784e-003 - 4.089000e+001 -3.042258e-001 -3.083033e+000 2.990557e-003 - 4.090000e+001 -2.832718e-001 -3.083787e+000 2.989457e-003 - 4.091000e+001 -2.579637e-001 -3.084541e+000 2.987738e-003 - 4.092000e+001 -2.286400e-001 -3.085295e+000 2.985794e-003 - 4.093000e+001 -1.956679e-001 -3.086049e+000 2.984076e-003 - 4.094000e+001 -1.594380e-001 -3.086803e+000 2.982978e-003 - 4.095000e+001 -1.203597e-001 -3.087557e+000 2.982757e-003 - 4.096000e+001 -7.885545e-002 -3.088311e+000 2.983461e-003 - 4.097000e+001 -3.535626e-002 -3.089065e+000 2.984929e-003 - 4.098000e+001 9.703828e-003 -3.089819e+000 2.986821e-003 - 4.099000e+001 5.589283e-002 -3.090573e+000 2.988700e-003 - 4.100000e+001 1.027862e-001 -3.091327e+000 2.990133e-003 - 4.101000e+001 1.499721e-001 -3.092081e+000 2.990792e-003 - 4.102000e+001 1.970570e-001 -3.092835e+000 2.990525e-003 - 4.103000e+001 2.436709e-001 -3.093589e+000 2.989395e-003 - 4.104000e+001 2.894722e-001 -3.094343e+000 2.987662e-003 - 4.105000e+001 3.341528e-001 -3.095097e+000 2.985726e-003 - 4.106000e+001 3.774419e-001 -3.095851e+000 2.984031e-003 - 4.107000e+001 4.191095e-001 -3.096605e+000 2.982971e-003 - 4.108000e+001 4.589688e-001 -3.097359e+000 2.982788e-003 - 4.109000e+001 4.968778e-001 -3.098113e+000 2.983523e-003 - 4.110000e+001 5.327388e-001 -3.098867e+000 2.985006e-003 - 4.111000e+001 5.664977e-001 -3.099621e+000 2.986892e-003 - 4.112000e+001 5.981414e-001 -3.100375e+000 2.988746e-003 - 4.113000e+001 6.276931e-001 -3.101129e+000 2.990139e-003 - 4.114000e+001 6.552076e-001 -3.101883e+000 2.990753e-003 - 4.115000e+001 6.807649e-001 -3.102637e+000 2.990447e-003 - 4.116000e+001 7.044623e-001 -3.103391e+000 2.989293e-003 - 4.117000e+001 7.264070e-001 -3.104145e+000 2.987558e-003 - 4.118000e+001 7.467075e-001 -3.104899e+000 2.985643e-003 - 4.119000e+001 7.654657e-001 -3.105653e+000 2.983991e-003 - 4.120000e+001 7.827693e-001 -3.106407e+000 2.982983e-003 - 4.121000e+001 7.986845e-001 -3.107161e+000 2.982852e-003 - 4.122000e+001 8.132512e-001 -3.107915e+000 2.983628e-003 - 4.123000e+001 8.264789e-001 -3.108669e+000 2.985130e-003 - 4.124000e+001 8.383443e-001 -3.109423e+000 2.987009e-003 - 4.125000e+001 8.487917e-001 -3.110177e+000 2.988831e-003 - 4.126000e+001 8.577347e-001 -3.110931e+000 2.990175e-003 - 4.127000e+001 8.650610e-001 -3.111685e+000 2.990731e-003 - 4.128000e+001 8.706379e-001 -3.112439e+000 2.990374e-003 - 4.129000e+001 8.743205e-001 -3.113193e+000 2.989185e-003 - 4.130000e+001 8.759610e-001 -3.113947e+000 2.987441e-003 - 4.131000e+001 8.754187e-001 -3.114701e+000 2.985543e-003 - 4.132000e+001 8.725709e-001 -3.115455e+000 2.983932e-003 - 4.133000e+001 8.673229e-001 -3.116209e+000 2.982981e-003 - 4.134000e+001 8.596183e-001 -3.116963e+000 2.982909e-003 - 4.135000e+001 8.494471e-001 -3.117717e+000 2.983732e-003 - 4.136000e+001 8.368523e-001 -3.118470e+000 2.985259e-003 - 4.137000e+001 8.219346e-001 -3.119224e+000 2.987136e-003 - 4.138000e+001 8.048538e-001 -3.119978e+000 2.988927e-003 - 4.139000e+001 7.858275e-001 -3.120732e+000 2.990218e-003 - 4.140000e+001 7.651272e-001 -3.121486e+000 2.990712e-003 - 4.141000e+001 7.430707e-001 -3.122240e+000 2.990294e-003 - 4.142000e+001 7.200121e-001 -3.122994e+000 2.989062e-003 - 4.143000e+001 6.963293e-001 -3.123748e+000 2.987299e-003 - 4.144000e+001 6.724095e-001 -3.124502e+000 2.985412e-003 - 4.145000e+001 6.486328e-001 -3.125256e+000 2.983839e-003 - 4.146000e+001 6.253562e-001 -3.126010e+000 2.982944e-003 - 4.147000e+001 6.028961e-001 -3.126764e+000 2.982935e-003 - 4.148000e+001 5.815132e-001 -3.127518e+000 2.983815e-003 - 4.149000e+001 5.613976e-001 -3.128272e+000 2.985380e-003 - 4.150000e+001 5.426571e-001 -3.129026e+000 2.987268e-003 - 4.151000e+001 5.253086e-001 -3.129780e+000 2.989042e-003 - 4.152000e+001 5.092717e-001 -3.130534e+000 2.990294e-003 - 4.153000e+001 4.943681e-001 -3.131288e+000 2.990734e-003 - 4.154000e+001 4.803236e-001 -3.132042e+000 2.990260e-003 - 4.155000e+001 4.667746e-001 -3.132796e+000 2.988982e-003 - 4.156000e+001 4.532792e-001 -3.133550e+000 2.987193e-003 - 4.157000e+001 4.393312e-001 -3.134304e+000 2.985306e-003 - 4.158000e+001 4.243779e-001 -3.135058e+000 2.983756e-003 - 4.159000e+001 4.078396e-001 -3.135812e+000 2.982903e-003 - 4.160000e+001 3.891318e-001 -3.136566e+000 2.982944e-003 - 4.161000e+001 3.676873e-001 -3.137320e+000 2.983869e-003 - 4.162000e+001 3.429792e-001 -3.138074e+000 2.985466e-003 - 4.163000e+001 3.145419e-001 -3.138828e+000 2.987364e-003 - 4.164000e+001 2.819912e-001 -3.139582e+000 2.989126e-003 - 4.165000e+001 2.450410e-001 -3.140336e+000 2.990345e-003 - 4.166000e+001 2.035171e-001 -3.141090e+000 2.990741e-003 - 4.167000e+001 1.573669e-001 -3.141844e+000 2.990223e-003 - 4.168000e+001 1.066644e-001 -3.142598e+000 2.988909e-003 - 4.169000e+001 5.161178e-002 -3.143352e+000 2.987102e-003 - 4.170000e+001 -7.464667e-003 -3.144106e+000 2.985218e-003 - 4.171000e+001 -7.012232e-002 -3.144860e+000 2.983691e-003 - 4.172000e+001 -1.358141e-001 -3.145614e+000 2.982874e-003 - 4.173000e+001 -2.039035e-001 -3.146368e+000 2.982957e-003 - 4.174000e+001 -2.736830e-001 -3.147122e+000 2.983919e-003 - 4.175000e+001 -3.443938e-001 -3.147876e+000 2.985539e-003 - 4.176000e+001 -4.152469e-001 -3.148630e+000 2.987442e-003 - 4.177000e+001 -4.854448e-001 -3.149384e+000 2.989190e-003 - 4.178000e+001 -5.542024e-001 -3.150138e+000 2.990381e-003 - 4.179000e+001 -6.207666e-001 -3.150892e+000 2.990741e-003 - 4.180000e+001 -6.844341e-001 -3.151646e+000 2.990188e-003 - 4.181000e+001 -7.445669e-001 -3.152400e+000 2.988851e-003 - 4.182000e+001 -8.006040e-001 -3.153154e+000 2.987037e-003 - 4.183000e+001 -8.520710e-001 -3.153908e+000 2.985163e-003 - 4.184000e+001 -8.985854e-001 -3.154662e+000 2.983663e-003 - 4.185000e+001 -9.398591e-001 -3.155416e+000 2.982882e-003 - 4.186000e+001 -9.756980e-001 -3.156170e+000 2.982999e-003 - 4.187000e+001 -1.005998e+000 -3.156924e+000 2.983986e-003 - 4.188000e+001 -1.030739e+000 -3.157678e+000 2.985614e-003 - 4.189000e+001 -1.049978e+000 -3.158432e+000 2.987506e-003 - 4.190000e+001 -1.063838e+000 -3.159186e+000 2.989225e-003 - 4.191000e+001 -1.072501e+000 -3.159940e+000 2.990374e-003 - 4.192000e+001 -1.076195e+000 -3.160693e+000 2.990691e-003 - 4.193000e+001 -1.075185e+000 -3.161447e+000 2.990104e-003 - 4.194000e+001 -1.069762e+000 -3.162201e+000 2.988749e-003 - 4.195000e+001 -1.060238e+000 -3.162955e+000 2.986938e-003 - 4.196000e+001 -1.046933e+000 -3.163709e+000 2.985090e-003 - 4.197000e+001 -1.030173e+000 -3.164463e+000 2.983632e-003 - 4.198000e+001 -1.010285e+000 -3.165217e+000 2.982900e-003 - 4.199000e+001 -9.875887e-001 -3.165971e+000 2.983063e-003 - 4.200000e+001 -9.623982e-001 -3.166725e+000 2.984082e-003 - 4.201000e+001 -9.350173e-001 -3.167479e+000 2.985720e-003 - 4.202000e+001 -9.057387e-001 -3.168233e+000 2.987597e-003 - 4.203000e+001 -8.748424e-001 -3.168987e+000 2.989279e-003 - 4.204000e+001 -8.425948e-001 -3.169741e+000 2.990379e-003 - 4.205000e+001 -8.092465e-001 -3.170495e+000 2.990644e-003 - 4.206000e+001 -7.750312e-001 -3.171249e+000 2.990015e-003 - 4.207000e+001 -7.401633e-001 -3.172003e+000 2.988637e-003 - 4.208000e+001 -7.048354e-001 -3.172757e+000 2.986830e-003 - 4.209000e+001 -6.692152e-001 -3.173511e+000 2.985012e-003 - 4.210000e+001 -6.334429e-001 -3.174265e+000 2.983604e-003 - 4.211000e+001 -5.976285e-001 -3.175019e+000 2.982933e-003 - 4.212000e+001 -5.618486e-001 -3.175773e+000 2.983153e-003 - 4.213000e+001 -5.261454e-001 -3.176527e+000 2.984213e-003 - 4.214000e+001 -4.905255e-001 -3.177281e+000 2.985867e-003 - 4.215000e+001 -4.549606e-001 -3.178035e+000 2.987730e-003 - 4.216000e+001 -4.193894e-001 -3.178789e+000 2.989372e-003 - 4.217000e+001 -3.837216e-001 -3.179543e+000 2.990412e-003 - 4.218000e+001 -3.478432e-001 -3.180297e+000 2.990611e-003 - 4.219000e+001 -3.116241e-001 -3.181051e+000 2.989922e-003 - 4.220000e+001 -2.749265e-001 -3.181805e+000 2.988503e-003 - 4.221000e+001 -2.376158e-001 -3.182559e+000 2.986683e-003 - 4.222000e+001 -1.995710e-001 -3.183313e+000 2.984882e-003 - 4.223000e+001 -1.606969e-001 -3.184067e+000 2.983516e-003 - 4.224000e+001 -1.209350e-001 -3.184821e+000 2.982903e-003 - 4.225000e+001 -8.027481e-002 -3.185575e+000 2.983185e-003 - 4.226000e+001 -3.876268e-002 -3.186329e+000 2.984297e-003 - 4.227000e+001 3.490580e-003 -3.187083e+000 2.985982e-003 - 4.228000e+001 4.630497e-002 -3.187837e+000 2.987849e-003 - 4.229000e+001 8.942955e-002 -3.188591e+000 2.989468e-003 - 4.230000e+001 1.325440e-001 -3.189345e+000 2.990464e-003 - 4.231000e+001 1.752638e-001 -3.190099e+000 2.990607e-003 - 4.232000e+001 2.171490e-001 -3.190853e+000 2.989865e-003 - 4.233000e+001 2.577164e-001 -3.191607e+000 2.988407e-003 - 4.234000e+001 2.964547e-001 -3.192361e+000 2.986570e-003 - 4.235000e+001 3.328425e-001 -3.193115e+000 2.984777e-003 - 4.236000e+001 3.663676e-001 -3.193869e+000 2.983444e-003 - 4.237000e+001 3.965481e-001 -3.194623e+000 2.982880e-003 - 4.238000e+001 4.229528e-001 -3.195377e+000 2.983216e-003 - 4.239000e+001 4.452213e-001 -3.196131e+000 2.984375e-003 - 4.240000e+001 4.630819e-001 -3.196885e+000 2.986090e-003 - 4.241000e+001 4.763671e-001 -3.197639e+000 2.987965e-003 - 4.242000e+001 4.850248e-001 -3.198393e+000 2.989567e-003 - 4.243000e+001 4.891259e-001 -3.199147e+000 2.990526e-003 - 4.244000e+001 4.888663e-001 -3.199901e+000 2.990621e-003 - 4.245000e+001 4.845645e-001 -3.200655e+000 2.989830e-003 - 4.246000e+001 4.766527e-001 -3.201409e+000 2.988334e-003 - 4.247000e+001 4.656644e-001 -3.202163e+000 2.986475e-003 - 4.248000e+001 4.522158e-001 -3.202916e+000 2.984682e-003 - 4.249000e+001 4.369841e-001 -3.203670e+000 2.983369e-003 - 4.250000e+001 4.206819e-001 -3.204424e+000 2.982838e-003 - 4.251000e+001 4.040305e-001 -3.205178e+000 2.983213e-003 - 4.252000e+001 3.877308e-001 -3.205932e+000 2.984407e-003 - 4.253000e+001 3.724357e-001 -3.206686e+000 2.986145e-003 - 4.254000e+001 3.587234e-001 -3.207440e+000 2.988025e-003 - 4.255000e+001 3.470733e-001 -3.208194e+000 2.989616e-003 - 4.256000e+001 3.378466e-001 -3.208948e+000 2.990551e-003 - 4.257000e+001 3.312701e-001 -3.209702e+000 2.990616e-003 - 4.258000e+001 3.274274e-001 -3.210456e+000 2.989797e-003 - 4.259000e+001 3.262547e-001 -3.211210e+000 2.988282e-003 - 4.260000e+001 3.275438e-001 -3.211964e+000 2.986419e-003 - 4.261000e+001 3.309505e-001 -3.212718e+000 2.984638e-003 - 4.262000e+001 3.360099e-001 -3.213472e+000 2.983348e-003 - 4.263000e+001 3.421559e-001 -3.214226e+000 2.982848e-003 - 4.264000e+001 3.487464e-001 -3.214980e+000 2.983253e-003 - 4.265000e+001 3.550903e-001 -3.215734e+000 2.984468e-003 - 4.266000e+001 3.604785e-001 -3.216488e+000 2.986212e-003 - 4.267000e+001 3.642143e-001 -3.217242e+000 2.988084e-003 - 4.268000e+001 3.656441e-001 -3.217996e+000 2.989652e-003 - 4.269000e+001 3.641859e-001 -3.218750e+000 2.990556e-003 - 4.270000e+001 3.593553e-001 -3.219504e+000 2.990591e-003 - 4.271000e+001 3.507867e-001 -3.220258e+000 2.989748e-003 - 4.272000e+001 3.382501e-001 -3.221012e+000 2.988224e-003 - 4.273000e+001 3.216614e-001 -3.221766e+000 2.986369e-003 - 4.274000e+001 3.010877e-001 -3.222520e+000 2.984610e-003 - 4.275000e+001 2.767451e-001 -3.223274e+000 2.983352e-003 - 4.276000e+001 2.489917e-001 -3.224028e+000 2.982886e-003 - 4.277000e+001 2.183139e-001 -3.224782e+000 2.983316e-003 - 4.278000e+001 1.853083e-001 -3.225536e+000 2.984542e-003 - 4.279000e+001 1.506591e-001 -3.226290e+000 2.986279e-003 - 4.280000e+001 1.151129e-001 -3.227044e+000 2.988124e-003 - 4.281000e+001 7.945120e-002 -3.227798e+000 2.989652e-003 - 4.282000e+001 4.446216e-002 -3.228552e+000 2.990512e-003 - 4.283000e+001 1.091312e-002 -3.229306e+000 2.990508e-003 - 4.284000e+001 -2.047554e-002 -3.230060e+000 2.989642e-003 - 4.285000e+001 -4.905378e-002 -3.230814e+000 2.988116e-003 - 4.286000e+001 -7.426183e-002 -3.231568e+000 2.986283e-003 - 4.287000e+001 -9.564589e-002 -3.232322e+000 2.984566e-003 - 4.288000e+001 -1.128692e-001 -3.233076e+000 2.983363e-003 - 4.289000e+001 -1.257184e-001 -3.233830e+000 2.982952e-003 - 4.290000e+001 -1.341045e-001 -3.234584e+000 2.983427e-003 - 4.291000e+001 -1.380601e-001 -3.235338e+000 2.984677e-003 - 4.292000e+001 -1.377316e-001 -3.236092e+000 2.986410e-003 - 4.293000e+001 -1.333680e-001 -3.236846e+000 2.988225e-003 - 4.294000e+001 -1.253070e-001 -3.237600e+000 2.989703e-003 - 4.295000e+001 -1.139589e-001 -3.238354e+000 2.990502e-003 - 4.296000e+001 -9.978911e-002 -3.239108e+000 2.990440e-003 - 4.297000e+001 -8.330039e-002 -3.239862e+000 2.989531e-003 - 4.298000e+001 -6.501547e-002 -3.240616e+000 2.987985e-003 - 4.299000e+001 -4.546074e-002 -3.241370e+000 2.986161e-003 - 4.300000e+001 -2.515171e-002 -3.242124e+000 2.984480e-003 - 4.301000e+001 -4.580471e-003 -3.242878e+000 2.983331e-003 - 4.302000e+001 1.579427e-002 -3.243632e+000 2.982980e-003 - 4.303000e+001 3.555468e-002 -3.244386e+000 2.983508e-003 - 4.304000e+001 5.432865e-002 -3.245140e+000 2.984791e-003 - 4.305000e+001 7.179236e-002 -3.245893e+000 2.986532e-003 - 4.306000e+001 8.767067e-002 -3.246647e+000 2.988325e-003 - 4.307000e+001 1.017358e-001 -3.247401e+000 2.989758e-003 - 4.308000e+001 1.138047e-001 -3.248155e+000 2.990498e-003 - 4.309000e+001 1.237354e-001 -3.248909e+000 2.990374e-003 - 4.310000e+001 1.314237e-001 -3.249663e+000 2.989417e-003 - 4.311000e+001 1.367985e-001 -3.250417e+000 2.987847e-003 - 4.312000e+001 1.398189e-001 -3.251171e+000 2.986026e-003 - 4.313000e+001 1.404711e-001 -3.251925e+000 2.984377e-003 - 4.314000e+001 1.387663e-001 -3.252679e+000 2.983282e-003 - 4.315000e+001 1.347397e-001 -3.253433e+000 2.982996e-003 - 4.316000e+001 1.284494e-001 -3.254187e+000 2.983586e-003 - 4.317000e+001 1.199772e-001 -3.254941e+000 2.984915e-003 - 4.318000e+001 1.094288e-001 -3.255695e+000 2.986675e-003 - 4.319000e+001 9.693449e-002 -3.256449e+000 2.988461e-003 - 4.320000e+001 8.264981e-002 -3.257203e+000 2.989858e-003 - 4.321000e+001 6.675533e-002 -3.257957e+000 2.990545e-003 - 4.322000e+001 4.945596e-002 -3.258711e+000 2.990362e-003 - 4.323000e+001 3.097906e-002 -3.259465e+000 2.989351e-003 - 4.324000e+001 1.157138e-002 -3.260219e+000 2.987743e-003 - 4.325000e+001 -8.505222e-003 -3.260973e+000 2.985909e-003 - 4.326000e+001 -2.897941e-002 -3.261727e+000 2.984273e-003 - 4.327000e+001 -4.957701e-002 -3.262481e+000 2.983211e-003 - 4.328000e+001 -7.002855e-002 -3.263235e+000 2.982971e-003 - 4.329000e+001 -9.007734e-002 -3.263989e+000 2.983607e-003 - 4.330000e+001 -1.094877e-001 -3.264743e+000 2.984973e-003 - 4.331000e+001 -1.280527e-001 -3.265497e+000 2.986752e-003 - 4.332000e+001 -1.456016e-001 -3.266251e+000 2.988534e-003 - 4.333000e+001 -1.620050e-001 -3.267005e+000 2.989907e-003 - 4.334000e+001 -1.771797e-001 -3.267759e+000 2.990556e-003 - 4.335000e+001 -1.910904e-001 -3.268513e+000 2.990331e-003 - 4.336000e+001 -2.037493e-001 -3.269267e+000 2.989283e-003 - 4.337000e+001 -2.152142e-001 -3.270021e+000 2.987655e-003 - 4.338000e+001 -2.255826e-001 -3.270775e+000 2.985821e-003 - 4.339000e+001 -2.349855e-001 -3.271529e+000 2.984204e-003 - 4.340000e+001 -2.435775e-001 -3.272283e+000 2.983180e-003 - 4.341000e+001 -2.515262e-001 -3.273037e+000 2.982984e-003 - 4.342000e+001 -2.590010e-001 -3.273791e+000 2.983663e-003 - 4.343000e+001 -2.661609e-001 -3.274545e+000 2.985059e-003 - 4.344000e+001 -2.731428e-001 -3.275299e+000 2.986851e-003 - 4.345000e+001 -2.800508e-001 -3.276053e+000 2.988624e-003 - 4.346000e+001 -2.869473e-001 -3.276807e+000 2.989971e-003 - 4.347000e+001 -2.938466e-001 -3.277561e+000 2.990581e-003 - 4.348000e+001 -3.007104e-001 -3.278315e+000 2.990314e-003 - 4.349000e+001 -3.074474e-001 -3.279069e+000 2.989232e-003 - 4.350000e+001 -3.139159e-001 -3.279823e+000 2.987585e-003 - 4.351000e+001 -3.199292e-001 -3.280577e+000 2.985750e-003 - 4.352000e+001 -3.252648e-001 -3.281331e+000 2.984152e-003 - 4.353000e+001 -3.296766e-001 -3.282085e+000 2.983160e-003 - 4.354000e+001 -3.329083e-001 -3.282839e+000 2.983001e-003 - 4.355000e+001 -3.347099e-001 -3.283593e+000 2.983713e-003 - 4.356000e+001 -3.348534e-001 -3.284347e+000 2.985129e-003 - 4.357000e+001 -3.331502e-001 -3.285101e+000 2.986923e-003 - 4.358000e+001 -3.294660e-001 -3.285855e+000 2.988678e-003 - 4.359000e+001 -3.237348e-001 -3.286609e+000 2.989992e-003 - 4.360000e+001 -3.159698e-001 -3.287363e+000 2.990560e-003 - 4.361000e+001 -3.062713e-001 -3.288116e+000 2.990254e-003 - 4.362000e+001 -2.948305e-001 -3.288870e+000 2.989145e-003 - 4.363000e+001 -2.819287e-001 -3.289624e+000 2.987487e-003 - 4.364000e+001 -2.679323e-001 -3.290378e+000 2.985665e-003 - 4.365000e+001 -2.532836e-001 -3.291132e+000 2.984098e-003 - 4.366000e+001 -2.384866e-001 -3.291886e+000 2.983150e-003 - 4.367000e+001 -2.240904e-001 -3.292640e+000 2.983039e-003 - 4.368000e+001 -2.106681e-001 -3.293394e+000 2.983792e-003 - 4.369000e+001 -1.987949e-001 -3.294148e+000 2.985234e-003 - 4.370000e+001 -1.890245e-001 -3.294902e+000 2.987032e-003 - 4.371000e+001 -1.818651e-001 -3.295656e+000 2.988769e-003 - 4.372000e+001 -1.777567e-001 -3.296410e+000 2.990047e-003 - 4.373000e+001 -1.770512e-001 -3.297164e+000 2.990570e-003 - 4.374000e+001 -1.799938e-001 -3.297918e+000 2.990220e-003 - 4.375000e+001 -1.867100e-001 -3.298672e+000 2.989076e-003 - 4.376000e+001 -1.971963e-001 -3.299426e+000 2.987403e-003 - 4.377000e+001 -2.113159e-001 -3.300180e+000 2.985586e-003 - 4.378000e+001 -2.287998e-001 -3.300934e+000 2.984045e-003 - 4.379000e+001 -2.492536e-001 -3.301688e+000 2.983136e-003 - 4.380000e+001 -2.721684e-001 -3.302442e+000 2.983068e-003 - 4.381000e+001 -2.969372e-001 -3.303196e+000 2.983858e-003 - 4.382000e+001 -3.228742e-001 -3.303950e+000 2.985321e-003 - 4.383000e+001 -3.492380e-001 -3.304704e+000 2.987119e-003 - 4.384000e+001 -3.752559e-001 -3.305458e+000 2.988836e-003 - 4.385000e+001 -4.001502e-001 -3.306212e+000 2.990077e-003 - 4.386000e+001 -4.231633e-001 -3.306966e+000 2.990555e-003 - 4.387000e+001 -4.435821e-001 -3.307720e+000 2.990161e-003 - 4.388000e+001 -4.607603e-001 -3.308474e+000 2.988986e-003 - 4.389000e+001 -4.741373e-001 -3.309228e+000 2.987300e-003 - 4.390000e+001 -4.832535e-001 -3.309982e+000 2.985491e-003 - 4.391000e+001 -4.877614e-001 -3.310736e+000 2.983978e-003 - 4.392000e+001 -4.874318e-001 -3.311490e+000 2.983110e-003 - 4.393000e+001 -4.821556e-001 -3.312244e+000 2.983087e-003 - 4.394000e+001 -4.719415e-001 -3.312998e+000 2.983915e-003 - 4.395000e+001 -4.569084e-001 -3.313752e+000 2.985401e-003 - 4.396000e+001 -4.372755e-001 -3.314506e+000 2.987201e-003 - 4.397000e+001 -4.133488e-001 -3.315260e+000 2.988901e-003 - 4.398000e+001 -3.855055e-001 -3.316014e+000 2.990108e-003 - 4.399000e+001 -3.541772e-001 -3.316768e+000 2.990546e-003 - 4.400000e+001 -3.198331e-001 -3.317522e+000 2.990115e-003 - 4.401000e+001 -2.829626e-001 -3.318276e+000 2.988914e-003 - 4.402000e+001 -2.440603e-001 -3.319030e+000 2.987222e-003 - 4.403000e+001 -2.036122e-001 -3.319784e+000 2.985428e-003 - 4.404000e+001 -1.620839e-001 -3.320538e+000 2.983947e-003 - 4.405000e+001 -1.199123e-001 -3.321292e+000 2.983121e-003 - 4.406000e+001 -7.749962e-002 -3.322046e+000 2.983140e-003 - 4.407000e+001 -3.521029e-002 -3.322800e+000 2.984000e-003 - 4.408000e+001 6.629464e-003 -3.323554e+000 2.985500e-003 - 4.409000e+001 4.772960e-002 -3.324308e+000 2.987292e-003 - 4.410000e+001 8.783253e-002 -3.325062e+000 2.988962e-003 - 4.411000e+001 1.267079e-001 -3.325816e+000 2.990125e-003 - 4.412000e+001 1.641468e-001 -3.326570e+000 2.990511e-003 - 4.413000e+001 1.999555e-001 -3.327324e+000 2.990034e-003 - 4.414000e+001 2.339501e-001 -3.328078e+000 2.988802e-003 - 4.415000e+001 2.659513e-001 -3.328832e+000 2.987100e-003 - 4.416000e+001 2.957815e-001 -3.329586e+000 2.985321e-003 - 4.417000e+001 3.232629e-001 -3.330339e+000 2.983877e-003 - 4.418000e+001 3.482174e-001 -3.331093e+000 2.983100e-003 - 4.419000e+001 3.704686e-001 -3.331847e+000 2.983172e-003 - 4.420000e+001 3.898455e-001 -3.332601e+000 2.984075e-003 - 4.421000e+001 4.061876e-001 -3.333355e+000 2.985600e-003 - 4.422000e+001 4.193509e-001 -3.334109e+000 2.987394e-003 - 4.423000e+001 4.292153e-001 -3.334863e+000 2.989043e-003 - 4.424000e+001 4.356912e-001 -3.335617e+000 2.990167e-003 - 4.425000e+001 4.387269e-001 -3.336371e+000 2.990506e-003 - 4.426000e+001 4.383143e-001 -3.337125e+000 2.989985e-003 - 4.427000e+001 4.344935e-001 -3.337879e+000 2.988722e-003 - 4.428000e+001 4.273565e-001 -3.338633e+000 2.987009e-003 - 4.429000e+001 4.170478e-001 -3.339387e+000 2.985242e-003 - 4.430000e+001 4.037637e-001 -3.340141e+000 2.983829e-003 - 4.431000e+001 3.877495e-001 -3.340895e+000 2.983096e-003 - 4.432000e+001 3.692940e-001 -3.341649e+000 2.983215e-003 - 4.433000e+001 3.487228e-001 -3.342403e+000 2.984156e-003 - 4.434000e+001 3.263902e-001 -3.343157e+000 2.985701e-003 - 4.435000e+001 3.026692e-001 -3.343911e+000 2.987494e-003 - 4.436000e+001 2.779423e-001 -3.344665e+000 2.989119e-003 - 4.437000e+001 2.525907e-001 -3.345419e+000 2.990202e-003 - 4.438000e+001 2.269855e-001 -3.346173e+000 2.990494e-003 - 4.439000e+001 2.014788e-001 -3.346927e+000 2.989927e-003 - 4.440000e+001 1.763965e-001 -3.347681e+000 2.988631e-003 - 4.441000e+001 1.520331e-001 -3.348435e+000 2.986906e-003 - 4.442000e+001 1.286485e-001 -3.349189e+000 2.985149e-003 - 4.443000e+001 1.064660e-001 -3.349943e+000 2.983765e-003 - 4.444000e+001 8.567358e-002 -3.350697e+000 2.983074e-003 - 4.445000e+001 6.642606e-002 -3.351451e+000 2.983237e-003 - 4.446000e+001 4.884940e-002 -3.352205e+000 2.984215e-003 - 4.447000e+001 3.304585e-002 -3.352959e+000 2.985782e-003 - 4.448000e+001 1.910002e-002 -3.353713e+000 2.987576e-003 - 4.449000e+001 7.085075e-003 -3.354467e+000 2.989182e-003 - 4.450000e+001 -2.931344e-003 -3.355221e+000 2.990231e-003 - 4.451000e+001 -1.088206e-002 -3.355975e+000 2.990483e-003 - 4.452000e+001 -1.669654e-002 -3.356729e+000 2.989880e-003 - 4.453000e+001 -2.029867e-002 -3.357483e+000 2.988561e-003 - 4.454000e+001 -2.160650e-002 -3.358237e+000 2.986832e-003 - 4.455000e+001 -2.053392e-002 -3.358991e+000 2.985090e-003 - 4.456000e+001 -1.699436e-002 -3.359745e+000 2.983739e-003 - 4.457000e+001 -1.090634e-002 -3.360499e+000 2.983092e-003 - 4.458000e+001 -2.200469e-003 -3.361253e+000 2.983296e-003 - 4.459000e+001 9.172282e-003 -3.362007e+000 2.984305e-003 - 4.460000e+001 2.323187e-002 -3.362761e+000 2.985884e-003 - 4.461000e+001 3.996038e-002 -3.363515e+000 2.987668e-003 - 4.462000e+001 5.929380e-002 -3.364269e+000 2.989244e-003 - 4.463000e+001 8.111508e-002 -3.365023e+000 2.990250e-003 - 4.464000e+001 1.052490e-001 -3.365777e+000 2.990453e-003 - 4.465000e+001 1.314592e-001 -3.366531e+000 2.989807e-003 - 4.466000e+001 1.594480e-001 -3.367285e+000 2.988461e-003 - 4.467000e+001 1.888592e-001 -3.368039e+000 2.986725e-003 - 4.468000e+001 2.192839e-001 -3.368793e+000 2.985001e-003 - 4.469000e+001 2.502686e-001 -3.369547e+000 2.983686e-003 - 4.470000e+001 2.813274e-001 -3.370301e+000 2.983084e-003 - 4.471000e+001 3.119549e-001 -3.371055e+000 2.983335e-003 - 4.472000e+001 3.416416e-001 -3.371809e+000 2.984380e-003 - 4.473000e+001 3.698907e-001 -3.372562e+000 2.985977e-003 - 4.474000e+001 3.962341e-001 -3.373316e+000 2.987756e-003 - 4.475000e+001 4.202490e-001 -3.374070e+000 2.989306e-003 - 4.476000e+001 4.415724e-001 -3.374824e+000 2.990271e-003 - 4.477000e+001 4.599142e-001 -3.375578e+000 2.990428e-003 - 4.478000e+001 4.750669e-001 -3.376332e+000 2.989742e-003 - 4.479000e+001 4.869127e-001 -3.377086e+000 2.988371e-003 - 4.480000e+001 4.954264e-001 -3.377840e+000 2.986631e-003 - 4.481000e+001 5.006749e-001 -3.378594e+000 2.984925e-003 - 4.482000e+001 5.028128e-001 -3.379348e+000 2.983646e-003 - 4.483000e+001 5.020738e-001 -3.380102e+000 2.983091e-003 - 4.484000e+001 4.987599e-001 -3.380856e+000 2.983388e-003 - 4.485000e+001 4.932263e-001 -3.381610e+000 2.984468e-003 - 4.486000e+001 4.858657e-001 -3.382364e+000 2.986081e-003 - 4.487000e+001 4.770906e-001 -3.383118e+000 2.987853e-003 - 4.488000e+001 4.673149e-001 -3.383872e+000 2.989375e-003 - 4.489000e+001 4.569369e-001 -3.384626e+000 2.990296e-003 - 4.490000e+001 4.463226e-001 -3.385380e+000 2.990404e-003 - 4.491000e+001 4.357914e-001 -3.386134e+000 2.989674e-003 - 4.492000e+001 4.256051e-001 -3.386888e+000 2.988274e-003 - 4.493000e+001 4.159595e-001 -3.387642e+000 2.986527e-003 - 4.494000e+001 4.069796e-001 -3.388396e+000 2.984835e-003 - 4.495000e+001 3.987191e-001 -3.389150e+000 2.983589e-003 - 4.496000e+001 3.911630e-001 -3.389904e+000 2.983079e-003 - 4.497000e+001 3.842343e-001 -3.390658e+000 2.983420e-003 - 4.498000e+001 3.778029e-001 -3.391412e+000 2.984535e-003 - 4.499000e+001 3.716977e-001 -3.392166e+000 2.986166e-003 - 4.500000e+001 3.657198e-001 -3.392920e+000 2.987934e-003 - 4.501000e+001 3.596575e-001 -3.393674e+000 2.989433e-003 - 4.502000e+001 3.532999e-001 -3.394428e+000 2.990317e-003 - 4.503000e+001 3.464515e-001 -3.395182e+000 2.990383e-003 - 4.504000e+001 3.389442e-001 -3.395936e+000 2.989617e-003 - 4.505000e+001 3.306470e-001 -3.396690e+000 2.988194e-003 - 4.506000e+001 3.214741e-001 -3.397444e+000 2.986443e-003 - 4.507000e+001 3.113884e-001 -3.398198e+000 2.984768e-003 - 4.508000e+001 3.004033e-001 -3.398952e+000 2.983556e-003 - 4.509000e+001 2.885796e-001 -3.399706e+000 2.983087e-003 - 4.510000e+001 2.760209e-001 -3.400460e+000 2.983469e-003 - 4.511000e+001 2.628648e-001 -3.401214e+000 2.984614e-003 - 4.512000e+001 2.492735e-001 -3.401968e+000 2.986256e-003 - 4.513000e+001 2.354209e-001 -3.402722e+000 2.988015e-003 - 4.514000e+001 2.214811e-001 -3.403476e+000 2.989485e-003 - 4.515000e+001 2.076149e-001 -3.404230e+000 2.990328e-003 - 4.516000e+001 1.939586e-001 -3.404984e+000 2.990351e-003 - 4.517000e+001 1.806133e-001 -3.405738e+000 2.989547e-003 - 4.518000e+001 1.676366e-001 -3.406492e+000 2.988103e-003 - 4.519000e+001 1.550374e-001 -3.407246e+000 2.986351e-003 - 4.520000e+001 1.427730e-001 -3.408000e+000 2.984696e-003 - 4.521000e+001 1.307499e-001 -3.408754e+000 2.983520e-003 - 4.522000e+001 1.188275e-001 -3.409508e+000 2.983095e-003 - 4.523000e+001 1.068249e-001 -3.410262e+000 2.983520e-003 - 4.524000e+001 9.453047e-002 -3.411016e+000 2.984694e-003 - 4.525000e+001 8.171320e-002 -3.411770e+000 2.986347e-003 - 4.526000e+001 6.813578e-002 -3.412524e+000 2.988096e-003 - 4.527000e+001 5.356828e-002 -3.413278e+000 2.989537e-003 - 4.528000e+001 3.780185e-002 -3.414032e+000 2.990340e-003 - 4.529000e+001 2.066158e-002 -3.414786e+000 2.990320e-003 - 4.530000e+001 2.017875e-003 -3.415539e+000 2.989481e-003 - 4.531000e+001 -1.820443e-002 -3.416293e+000 2.988019e-003 - 4.532000e+001 -4.001954e-002 -3.417047e+000 2.986271e-003 - 4.533000e+001 -6.337736e-002 -3.417801e+000 2.984640e-003 - 4.534000e+001 -8.816324e-002 -3.418555e+000 2.983503e-003 - 4.535000e+001 -1.142011e-001 -3.419309e+000 2.983125e-003 - 4.536000e+001 -1.412598e-001 -3.420063e+000 2.983591e-003 - 4.537000e+001 -1.690615e-001 -3.420817e+000 2.984793e-003 - 4.538000e+001 -1.972937e-001 -3.421571e+000 2.986453e-003 - 4.539000e+001 -2.256212e-001 -3.422325e+000 2.988186e-003 - 4.540000e+001 -2.537004e-001 -3.423079e+000 2.989591e-003 - 4.541000e+001 -2.811932e-001 -3.423833e+000 2.990346e-003 - 4.542000e+001 -3.077799e-001 -3.424587e+000 2.990275e-003 - 4.543000e+001 -3.331720e-001 -3.425341e+000 2.989395e-003 - 4.544000e+001 -3.571219e-001 -3.426095e+000 2.987910e-003 - 4.545000e+001 -3.794307e-001 -3.426849e+000 2.986162e-003 - 4.546000e+001 -3.999537e-001 -3.427603e+000 2.984556e-003 - 4.547000e+001 -4.186018e-001 -3.428357e+000 2.983462e-003 - 4.548000e+001 -4.353411e-001 -3.429111e+000 2.983134e-003 - 4.549000e+001 -4.501887e-001 -3.429865e+000 2.983650e-003 - 4.550000e+001 -4.632066e-001 -3.430619e+000 2.984889e-003 - 4.551000e+001 -4.744927e-001 -3.431373e+000 2.986565e-003 - 4.552000e+001 -4.841716e-001 -3.432127e+000 2.988290e-003 - 4.553000e+001 -4.923827e-001 -3.432881e+000 2.989666e-003 - 4.554000e+001 -4.992701e-001 -3.433635e+000 2.990377e-003 - 4.555000e+001 -5.049707e-001 -3.434389e+000 2.990258e-003 - 4.556000e+001 -5.096056e-001 -3.435143e+000 2.989336e-003 - 4.557000e+001 -5.132720e-001 -3.435897e+000 2.987824e-003 - 4.558000e+001 -5.160367e-001 -3.436651e+000 2.986069e-003 - 4.559000e+001 -5.179337e-001 -3.437405e+000 2.984477e-003 - 4.560000e+001 -5.189629e-001 -3.438159e+000 2.983415e-003 - 4.561000e+001 -5.190916e-001 -3.438913e+000 2.983128e-003 - 4.562000e+001 -5.182595e-001 -3.439667e+000 2.983683e-003 - 4.563000e+001 -5.163842e-001 -3.440421e+000 2.984950e-003 - 4.564000e+001 -5.133695e-001 -3.441175e+000 2.986637e-003 - 4.565000e+001 -5.091143e-001 -3.441929e+000 2.988354e-003 - 4.566000e+001 -5.035224e-001 -3.442683e+000 2.989704e-003 - 4.567000e+001 -4.965112e-001 -3.443437e+000 2.990377e-003 - 4.568000e+001 -4.880210e-001 -3.444191e+000 2.990219e-003 - 4.569000e+001 -4.780216e-001 -3.444945e+000 2.989265e-003 - 4.570000e+001 -4.665184e-001 -3.445699e+000 2.987737e-003 - 4.571000e+001 -4.535550e-001 -3.446453e+000 2.985987e-003 - 4.572000e+001 -4.392143e-001 -3.447207e+000 2.984419e-003 - 4.573000e+001 -4.236170e-001 -3.447961e+000 2.983395e-003 - 4.574000e+001 -4.069173e-001 -3.448715e+000 2.983153e-003 - 4.575000e+001 -3.892969e-001 -3.449469e+000 2.983748e-003 - 4.576000e+001 -3.709574e-001 -3.450223e+000 2.985042e-003 - 4.577000e+001 -3.521105e-001 -3.450977e+000 2.986735e-003 - 4.578000e+001 -3.329692e-001 -3.451731e+000 2.988436e-003 - 4.579000e+001 -3.137373e-001 -3.452485e+000 2.989751e-003 - 4.580000e+001 -2.946006e-001 -3.453239e+000 2.990377e-003 - 4.581000e+001 -2.757190e-001 -3.453993e+000 2.990171e-003 - 4.582000e+001 -2.572200e-001 -3.454747e+000 2.989178e-003 - 4.583000e+001 -2.391953e-001 -3.455501e+000 2.987627e-003 - 4.584000e+001 -2.216989e-001 -3.456255e+000 2.985877e-003 - 4.585000e+001 -2.047483e-001 -3.457009e+000 2.984330e-003 - 4.586000e+001 -1.883279e-001 -3.457762e+000 2.983346e-003 - 4.587000e+001 -1.723950e-001 -3.458516e+000 2.983151e-003 - 4.588000e+001 -1.568881e-001 -3.459270e+000 2.983793e-003 - 4.589000e+001 -1.417357e-001 -3.460024e+000 2.985122e-003 - 4.590000e+001 -1.268665e-001 -3.460778e+000 2.986832e-003 - 4.591000e+001 -1.122202e-001 -3.461532e+000 2.988529e-003 - 4.592000e+001 -9.775690e-002 -3.462286e+000 2.989822e-003 - 4.593000e+001 -8.346579e-002 -3.463040e+000 2.990413e-003 - 4.594000e+001 -6.937170e-002 -3.463794e+000 2.990168e-003 - 4.595000e+001 -5.553931e-002 -3.464548e+000 2.989141e-003 - 4.596000e+001 -4.207456e-002 -3.465302e+000 2.987569e-003 - 4.597000e+001 -2.912286e-002 -3.466056e+000 2.985814e-003 - 4.598000e+001 -1.686426e-002 -3.466810e+000 2.984280e-003 - 4.599000e+001 -5.505608e-003 -3.467564e+000 2.983320e-003 - 4.600000e+001 4.729938e-003 -3.468318e+000 2.983156e-003 - 4.601000e+001 1.361554e-002 -3.469072e+000 2.983825e-003 - 4.602000e+001 2.093476e-002 -3.469826e+000 2.985172e-003 - 4.603000e+001 2.649634e-002 -3.470580e+000 2.986884e-003 - 4.604000e+001 3.014881e-002 -3.471334e+000 2.988567e-003 - 4.605000e+001 3.179399e-002 -3.472088e+000 2.989833e-003 - 4.606000e+001 3.139865e-002 -3.472842e+000 2.990392e-003 - 4.607000e+001 2.900337e-002 -3.473596e+000 2.990116e-003 - 4.608000e+001 2.472809e-002 -3.474350e+000 2.989070e-003 - 4.609000e+001 1.877379e-002 -3.475104e+000 2.987496e-003 - 4.610000e+001 1.142000e-002 -3.475858e+000 2.985757e-003 - 4.611000e+001 3.018033e-003 -3.476612e+000 2.984254e-003 - 4.612000e+001 -6.019798e-003 -3.477366e+000 2.983336e-003 - 4.613000e+001 -1.523467e-002 -3.478120e+000 2.983214e-003 - 4.614000e+001 -2.413886e-002 -3.478874e+000 2.983916e-003 - 4.615000e+001 -3.223557e-002 -3.479628e+000 2.985278e-003 - 4.616000e+001 -3.904017e-002 -3.480382e+000 2.986986e-003 - 4.617000e+001 -4.410169e-002 -3.481136e+000 2.988642e-003 - 4.618000e+001 -4.702355e-002 -3.481890e+000 2.989867e-003 - 4.619000e+001 -4.748238e-002 -3.482644e+000 2.990376e-003 - 4.620000e+001 -4.524399e-002 -3.483398e+000 2.990053e-003 - 4.621000e+001 -4.017554e-002 -3.484152e+000 2.988973e-003 - 4.622000e+001 -3.225328e-002 -3.484906e+000 2.987384e-003 - 4.623000e+001 -2.156526e-002 -3.485660e+000 2.985653e-003 - 4.624000e+001 -8.308873e-003 -3.486414e+000 2.984179e-003 - 4.625000e+001 7.216767e-003 -3.487168e+000 2.983304e-003 - 4.626000e+001 2.462337e-002 -3.487922e+000 2.983229e-003 - 4.627000e+001 4.345032e-002 -3.488676e+000 2.983973e-003 - 4.628000e+001 6.318510e-002 -3.489430e+000 2.985362e-003 - 4.629000e+001 8.328627e-002 -3.490184e+000 2.987076e-003 - 4.630000e+001 1.032079e-001 -3.490938e+000 2.988720e-003 - 4.631000e+001 1.224243e-001 -3.491692e+000 2.989914e-003 - 4.632000e+001 1.404536e-001 -3.492446e+000 2.990384e-003 - 4.633000e+001 1.568794e-001 -3.493200e+000 2.990023e-003 - 4.634000e+001 1.713688e-001 -3.493954e+000 2.988915e-003 - 4.635000e+001 1.836866e-001 -3.494708e+000 2.987314e-003 - 4.636000e+001 1.937046e-001 -3.495462e+000 2.985591e-003 - 4.637000e+001 2.014047e-001 -3.496216e+000 2.984142e-003 - 4.638000e+001 2.068777e-001 -3.496970e+000 2.983303e-003 - 4.639000e+001 2.103158e-001 -3.497724e+000 2.983266e-003 - 4.640000e+001 2.119999e-001 -3.498478e+000 2.984040e-003 - 4.641000e+001 2.122831e-001 -3.499232e+000 2.985444e-003 - 4.642000e+001 2.115701e-001 -3.499985e+000 2.987153e-003 - 4.643000e+001 2.102943e-001 -3.500739e+000 2.988771e-003 - 4.644000e+001 2.088937e-001 -3.501493e+000 2.989926e-003 - 4.645000e+001 2.077862e-001 -3.502247e+000 2.990350e-003 - 4.646000e+001 2.073468e-001 -3.503001e+000 2.989948e-003 - 4.647000e+001 2.078868e-001 -3.503755e+000 2.988812e-003 - 4.648000e+001 2.096367e-001 -3.504509e+000 2.987204e-003 - 4.649000e+001 2.127329e-001 -3.505263e+000 2.985495e-003 - 4.650000e+001 2.172102e-001 -3.506017e+000 2.984081e-003 - 4.651000e+001 2.229989e-001 -3.506771e+000 2.983289e-003 - 4.652000e+001 2.299280e-001 -3.507525e+000 2.983302e-003 - 4.653000e+001 2.377332e-001 -3.508279e+000 2.984118e-003 - 4.654000e+001 2.460704e-001 -3.509033e+000 2.985548e-003 - 4.655000e+001 2.545323e-001 -3.509787e+000 2.987260e-003 - 4.656000e+001 2.626691e-001 -3.510541e+000 2.988860e-003 - 4.657000e+001 2.700111e-001 -3.511295e+000 2.989979e-003 - 4.658000e+001 2.760920e-001 -3.512049e+000 2.990359e-003 - 4.659000e+001 2.804722e-001 -3.512803e+000 2.989913e-003 - 4.660000e+001 2.827601e-001 -3.513557e+000 2.988743e-003 - 4.661000e+001 2.826317e-001 -3.514311e+000 2.987118e-003 - 4.662000e+001 2.798459e-001 -3.515065e+000 2.985414e-003 - 4.663000e+001 2.742557e-001 -3.515819e+000 2.984022e-003 - 4.664000e+001 2.658146e-001 -3.516573e+000 2.983265e-003 - 4.665000e+001 2.545781e-001 -3.517327e+000 2.983316e-003 - 4.666000e+001 2.406999e-001 -3.518081e+000 2.984163e-003 - 4.667000e+001 2.244233e-001 -3.518835e+000 2.985610e-003 - 4.668000e+001 2.060686e-001 -3.519589e+000 2.987321e-003 - 4.669000e+001 1.860167e-001 -3.520343e+000 2.988902e-003 - 4.670000e+001 1.646905e-001 -3.521097e+000 2.989989e-003 - 4.671000e+001 1.425343e-001 -3.521851e+000 2.990331e-003 - 4.672000e+001 1.199934e-001 -3.522605e+000 2.989852e-003 - 4.673000e+001 9.749380e-002 -3.523359e+000 2.988663e-003 - 4.674000e+001 7.542381e-002 -3.524113e+000 2.987038e-003 - 4.675000e+001 5.411879e-002 -3.524867e+000 2.985353e-003 - 4.676000e+001 3.384880e-002 -3.525621e+000 2.983998e-003 - 4.677000e+001 1.481049e-002 -3.526375e+000 2.983287e-003 - 4.678000e+001 -2.876679e-003 -3.527129e+000 2.983383e-003 - 4.679000e+001 -1.916977e-002 -3.527883e+000 2.984265e-003 - 4.680000e+001 -3.409753e-002 -3.528637e+000 2.985728e-003 - 4.681000e+001 -4.775161e-002 -3.529391e+000 2.987432e-003 - 4.682000e+001 -6.027465e-002 -3.530145e+000 2.988984e-003 - 4.683000e+001 -7.184583e-002 -3.530899e+000 2.990026e-003 - 4.684000e+001 -8.266497e-002 -3.531653e+000 2.990316e-003 - 4.685000e+001 -9.293596e-002 -3.532407e+000 2.989788e-003 - 4.686000e+001 -1.028508e-001 -3.533161e+000 2.988563e-003 - 4.687000e+001 -1.125747e-001 -3.533915e+000 2.986922e-003 - 4.688000e+001 -1.222340e-001 -3.534669e+000 2.985244e-003 - 4.689000e+001 -1.319063e-001 -3.535423e+000 2.983916e-003 - 4.690000e+001 -1.416145e-001 -3.536177e+000 2.983245e-003 - 4.691000e+001 -1.513247e-001 -3.536931e+000 2.983386e-003 - 4.692000e+001 -1.609475e-001 -3.537685e+000 2.984307e-003 - 4.693000e+001 -1.703436e-001 -3.538439e+000 2.985795e-003 - 4.694000e+001 -1.793320e-001 -3.539193e+000 2.987508e-003 - 4.695000e+001 -1.877020e-001 -3.539947e+000 2.989050e-003 - 4.696000e+001 -1.952261e-001 -3.540701e+000 2.990069e-003 - 4.697000e+001 -2.016752e-001 -3.541455e+000 2.990330e-003 - 4.698000e+001 -2.068333e-001 -3.542209e+000 2.989775e-003 - 4.699000e+001 -2.105124e-001 -3.542962e+000 2.988534e-003 - 4.700000e+001 -2.125651e-001 -3.543716e+000 2.986891e-003 - 4.701000e+001 -2.128957e-001 -3.544470e+000 2.985227e-003 - 4.702000e+001 -2.114679e-001 -3.545224e+000 2.983924e-003 - 4.703000e+001 -2.083097e-001 -3.545978e+000 2.983284e-003 - 4.704000e+001 -2.035136e-001 -3.546732e+000 2.983451e-003 - 4.705000e+001 -1.972345e-001 -3.547486e+000 2.984385e-003 - 4.706000e+001 -1.896828e-001 -3.548240e+000 2.985868e-003 - 4.707000e+001 -1.811152e-001 -3.548994e+000 2.987555e-003 - 4.708000e+001 -1.718219e-001 -3.549748e+000 2.989056e-003 - 4.709000e+001 -1.621128e-001 -3.550502e+000 2.990024e-003 - 4.710000e+001 -1.523022e-001 -3.551256e+000 2.990236e-003 - 4.711000e+001 -1.426924e-001 -3.552010e+000 2.989645e-003 - 4.712000e+001 -1.335594e-001 -3.552764e+000 2.988388e-003 - 4.713000e+001 -1.251389e-001 -3.553518e+000 2.986757e-003 - 4.714000e+001 -1.176147e-001 -3.554272e+000 2.985131e-003 - 4.715000e+001 -1.111103e-001 -3.555026e+000 2.983887e-003 - 4.716000e+001 -1.056836e-001 -3.555780e+000 2.983314e-003 - 4.717000e+001 -1.013250e-001 -3.556534e+000 2.983547e-003 - 4.718000e+001 -9.795979e-002 -3.557288e+000 2.984532e-003 - 4.719000e+001 -9.545306e-002 -3.558042e+000 2.986041e-003 - 4.720000e+001 -9.361892e-002 -3.558796e+000 2.987725e-003 - 4.721000e+001 -9.223174e-002 -3.559550e+000 2.989194e-003 - 4.722000e+001 -9.103962e-002 -3.560304e+000 2.990108e-003 - 4.723000e+001 -8.977921e-002 -3.561058e+000 2.990254e-003 - 4.724000e+001 -8.819091e-002 -3.561812e+000 2.989599e-003 - 4.725000e+001 -8.603370e-002 -3.562566e+000 2.988290e-003 - 4.726000e+001 -8.309880e-002 -3.563320e+000 2.986628e-003 - 4.727000e+001 -7.922137e-002 -3.564074e+000 2.984995e-003 - 4.728000e+001 -7.428962e-002 -3.564828e+000 2.983767e-003 - 4.729000e+001 -6.825097e-002 -3.565582e+000 2.983229e-003 - 4.730000e+001 -6.111489e-002 -3.566336e+000 2.983504e-003 - 4.731000e+001 -5.295225e-002 -3.567090e+000 2.984529e-003 - 4.732000e+001 -4.389150e-002 -3.567844e+000 2.986068e-003 - 4.733000e+001 -3.411175e-002 -3.568598e+000 2.987766e-003 - 4.734000e+001 -2.383330e-002 -3.569352e+000 2.989233e-003 - 4.735000e+001 -1.330620e-002 -3.570106e+000 2.990133e-003 - 4.736000e+001 -2.797566e-003 -3.570860e+000 2.990261e-003 - 4.737000e+001 7.421720e-003 -3.571614e+000 2.989588e-003 - 4.738000e+001 1.708998e-002 -3.572368e+000 2.988271e-003 - 4.739000e+001 2.596682e-002 -3.573122e+000 2.986614e-003 - 4.740000e+001 3.384350e-002 -3.573876e+000 2.985000e-003 - 4.741000e+001 4.055121e-002 -3.574630e+000 2.983800e-003 - 4.742000e+001 4.596670e-002 -3.575384e+000 2.983292e-003 - 4.743000e+001 5.001509e-002 -3.576138e+000 2.983591e-003 - 4.744000e+001 5.266987e-002 -3.576892e+000 2.984625e-003 - 4.745000e+001 5.395000e-002 -3.577646e+000 2.986153e-003 - 4.746000e+001 5.391470e-002 -3.578400e+000 2.987819e-003 - 4.747000e+001 5.265602e-002 -3.579154e+000 2.989237e-003 - 4.748000e+001 5.029010e-002 -3.579908e+000 2.990079e-003 - 4.749000e+001 4.694742e-002 -3.580662e+000 2.990150e-003 - 4.750000e+001 4.276304e-002 -3.581416e+000 2.989434e-003 - 4.751000e+001 3.786728e-002 -3.582170e+000 2.988097e-003 - 4.752000e+001 3.237762e-002 -3.582924e+000 2.986449e-003 - 4.753000e+001 2.639226e-002 -3.583678e+000 2.984871e-003 - 4.754000e+001 1.998599e-002 -3.584432e+000 2.983731e-003 - 4.755000e+001 1.320837e-002 -3.585185e+000 2.983294e-003 - 4.756000e+001 6.084624e-003 -3.585939e+000 2.983665e-003 - 4.757000e+001 -1.381011e-003 -3.586693e+000 2.984758e-003 - 4.758000e+001 -9.199539e-003 -3.587447e+000 2.986322e-003 - 4.759000e+001 -1.738958e-002 -3.588201e+000 2.987997e-003 - 4.760000e+001 -2.596829e-002 -3.588955e+000 2.989395e-003 - 4.761000e+001 -3.494154e-002 -3.589709e+000 2.990193e-003 - 4.762000e+001 -4.429393e-002 -3.590463e+000 2.990207e-003 - 4.763000e+001 -5.397953e-002 -3.591217e+000 2.989431e-003 - 4.764000e+001 -6.391390e-002 -3.591971e+000 2.988042e-003 - 4.765000e+001 -7.396809e-002 -3.592725e+000 2.986357e-003 - 4.766000e+001 -8.396519e-002 -3.593479e+000 2.984763e-003 - 4.767000e+001 -9.367980e-002 -3.594233e+000 2.983627e-003 - 4.768000e+001 -1.028407e-001 -3.594987e+000 2.983209e-003 - 4.769000e+001 -1.111364e-001 -3.595741e+000 2.983606e-003 - 4.770000e+001 -1.182245e-001 -3.596495e+000 2.984727e-003 - 4.771000e+001 -1.237429e-001 -3.597249e+000 2.986313e-003 - 4.772000e+001 -1.273236e-001 -3.598003e+000 2.987999e-003 - 4.773000e+001 -1.286085e-001 -3.598757e+000 2.989398e-003 - 4.774000e+001 -1.272651e-001 -3.599511e+000 2.990192e-003 - 4.775000e+001 -1.230030e-001 -3.600265e+000 2.990200e-003 - 4.776000e+001 -1.155891e-001 -3.601019e+000 2.989422e-003 - 4.777000e+001 -1.048610e-001 -3.601773e+000 2.988040e-003 - 4.778000e+001 -9.073814e-002 -3.602527e+000 2.986373e-003 - 4.779000e+001 -7.322944e-002 -3.603281e+000 2.984807e-003 - 4.780000e+001 -5.243770e-002 -3.604035e+000 2.983702e-003 - 4.781000e+001 -2.855960e-002 -3.604789e+000 2.983312e-003 - 4.782000e+001 -1.881734e-003 -3.605543e+000 2.983725e-003 - 4.783000e+001 2.722732e-002 -3.606297e+000 2.984844e-003 - 4.784000e+001 5.832875e-002 -3.607051e+000 2.986405e-003 - 4.785000e+001 9.092838e-002 -3.607805e+000 2.988047e-003 - 4.786000e+001 1.244942e-001 -3.608559e+000 2.989389e-003 - 4.787000e+001 1.584753e-001 -3.609313e+000 2.990119e-003 - 4.788000e+001 1.923222e-001 -3.610067e+000 2.990071e-003 - 4.789000e+001 2.255064e-001 -3.610821e+000 2.989254e-003 - 4.790000e+001 2.575389e-001 -3.611575e+000 2.987860e-003 - 4.791000e+001 2.879875e-001 -3.612329e+000 2.986210e-003 - 4.792000e+001 3.164898e-001 -3.613083e+000 2.984688e-003 - 4.793000e+001 3.427644e-001 -3.613837e+000 2.983648e-003 - 4.794000e+001 3.666170e-001 -3.614591e+000 2.983332e-003 - 4.795000e+001 3.879423e-001 -3.615345e+000 2.983816e-003 - 4.796000e+001 4.067226e-001 -3.616099e+000 2.984988e-003 - 4.797000e+001 4.230209e-001 -3.616853e+000 2.986579e-003 - 4.798000e+001 4.369715e-001 -3.617607e+000 2.988221e-003 - 4.799000e+001 4.487667e-001 -3.618361e+000 2.989534e-003 - 4.800000e+001 4.586409e-001 -3.619115e+000 2.990217e-003 - 4.801000e+001 4.668542e-001 -3.619869e+000 2.990109e-003 - 4.802000e+001 4.736736e-001 -3.620623e+000 2.989234e-003 - 4.803000e+001 4.793561e-001 -3.621377e+000 2.987793e-003 - 4.804000e+001 4.841321e-001 -3.622131e+000 2.986114e-003 - 4.805000e+001 4.881909e-001 -3.622885e+000 2.984584e-003 - 4.806000e+001 4.916689e-001 -3.623639e+000 2.983554e-003 - 4.807000e+001 4.946417e-001 -3.624393e+000 2.983263e-003 - 4.808000e+001 4.971191e-001 -3.625147e+000 2.983775e-003 - 4.809000e+001 4.990449e-001 -3.625901e+000 2.984974e-003 - 4.810000e+001 5.002992e-001 -3.626655e+000 2.986583e-003 - 4.811000e+001 5.007061e-001 -3.627408e+000 2.988230e-003 - 4.812000e+001 5.000430e-001 -3.628162e+000 2.989540e-003 - 4.813000e+001 4.980537e-001 -3.628916e+000 2.990211e-003 - 4.814000e+001 4.944627e-001 -3.629670e+000 2.990092e-003 - 4.815000e+001 4.889909e-001 -3.630424e+000 2.989213e-003 - 4.816000e+001 4.813715e-001 -3.631178e+000 2.987777e-003 - 4.817000e+001 4.713654e-001 -3.631932e+000 2.986117e-003 - 4.818000e+001 4.587749e-001 -3.632686e+000 2.984616e-003 - 4.819000e+001 4.434556e-001 -3.633440e+000 2.983619e-003 - 4.820000e+001 4.253256e-001 -3.634194e+000 2.983356e-003 - 4.821000e+001 4.043713e-001 -3.634948e+000 2.983885e-003 - 4.822000e+001 3.806504e-001 -3.635702e+000 2.985081e-003 - 4.823000e+001 3.542905e-001 -3.636456e+000 2.986665e-003 - 4.824000e+001 3.254857e-001 -3.637210e+000 2.988267e-003 - 4.825000e+001 2.944889e-001 -3.637964e+000 2.989518e-003 - 4.826000e+001 2.616027e-001 -3.638718e+000 2.990127e-003 - 4.827000e+001 2.271674e-001 -3.639472e+000 2.989955e-003 - 4.828000e+001 1.915482e-001 -3.640226e+000 2.989042e-003 - 4.829000e+001 1.551217e-001 -3.640980e+000 2.987600e-003 - 4.830000e+001 1.182627e-001 -3.641734e+000 2.985963e-003 - 4.831000e+001 8.133148e-002 -3.642488e+000 2.984512e-003 - 4.832000e+001 4.466268e-002 -3.643242e+000 2.983585e-003 - 4.833000e+001 8.556424e-003 -3.643996e+000 2.983397e-003 - 4.834000e+001 -2.672850e-002 -3.644750e+000 2.983994e-003 - 4.835000e+001 -6.097877e-002 -3.645504e+000 2.985239e-003 - 4.836000e+001 -9.402788e-002 -3.646258e+000 2.986843e-003 - 4.837000e+001 -1.257550e-001 -3.647012e+000 2.988436e-003 - 4.838000e+001 -1.560815e-001 -3.647766e+000 2.989648e-003 - 4.839000e+001 -1.849649e-001 -3.648520e+000 2.990200e-003 - 4.840000e+001 -2.123923e-001 -3.649274e+000 2.989962e-003 - 4.841000e+001 -2.383717e-001 -3.650028e+000 2.988986e-003 - 4.842000e+001 -2.629234e-001 -3.650782e+000 2.987497e-003 - 4.843000e+001 -2.860718e-001 -3.651536e+000 2.985836e-003 - 4.844000e+001 -3.078372e-001 -3.652290e+000 2.984385e-003 - 4.845000e+001 -3.282291e-001 -3.653044e+000 2.983479e-003 - 4.846000e+001 -3.472414e-001 -3.653798e+000 2.983329e-003 - 4.847000e+001 -3.648490e-001 -3.654552e+000 2.983969e-003 - 4.848000e+001 -3.810065e-001 -3.655306e+000 2.985253e-003 - 4.849000e+001 -3.956491e-001 -3.656060e+000 2.986885e-003 - 4.850000e+001 -4.086954e-001 -3.656814e+000 2.988490e-003 - 4.851000e+001 -4.200516e-001 -3.657568e+000 2.989700e-003 - 4.852000e+001 -4.296171e-001 -3.658322e+000 2.990238e-003 - 4.853000e+001 -4.372914e-001 -3.659076e+000 2.989981e-003 - 4.854000e+001 -4.429812e-001 -3.659830e+000 2.988989e-003 - 4.855000e+001 -4.466066e-001 -3.660584e+000 2.987492e-003 - 4.856000e+001 -4.481086e-001 -3.661338e+000 2.985833e-003 - 4.857000e+001 -4.474532e-001 -3.662092e+000 2.984395e-003 - 4.858000e+001 -4.446364e-001 -3.662846e+000 2.983509e-003 - 4.859000e+001 -4.396859e-001 -3.663600e+000 2.983378e-003 - 4.860000e+001 -4.326615e-001 -3.664354e+000 2.984030e-003 - 4.861000e+001 -4.236540e-001 -3.665108e+000 2.985313e-003 - 4.862000e+001 -4.127815e-001 -3.665862e+000 2.986929e-003 - 4.863000e+001 -4.001848e-001 -3.666616e+000 2.988504e-003 - 4.864000e+001 -3.860214e-001 -3.667370e+000 2.989674e-003 - 4.865000e+001 -3.704578e-001 -3.668124e+000 2.990170e-003 - 4.866000e+001 -3.536626e-001 -3.668878e+000 2.989880e-003 - 4.867000e+001 -3.357988e-001 -3.669631e+000 2.988871e-003 - 4.868000e+001 -3.170168e-001 -3.670385e+000 2.987378e-003 - 4.869000e+001 -2.974487e-001 -3.671139e+000 2.985745e-003 - 4.870000e+001 -2.772035e-001 -3.671893e+000 2.984353e-003 - 4.871000e+001 -2.563645e-001 -3.672647e+000 2.983523e-003 - 4.872000e+001 -2.349881e-001 -3.673401e+000 2.983448e-003 - 4.873000e+001 -2.131055e-001 -3.674155e+000 2.984146e-003 - 4.874000e+001 -1.907252e-001 -3.674909e+000 2.985455e-003 - 4.875000e+001 -1.678382e-001 -3.675663e+000 2.987072e-003 - 4.876000e+001 -1.444244e-001 -3.676417e+000 2.988623e-003 - 4.877000e+001 -1.204601e-001 -3.677171e+000 2.989748e-003 - 4.878000e+001 -9.592627e-002 -3.677925e+000 2.990188e-003 - 4.879000e+001 -7.081694e-002 -3.678679e+000 2.989841e-003 - 4.880000e+001 -4.514721e-002 -3.679433e+000 2.988785e-003 - 4.881000e+001 -1.896035e-002 -3.680187e+000 2.987263e-003 - 4.882000e+001 7.666454e-003 -3.680941e+000 2.985625e-003 - 4.883000e+001 3.461817e-002 -3.681695e+000 2.984249e-003 - 4.884000e+001 6.174004e-002 -3.682449e+000 2.983453e-003 - 4.885000e+001 8.883805e-002 -3.683203e+000 2.983421e-003 - 4.886000e+001 1.156817e-001 -3.683957e+000 2.984161e-003 - 4.887000e+001 1.420088e-001 -3.684711e+000 2.985502e-003 - 4.888000e+001 1.675330e-001 -3.685465e+000 2.987135e-003 - 4.889000e+001 1.919521e-001 -3.686219e+000 2.988685e-003 - 4.890000e+001 2.149583e-001 -3.686973e+000 2.989794e-003 - 4.891000e+001 2.362490e-001 -3.687727e+000 2.990209e-003 - 4.892000e+001 2.555377e-001 -3.688481e+000 2.989836e-003 - 4.893000e+001 2.725645e-001 -3.689235e+000 2.988761e-003 - 4.894000e+001 2.871061e-001 -3.689989e+000 2.987232e-003 - 4.895000e+001 2.989836e-001 -3.690743e+000 2.985601e-003 - 4.896000e+001 3.080688e-001 -3.691497e+000 2.984244e-003 - 4.897000e+001 3.142883e-001 -3.692251e+000 2.983473e-003 - 4.898000e+001 3.176250e-001 -3.693005e+000 2.983466e-003 - 4.899000e+001 3.181173e-001 -3.693759e+000 2.984221e-003 - 4.900000e+001 3.158557e-001 -3.694513e+000 2.985562e-003 - 4.901000e+001 3.109769e-001 -3.695267e+000 2.987178e-003 - 4.902000e+001 3.036569e-001 -3.696021e+000 2.988695e-003 - 4.903000e+001 2.941017e-001 -3.696775e+000 2.989762e-003 - 4.904000e+001 2.825377e-001 -3.697529e+000 2.990136e-003 - 4.905000e+001 2.692014e-001 -3.698283e+000 2.989730e-003 - 4.906000e+001 2.543295e-001 -3.699037e+000 2.988641e-003 - 4.907000e+001 2.381500e-001 -3.699791e+000 2.987121e-003 - 4.908000e+001 2.208741e-001 -3.700545e+000 2.985522e-003 - 4.909000e+001 2.026902e-001 -3.701299e+000 2.984215e-003 - 4.910000e+001 1.837599e-001 -3.702053e+000 2.983504e-003 - 4.911000e+001 1.642162e-001 -3.702807e+000 2.983553e-003 - 4.912000e+001 1.441642e-001 -3.703561e+000 2.984350e-003 - 4.913000e+001 1.236833e-001 -3.704315e+000 2.985711e-003 - 4.914000e+001 1.028323e-001 -3.705069e+000 2.987317e-003 - 4.915000e+001 8.165557e-002 -3.705823e+000 2.988798e-003 - 4.916000e+001 6.019017e-002 -3.706577e+000 2.989808e-003 - 4.917000e+001 3.847424e-002 -3.707331e+000 2.990115e-003 - 4.918000e+001 1.655491e-002 -3.708085e+000 2.989647e-003 - 4.919000e+001 -5.504183e-003 -3.708839e+000 2.988509e-003 - 4.920000e+001 -2.761642e-002 -3.709593e+000 2.986966e-003 - 4.921000e+001 -4.966738e-002 -3.710347e+000 2.985372e-003 - 4.922000e+001 -7.151195e-002 -3.711101e+000 2.984099e-003 - 4.923000e+001 -9.297379e-002 -3.711855e+000 2.983440e-003 - 4.924000e+001 -1.138471e-001 -3.712608e+000 2.983552e-003 - 4.925000e+001 -1.339011e-001 -3.713362e+000 2.984409e-003 - 4.926000e+001 -1.528862e-001 -3.714116e+000 2.985815e-003 - 4.927000e+001 -1.705428e-001 -3.714870e+000 2.987445e-003 - 4.928000e+001 -1.866112e-001 -3.715624e+000 2.988924e-003 - 4.929000e+001 -2.008429e-001 -3.716378e+000 2.989910e-003 - 4.930000e+001 -2.130120e-001 -3.717132e+000 2.990176e-003 - 4.931000e+001 -2.229263e-001 -3.717886e+000 2.989659e-003 - 4.932000e+001 -2.304382e-001 -3.718640e+000 2.988476e-003 - 4.933000e+001 -2.354533e-001 -3.719394e+000 2.986899e-003 - 4.934000e+001 -2.379373e-001 -3.720148e+000 2.985290e-003 - 4.935000e+001 -2.379208e-001 -3.720902e+000 2.984018e-003 - 4.936000e+001 -2.355007e-001 -3.721656e+000 2.983378e-003 - 4.937000e+001 -2.308387e-001 -3.722410e+000 2.983517e-003 - 4.938000e+001 -2.241574e-001 -3.723164e+000 2.984403e-003 - 4.939000e+001 -2.157329e-001 -3.723918e+000 2.985833e-003 - 4.940000e+001 -2.058849e-001 -3.724672e+000 2.987477e-003 - 4.941000e+001 -1.949655e-001 -3.725426e+000 2.988957e-003 - 4.942000e+001 -1.833455e-001 -3.726180e+000 2.989935e-003 - 4.943000e+001 -1.714003e-001 -3.726934e+000 2.990187e-003 - 4.944000e+001 -1.594955e-001 -3.727688e+000 2.989655e-003 - 4.945000e+001 -1.479734e-001 -3.728442e+000 2.988463e-003 - 4.946000e+001 -1.371401e-001 -3.729196e+000 2.986885e-003 - 4.947000e+001 -1.272551e-001 -3.729950e+000 2.985284e-003 - 4.948000e+001 -1.185225e-001 -3.730704e+000 2.984028e-003 - 4.949000e+001 -1.110862e-001 -3.731458e+000 2.983406e-003 - 4.950000e+001 -1.050267e-001 -3.732212e+000 2.983560e-003 - 4.951000e+001 -1.003619e-001 -3.732966e+000 2.984453e-003 - 4.952000e+001 -9.705098e-002 -3.733720e+000 2.985876e-003 - 4.953000e+001 -9.500064e-002 -3.734474e+000 2.987501e-003 - 4.954000e+001 -9.407387e-002 -3.735228e+000 2.988953e-003 - 4.955000e+001 -9.410071e-002 -3.735982e+000 2.989898e-003 - 4.956000e+001 -9.489022e-002 -3.736736e+000 2.990120e-003 - 4.957000e+001 -9.624299e-002 -3.737490e+000 2.989571e-003 - 4.958000e+001 -9.796354e-002 -3.738244e+000 2.988378e-003 - 4.959000e+001 -9.987194e-002 -3.738998e+000 2.986819e-003 - 4.960000e+001 -1.018139e-001 -3.739752e+000 2.985253e-003 - 4.961000e+001 -1.036689e-001 -3.740506e+000 2.984043e-003 - 4.962000e+001 -1.053559e-001 -3.741260e+000 2.983468e-003 - 4.963000e+001 -1.068364e-001 -3.742014e+000 2.983659e-003 - 4.964000e+001 -1.081146e-001 -3.742768e+000 2.984571e-003 - 4.965000e+001 -1.092346e-001 -3.743522e+000 2.985989e-003 - 4.966000e+001 -1.102751e-001 -3.744276e+000 2.987585e-003 - 4.967000e+001 -1.113423e-001 -3.745030e+000 2.988989e-003 - 4.968000e+001 -1.125601e-001 -3.745784e+000 2.989876e-003 - 4.969000e+001 -1.140597e-001 -3.746538e+000 2.990042e-003 - 4.970000e+001 -1.159688e-001 -3.747292e+000 2.989450e-003 - 4.971000e+001 -1.184000e-001 -3.748046e+000 2.988238e-003 - 4.972000e+001 -1.214412e-001 -3.748800e+000 2.986688e-003 - 4.973000e+001 -1.251460e-001 -3.749554e+000 2.985159e-003 - 4.974000e+001 -1.295272e-001 -3.750308e+000 2.984006e-003 - 4.975000e+001 -1.345520e-001 -3.751062e+000 2.983498e-003 - 4.976000e+001 -1.401398e-001 -3.751816e+000 2.983753e-003 - 4.977000e+001 -1.461627e-001 -3.752570e+000 2.984711e-003 - 4.978000e+001 -1.524491e-001 -3.753324e+000 2.986150e-003 - 4.979000e+001 -1.587896e-001 -3.754078e+000 2.987735e-003 - 4.980000e+001 -1.649447e-001 -3.754831e+000 2.989098e-003 - 4.981000e+001 -1.706552e-001 -3.755585e+000 2.989923e-003 - 4.982000e+001 -1.756526e-001 -3.756339e+000 2.990017e-003 - 4.983000e+001 -1.796716e-001 -3.757093e+000 2.989358e-003 - 4.984000e+001 -1.824607e-001 -3.757847e+000 2.988096e-003 - 4.985000e+001 -1.837943e-001 -3.758601e+000 2.986522e-003 - 4.986000e+001 -1.834815e-001 -3.759355e+000 2.985000e-003 - 4.987000e+001 -1.813744e-001 -3.760109e+000 2.983884e-003 - 4.988000e+001 -1.773738e-001 -3.760863e+000 2.983435e-003 - 4.989000e+001 -1.714326e-001 -3.761617e+000 2.983758e-003 - 4.990000e+001 -1.635561e-001 -3.762371e+000 2.984781e-003 - 4.991000e+001 -1.538005e-001 -3.763125e+000 2.986270e-003 - 4.992000e+001 -1.422686e-001 -3.763879e+000 2.987882e-003 - 4.993000e+001 -1.291027e-001 -3.764633e+000 2.989245e-003 - 4.994000e+001 -1.144772e-001 -3.765387e+000 2.990044e-003 - 4.995000e+001 -9.858902e-002 -3.766141e+000 2.990093e-003 - 4.996000e+001 -8.164740e-002 -3.766895e+000 2.989380e-003 - 4.997000e+001 -6.386424e-002 -3.767649e+000 2.988065e-003 - 4.998000e+001 -4.544455e-002 -3.768403e+000 2.986448e-003 - 4.999000e+001 -2.657826e-002 -3.769157e+000 2.984901e-003 - 5.000000e+001 -7.433535e-003 -3.769911e+000 2.983777e-003 - 5.001000e+001 1.184793e-002 -3.770665e+000 2.983338e-003 - 5.002000e+001 3.115339e-002 -3.771419e+000 2.983684e-003 - 5.003000e+001 5.039923e-002 -3.772173e+000 2.984737e-003 - 5.004000e+001 6.952890e-002 -3.772927e+000 2.986256e-003 - 5.005000e+001 8.850874e-002 -3.773681e+000 2.987893e-003 - 5.006000e+001 1.073221e-001 -3.774435e+000 2.989274e-003 - 5.007000e+001 1.259622e-001 -3.775189e+000 2.990084e-003 - 5.008000e+001 1.444238e-001 -3.775943e+000 2.990139e-003 - 5.009000e+001 1.626954e-001 -3.776697e+000 2.989427e-003 - 5.010000e+001 1.807507e-001 -3.777451e+000 2.988114e-003 - 5.011000e+001 1.985423e-001 -3.778205e+000 2.986499e-003 - 5.012000e+001 2.159955e-001 -3.778959e+000 2.984953e-003 - 5.013000e+001 2.330049e-001 -3.779713e+000 2.983829e-003 - 5.014000e+001 2.494330e-001 -3.780467e+000 2.983383e-003 - 5.015000e+001 2.651108e-001 -3.781221e+000 2.983714e-003 - 5.016000e+001 2.798414e-001 -3.781975e+000 2.984742e-003 - 5.017000e+001 2.934055e-001 -3.782729e+000 2.986228e-003 - 5.018000e+001 3.055691e-001 -3.783483e+000 2.987828e-003 - 5.019000e+001 3.160933e-001 -3.784237e+000 2.989173e-003 - 5.020000e+001 3.247444e-001 -3.784991e+000 2.989958e-003 - 5.021000e+001 3.313057e-001 -3.785745e+000 2.990005e-003 - 5.022000e+001 3.355888e-001 -3.786499e+000 2.989309e-003 - 5.023000e+001 3.374439e-001 -3.787253e+000 2.988034e-003 - 5.024000e+001 3.367693e-001 -3.788007e+000 2.986478e-003 - 5.025000e+001 3.335195e-001 -3.788761e+000 2.985003e-003 - 5.026000e+001 3.277097e-001 -3.789515e+000 2.983950e-003 - 5.027000e+001 3.194188e-001 -3.790269e+000 2.983562e-003 - 5.028000e+001 3.087894e-001 -3.791023e+000 2.983924e-003 - 5.029000e+001 2.960239e-001 -3.791777e+000 2.984949e-003 - 5.030000e+001 2.813789e-001 -3.792531e+000 2.986395e-003 - 5.031000e+001 2.651564e-001 -3.793285e+000 2.987922e-003 - 5.032000e+001 2.476928e-001 -3.794039e+000 2.989173e-003 - 5.033000e+001 2.293464e-001 -3.794793e+000 2.989858e-003 - 5.034000e+001 2.104836e-001 -3.795547e+000 2.989817e-003 - 5.035000e+001 1.914651e-001 -3.796301e+000 2.989061e-003 - 5.036000e+001 1.726316e-001 -3.797054e+000 2.987767e-003 - 5.037000e+001 1.542915e-001 -3.797808e+000 2.986237e-003 - 5.038000e+001 1.367095e-001 -3.798562e+000 2.984830e-003 - 5.039000e+001 1.200973e-001 -3.799316e+000 2.983876e-003 - 5.040000e+001 1.046074e-001 -3.800070e+000 2.983601e-003 - 5.041000e+001 9.032967e-002 -3.800824e+000 2.984071e-003 - 5.042000e+001 7.729048e-002 -3.801578e+000 2.985180e-003 - 5.043000e+001 6.545553e-002 -3.802332e+000 2.986671e-003 - 5.044000e+001 5.473511e-002 -3.803086e+000 2.988196e-003 - 5.045000e+001 4.499208e-002 -3.803840e+000 2.989400e-003 - 5.046000e+001 3.605181e-002 -3.804594e+000 2.990001e-003 - 5.047000e+001 2.771381e-002 -3.805348e+000 2.989854e-003 - 5.048000e+001 1.976411e-002 -3.806102e+000 2.988989e-003 - 5.049000e+001 1.198799e-002 -3.806856e+000 2.987599e-003 - 5.050000e+001 4.182230e-003 -3.807610e+000 2.986005e-003 - 5.051000e+001 -3.833700e-003 -3.808364e+000 2.984572e-003 - 5.052000e+001 -1.220802e-002 -3.809118e+000 2.983634e-003 - 5.053000e+001 -2.104913e-002 -3.809872e+000 2.983412e-003 - 5.054000e+001 -3.042050e-002 -3.810626e+000 2.983962e-003 - 5.055000e+001 -4.033818e-002 -3.811380e+000 2.985162e-003 - 5.056000e+001 -5.077089e-002 -3.812134e+000 2.986740e-003 - 5.057000e+001 -6.164277e-002 -3.812888e+000 2.988337e-003 - 5.058000e+001 -7.283832e-002 -3.813642e+000 2.989587e-003 - 5.059000e+001 -8.420938e-002 -3.814396e+000 2.990204e-003 - 5.060000e+001 -9.558351e-002 -3.815150e+000 2.990044e-003 - 5.061000e+001 -1.067733e-001 -3.815904e+000 2.989141e-003 - 5.062000e+001 -1.175863e-001 -3.816658e+000 2.987698e-003 - 5.063000e+001 -1.278342e-001 -3.817412e+000 2.986041e-003 - 5.064000e+001 -1.373419e-001 -3.818166e+000 2.984547e-003 - 5.065000e+001 -1.459548e-001 -3.818920e+000 2.983555e-003 - 5.066000e+001 -1.535448e-001 -3.819674e+000 2.983291e-003 - 5.067000e+001 -1.600145e-001 -3.820428e+000 2.983813e-003 - 5.068000e+001 -1.652985e-001 -3.821182e+000 2.985001e-003 - 5.069000e+001 -1.693639e-001 -3.821936e+000 2.986582e-003 - 5.070000e+001 -1.722077e-001 -3.822690e+000 2.988198e-003 - 5.071000e+001 -1.738532e-001 -3.823444e+000 2.989480e-003 - 5.072000e+001 -1.743444e-001 -3.824198e+000 2.990141e-003 - 5.073000e+001 -1.737400e-001 -3.824952e+000 2.990034e-003 - 5.074000e+001 -1.721062e-001 -3.825706e+000 2.989191e-003 - 5.075000e+001 -1.695106e-001 -3.826460e+000 2.987807e-003 - 5.076000e+001 -1.660154e-001 -3.827214e+000 2.986203e-003 - 5.077000e+001 -1.616724e-001 -3.827968e+000 2.984745e-003 - 5.078000e+001 -1.565189e-001 -3.828722e+000 2.983767e-003 - 5.079000e+001 -1.505757e-001 -3.829476e+000 2.983488e-003 - 5.080000e+001 -1.438464e-001 -3.830230e+000 2.983966e-003 - 5.081000e+001 -1.363191e-001 -3.830984e+000 2.985082e-003 - 5.082000e+001 -1.279696e-001 -3.831738e+000 2.986573e-003 - 5.083000e+001 -1.187663e-001 -3.832492e+000 2.988091e-003 - 5.084000e+001 -1.086762e-001 -3.833246e+000 2.989285e-003 - 5.085000e+001 -9.767222e-002 -3.834000e+000 2.989881e-003 - 5.086000e+001 -8.574053e-002 -3.834754e+000 2.989747e-003 - 5.087000e+001 -7.288773e-002 -3.835508e+000 2.988921e-003 - 5.088000e+001 -5.914752e-002 -3.836262e+000 2.987599e-003 - 5.089000e+001 -4.458611e-002 -3.837016e+000 2.986095e-003 - 5.090000e+001 -2.930590e-002 -3.837770e+000 2.984761e-003 - 5.091000e+001 -1.344725e-002 -3.838524e+000 2.983910e-003 - 5.092000e+001 2.812104e-003 -3.839277e+000 2.983740e-003 - 5.093000e+001 1.926000e-002 -3.840031e+000 2.984289e-003 - 5.094000e+001 3.565516e-002 -3.840785e+000 2.985426e-003 - 5.095000e+001 5.173475e-002 -3.841539e+000 2.986881e-003 - 5.096000e+001 6.722382e-002 -3.842293e+000 2.988312e-003 - 5.097000e+001 8.184616e-002 -3.843047e+000 2.989380e-003 - 5.098000e+001 9.533620e-002 -3.843801e+000 2.989833e-003 - 5.099000e+001 1.074511e-001 -3.844555e+000 2.989563e-003 - 5.100000e+001 1.179827e-001 -3.845309e+000 2.988630e-003 - 5.101000e+001 1.267682e-001 -3.846063e+000 2.987250e-003 - 5.102000e+001 1.336992e-001 -3.846817e+000 2.985744e-003 - 5.103000e+001 1.387292e-001 -3.847571e+000 2.984467e-003 - 5.104000e+001 1.418776e-001 -3.848325e+000 2.983720e-003 - 5.105000e+001 1.432309e-001 -3.849079e+000 2.983685e-003 - 5.106000e+001 1.429412e-001 -3.849833e+000 2.984375e-003 - 5.107000e+001 1.412212e-001 -3.850587e+000 2.985637e-003 - 5.108000e+001 1.383359e-001 -3.851341e+000 2.987180e-003 - 5.109000e+001 1.345920e-001 -3.852095e+000 2.988648e-003 - 5.110000e+001 1.303249e-001 -3.852849e+000 2.989700e-003 - 5.111000e+001 1.258839e-001 -3.853603e+000 2.990088e-003 - 5.112000e+001 1.216166e-001 -3.854357e+000 2.989715e-003 - 5.113000e+001 1.178531e-001 -3.855111e+000 2.988661e-003 - 5.114000e+001 1.148903e-001 -3.855865e+000 2.987160e-003 - 5.115000e+001 1.129781e-001 -3.856619e+000 2.985554e-003 - 5.116000e+001 1.123076e-001 -3.857373e+000 2.984210e-003 - 5.117000e+001 1.130013e-001 -3.858127e+000 2.983439e-003 - 5.118000e+001 1.151072e-001 -3.858881e+000 2.983420e-003 - 5.119000e+001 1.185959e-001 -3.859635e+000 2.984164e-003 - 5.120000e+001 1.233618e-001 -3.860389e+000 2.985505e-003 - 5.121000e+001 1.292270e-001 -3.861143e+000 2.987139e-003 - 5.122000e+001 1.359498e-001 -3.861897e+000 2.988697e-003 - 5.123000e+001 1.432353e-001 -3.862651e+000 2.989826e-003 - 5.124000e+001 1.507491e-001 -3.863405e+000 2.990268e-003 - 5.125000e+001 1.581330e-001 -3.864159e+000 2.989924e-003 - 5.126000e+001 1.650209e-001 -3.864913e+000 2.988871e-003 - 5.127000e+001 1.710562e-001 -3.865667e+000 2.987347e-003 - 5.128000e+001 1.759080e-001 -3.866421e+000 2.985696e-003 - 5.129000e+001 1.792868e-001 -3.867175e+000 2.984294e-003 - 5.130000e+001 1.809570e-001 -3.867929e+000 2.983456e-003 - 5.131000e+001 1.807480e-001 -3.868683e+000 2.983370e-003 - 5.132000e+001 1.785617e-001 -3.869437e+000 2.984052e-003 - 5.133000e+001 1.743767e-001 -3.870191e+000 2.985343e-003 - 5.134000e+001 1.682490e-001 -3.870945e+000 2.986945e-003 - 5.135000e+001 1.603087e-001 -3.871699e+000 2.988493e-003 - 5.136000e+001 1.507543e-001 -3.872453e+000 2.989637e-003 - 5.137000e+001 1.398429e-001 -3.873207e+000 2.990119e-003 - 5.138000e+001 1.278786e-001 -3.873961e+000 2.989836e-003 - 5.139000e+001 1.151992e-001 -3.874715e+000 2.988861e-003 - 5.140000e+001 1.021606e-001 -3.875469e+000 2.987422e-003 - 5.141000e+001 8.912230e-002 -3.876223e+000 2.985851e-003 - 5.142000e+001 7.643163e-002 -3.876977e+000 2.984511e-003 - 5.143000e+001 6.441013e-002 -3.877731e+000 2.983707e-003 - 5.144000e+001 5.334091e-002 -3.878485e+000 2.983618e-003 - 5.145000e+001 4.345844e-002 -3.879239e+000 2.984258e-003 - 5.146000e+001 3.494082e-002 -3.879993e+000 2.985470e-003 - 5.147000e+001 2.790497e-002 -3.880747e+000 2.986969e-003 - 5.148000e+001 2.240478e-002 -3.881501e+000 2.988403e-003 - 5.149000e+001 1.843223e-002 -3.882254e+000 2.989441e-003 - 5.150000e+001 1.592124e-002 -3.883008e+000 2.989845e-003 - 5.151000e+001 1.475406e-002 -3.883762e+000 2.989526e-003 - 5.152000e+001 1.476962e-002 -3.884516e+000 2.988563e-003 - 5.153000e+001 1.577344e-002 -3.885270e+000 2.987187e-003 - 5.154000e+001 1.754843e-002 -3.886024e+000 2.985722e-003 - 5.155000e+001 1.986611e-002 -3.886778e+000 2.984512e-003 - 5.156000e+001 2.249753e-002 -3.887532e+000 2.983841e-003 - 5.157000e+001 2.522341e-002 -3.888286e+000 2.983866e-003 - 5.158000e+001 2.784306e-002 -3.889040e+000 2.984580e-003 - 5.159000e+001 3.018154e-002 -3.889794e+000 2.985813e-003 - 5.160000e+001 3.209496e-002 -3.890548e+000 2.987275e-003 - 5.161000e+001 3.347363e-002 -3.891302e+000 2.988621e-003 - 5.162000e+001 3.424312e-002 -3.892056e+000 2.989533e-003 - 5.163000e+001 3.436324e-002 -3.892810e+000 2.989796e-003 - 5.164000e+001 3.382514e-002 -3.893564e+000 2.989345e-003 - 5.165000e+001 3.264689e-002 -3.894318e+000 2.988283e-003 - 5.166000e+001 3.086787e-002 -3.895072e+000 2.986856e-003 - 5.167000e+001 2.854235e-002 -3.895826e+000 2.985397e-003 - 5.168000e+001 2.573279e-002 -3.896580e+000 2.984249e-003 - 5.169000e+001 2.250317e-002 -3.897334e+000 2.983683e-003 - 5.170000e+001 1.891294e-002 -3.898088e+000 2.983838e-003 - 5.171000e+001 1.501180e-002 -3.898842e+000 2.984683e-003 - 5.172000e+001 1.083562e-002 -3.899596e+000 2.986026e-003 - 5.173000e+001 6.403784e-003 -3.900350e+000 2.987558e-003 - 5.174000e+001 1.718012e-003 -3.901104e+000 2.988925e-003 - 5.175000e+001 -3.237353e-003 -3.901858e+000 2.989806e-003 - 5.176000e+001 -8.493625e-003 -3.902612e+000 2.989995e-003 - 5.177000e+001 -1.409482e-002 -3.903366e+000 2.989442e-003 - 5.178000e+001 -2.009372e-002 -3.904120e+000 2.988266e-003 - 5.179000e+001 -2.654718e-002 -3.904874e+000 2.986735e-003 - 5.180000e+001 -3.351116e-002 -3.905628e+000 2.985198e-003 - 5.181000e+001 -4.103561e-002 -3.906382e+000 2.984008e-003 - 5.182000e+001 -4.915978e-002 -3.907136e+000 2.983442e-003 - 5.183000e+001 -5.790806e-002 -3.907890e+000 2.983634e-003 - 5.184000e+001 -6.728675e-002 -3.908644e+000 2.984545e-003 - 5.185000e+001 -7.728182e-002 -3.909398e+000 2.985971e-003 - 5.186000e+001 -8.785794e-002 -3.910152e+000 2.987589e-003 - 5.187000e+001 -9.895866e-002 -3.910906e+000 2.989029e-003 - 5.188000e+001 -1.105078e-001 -3.911660e+000 2.989964e-003 - 5.189000e+001 -1.224119e-001 -3.912414e+000 2.990181e-003 - 5.190000e+001 -1.345636e-001 -3.913168e+000 2.989628e-003 - 5.191000e+001 -1.468456e-001 -3.913922e+000 2.988429e-003 - 5.192000e+001 -1.591350e-001 -3.914676e+000 2.986856e-003 - 5.193000e+001 -1.713079e-001 -3.915430e+000 2.985265e-003 - 5.194000e+001 -1.832433e-001 -3.916184e+000 2.984017e-003 - 5.195000e+001 -1.948275e-001 -3.916938e+000 2.983397e-003 - 5.196000e+001 -2.059568e-001 -3.917692e+000 2.983542e-003 - 5.197000e+001 -2.165397e-001 -3.918446e+000 2.984418e-003 - 5.198000e+001 -2.264985e-001 -3.919200e+000 2.985824e-003 - 5.199000e+001 -2.357693e-001 -3.919954e+000 2.987436e-003 - 5.200000e+001 -2.443013e-001 -3.920708e+000 2.988888e-003 - 5.201000e+001 -2.520553e-001 -3.921462e+000 2.989852e-003 - 5.202000e+001 -2.590008e-001 -3.922216e+000 2.990110e-003 - 5.203000e+001 -2.651136e-001 -3.922970e+000 2.989610e-003 - 5.204000e+001 -2.703723e-001 -3.923724e+000 2.988469e-003 - 5.205000e+001 -2.747550e-001 -3.924477e+000 2.986953e-003 - 5.206000e+001 -2.782363e-001 -3.925231e+000 2.985410e-003 - 5.207000e+001 -2.807847e-001 -3.925985e+000 2.984194e-003 - 5.208000e+001 -2.823608e-001 -3.926739e+000 2.983580e-003 - 5.209000e+001 -2.829163e-001 -3.927493e+000 2.983705e-003 - 5.210000e+001 -2.823942e-001 -3.928247e+000 2.984534e-003 - 5.211000e+001 -2.807298e-001 -3.929001e+000 2.985870e-003 - 5.212000e+001 -2.778526e-001 -3.929755e+000 2.987401e-003 - 5.213000e+001 -2.736898e-001 -3.930509e+000 2.988773e-003 - 5.214000e+001 -2.681699e-001 -3.931263e+000 2.989669e-003 - 5.215000e+001 -2.612269e-001 -3.932017e+000 2.989887e-003 - 5.216000e+001 -2.528054e-001 -3.932771e+000 2.989381e-003 - 5.217000e+001 -2.428651e-001 -3.933525e+000 2.988273e-003 - 5.218000e+001 -2.313853e-001 -3.934279e+000 2.986825e-003 - 5.219000e+001 -2.183687e-001 -3.935033e+000 2.985374e-003 - 5.220000e+001 -2.038446e-001 -3.935787e+000 2.984258e-003 - 5.221000e+001 -1.878710e-001 -3.936541e+000 2.983737e-003 - 5.222000e+001 -1.705350e-001 -3.937295e+000 2.983929e-003 - 5.223000e+001 -1.519531e-001 -3.938049e+000 2.984787e-003 - 5.224000e+001 -1.322689e-001 -3.938803e+000 2.986108e-003 - 5.225000e+001 -1.116501e-001 -3.939557e+000 2.987580e-003 - 5.226000e+001 -9.028478e-002 -3.940311e+000 2.988860e-003 - 5.227000e+001 -6.837576e-002 -3.941065e+000 2.989647e-003 - 5.228000e+001 -4.613526e-002 -3.941819e+000 2.989759e-003 - 5.229000e+001 -2.377856e-002 -3.942573e+000 2.989169e-003 - 5.230000e+001 -1.517767e-003 -3.943327e+000 2.988014e-003 - 5.231000e+001 2.044425e-002 -3.944081e+000 2.986564e-003 - 5.232000e+001 4.191933e-002 -3.944835e+000 2.985157e-003 - 5.233000e+001 6.273875e-002 -3.945589e+000 2.984122e-003 - 5.234000e+001 8.275686e-002 -3.946343e+000 2.983705e-003 - 5.235000e+001 1.018536e-001 -3.947097e+000 2.984004e-003 - 5.236000e+001 1.199356e-001 -3.947851e+000 2.984953e-003 - 5.237000e+001 1.369359e-001 -3.948605e+000 2.986331e-003 - 5.238000e+001 1.528130e-001 -3.949359e+000 2.987820e-003 - 5.239000e+001 1.675475e-001 -3.950113e+000 2.989072e-003 - 5.240000e+001 1.811392e-001 -3.950867e+000 2.989796e-003 - 5.241000e+001 1.936021e-001 -3.951621e+000 2.989821e-003 - 5.242000e+001 2.049605e-001 -3.952375e+000 2.989137e-003 - 5.243000e+001 2.152434e-001 -3.953129e+000 2.987898e-003 - 5.244000e+001 2.244797e-001 -3.953883e+000 2.986390e-003 - 5.245000e+001 2.326944e-001 -3.954637e+000 2.984960e-003 - 5.246000e+001 2.399043e-001 -3.955391e+000 2.983939e-003 - 5.247000e+001 2.461158e-001 -3.956145e+000 2.983567e-003 - 5.248000e+001 2.513225e-001 -3.956899e+000 2.983932e-003 - 5.249000e+001 2.555052e-001 -3.957653e+000 2.984954e-003 - 5.250000e+001 2.586323e-001 -3.958407e+000 2.986400e-003 - 5.251000e+001 2.606611e-001 -3.959161e+000 2.987937e-003 - 5.252000e+001 2.615407e-001 -3.959915e+000 2.989213e-003 - 5.253000e+001 2.612153e-001 -3.960669e+000 2.989933e-003 - 5.254000e+001 2.596279e-001 -3.961423e+000 2.989930e-003 - 5.255000e+001 2.567248e-001 -3.962177e+000 2.989202e-003 - 5.256000e+001 2.524595e-001 -3.962931e+000 2.987915e-003 - 5.257000e+001 2.467970e-001 -3.963685e+000 2.986361e-003 - 5.258000e+001 2.397168e-001 -3.964439e+000 2.984897e-003 - 5.259000e+001 2.312159e-001 -3.965193e+000 2.983859e-003 - 5.260000e+001 2.213109e-001 -3.965947e+000 2.983485e-003 - 5.261000e+001 2.100381e-001 -3.966700e+000 2.983864e-003 - 5.262000e+001 1.974543e-001 -3.967454e+000 2.984907e-003 - 5.263000e+001 1.836349e-001 -3.968208e+000 2.986378e-003 - 5.264000e+001 1.686722e-001 -3.968962e+000 2.987938e-003 - 5.265000e+001 1.526726e-001 -3.969716e+000 2.989230e-003 - 5.266000e+001 1.357529e-001 -3.970470e+000 2.989960e-003 - 5.267000e+001 1.180373e-001 -3.971224e+000 2.989962e-003 - 5.268000e+001 9.965280e-002 -3.971978e+000 2.989236e-003 - 5.269000e+001 8.072641e-002 -3.972732e+000 2.987949e-003 - 5.270000e+001 6.138159e-002 -3.973486e+000 2.986397e-003 - 5.271000e+001 4.173596e-002 -3.974240e+000 2.984935e-003 - 5.272000e+001 2.189951e-002 -3.974994e+000 2.983899e-003 - 5.273000e+001 1.973930e-003 -3.975748e+000 2.983526e-003 - 5.274000e+001 -1.794731e-002 -3.976502e+000 2.983899e-003 - 5.275000e+001 -3.777782e-002 -3.977256e+000 2.984931e-003 - 5.276000e+001 -5.743648e-002 -3.978010e+000 2.986383e-003 - 5.277000e+001 -7.684481e-002 -3.978764e+000 2.987918e-003 - 5.278000e+001 -9.592412e-002 -3.979518e+000 2.989184e-003 - 5.279000e+001 -1.145923e-001 -3.980272e+000 2.989891e-003 - 5.280000e+001 -1.327608e-001 -3.981026e+000 2.989880e-003 - 5.281000e+001 -1.503319e-001 -3.981780e+000 2.989154e-003 - 5.282000e+001 -1.671971e-001 -3.982534e+000 2.987884e-003 - 5.283000e+001 -1.832354e-001 -3.983288e+000 2.986362e-003 - 5.284000e+001 -1.983139e-001 -3.984042e+000 2.984942e-003 - 5.285000e+001 -2.122888e-001 -3.984796e+000 2.983950e-003 - 5.286000e+001 -2.250076e-001 -3.985550e+000 2.983614e-003 - 5.287000e+001 -2.363134e-001 -3.986304e+000 2.984012e-003 - 5.288000e+001 -2.460491e-001 -3.987058e+000 2.985047e-003 - 5.289000e+001 -2.540637e-001 -3.987812e+000 2.986480e-003 - 5.290000e+001 -2.602182e-001 -3.988566e+000 2.987977e-003 - 5.291000e+001 -2.643928e-001 -3.989320e+000 2.989192e-003 - 5.292000e+001 -2.664934e-001 -3.990074e+000 2.989845e-003 - 5.293000e+001 -2.664577e-001 -3.990828e+000 2.989787e-003 - 5.294000e+001 -2.642611e-001 -3.991582e+000 2.989031e-003 - 5.295000e+001 -2.599209e-001 -3.992336e+000 2.987754e-003 - 5.296000e+001 -2.534991e-001 -3.993090e+000 2.986251e-003 - 5.297000e+001 -2.451033e-001 -3.993844e+000 2.984871e-003 - 5.298000e+001 -2.348865e-001 -3.994598e+000 2.983934e-003 - 5.299000e+001 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2.986697e-003 - 5.316000e+001 -1.538153e-002 -4.008170e+000 2.988172e-003 - 5.317000e+001 -1.077370e-002 -4.008923e+000 2.989325e-003 - 5.318000e+001 -6.687857e-003 -4.009677e+000 2.989888e-003 - 5.319000e+001 -2.935294e-003 -4.010431e+000 2.989734e-003 - 5.320000e+001 6.659543e-004 -4.011185e+000 2.988897e-003 - 5.321000e+001 4.281236e-003 -4.011939e+000 2.987569e-003 - 5.322000e+001 8.050523e-003 -4.012693e+000 2.986057e-003 - 5.323000e+001 1.208120e-002 -4.013447e+000 2.984710e-003 - 5.324000e+001 1.644276e-002 -4.014201e+000 2.983837e-003 - 5.325000e+001 2.116364e-002 -4.014955e+000 2.983642e-003 - 5.326000e+001 2.623037e-002 -4.015709e+000 2.984169e-003 - 5.327000e+001 3.158907e-002 -4.016463e+000 2.985295e-003 - 5.328000e+001 3.714912e-002 -4.017217e+000 2.986761e-003 - 5.329000e+001 4.278882e-002 -4.017971e+000 2.988228e-003 - 5.330000e+001 4.836279e-002 -4.018725e+000 2.989358e-003 - 5.331000e+001 5.371055e-002 -4.019479e+000 2.989891e-003 - 5.332000e+001 5.866593e-002 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3.219267e-002 -4.033051e+000 2.984644e-003 - 5.350000e+001 2.892246e-002 -4.033805e+000 2.983846e-003 - 5.351000e+001 2.627767e-002 -4.034559e+000 2.983729e-003 - 5.352000e+001 2.429185e-002 -4.035313e+000 2.984317e-003 - 5.353000e+001 2.296103e-002 -4.036067e+000 2.985474e-003 - 5.354000e+001 2.224531e-002 -4.036821e+000 2.986930e-003 - 5.355000e+001 2.207241e-002 -4.037575e+000 2.988348e-003 - 5.356000e+001 2.234295e-002 -4.038329e+000 2.989400e-003 - 5.357000e+001 2.293711e-002 -4.039083e+000 2.989842e-003 - 5.358000e+001 2.372234e-002 -4.039837e+000 2.989573e-003 - 5.359000e+001 2.456157e-002 -4.040591e+000 2.988655e-003 - 5.360000e+001 2.532159e-002 -4.041345e+000 2.987301e-003 - 5.361000e+001 2.588110e-002 -4.042099e+000 2.985825e-003 - 5.362000e+001 2.613786e-002 -4.042853e+000 2.984569e-003 - 5.363000e+001 2.601471e-002 -4.043607e+000 2.983826e-003 - 5.364000e+001 2.546407e-002 -4.044361e+000 2.983767e-003 - 5.365000e+001 2.447069e-002 -4.045115e+000 2.984408e-003 - 5.366000e+001 2.305243e-002 -4.045869e+000 2.985599e-003 - 5.367000e+001 2.125922e-002 -4.046623e+000 2.987065e-003 - 5.368000e+001 1.917010e-002 -4.047377e+000 2.988465e-003 - 5.369000e+001 1.688861e-002 -4.048131e+000 2.989475e-003 - 5.370000e+001 1.453674e-002 -4.048885e+000 2.989860e-003 - 5.371000e+001 1.224787e-002 -4.049639e+000 2.989531e-003 - 5.372000e+001 1.015898e-002 -4.050393e+000 2.988561e-003 - 5.373000e+001 8.402674e-003 -4.051147e+000 2.987175e-003 - 5.374000e+001 7.099318e-003 -4.051900e+000 2.985692e-003 - 5.375000e+001 6.349877e-003 -4.052654e+000 2.984456e-003 - 5.376000e+001 6.229709e-003 -4.053408e+000 2.983755e-003 - 5.377000e+001 6.783694e-003 -4.054162e+000 2.983752e-003 - 5.378000e+001 8.022947e-003 -4.054916e+000 2.984450e-003 - 5.379000e+001 9.923265e-003 -4.055670e+000 2.985690e-003 - 5.380000e+001 1.242540e-002 -4.056424e+000 2.987185e-003 - 5.381000e+001 1.543709e-002 -4.057178e+000 2.988591e-003 - 5.382000e+001 1.883680e-002 -4.057932e+000 2.989582e-003 - 5.383000e+001 2.247888e-002 -4.058686e+000 2.989928e-003 - 5.384000e+001 2.619992e-002 -4.059440e+000 2.989548e-003 - 5.385000e+001 2.982597e-002 -4.060194e+000 2.988527e-003 - 5.386000e+001 3.318021e-002 -4.060948e+000 2.987099e-003 - 5.387000e+001 3.609077e-002 -4.061702e+000 2.985590e-003 - 5.388000e+001 3.839819e-002 -4.062456e+000 2.984349e-003 - 5.389000e+001 3.996231e-002 -4.063210e+000 2.983662e-003 - 5.390000e+001 4.066817e-002 -4.063964e+000 2.983689e-003 - 5.391000e+001 4.043077e-002 -4.064718e+000 2.984426e-003 - 5.392000e+001 3.919833e-002 -4.065472e+000 2.985704e-003 - 5.393000e+001 3.695421e-002 -4.066226e+000 2.987229e-003 - 5.394000e+001 3.371717e-002 -4.066980e+000 2.988653e-003 - 5.395000e+001 2.954026e-002 -4.067734e+000 2.989647e-003 - 5.396000e+001 2.450832e-002 -4.068488e+000 2.989983e-003 - 5.397000e+001 1.873432e-002 -4.069242e+000 2.989585e-003 - 5.398000e+001 1.235480e-002 -4.069996e+000 2.988541e-003 - 5.399000e+001 5.524565e-003 -4.070750e+000 2.987091e-003 - 5.400000e+001 -1.588934e-003 -4.071504e+000 2.985567e-003 - 5.401000e+001 -8.811368e-003 -4.072258e+000 2.984318e-003 - 5.402000e+001 -1.596714e-002 -4.073012e+000 2.983631e-003 - 5.403000e+001 -2.288463e-002 -4.073766e+000 2.983664e-003 - 5.404000e+001 -2.940079e-002 -4.074520e+000 2.984410e-003 - 5.405000e+001 -3.536512e-002 -4.075274e+000 2.985695e-003 - 5.406000e+001 -4.064275e-002 -4.076028e+000 2.987226e-003 - 5.407000e+001 -4.511669e-002 -4.076782e+000 2.988650e-003 - 5.408000e+001 -4.868925e-002 -4.077536e+000 2.989642e-003 - 5.409000e+001 -5.128273e-002 -4.078290e+000 2.989975e-003 - 5.410000e+001 -5.283934e-002 -4.079044e+000 2.989574e-003 - 5.411000e+001 -5.332072e-002 -4.079798e+000 2.988532e-003 - 5.412000e+001 -5.270693e-002 -4.080552e+000 2.987089e-003 - 5.413000e+001 -5.099526e-002 -4.081306e+000 2.985575e-003 - 5.414000e+001 -4.819895e-002 -4.082060e+000 2.984338e-003 - 5.415000e+001 -4.434586e-002 -4.082814e+000 2.983662e-003 - 5.416000e+001 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5.433000e+001 1.106527e-001 -4.096385e+000 2.988615e-003 - 5.434000e+001 1.168494e-001 -4.097139e+000 2.989535e-003 - 5.435000e+001 1.221396e-001 -4.097893e+000 2.989813e-003 - 5.436000e+001 1.265037e-001 -4.098647e+000 2.989388e-003 - 5.437000e+001 1.299471e-001 -4.099401e+000 2.988360e-003 - 5.438000e+001 1.325002e-001 -4.100155e+000 2.986970e-003 - 5.439000e+001 1.342171e-001 -4.100909e+000 2.985540e-003 - 5.440000e+001 1.351733e-001 -4.101663e+000 2.984402e-003 - 5.441000e+001 1.354627e-001 -4.102417e+000 2.983817e-003 - 5.442000e+001 1.351927e-001 -4.103171e+000 2.983921e-003 - 5.443000e+001 1.344798e-001 -4.103925e+000 2.984686e-003 - 5.444000e+001 1.334434e-001 -4.104679e+000 2.985933e-003 - 5.445000e+001 1.322004e-001 -4.105433e+000 2.987371e-003 - 5.446000e+001 1.308592e-001 -4.106187e+000 2.988665e-003 - 5.447000e+001 1.295137e-001 -4.106941e+000 2.989516e-003 - 5.448000e+001 1.282390e-001 -4.107695e+000 2.989728e-003 - 5.449000e+001 1.270867e-001 -4.108449e+000 2.989253e-003 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2.984266e-003 - 5.467000e+001 6.709781e-002 -4.122021e+000 2.983820e-003 - 5.468000e+001 5.774379e-002 -4.122775e+000 2.984062e-003 - 5.469000e+001 4.797052e-002 -4.123529e+000 2.984936e-003 - 5.470000e+001 3.792838e-002 -4.124283e+000 2.986240e-003 - 5.471000e+001 2.777312e-002 -4.125037e+000 2.987671e-003 - 5.472000e+001 1.765817e-002 -4.125791e+000 2.988897e-003 - 5.473000e+001 7.727103e-003 -4.126545e+000 2.989634e-003 - 5.474000e+001 -1.893423e-003 -4.127299e+000 2.989708e-003 - 5.475000e+001 -1.109968e-002 -4.128053e+000 2.989102e-003 - 5.476000e+001 -1.981563e-002 -4.128807e+000 2.987954e-003 - 5.477000e+001 -2.799598e-002 -4.129561e+000 2.986529e-003 - 5.478000e+001 -3.562751e-002 -4.130315e+000 2.985156e-003 - 5.479000e+001 -4.272837e-002 -4.131069e+000 2.984154e-003 - 5.480000e+001 -4.934552e-002 -4.131823e+000 2.983757e-003 - 5.481000e+001 -5.555035e-002 -4.132577e+000 2.984058e-003 - 5.482000e+001 -6.143272e-002 -4.133331e+000 2.984990e-003 - 5.483000e+001 -6.709375e-002 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1.992514e-002 -4.234364e+000 2.989680e-003 - 5.617000e+001 2.017790e-002 -4.235118e+000 2.989381e-003 - 5.618000e+001 2.017602e-002 -4.235872e+000 2.988478e-003 - 5.619000e+001 1.971768e-002 -4.236626e+000 2.987179e-003 - 5.620000e+001 1.863633e-002 -4.237380e+000 2.985783e-003 - 5.621000e+001 1.681048e-002 -4.238134e+000 2.984614e-003 - 5.622000e+001 1.417099e-002 -4.238888e+000 2.983942e-003 - 5.623000e+001 1.070535e-002 -4.239642e+000 2.983924e-003 - 5.624000e+001 6.458741e-003 -4.240396e+000 2.984566e-003 - 5.625000e+001 1.531875e-003 -4.241150e+000 2.985718e-003 - 5.626000e+001 -3.924399e-003 -4.241904e+000 2.987115e-003 - 5.627000e+001 -9.717265e-003 -4.242658e+000 2.988434e-003 - 5.628000e+001 -1.562254e-002 -4.243412e+000 2.989370e-003 - 5.629000e+001 -2.139703e-002 -4.244166e+000 2.989706e-003 - 5.630000e+001 -2.679209e-002 -4.244920e+000 2.989365e-003 - 5.631000e+001 -3.156741e-002 -4.245674e+000 2.988425e-003 - 5.632000e+001 -3.550447e-002 -4.246428e+000 2.987101e-003 - 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2.983920e-003 - 5.650000e+001 2.119137e-002 -4.260000e+000 2.984637e-003 - 5.651000e+001 2.200380e-002 -4.260754e+000 2.985848e-003 - 5.652000e+001 2.208394e-002 -4.261508e+000 2.987273e-003 - 5.653000e+001 2.159236e-002 -4.262262e+000 2.988585e-003 - 5.654000e+001 2.072651e-002 -4.263016e+000 2.989480e-003 - 5.655000e+001 1.970877e-002 -4.263769e+000 2.989754e-003 - 5.656000e+001 1.877277e-002 -4.264523e+000 2.989342e-003 - 5.657000e+001 1.814911e-002 -4.265277e+000 2.988339e-003 - 5.658000e+001 1.805096e-002 -4.266031e+000 2.986975e-003 - 5.659000e+001 1.866051e-002 -4.266785e+000 2.985565e-003 - 5.660000e+001 2.011700e-002 -4.267539e+000 2.984433e-003 - 5.661000e+001 2.250698e-002 -4.268293e+000 2.983841e-003 - 5.662000e+001 2.585737e-002 -4.269047e+000 2.983924e-003 - 5.663000e+001 3.013173e-002 -4.269801e+000 2.984665e-003 - 5.664000e+001 3.522995e-002 -4.270555e+000 2.985890e-003 - 5.665000e+001 4.099151e-002 -4.271309e+000 2.987319e-003 - 5.666000e+001 4.720195e-002 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3.734364e-003 -4.284881e+000 2.988228e-003 - 5.684000e+001 -8.766071e-003 -4.285635e+000 2.986854e-003 - 5.685000e+001 -2.091821e-002 -4.286389e+000 2.985462e-003 - 5.686000e+001 -3.239439e-002 -4.287143e+000 2.984373e-003 - 5.687000e+001 -4.290206e-002 -4.287897e+000 2.983838e-003 - 5.688000e+001 -5.219541e-002 -4.288651e+000 2.983980e-003 - 5.689000e+001 -6.008447e-002 -4.289405e+000 2.984765e-003 - 5.690000e+001 -6.644139e-002 -4.290159e+000 2.986013e-003 - 5.691000e+001 -7.120349e-002 -4.290913e+000 2.987434e-003 - 5.692000e+001 -7.437315e-002 -4.291667e+000 2.988700e-003 - 5.693000e+001 -7.601452e-002 -4.292421e+000 2.989521e-003 - 5.694000e+001 -7.624743e-002 -4.293175e+000 2.989708e-003 - 5.695000e+001 -7.523884e-002 -4.293929e+000 2.989219e-003 - 5.696000e+001 -7.319236e-002 -4.294683e+000 2.988168e-003 - 5.697000e+001 -7.033643e-002 -4.295437e+000 2.986797e-003 - 5.698000e+001 -6.691190e-002 -4.296191e+000 2.985423e-003 - 5.699000e+001 -6.315966e-002 -4.296945e+000 2.984362e-003 - 5.700000e+001 -5.930894e-002 -4.297699e+000 2.983861e-003 - 5.701000e+001 -5.556691e-002 -4.298453e+000 2.984033e-003 - 5.702000e+001 -5.211011e-002 -4.299207e+000 2.984837e-003 - 5.703000e+001 -4.907804e-002 -4.299961e+000 2.986088e-003 - 5.704000e+001 -4.656926e-002 -4.300715e+000 2.987494e-003 - 5.705000e+001 -4.463997e-002 -4.301469e+000 2.988730e-003 - 5.706000e+001 -4.330515e-002 -4.302223e+000 2.989512e-003 - 5.707000e+001 -4.254200e-002 -4.302977e+000 2.989660e-003 - 5.708000e+001 -4.229535e-002 -4.303731e+000 2.989140e-003 - 5.709000e+001 -4.248472e-002 -4.304485e+000 2.988072e-003 - 5.710000e+001 -4.301235e-002 -4.305239e+000 2.986705e-003 - 5.711000e+001 -4.377177e-002 -4.305992e+000 2.985353e-003 - 5.712000e+001 -4.465639e-002 -4.306746e+000 2.984330e-003 - 5.713000e+001 -4.556735e-002 -4.307500e+000 2.983873e-003 - 5.714000e+001 -4.642037e-002 -4.308254e+000 2.984087e-003 - 5.715000e+001 -4.715106e-002 -4.309008e+000 2.984923e-003 - 5.716000e+001 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2.989550e-003 - 5.733000e+001 -5.517111e-002 -4.322580e+000 2.989618e-003 - 5.734000e+001 -5.482565e-002 -4.323334e+000 2.989028e-003 - 5.735000e+001 -5.376988e-002 -4.324088e+000 2.987919e-003 - 5.736000e+001 -5.187383e-002 -4.324842e+000 2.986546e-003 - 5.737000e+001 -4.903183e-002 -4.325596e+000 2.985227e-003 - 5.738000e+001 -4.517049e-002 -4.326350e+000 2.984268e-003 - 5.739000e+001 -4.025535e-002 -4.327104e+000 2.983889e-003 - 5.740000e+001 -3.429558e-002 -4.327858e+000 2.984179e-003 - 5.741000e+001 -2.734655e-002 -4.328612e+000 2.985069e-003 - 5.742000e+001 -1.950988e-002 -4.329366e+000 2.986352e-003 - 5.743000e+001 -1.093107e-002 -4.330120e+000 2.987731e-003 - 5.744000e+001 -1.794583e-003 -4.330874e+000 2.988887e-003 - 5.745000e+001 7.683312e-003 -4.331628e+000 2.989552e-003 - 5.746000e+001 1.726365e-002 -4.332382e+000 2.989572e-003 - 5.747000e+001 2.669538e-002 -4.333136e+000 2.988944e-003 - 5.748000e+001 3.572697e-002 -4.333890e+000 2.987813e-003 - 5.749000e+001 4.411833e-002 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5.374917e-002 -4.347462e+000 2.984261e-003 - 5.767000e+001 5.486226e-002 -4.348216e+000 2.985224e-003 - 5.768000e+001 5.710481e-002 -4.348969e+000 2.986547e-003 - 5.769000e+001 6.046664e-002 -4.349723e+000 2.987922e-003 - 5.770000e+001 6.487949e-002 -4.350477e+000 2.989033e-003 - 5.771000e+001 7.022062e-002 -4.351231e+000 2.989623e-003 - 5.772000e+001 7.631914e-002 -4.351985e+000 2.989556e-003 - 5.773000e+001 8.296459e-002 -4.352739e+000 2.988846e-003 - 5.774000e+001 8.991742e-002 -4.353493e+000 2.987657e-003 - 5.775000e+001 9.692077e-002 -4.354247e+000 2.986264e-003 - 5.776000e+001 1.037129e-001 -4.355001e+000 2.984989e-003 - 5.777000e+001 1.100398e-001 -4.355755e+000 2.984125e-003 - 5.778000e+001 1.156666e-001 -4.356509e+000 2.983875e-003 - 5.779000e+001 1.203891e-001 -4.357263e+000 2.984296e-003 - 5.780000e+001 1.240418e-001 -4.358017e+000 2.985291e-003 - 5.781000e+001 1.265051e-001 -4.358771e+000 2.986630e-003 - 5.782000e+001 1.277096e-001 -4.359525e+000 2.988003e-003 - 5.783000e+001 1.276374e-001 -4.360279e+000 2.989093e-003 - 5.784000e+001 1.263215e-001 -4.361033e+000 2.989648e-003 - 5.785000e+001 1.238417e-001 -4.361787e+000 2.989540e-003 - 5.786000e+001 1.203190e-001 -4.362541e+000 2.988792e-003 - 5.787000e+001 1.159076e-001 -4.363295e+000 2.987577e-003 - 5.788000e+001 1.107855e-001 -4.364049e+000 2.986175e-003 - 5.789000e+001 1.051442e-001 -4.364803e+000 2.984909e-003 - 5.790000e+001 9.917808e-002 -4.365557e+000 2.984073e-003 - 5.791000e+001 9.307404e-002 -4.366311e+000 2.983860e-003 - 5.792000e+001 8.700176e-002 -4.367065e+000 2.984320e-003 - 5.793000e+001 8.110545e-002 -4.367819e+000 2.985349e-003 - 5.794000e+001 7.549725e-002 -4.368573e+000 2.986707e-003 - 5.795000e+001 7.025264e-002 -4.369327e+000 2.988081e-003 - 5.796000e+001 6.540825e-002 -4.370081e+000 2.989155e-003 - 5.797000e+001 6.096182e-002 -4.370835e+000 2.989680e-003 - 5.798000e+001 5.687459e-002 -4.371589e+000 2.989535e-003 - 5.799000e+001 5.307564e-002 -4.372343e+000 2.988753e-003 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2.984000e-003 - 5.817000e+001 -5.141627e-002 -4.385915e+000 2.983849e-003 - 5.818000e+001 -5.746128e-002 -4.386669e+000 2.984373e-003 - 5.819000e+001 -6.276187e-002 -4.387423e+000 2.985451e-003 - 5.820000e+001 -6.723545e-002 -4.388177e+000 2.986833e-003 - 5.821000e+001 -7.083249e-002 -4.388931e+000 2.988201e-003 - 5.822000e+001 -7.353866e-002 -4.389685e+000 2.989239e-003 - 5.823000e+001 -7.537515e-002 -4.390439e+000 2.989707e-003 - 5.824000e+001 -7.639717e-002 -4.391192e+000 2.989499e-003 - 5.825000e+001 -7.669054e-002 -4.391946e+000 2.988661e-003 - 5.826000e+001 -7.636687e-002 -4.392700e+000 2.987386e-003 - 5.827000e+001 -7.555744e-002 -4.393454e+000 2.985968e-003 - 5.828000e+001 -7.440611e-002 -4.394208e+000 2.984735e-003 - 5.829000e+001 -7.306184e-002 -4.394962e+000 2.983971e-003 - 5.830000e+001 -7.167104e-002 -4.395716e+000 2.983854e-003 - 5.831000e+001 -7.037029e-002 -4.396470e+000 2.984411e-003 - 5.832000e+001 -6.927975e-002 -4.397224e+000 2.985513e-003 - 5.833000e+001 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2.989739e-003 - 5.850000e+001 -8.305902e-002 -4.410796e+000 2.989470e-003 - 5.851000e+001 -8.162980e-002 -4.411550e+000 2.988579e-003 - 5.852000e+001 -7.974466e-002 -4.412304e+000 2.987273e-003 - 5.853000e+001 -7.745109e-002 -4.413058e+000 2.985852e-003 - 5.854000e+001 -7.480636e-002 -4.413812e+000 2.984643e-003 - 5.855000e+001 -7.187339e-002 -4.414566e+000 2.983927e-003 - 5.856000e+001 -6.871651e-002 -4.415320e+000 2.983867e-003 - 5.857000e+001 -6.539754e-002 -4.416074e+000 2.984479e-003 - 5.858000e+001 -6.197229e-002 -4.416828e+000 2.985620e-003 - 5.859000e+001 -5.848788e-002 -4.417582e+000 2.987027e-003 - 5.860000e+001 -5.498077e-002 -4.418336e+000 2.988376e-003 - 5.861000e+001 -5.147590e-002 -4.419090e+000 2.989356e-003 - 5.862000e+001 -4.798662e-002 -4.419844e+000 2.989741e-003 - 5.863000e+001 -4.451575e-002 -4.420598e+000 2.989443e-003 - 5.864000e+001 -4.105728e-002 -4.421352e+000 2.988530e-003 - 5.865000e+001 -3.759885e-002 -4.422106e+000 2.987213e-003 - 5.866000e+001 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L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of fitting the Debye model to experimental Debye-Waller -factors. - -In this example, we build a fit recipe that uses an external function that can -simulate a atomic displacement parameters using the Debye model. This serves as -an example of how to utilize python functions in a fit and extend them with -SrFit without writing additional code. This example also demonstrates guide a -refinement with restraints. - -Instructions - -Run the example and then read the 'makeRecipe' code to see how to use a python -function as a profile generator. - -Extensions - -- Don't hardcode the mass of lead in the fitting equation. Turn it into a - Parameter and refine it. There are two ways to do this. Try to figure out - both. -""" - -import numpy -from gaussianrecipe import scipyOptimize - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) - -# The data -data = """\ -015.0 0.00334 0.00013 -050.0 0.00508 0.00022 -100.0 0.00830 0.00040 -150.0 0.01252 0.00071 -200.0 0.01792 0.00100 -250.0 0.02304 0.00120 -300.0 0.02737 0.00140 -350.0 0.03085 0.00160 -400.0 0.03484 0.00190 -450.0 0.03774 0.00220 -500.0 0.03946 0.00250 -""" - -###### -# Example Code - - -def makeRecipe(): - """Make the recipe for the fit. - - The instructions for what we want to refine, and how to refine it - will be defined within a FitRecipe instance. The job of a FitRecipe - is to collect and associate all the data, the fitting equations, - fitting variables, constraints and restrations. We will demonstrate - each of these within the code. - - Data is held within a Profile object. The Profile is simply a - container that holds the data, and the theoretical profile once it - has been calculated. - - Data is associated with a fitting equation within a FitContribution. - The FitContribution defines the equation and parameters that will be - adjusted to fit the data. The fitting equation can be defined within - a function or optionally within the ProfileGenerator class. We won't - need the ProfileGenerator class in this example since the signature - of the fitting equation (the 'debye' function defined below) is so - simple. The FitContribution also defines the residual function to - optimize for the data/equation pair. This can be modified, but we - won't do that here. - """ - - # The Profile - # Create a Profile to hold the experimental and calculated signal. - profile = Profile() - - # Load data and add it to the profile. It is our responsibility to get our - # data into the profile. - xydy = numpy.array(data.split(), dtype=float).reshape(-1, 3) - x, y, dy = xydy.T - profile.setObservedProfile(x, y, dy) - - # The FitContribution - # The FitContribution associates the profile with the Debye function. - contribution = FitContribution("pb") - # Tell the contribution about the Profile. We will need to use the - # independent variable (the temperature) from the data to calculate the - # theoretical signal, so give it an informative name ('T') that we can use - # later. - contribution.setProfile(profile, xname="T") - - # We now need to create the fitting equation. We tell the FitContribution - # to use the 'debye' function defined below. The 'registerFunction' method - # will let us do this. Since we haven't told it otherwise, - # 'registerFunction' will extract the name of the function ('debye') and - # the names of the arguments ('T', 'm', 'thetaD'). These arguments will - # become Parameters of the FitContribution. Since we named the x-variable - # 'T' above, the 'T' in the 'debye' equation will refer to this x-variable - # whenever it is used. - contribution.registerFunction(debye) - - # Now we can create the fitting equation. We want to extend the 'debye' - # equation by adding a vertical offset. We could wrap 'debye' in a new - # function with an offset, and register that instead of 'debye', but what - # we do here is easier. - # - # When we set the fitting equation, we do not need to specify the - # Parameters to the 'debye' function since the FitContribution already - # knows what they are. If we choose to specify the arguments, we can make - # adjustments to their input values. We wish to have the thetaD value in - # the debye equation to be positive, so we specify the input as abs(thetaD) - # in the equation below. Furthermore, we know 'm', the mass of lead, so we - # can specify that as well. - contribution.setEquation("debye(T, 207.2, abs(thetaD)) + offset") - - # The FitRecipe - # The FitRecipe lets us define what we want to fit. It is where we can - # create variables, constraints and restraints. If we had multiple profiles - # to fit simultaneously, the contribution from each could be added to the - # recipe. - recipe = FitRecipe() - recipe.addContribution(contribution) - - # Specify which Parameters we want to refine. - - # Vary the offset - recipe.addVar(contribution.offset, 0) - # We also vary the Debye temperature. - recipe.addVar(contribution.thetaD, 100) - - # We would like to 'suggest' that the offset should remain positive. This - # is somethine that we know about the system that might help the refinement - # converge to a physically reasonable result. We will do this with a soft - # constraint, or restraint. Here we restrain the offset variable to between - # 0 and infinity. We tell the recipe that we want to scale the penalty for - # breaking the restraint by the point-average chi^2 value so that the - # restraint is roughly as significant as any other data point throughout - # the fit. - recipe.restrain(recipe.offset, lb=0, scaled=True) - - # We're done setting up the recipe. We can now do other things with it. - return recipe - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # Plot this. - # Note that since the contribution was given the name "pb", it is - # accessible from the recipe with this name. This is a useful way to - # organize multiple contributions to a fit. - T = recipe.pb.profile.x - U = recipe.pb.profile.y - Ucalc = recipe.pb.profile.ycalc - - import pylab - - pylab.plot(T, U, "o", label="Pb $U_{iso}$ Data") - pylab.plot(T, Ucalc) - pylab.xlabel("T (K)") - pylab.ylabel(r"$U_{iso} (\AA^2)$") - pylab.legend(loc=(0.0, 0.8)) - - pylab.show() - return - - -def main(): - """The workflow of creating, running and inspecting a fit.""" - - # Create the recipe - recipe = makeRecipe() - - # Refine using the optimizer of your choice - scipyOptimize(recipe) - - # Get the results. - res = FitResults(recipe) - - # Print the results - res.printResults() - - # Plot the results - plotResults(recipe) - - return - - -# Functions required for calculation of Debye curve. Feel free to skip these, -# as we treat them as if existing in some external library that we cannot -# modify. - - -def debye(T, m, thetaD): - """A wrapped version of 'adps' that can handle an array of - T-values.""" - y = numpy.array([adps(m, thetaD, x) for x in T]) - return y - - -def adps(m, thetaD, T): - """Calculates atomic displacement factors within the Debye model. - - = (3h^2/4 pi^2 m kB thetaD)(phi(thetaD/T)/(ThetaD/T) + 1/4) - - arguments: - m -- float -- mass of the ion in atomic mass units (e.g., C = 12) - thetaD -- float -- Debye Temperature - T -- float -- temperature. - - return: - Uiso -- float -- the thermal factor from the Debye recipe at temp T - """ - h = 6.6260755e-34 # Planck's constant. J.s of m^2.kg/s - kB = 1.3806503e-23 # Boltzmann's constant. J/K - amu = 1.66053886e-27 # Atomic mass unit. kg - - def __phi(x): - """Evaluates the phi integral needed in Debye calculation. - - phi(x) = (1/x) int_0^x xi/(exp(xi)-1) dxi - - arguments: - x -- float -- value of thetaD (Debye temperature)/T - - returns: - phi -- float -- value of the phi function - """ - - def __debyeKernel(xi): - """Function needed by debye calculators.""" - y = xi / (numpy.exp(xi) - 1) - return y - - import scipy.integrate - - int = scipy.integrate.quad(__debyeKernel, 0, x) - phi = (1 / x) * int[0] - - return phi - - m = m * amu - u2 = (3 * h**2 / (4 * numpy.pi**2 * m * kB * thetaD)) * ( - __phi(thetaD / T) / (thetaD / T) + 1.0 / 4.0 - ) - - return u2 * 1e20 - - -if __name__ == "__main__": - - main() - -# End of file diff --git a/docs/examples/srfit_ex/debyemodelII.py b/docs/examples/srfit_ex/debyemodelII.py deleted file mode 100644 index 0aace44..0000000 --- a/docs/examples/srfit_ex/debyemodelII.py +++ /dev/null @@ -1,162 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of fitting the Debye recipe to experimental Debye-Waller -factors. - -This is an extension of example in debyemodel.py. The recipe we create will -simultaneously fit the low and high temperature parts of the experimental data -with the same Debye temperature, but different offsets. This example also -introduces constraints. - -Instructions - -Run the example and then read through the 'makeRecipeII' code to learn about -multi-profile recipes. You will learn how to constrain related information -between the fit contributions. - -Extensions - -- Play with the fit ranges and see if you can improve the fit. -- The Debye temperature parameters from the two contributions can be - constrained without creating a new variable. Try to figure out how that is - done. -""" - -from debyemodel import makeRecipe, scipyOptimize - -from diffpy.srfit.fitbase import FitRecipe, FitResults - -###### -# Example Code - - -def makeRecipeII(): - """Make a recipe for fitting low and high temperature regions. - - We will fit the low and high temperature parts of Debye curve - simultaneously with the same Debye temperature, but different - offsets. - - We will make two FitRecipes using the makeRecipe function from - debyemodel.py and extract the configured FitContribution from each. - We will use different fitting ranges for each FitContribution and - constrain the Debye temperature in each FitContribution to be the - same. - """ - - # We'll throw these away. We just want the FitContributions that are - # configured within the recipes. - m1 = makeRecipe() - m2 = makeRecipe() - # These are the FitContributions (we named them "pb" in the debyemodel - # example). - lowT = m1.pb - highT = m2.pb - # Let's rename the FitContributions to something more meaningful for this - # example. - lowT.name = "lowT" - highT.name = "highT" - - # Now create a fresh FitRecipe to work with and add to it the two - # FitContributions. - recipe = FitRecipe() - recipe.addContribution(lowT) - recipe.addContribution(highT) - - # Change the fit ranges of the Profiles embedded within the - # FitContributions. We want to fit one of the contributions at low - # temperature, and one at high. - lowT.profile.setCalculationRange(0, 150) - highT.profile.setCalculationRange(400, 500) - - # Vary the offset from each FitContribution separately, while keeping the - # Debye temperatures the same. We give each offset variable a different - # name in the recipe so it retains its identity. - recipe.addVar(recipe.lowT.offset, name="lowToffset") - recipe.addVar(recipe.highT.offset, name="highToffset") - # We create a new Variable and use the recipe's "constrain" method to - # associate the Debye temperature parameters with that variable. - recipe.newVar("thetaD", 100) - recipe.constrain(recipe.lowT.thetaD, "thetaD") - recipe.constrain(recipe.highT.thetaD, "thetaD") - return recipe - - -def plotResults(recipe): - """Display the results contained within a refined FitRecipe.""" - - # The variable values are returned in the order in which the variables were - # added to the FitRecipe. - lowToffset, highToffset, thetaD = recipe.getValues() - - # We want to extend the fitting range to its full extent so we can get a - # nice full plot. - recipe.lowT.profile.setCalculationRange(xmin="obs", xmax="obs") - recipe.highT.profile.setCalculationRange(xmin="obs", xmax="obs") - T = recipe.lowT.profile.x - U = recipe.lowT.profile.y - # We can use a FitContribution's 'evaluateEquation' method to evaluate - # expressions involving the Parameters and other aspects of the - # FitContribution. Here we evaluate the fitting equation, which is always - # accessed using the name "eq". We access it this way (rather than through - # the Profile's ycalc attribute) because we changed the calculation range - # above, and we therefore need to recalculate the profile. - lowU = recipe.lowT.evaluateEquation("eq") - highU = recipe.highT.evaluateEquation("eq") - - # Now we can plot this. - import pylab - - pylab.plot(T, U, "o", label="Pb $U_{iso}$ Data") - lbl1 = r"$T_d$=%3.1f K, lowToff=%1.5f $\AA^2$" % (abs(thetaD), lowToffset) - lbl2 = r"$T_d$=%3.1f K, highToff=%1.5f $\AA^2$" % ( - abs(thetaD), - highToffset, - ) - pylab.plot(T, lowU, label=lbl1) - pylab.plot(T, highU, label=lbl2) - pylab.xlabel("T (K)") - pylab.ylabel(r"$U_{iso} (\AA^2)$") - pylab.legend(loc=(0.0, 0.8)) - - pylab.show() - return - - -def main(): - - # Create the recipe - recipe = makeRecipeII() - - # Refine using the optimizer of your choice - scipyOptimize(recipe) - - # Get the results in a FitResults object. - res = FitResults(recipe) - - # Print the results - res.printResults() - - # Plot the results - plotResults(recipe) - - return - - -if __name__ == "__main__": - - main() - -# End of file diff --git a/docs/examples/srfit_ex/ellipsoidsas.py b/docs/examples/srfit_ex/ellipsoidsas.py deleted file mode 100644 index 23ee5f0..0000000 --- a/docs/examples/srfit_ex/ellipsoidsas.py +++ /dev/null @@ -1,130 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2010 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of a refinement of SAS I(Q) data to an ellipsoidal model.""" - -from gaussianrecipe import scipyOptimize - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) -from diffpy.srfit.sas import SASGenerator, SASParser - -###### -# Example Code - - -def makeRecipe(datname): - """Create a fitting recipe for ellipsoidal SAS data.""" - - # The Profile - # This will be used to store the observed and calculated I(Q) data. - profile = Profile() - - # Load data and add it to the Profile. We use a SASParser to load the data - # properly and pass the metadata along. - parser = SASParser() - parser.parseFile(datname) - profile.loadParsedData(parser) - - # The ProfileGenerator - # The SASGenerator is for configuring and calculating a SAS profile. We use - # a sas model to configure and serve as the calculation engine of the - # generator. This allows us to use the full sas model creation - # capabilities, and tie this into SrFit when we want to fit a model to - # data. The documentation for the various sas models can be found at - # http://www.sasview.org. - from sas.models.EllipsoidModel import EllipsoidModel - - model = EllipsoidModel() - generator = SASGenerator("generator", model) - - # The FitContribution - # Here we associate the Profile and ProfileGenerator, as has been done - # before. - contribution = FitContribution("ellipsoid") - contribution.addProfileGenerator(generator) - contribution.setProfile(profile, xname="q") - - # We want to fit the log of the signal to the log of the data so that the - # higher-Q information remains significant. There are no I(Q) uncertainty - # values with the data, so we do not need to worry about the effect this - # will have on the estimated parameter uncertainties. - contribution.setResidualEquation("log(eq) - log(y)") - - # Make the FitRecipe and add the FitContribution. - recipe = FitRecipe() - recipe.addContribution(contribution) - - # Configure the fit variables - # The SASGenerator uses the parameters from the params and dispersion - # attributes of the model. These vary from model to model, but are adopted - # as SrFit Parameters within the generator. Whereas the dispersion - # parameters are accessible as, e.g. "radius.width", within the - # SASGenerator these are named like "radius_width". - # - # We want to fit the scale factor, radii and background factors. - recipe.addVar(generator.scale, 1) - recipe.addVar(generator.radius_a, 50) - recipe.addVar(generator.radius_b, 500) - recipe.addVar(generator.background, 0) - - # Give the recipe away so it can be used! - return recipe - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # All this should be pretty familiar by now. - r = recipe.ellipsoid.profile.x - y = recipe.ellipsoid.profile.y - ycalc = recipe.ellipsoid.profile.ycalc - diff = y - ycalc + min(y) - - import pylab - - pylab.loglog(r, y, "bo", label="I(Q) Data") - pylab.loglog(r, ycalc, "r-", label="I(Q) Fit") - pylab.loglog(r, diff, "g-", label="I(Q) diff") - pylab.xlabel(r"$Q (\AA^{-1})$") - pylab.ylabel("$I (arb. units)$") - pylab.legend(loc=1) - - pylab.show() - return - - -if __name__ == "__main__": - - # Make the data and the recipe - data = "data/sas_ellipsoid_testdata.txt" - - # Make the recipe - recipe = makeRecipe(data) - - # Optimize - scipyOptimize(recipe) - - # Generate and print the FitResults - res = FitResults(recipe) - res.printResults() - - # Plot! - plotResults(recipe) - -# End of file diff --git a/docs/examples/srfit_ex/gaussiangenerator.py b/docs/examples/srfit_ex/gaussiangenerator.py deleted file mode 100644 index fedff5a..0000000 --- a/docs/examples/srfit_ex/gaussiangenerator.py +++ /dev/null @@ -1,180 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of using ProfileGenerators in FitContributions. - -This is an example of building a ProfileGenerator and using it in a -FitContribution in order to fit a Gaussian profile. The recipe creation is much -like in gaussianrecipe.py, except that it uses our custom GaussianGenerator -class. ProfileGenerators are usually used to organize profile calculators that -require more information than can be conveniently passed into a function call, -but can be used for simple calculations as well. The GaussianGenerator class -is an example of a ProfileGenerator that can be used by a FitContribution to -help generate a the profile. - -Instructions - -Run gaussianrecipe.py and this example. Note how the output is identical. Next -read through 'GaussianGenerator' class. This provides a simple example of how -to create a custom ProfileGenerator. Finally read the 'makeRecipe' code to see -how the GaussianGenerator is used. Contrast this to the 'makeRecipe' section -in gaussianrecipe.py. - -Extensions - -- Remove the amplitude from GaussianGenerator and instead use the 'setEquation' - method of the FitContribution to account for it. Note that the - GaussianGenerator will be accessible by its name, "g". -""" - -from numpy import exp - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - Profile, - ProfileGenerator, -) - -###### -# Example Code - - -class GaussianGenerator(ProfileGenerator): - """A class for calculating a Gaussian profile. - - Generating a Gaussian is not difficult, as was shown in - gaussianrecipe.py. Here we create a class that encapsulates this - functionality. Placing this class in a python module would make it - possible to import it and reuse it, thereby saving future code - writing and debugging. - - The purpose of a ProfileGenerator is to 1) provide a function that - generates a profile signal 2) organize the Parameters required for - the calculation - - Thus, this class overloads the __init__ method to create the - necessary Parameters for the calculation, and the __call__ method to - generate the signal. - """ - - def __init__(self, name): - """Define the generator. - - Note that a ProfileGenerator needs a name passed in the initializer. - This makes it so the generator can be referenced by name when it is - part of a FitContribution. - - Here we create the Parameters for the calculation. - - A -- The amplitude - x0 -- The center - sigma -- The width - """ - # This initializes various parts of the generator - ProfileGenerator.__init__(self, name) - - # Here we create new Parameters using the '_newParameter' method of - # ProfileGenerator. The signature is - # _newParameter(name, value). - # See the API for full details. - self._newParameter("A", 1.0) - self._newParameter("x0", 0.0) - self._newParameter("sigma", 1.0) - return - - def __call__(self, x): - """Calculate the profile. - - Here we calculate the Gaussian profile given the independent - variable, x. We will define it as we did in gaussianrecipe.py. - """ - # First we must get the values of the Parameters. Since we used - # _newParameter to create them, the Parameters are accessible as - # attributes by name. - A = self.A.value - x0 = self.x0.value - sigma = self.sigma.value - - # Now we can use them. Note that we imported exp from numpy at the top - # of the module. - y = A * exp(-0.5 * (x - x0) ** 2 / sigma**2) - - # Now return the value. - return y - - -# End class GaussianGenerator - - -def makeRecipe(): - """Create a recipe that uses the GaussianGenerator. - - This will create a FitContribution that uses the GaussianGenerator, - associate this with a Profile, and use this to define a FitRecipe. - """ - - # The Profile - # Create a Profile to hold the experimental and calculated signal. - profile = Profile() - - # Load data and add it to the profile. This uses the loadtxt function from - # numpy. - profile.loadtxt("data/gaussian.dat") - - # The ProfileGenerator - # Create a GaussianGenerator named "g". This will be the name we use to - # refer to the generator from within the FitContribution equation. - generator = GaussianGenerator("g") - - # The FitContribution - # Create a FitContribution that will associate the Profile with the - # GaussianGenerator. The GaussianGenerator will be accessible as an - # attribute of the FitContribution by its name ("g"). Note that this will - # set the fitting equation to "g", which calls the GaussianGenerator. - contribution = FitContribution("g1") - contribution.addProfileGenerator(generator) - contribution.setProfile(profile) - - # The FitRecipe - # Now we create the FitRecipe and add the FitContribution. - recipe = FitRecipe() - recipe.addContribution(contribution) - - # Specify which Parameters we want to vary in the fit. This will add - # Variables to the FitRecipe that directly modify the Parameters of the - # FitContribution. - # - # We create a variable for each Parameter of the GaussianGenerator. Note - # that the Parameters belong to the GaussianGenerator, not the - # FitContribution as in gaussianrecipe.py. We initialize parameters as in - # gaussianrecipe.py so we can expect the same output. - recipe.addVar(generator.A, 1) - recipe.addVar(generator.x0, 5) - recipe.addVar(generator.sigma, name="sig") - recipe.sig.value = 1 - - # Give the recipe away so it can be used! - return recipe - - -if __name__ == "__main__": - - # We can use main from gaussianrecipe.py, since this doesn't care if we use - # a ProfileGenerator or not. - from gaussianrecipe import main - - main() - -# End of file diff --git a/docs/examples/srfit_ex/gaussianrecipe.py b/docs/examples/srfit_ex/gaussianrecipe.py deleted file mode 100644 index 646afc7..0000000 --- a/docs/examples/srfit_ex/gaussianrecipe.py +++ /dev/null @@ -1,214 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of fitting a Gaussian to simulated data. - -This is an example of building a fit recipe that can be driven by an optimizer -to fit a Gaussian profile to simulated data. The purpose of this example is -familiarize the developer with the objects involved in defining a SrFit -refinement recipe. - -Instructions - -If you have not yet run the example, run it and inspect the output. The example -script is driven by the 'main' method defined below. Take a look at that method -to get an understanding of how a fit recipe can be used once created. After -that, read the 'makeRecipe' code to see what goes into a fit recipe. After -that, read the 'scipyOptimize' code to see how the refinement is executed. -Finally, read the 'plotResults' code to see how to extracts the refined profile -and plot it. - -Extensions - -After reading through the code, try to perform the following tasks. The process -will leave you with a much better understanding of how SrFit works. - -- Play around with setting the values of the Variables and Parameters. What - happens to the associated Parameter when you change a variable value? What - happens to the variable when you change the Parameter value? -- Modify the fitting equation by adding a constant. See if that improves the - fit. -- Create a FitRecipe to fit the Lorentzian profile in the data/lorentzian.dat - file. -""" - -from __future__ import print_function - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) - -###### -# Example Code - - -def main(): - """The workflow of creating, running and inspecting a fit.""" - - # Start by creating the recipe. The recipe describes the data to be fit, - # the profile generator used to simulate the data and the variables that - # will be tuned by the optimizer. - recipe = makeRecipe() - - # Refine using the optimizer of your choice. - scipyOptimize(recipe) - - # Get the results in a FitResults object. The FitResults object stores the - # current state of the recipe, and uses it to calculate useful statistics - # about the fit. - res = FitResults(recipe) - - # Print the results. - res.printResults() - - # Plot the results. - plotResults(recipe) - - return - - -def makeRecipe(): - """Make a FitRecipe for fitting a Gaussian curve to data. - - The instructions for what we want to refine, and how to refine it - will be defined within a FitRecipe instance. The job of a FitRecipe - is to collect and associate all the data, the fitting equations, - fitting variables, constraints and restraints. The configured recipe - provides a 'residual' function and the initial variable values that - an optimizer can use to refine the variables to minimize the - disagreement between the calculated profile and the data. - - Once we define the FitRecipe, we can send it an optimizer to be - optimized. See the 'scipyOptimize' function. - """ - - # The Profile - # Create a Profile to hold the experimental and calculated signal. - profile = Profile() - - # Load data and add it to the profile. This uses the loadtxt function from - # numpy. - profile.loadtxt("data/gaussian.dat") - - # The FitContribution - # The FitContribution associates the Profile with a fitting equation. The - # FitContribution also stores the parameters of the fitting equation. We - # give our FitContribution then name "g1". We will be able to access the - # FitContribution by that name within the FitRecipe. - contribution = FitContribution("g1") - # Tell the FitContribution about the Profile. The FitContribution will give - # us access to the data held within the Profile. Here, we can tell it what - # name we want to use for the independent variable. We tell it to use the - # name "x". - contribution.setProfile(profile, xname="x") - - # Now we need to create a fitting equation. We do that by writing out the - # equation as a string. The FitContribution will turn this into a callable - # function internally. In the process, it extracts all the parameters from - # the equation (A, x, x0, sigma) and turns them into Parameter objects - # internally. These objects can be accessed as attributes of the - # contribution by name. Since we told the contribution that our - # independent variable is named "x", this value will be substituted into - # the fitting equation whenever it is called. - contribution.setEquation("A * exp(-0.5*(x-x0)**2/sigma**2)") - - # To demonstrate how these parameters are used, we will give "A" an initial - # value. Note that Parameters are not numbers, but are containers for - # numbers. To get or modify the value of a parameter, use its 'value' - # attribute. Parameters also have a 'name' attribute. - contribution.A.value = 1.0 - - # The FitRecipe - # The FitRecipe lets us define what we want to fit. It is where we can - # create variables, constraints and restraints. - recipe = FitRecipe() - - # Here we tell the FitRecipe to use our FitContribution. When the FitRecipe - # calculates its residual function, it will call on the FitContribution to - # do part of the work. - recipe.addContribution(contribution) - - # Specify which Parameters we want to vary in the fit. This will add - # Variables to the FitRecipe that directly modify the Parameters of the - # FitContribution. - # - # Here we create a Variable for the 'A' Parameter from our fit equation. - # The resulting Variable will be named 'A' as well, but it will be accessed - # via the FitRecipe. - recipe.addVar(contribution.A) - # Here we create the Variable for 'x0' and give it an initial value of 5. - recipe.addVar(contribution.x0, 5) - # Here we create a Variable named 'sig', which is tied to the 'sigma' - # Parameter of our FitContribution. We give it an initial value through the - # FitRecipe instance. - recipe.addVar(contribution.sigma, name="sig") - recipe.sig.value = 1 - - return recipe - - -def scipyOptimize(recipe): - """Optimize the recipe created above using scipy. - - The FitRecipe we created in makeRecipe has a 'residual' method that - we can be minimized using a scipy optimizer. The details are - described in the source. - """ - - # We're going to use the least-squares (Levenberg-Marquardt) optimizer from - # scipy. We simply have to give it the function to minimize - # (recipe.residual) and the starting values of the Variables - # (recipe.getValues()). - from scipy.optimize.minpack import leastsq - - print("Fit using scipy's LM optimizer") - leastsq(recipe.residual, recipe.getValues()) - - return - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # We can access the data and fit profile through the Profile we created - # above. We get to it through our FitContribution, which we named "g1". - # - # The independent variable. This is always under the "x" attribute. - x = recipe.g1.profile.x - # The observed profile that we loaded earlier, the "y" attribute. - y = recipe.g1.profile.y - # The calculated profile, the "ycalc" attribute. - ycalc = recipe.g1.profile.ycalc - - # This stuff is specific to pylab from the matplotlib distribution. - import pylab - - pylab.plot(x, y, "b.", label="observed Gaussian") - pylab.plot(x, ycalc, "g-", label="calculated Gaussian") - pylab.legend(loc=(0.0, 0.8)) - pylab.xlabel("x") - pylab.ylabel("y") - - pylab.show() - return - - -if __name__ == "__main__": - - main() - -# End of file diff --git a/docs/examples/srfit_ex/interface.py b/docs/examples/srfit_ex/interface.py deleted file mode 100644 index 6b0daca..0000000 --- a/docs/examples/srfit_ex/interface.py +++ /dev/null @@ -1,78 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of fitting a Gaussian to simulated data. - -This is like gaussianrecipe.py, but it uses a shorthand interface -defined in the diffpy.srfit.interface.interface.py module. -""" - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) - -###### -# Example Code - - -def main(): - - p = Profile() - p.loadtxt("data/gaussian.dat") - - # FitContribution operations - # "<<" - Inject a parameter value - c = FitContribution("g1") - c.setProfile(p) - c.setEquation("A * exp(-0.5*(x-x0)**2/sigma**2)") - c.A << 0.5 - c.x0 << 5 - c.sigma << 1 - - # FitRecipe operations - # "|=" - Union of necessary components. - # "+=" - Add Parameter or create a new one. Each tuple is a set of - # arguments for either setVar or addVar. - # "*=" - Constrain a parameter. Think of "*" as a push-pin holding one - # parameter's value to that of another. - # "%=" - Restrain a parameter or equation. Think of "%" as a rope - # loosely tying parameters to a value. - r = FitRecipe() - r |= c - r += (c.A, 0.5), (c.x0, 5), ("sig", 1) - r *= c.sigma, "sig" - r %= c.A, 0.5, 0.5 - - from gaussianrecipe import scipyOptimize - - scipyOptimize(r) - - res = FitResults(r) - # Print the results. - res.printResults() - # Plot the results. - from gaussianrecipe import plotResults - - plotResults(r) - - return - - -if __name__ == "__main__": - main() - -# End of file diff --git a/docs/examples/srfit_ex/npintensity.py b/docs/examples/srfit_ex/npintensity.py deleted file mode 100644 index 210aa4c..0000000 --- a/docs/examples/srfit_ex/npintensity.py +++ /dev/null @@ -1,531 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of using ProfileGenerators in FitContributions. - -This is an example of building a ProfileGenerator and using it in a -FitContribution in order to fit theoretical intensity data. ProfileGenerators -are used to organize profile calculators that require more information than can -be conveniently passed into a function call. The IntensityGenerator class is -an example of a ProfileGenerator that can be used by a FitContribution to help -generate a the profile. - -Instructions - -Run the example and note the last line of the output. It will be described in -the code. Then read through 'IntensityGenerator' class. This will motivate the -need for the ProfileGenerator class. Next read the 'makeRecipe' code. This -will demonstrate how to use the generator, the structure container needed by -the generator and introduce new operations that can be used in a registered -equation. - -Extensions - -- The IntensityGenerator class uses the 'addParameterSet' method to associate - the structure adapter (DiffpyStructureParSet) with the generator. Most SrFit - classes have an 'addParameterSet' class and can store ParameterSet objects. - Grab the phase object from the IntensityGenerator and try to add it to other - objects used in the fit recipe. Create variables from the moved Parameters - rather than from the 'phase' that lives in the IntensityGenerator and see if - everything still refines. -""" - -from __future__ import print_function - -import numpy -from gaussianrecipe import scipyOptimize - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, - ProfileGenerator, -) -from diffpy.srfit.structure.diffpyparset import DiffpyStructureParSet - -###### -# Example Code - - -class IntensityGenerator(ProfileGenerator): - """A class for calculating intensity using the Debye equation. - - Calculating intensity from a structure is difficult in general. This - class takes a diffpy.structure.Structure instance and from that - generates a theoretical intensity signal. Unlike the example in - gaussianrecipe.py, the intensity generator is not simple. It must - take a structure object and some Parameters, and from that generate - a signal. At the same time, the structure itself (the lattice, atom - positions, thermal parameters, etc.) needs to be refinable. Thus we - define this ProfileGenerator to help us interface which exposes the - Parameters required by the calculation and provides a way for a - FitContribution to perform that calculation. - - The purpose of a ProfileGenerator is to 1) provide a function that - generates a profile signal 2) organize the Parameters required for - the calculation - - This generator wraps the 'iofq' function defined below. Knowledge of - this function is not required for this example. - """ - - def __init__(self, name): - """Define our generator. - - In this example we will keep count of how many times the - calculation gets performed. The 'count' attribute will be used - to store the count. - """ - ProfileGenerator.__init__(self, name) - # Count the calls - self.count = 0 - return - - def setStructure(self, strufile): - """Set the structure used in the calculation. - - strufile -- The name of a structure file. A - diffpy.structure.Structure object will be created from - the file, and that object will be passed to the 'iofq' - function whenever it is called. - - This will create the refinement Parameters using the - DiffpyStructureParSet adapter from diffpy.srfit.structure.diffpyparset. - DiffpyStructureParSet is a ParameterSet object that organizes and gives - attribute access to Parameters and ParameterSets adapted from a diffpy - Structure object. The Parameters embedded in the DiffpyStructureParSet - are proxies for attributes of the diffpy.structure.Structure object - that is needed by the 'iofq' function. The Parameters will be - accessible by name under the 'phase' attribute of this generator, and - are organized hierarchically: - - phase - - lattice (retrieved with 'getLattice') - - a - - b - - c - - alpha - - beta - - gamma - - scatterers (retrieved with 'getScatterers') - - atom1 (the name depends on the element) - - x - - y - - z - - occ - - U11 - - U22 - - U33 - - U12 - - U13 - - U23 - - Uiso - - etc. - - The diffpy.structure.Structure instance is held within the - DiffpyStructureParSet as the 'stru' attribute. - """ - # Load the structure from file - from diffpy.structure import Structure - - stru = Structure() - stru.read(strufile) - - # Create a ParameterSet designed to interface with - # diffpy.structure.Structure objects that organizes the Parameter - # hierarchy. Note that the DiffpyStructureParSet holds a handle to the - # loaded structure that we use in the __call__ method below. - # - # We pass the diffpy.structure.Structure instance, and give the - # DiffpyStructureParSet the name "phase". - parset = DiffpyStructureParSet("phase", stru) - - # Put this ParameterSet in the ProfileGenerator. - self.addParameterSet(parset) - - return - - def __call__(self, q): - """Calculate the intensity. - - This ProfileGenerator will be used in a FitContribution that - will be optimized to fit some data. By the time this function - is evaluated, the diffpy.structure.Structure instance has been - updated by the optimizer via the DiffpyStructureParSet defined - in setStructure. Thus, we need only call iofq with the internal - structure object. - """ - self.count += 1 - print("iofq called", self.count) - return iofq(self.phase.stru, q) - - -# End class IntensityGenerator - - -def makeRecipe(strufile, datname): - """Create a recipe that uses the IntensityGenerator. - - This will create a FitContribution that uses the IntensityGenerator, - associate this with a Profile, and use this to define a FitRecipe. - """ - - # The Profile - # Create a Profile. This will hold the experimental and calculated signal. - profile = Profile() - - # Load data and add it to the profile - x, y, u = profile.loadtxt(datname) - - # The ProfileGenerator - # Create an IntensityGenerator named "I". This will be the name we use to - # refer to the generator from within the FitContribution equation. We also - # need to load the model structure we're using. - generator = IntensityGenerator("I") - generator.setStructure(strufile) - - # The FitContribution - # Create a FitContribution, that will associate the Profile with the - # ProfileGenerator. The ProfileGenerator will be accessible as an - # attribute of the FitContribution by its name ("I"). We also want to tell - # the FitContribution to name the x-variable of the profile "q", so we can - # use it in equations with this name. - contribution = FitContribution("bucky") - contribution.addProfileGenerator(generator) - contribution.setProfile(profile, xname="q") - - # Now we're ready to define the fitting equation for the FitContribution. - # We need to modify the intensity calculation, and we'll do that from - # within the fitting equation for the sake of instruction. We want to - # modify the calculation in three ways. We want to scale it, add a - # polynomial background, and broaden the peaks. - # - # There is added benefit for defining these operations outside of the - # IntensityGenerator. By combining the different parts of the calculation - # within the fitting equation, the time-consuming iofq calculation is only - # performed when a structural Parameter is changed. If only non-structural - # parameters are changed, such as the background and broadening Parameters, - # then then previously computed iofq value will be used to compute the - # contribution equation. The benefit in this is very apparent when - # refining the recipe with the LM optimizer, which only changes two - # variables at a time most of the time. Note in the refinement output how - # many times the residual is calculated, versus how many times iofq is - # called when using the scipyOptimize function. - - # We will define the background as a string. - - bkgdstr = "b0 + b1*q + b2*q**2 + b3*q**3 + b4*q**4 + b5*q**5 + b6*q**6 +\ - b7*q**7 + b8*q**8 + b9*q**9" - - # This creates a callable equation named "bkgd" within the FitContribution, - # and turns the polynomial coefficients into Parameters. - contribution.registerStringFunction(bkgdstr, "bkgd") - - # We will create the broadening function that we need by creating a python - # function and registering it with the FitContribution. - pi = numpy.pi - exp = numpy.exp - - def gaussian(q, q0, width): - return ( - 1 - / (2 * pi * width**2) ** 0.5 - * exp(-0.5 * ((q - q0) / width) ** 2) - ) - - # This registers the python function and extracts the name and creates - # Parameters from the arguments. - contribution.registerFunction(gaussian) - - # Center the Gaussian so it is not truncated. - contribution.q0.value = x[len(x) // 2] - - # Now we can incorporate the scale and bkgd into our calculation. We also - # convolve the signal with the Gaussian to broaden it. Recall that we don't - # need to supply arguments to the registered functions unless we want to - # make changes to their input values. - contribution.setEquation("scale * convolve(I, gaussian) + bkgd") - - # Make the FitRecipe and add the FitContribution. - recipe = FitRecipe() - recipe.addContribution(contribution) - - # Specify which parameters we want to refine. - recipe.addVar(contribution.b0, 0) - recipe.addVar(contribution.b1, 0) - recipe.addVar(contribution.b2, 0) - recipe.addVar(contribution.b3, 0) - recipe.addVar(contribution.b4, 0) - recipe.addVar(contribution.b5, 0) - recipe.addVar(contribution.b6, 0) - recipe.addVar(contribution.b7, 0) - recipe.addVar(contribution.b8, 0) - recipe.addVar(contribution.b9, 0) - - # We also want to adjust the scale and the convolution width - recipe.addVar(contribution.scale, 1) - recipe.addVar(contribution.width, 0.1) - - # We can also refine structural parameters. Here we extract the - # DiffpyStructureParSet from the intensity generator and use the parameters - # like we would any others. - phase = generator.phase - - # We want to allow for isotropic expansion, so we'll constrain the lattice - # parameters to the same value (the lattice is cubic). Note that we - # constrain to the "a" Parameter directly. In previous examples, we - # constrained to a Variable by name. This has the same effect. - lattice = phase.getLattice() - a = lattice.a - recipe.addVar(a) - recipe.constrain(lattice.b, a) - recipe.constrain(lattice.c, a) - # We want to refine the thermal parameters as well. We will add a new - # Variable that we call "Uiso" and constrain the atomic Uiso values to - # this. Note that we don't give Uiso an initial value. The initial value - # will be inferred from the following constraints. - Uiso = recipe.newVar("Uiso") - for atom in phase.getScatterers(): - recipe.constrain(atom.Uiso, Uiso) - - # Give the recipe away so it can be used! - return recipe - - -def main(): - - # Make the data and the recipe - strufile = "data/C60.stru" - q = numpy.arange(1, 20, 0.05) - makeData(strufile, q, "C60.iq", 1.0, 100.68, 0.005, 0.13, 2) - - # Make the recipe - recipe = makeRecipe(strufile, "C60.iq") - - # Optimize - scipyOptimize(recipe) - - # Generate and print the FitResults - res = FitResults(recipe) - # We want to see how much speed-up we get from bringing the scale and - # background outside of the intensity generator. Get the number of calls - # to the residual function from the FitRecipe, and the number of calls to - # 'iofq' from the IntensityGenerator. - rescount = recipe.fithooks[0].count - calcount = recipe.bucky.I.count - footer = "iofq called %i%% of the time" % int(100.0 * calcount / rescount) - res.printResults(footer=footer) - - # Plot! - plotResults(recipe) - - return - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # All this should be pretty familiar by now. - q = recipe.bucky.profile.x - - Imeas = recipe.bucky.profile.y - Icalc = recipe.bucky.profile.ycalc - bkgd = recipe.bucky.evaluateEquation("bkgd") - diff = Imeas - Icalc - - import pylab - - pylab.plot(q, Imeas, "ob", label="I(Q) Data") - pylab.plot(q, Icalc, "r-", label="I(Q) Fit") - pylab.plot(q, diff, "g-", label="I(Q) diff") - pylab.plot(q, bkgd, "c-", label="Bkgd. Fit") - pylab.xlabel(r"$Q (\AA^{-1})$") - pylab.ylabel("Intensity (arb. units)") - pylab.legend(loc=1) - - pylab.show() - return - - -def iofq(S, q): - """Calculate I(Q) (X-ray) using the Debye Equation. - - I(Q) = 2 sum(i,j) f_i(Q) f_j(Q) sinc(rij Q) exp(-0.5 ssij Q**2) - (The exponential term is the Debye-Waller factor.) - - S -- A diffpy.structure.Structure instance. It is assumed that the - structure is that of an isolated scatterer. Periodic boundary - conditions are not applied. - q -- The q-points to calculate over. - - This uses cctbx for the calculation of the f_i if it is available, - otherwise f_i = 1. - """ - # The functions we need - sinc = numpy.sinc - exp = numpy.exp - pi = numpy.pi - - # The brute-force calculation is very slow. Thus we optimize a little bit. - - # The precision of distance measurements - deltad = 1e-6 - dmult = int(1 / deltad) - deltau = deltad**2 - umult = int(1 / deltau) - - pairdict = {} - elcount = {} - n = len(S) - for i in range(n): - - # count the number of each element - eli = S[i].element - m = elcount.get(eli, 0) - elcount[eli] = m + 1 - - for j in range(i + 1, n): - - elj = S[j].element - - # Get the pair - els = [eli, elj] - els.sort() - - # Get the distance to the desired precision - d = S.distance(i, j) - D = int(d * dmult) - - # Get the DW factor to the same precision - ss = S[i].Uisoequiv + S[j].Uisoequiv - SS = int(ss * umult) - - # Record the multiplicity of this pair - key = (els[0], els[1], D, SS) - mult = pairdict.get(key, 0) - pairdict[key] = mult + 1 - - # Now we can calculate IofQ from the pair dictionary. Making the dictionary - # first reduces the amount of calls to sinc and exp we have to make. - - # First we must cache the scattering factors - fdict = {} - for el in elcount: - fdict[el] = getXScatteringFactor(el, q) - - # Now we can compute I(Q) for the i != j pairs - y = 0 - x = q * deltad / pi - for key, mult in pairdict.items(): - eli = key[0] - elj = key[1] - fi = fdict[eli] - fj = fdict[elj] - D = key[2] - SS = key[3] - - # Note that numpy's sinc(x) = sin(x*pi)/(x*pi) - y += fi * fj * mult * sinc(x * D) * exp(-0.5 * SS * deltau * q**2) - - # We must multiply by 2 since we only counted j > i pairs. - y *= 2 - - # Now we must add in the i == j pairs. - for el, f in fdict.items(): - y += f**2 * elcount[el] - - # And that's it! - - return y - - -def getXScatteringFactor(el, q): - """Get the x-ray scattering factor for an element over the q range. - - If cctbx is not available, f(q) = 1 is used. - """ - try: - import cctbx.eltbx.xray_scattering as xray - - wk1995 = xray.wk1995(el) - g = wk1995.fetch() - # at_stol - at sin(theta)/lambda = Q/(4*pi) - f = numpy.asarray(map(g.at_stol, q / (4 * numpy.pi))) - return f - except ImportError: - return 1 - - -def makeData(strufile, q, datname, scale, a, Uiso, sig, bkgc, nl=1): - """Make some fake data and save it to file. - - Make some data to fit. This uses iofq to calculate an intensity curve, and - adds to it a background, broadens the peaks, and noise. - - strufile-- A filename holding the sample structure - q -- The q-range to calculate over. - datname -- The name of the file we're saving to. - scale -- The scale factor - a -- The lattice constant to use - Uiso -- The thermal factor for all atoms - sig -- The broadening factor - bkgc -- A parameter that gives minor control of the background. - nl -- Noise level (0, inf), default 1, larger -> less noise. - """ - - from diffpy.structure import Structure - - S = Structure() - S.read(strufile) - - # Set the lattice parameters - S.lattice.setLatPar(a, a, a) - - # Set a DW factor - for a in S: - a.Uisoequiv = Uiso - y = iofq(S, q) - - # We want to broaden the peaks as well. This simulates instrument effects. - q0 = q[len(q) // 2] - g = numpy.exp(-0.5 * ((q - q0) / sig) ** 2) - y = numpy.convolve(y, g, mode="same") / sum(g) - - # Add a polynomial background. - bkgd = (q + bkgc) ** 2 * (1.5 * max(q) - q) ** 5 - bkgd *= 0.2 * max(y) / max(bkgd) - - y += bkgd - - # Multiply by a scale factor - y *= scale - - # Calculate the uncertainty - u = (y / nl) ** 0.5 - - # And apply the noise - if nl > 0: - y = numpy.random.poisson(y * nl) / nl - - # Now save it - numpy.savetxt(datname, numpy.transpose([q, y, u])) - return - - -if __name__ == "__main__": - - main() - -# End of file diff --git a/docs/examples/srfit_ex/npintensityII.py b/docs/examples/srfit_ex/npintensityII.py deleted file mode 100644 index bd3a32f..0000000 --- a/docs/examples/srfit_ex/npintensityII.py +++ /dev/null @@ -1,279 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of extracting information from multiple data sets -simultaneously. - -This example builds on npintensitygenerator.py, and uses IntensityGenerator -from that example to build a recipe that simultaneously refines two data sets -generated from the same structure. - -Instructions - -Run the example and then read through the 'makeRecipe' code. You will see how -to refine a single structure to two data sets. - -Extensions - -- In 'makeRecipe' the fit contributions are identically configured except for - the profile. Factor out that configuration code and apply it in the - 'makeRecipe' method. This will reduce the amount of code required to get the - job done, make it clearer what is being done and therefore reduce potential - mistakes in the code. This encapsulation of configuration workflow is the - first step towards writing a user interface. -""" - -import numpy -from gaussianrecipe import scipyOptimize -from npintensity import IntensityGenerator, makeData - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) - -###### -# Example Code - - -def makeRecipe(strufile, datname1, datname2): - """Create a recipe that uses the IntensityGenerator. - - We will create two FitContributions that use the IntensityGenerator - from npintensitygenerator.py and associate each of these with a - Profile, and use this to define a FitRecipe. - - Both simulated data sets come from the same structure. We're going - to make two FitContributions that are identical, except for the - profile that is held in each. We're going to assure that the - structures are identical by using the same DiffpyStructureParSet - (which is generated by the IntensityGenerator when we load the - structure) in both generators. - """ - - # The Profiles - # Create two Profiles for the two FitContributions. - profile1 = Profile() - profile2 = Profile() - - # Load data into the Profiles - profile1.loadtxt(datname1) - x, y, u = profile2.loadtxt(datname2) - - # The ProfileGenerators - # Create two IntensityGenerators named "I". There will not be a name - # conflict, since the name is only meaningful within the FitContribution - # that holds the ProfileGenerator. Load the structure into one and make - # sure that the second ProfileGenerator is using the same - # DiffyStructureParSet. This will assure that both ProfileGenerators are - # using the exact same Parameters, and underlying Structure object in the - # calculation of the profile. - generator1 = IntensityGenerator("I") - generator1.setStructure(strufile) - generator2 = IntensityGenerator("I") - generator2.addParameterSet(generator1.phase) - - # The FitContributions - # Create the FitContributions. - contribution1 = FitContribution("bucky1") - contribution1.addProfileGenerator(generator1) - contribution1.setProfile(profile1, xname="q") - contribution2 = FitContribution("bucky2") - contribution2.addProfileGenerator(generator2) - contribution2.setProfile(profile2, xname="q") - - # Now we're ready to define the fitting equation for each FitContribution. - # The functions registered below will be independent, even though they take - # the same form and use the same Parameter names. By default, Parameters - # in different contributions are different Parameters even if they have the - # same names. FitContributions are isolated namespaces than only share - # information if you tell them to by using addParameter or addParameterSet. - bkgdstr = "b0 + b1*q + b2*q**2 + b3*q**3 + b4*q**4 + b5*q**5 + b6*q**6 +\ - b7*q**7 +b8*q**8 + b9*q**9" - - contribution1.registerStringFunction(bkgdstr, "bkgd") - contribution2.registerStringFunction(bkgdstr, "bkgd") - - # We will create the broadening function by registering a python function. - pi = numpy.pi - exp = numpy.exp - - def gaussian(q, q0, width): - return ( - 1 - / (2 * pi * width**2) ** 0.5 - * exp(-0.5 * ((q - q0) / width) ** 2) - ) - - contribution1.registerFunction(gaussian) - contribution2.registerFunction(gaussian) - # Center the gaussian - contribution1.q0.value = x[len(x) // 2] - contribution2.q0.value = x[len(x) // 2] - - # Now we can incorporate the scale and bkgd into our calculation. We also - # convolve the signal with the gaussian to broaden it. - contribution1.setEquation("scale * convolve(I, gaussian) + bkgd") - contribution2.setEquation("scale * convolve(I, gaussian) + bkgd") - - # Make a FitRecipe and associate the FitContributions. - recipe = FitRecipe() - recipe.addContribution(contribution1) - recipe.addContribution(contribution2) - - # Specify which Parameters we want to refine. We want to refine the - # background that we just defined in the FitContributions. We have to do - # this separately for each FitContribution. We tag the variables so it is - # easy to retrieve the background variables. - recipe.addVar(contribution1.b0, 0, name="b1_0", tag="bcoeffs1") - recipe.addVar(contribution1.b1, 0, name="b1_1", tag="bcoeffs1") - recipe.addVar(contribution1.b2, 0, name="b1_2", tag="bcoeffs1") - recipe.addVar(contribution1.b3, 0, name="b1_3", tag="bcoeffs1") - recipe.addVar(contribution1.b4, 0, name="b1_4", tag="bcoeffs1") - recipe.addVar(contribution1.b5, 0, name="b1_5", tag="bcoeffs1") - recipe.addVar(contribution1.b6, 0, name="b1_6", tag="bcoeffs1") - recipe.addVar(contribution1.b7, 0, name="b1_7", tag="bcoeffs1") - recipe.addVar(contribution1.b8, 0, name="b1_8", tag="bcoeffs1") - recipe.addVar(contribution1.b9, 0, name="b1_9", tag="bcoeffs1") - recipe.addVar(contribution2.b0, 0, name="b2_0", tag="bcoeffs2") - recipe.addVar(contribution2.b1, 0, name="b2_1", tag="bcoeffs2") - recipe.addVar(contribution2.b2, 0, name="b2_2", tag="bcoeffs2") - recipe.addVar(contribution2.b3, 0, name="b2_3", tag="bcoeffs2") - recipe.addVar(contribution2.b4, 0, name="b2_4", tag="bcoeffs2") - recipe.addVar(contribution2.b5, 0, name="b2_5", tag="bcoeffs2") - recipe.addVar(contribution2.b6, 0, name="b2_6", tag="bcoeffs2") - recipe.addVar(contribution2.b7, 0, name="b2_7", tag="bcoeffs2") - recipe.addVar(contribution2.b8, 0, name="b2_8", tag="bcoeffs2") - recipe.addVar(contribution2.b9, 0, name="b2_9", tag="bcoeffs2") - - # We also want to adjust the scale and the convolution width - recipe.addVar(contribution1.scale, 1, name="scale1") - recipe.addVar(contribution1.width, 0.1, name="width1") - recipe.addVar(contribution2.scale, 1, name="scale2") - recipe.addVar(contribution2.width, 0.1, name="width2") - - # We can also refine structural parameters. We only have to do this once, - # since each generator holds the same DiffpyStructureParSet. - phase = generator1.phase - lattice = phase.getLattice() - a = recipe.addVar(lattice.a) - # We want to allow for isotropic expansion, so we'll make constraints for - # that. - recipe.constrain(lattice.b, a) - recipe.constrain(lattice.c, a) - # We want to refine the thermal parameters as well. We will add a new - # variable that we call "Uiso" and constrain the atomic Uiso values to - # this. Note that we don't give Uiso an initial value. The initial value - # will be inferred from the subsequent constraints. - Uiso = recipe.newVar("Uiso") - for atom in phase.getScatterers(): - recipe.constrain(atom.Uiso, Uiso) - - # Give the recipe away so it can be used! - return recipe - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # plotting song and dance - q = recipe.bucky1.profile.x - - # Plot this for fun. - I1 = recipe.bucky1.profile.y - Icalc1 = recipe.bucky1.profile.ycalc - bkgd1 = recipe.bucky1.evaluateEquation("bkgd") - diff1 = I1 - Icalc1 - I2 = recipe.bucky2.profile.y - Icalc2 = recipe.bucky2.profile.ycalc - bkgd2 = recipe.bucky2.evaluateEquation("bkgd") - diff2 = I2 - Icalc2 - offset = 1.2 * max(I2) * numpy.ones_like(I2) - I1 += offset - Icalc1 += offset - bkgd1 += offset - diff1 += offset - - import pylab - - pylab.subplot(2, 1, 1) - pylab.plot(q, I1, "bo", label="I1(Q) Data") - pylab.plot(q, Icalc1, "r-", label="I1(Q) Fit") - pylab.plot(q, diff1, "g-", label="I1(Q) diff") - pylab.plot(q, bkgd1, "c-", label="Bkgd1 Fit") - pylab.legend(loc=1) - - pylab.subplot(2, 1, 2) - pylab.plot(q, I2, "bo", label="I2(Q) Data") - pylab.plot(q, Icalc2, "r-", label="I2(Q) Fit") - pylab.plot(q, diff2, "g-", label="I2(Q) diff") - pylab.plot(q, bkgd2, "c-", label="Bkgd2 Fit") - pylab.xlabel(r"$Q (\AA^{-1})$") - pylab.ylabel("Intensity (arb. units)") - pylab.legend(loc=1) - - pylab.show() - return - - -def main(): - - # Make two different data sets, each from the same structure, but with - # different scale, noise, broadening and background. - strufile = "data/C60.stru" - q = numpy.arange(1, 20, 0.05) - makeData(strufile, q, "C60_1.iq", 8.1, 101.68, 0.008, 0.12, 2, 0.01) - makeData(strufile, q, "C60_2.iq", 3.2, 101.68, 0.02, 0.003, 0, 1) - - # Make the recipe - recipe = makeRecipe(strufile, "C60_1.iq", "C60_2.iq") - - # Optimize - # Since the backgrounds have a large effect on the profile, we will refine - # them first, but do so separately. - # To refine the background from the first contribution, we will fix - # all other parameters and give the second contribution no weight in the - # fit. - recipe.fix("all") - recipe.free("bcoeffs1") - recipe.setWeight(recipe.bucky2, 0) - scipyOptimize(recipe) - # Now do the same for the second background - recipe.fix("all") - recipe.free("bcoeffs1") - recipe.setWeight(recipe.bucky2, 1) - recipe.setWeight(recipe.bucky1, 0) - scipyOptimize(recipe) - # Now refine everything with the structure parameters included - recipe.free("all") - recipe.setWeight(recipe.bucky1, 1) - scipyOptimize(recipe) - - # Generate and print the FitResults - res = FitResults(recipe) - res.printResults() - - # Plot! - plotResults(recipe) - - return - - -if __name__ == "__main__": - - main() - -# End of file diff --git a/docs/examples/srfit_ex/nppdfcrystal.py b/docs/examples/srfit_ex/nppdfcrystal.py deleted file mode 100644 index 0c098ef..0000000 --- a/docs/examples/srfit_ex/nppdfcrystal.py +++ /dev/null @@ -1,129 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of fitting a crystal-like nanoparticle (nanocrystal) PDF. - -This is an example of modeling the PDF from a nanocrystal as an -attenuated bulk PDF. This involves a crystal PDF calculation and a -spherical nanoparticle characteristic function. The equation we model is -Gnano(r) = f(r) * Gbulk(r), where f(r) is the nanoparticle -characteristic function for the nanoparticle shape. Functions for -calculating the characteristic function in the -diffpy.srfit.pdf.characteristicfunctions module. -""" - -import numpy -from gaussianrecipe import scipyOptimize -from pyobjcryst import loadCrystal - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) -from diffpy.srfit.pdf import PDFGenerator, PDFParser - - -def makeRecipe(ciffile, grdata): - """Make a recipe to model a crystal-like nanoparticle PDF.""" - - # Set up a PDF fit as has been done in other examples. - pdfprofile = Profile() - - pdfparser = PDFParser() - pdfparser.parseFile(grdata) - pdfprofile.loadParsedData(pdfparser) - pdfprofile.setCalculationRange(xmin=0.1, xmax=20) - - pdfcontribution = FitContribution("pdf") - pdfcontribution.setProfile(pdfprofile, xname="r") - - pdfgenerator = PDFGenerator("G") - pdfgenerator.setQmax(30.0) - stru = loadCrystal(ciffile) - pdfgenerator.setStructure(stru) - pdfcontribution.addProfileGenerator(pdfgenerator) - - # Register the nanoparticle shape factor. - from diffpy.srfit.pdf.characteristicfunctions import sphericalCF - - pdfcontribution.registerFunction(sphericalCF, name="f") - - # Now we set up the fitting equation. - pdfcontribution.setEquation("f * G") - - # Now make the recipe. Make sure we fit the characteristic function shape - # parameters, in this case 'psize', which is the diameter of the particle. - recipe = FitRecipe() - recipe.addContribution(pdfcontribution) - - phase = pdfgenerator.phase - for par in phase.sgpars: - recipe.addVar(par) - - recipe.addVar(pdfcontribution.psize, 20) - recipe.addVar(pdfgenerator.scale, 1) - recipe.addVar(pdfgenerator.delta2, 0) - recipe.B11_0 = 0.1 - - return recipe - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # All this should be pretty familiar by now. - r = recipe.pdf.profile.x - g = recipe.pdf.profile.y - gcalc = recipe.pdf.profile.ycalc - diffzero = -0.8 * max(g) * numpy.ones_like(g) - diff = g - gcalc + diffzero - - gcryst = recipe.pdf.evaluateEquation("G") - gcryst /= recipe.scale.value - - fr = recipe.pdf.evaluateEquation("f") - fr *= max(g) / fr[0] - - import pylab - - pylab.plot(r, g, "bo", label="G(r) Data") - pylab.plot(r, gcryst, "y--", label="G(r) Crystal") - pylab.plot(r, fr, "k--", label="f(r) calculated (scaled)") - pylab.plot(r, gcalc, "r-", label="G(r) Fit") - pylab.plot(r, diff, "g-", label="G(r) diff") - pylab.plot(r, diffzero, "k-") - pylab.xlabel(r"$r (\AA)$") - pylab.ylabel(r"$G (\AA^{-2})$") - pylab.legend(loc=1) - - pylab.show() - return - - -if __name__ == "__main__": - - ciffile = "data/pb.cif" - grdata = "data/pb_100_qmin1.gr" - - recipe = makeRecipe(ciffile, grdata) - scipyOptimize(recipe) - - res = FitResults(recipe) - res.printResults() - - plotResults(recipe) - -# End of file diff --git a/docs/examples/srfit_ex/nppdfobjcryst.py b/docs/examples/srfit_ex/nppdfobjcryst.py deleted file mode 100644 index a05dbaa..0000000 --- a/docs/examples/srfit_ex/nppdfobjcryst.py +++ /dev/null @@ -1,257 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of a nanoparticle PDF refinement using DebyePDFGenerator. - -This example is similar to crystalpdfobjcryst.py, except that it uses -the DebyePDFGenerator from SrReal to refine a pyobjcryst Molecule. -""" - -import numpy - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) -from diffpy.srfit.pdf import DebyePDFGenerator - -###### -# Example Code - - -def makeRecipe(molecule, datname): - """Create a recipe that uses the DebyePDFGenerator.""" - - # The Profile - profile = Profile() - - # Load data and add it to the profile - profile.loadtxt(datname) - profile.setCalculationRange(xmin=1.2, xmax=8) - - # The ProfileGenerator - # Create a DebyePDFGenerator named "G". - generator = DebyePDFGenerator("G") - generator.setStructure(molecule) - # These are metadata needed by the generator - generator.setQmin(0.68) - generator.setQmax(22) - - # The FitContribution - contribution = FitContribution("bucky") - contribution.addProfileGenerator(generator) - contribution.setProfile(profile, xname="r") - - # Make a FitRecipe. - recipe = FitRecipe() - recipe.addContribution(contribution) - - # Specify which parameters we want to refine. We'll be using the - # MoleculeParSet within the generator, so let's get a handle to it. See the - # diffpy.srfit.structure.objcryststructure module for more information - # about the MoleculeParSet hierarchy. - c60 = generator.phase - - # First, the isotropic thermal displacement factor. - Biso = recipe.newVar("Biso") - for atom in c60.getScatterers(): - - # We have defined a 'center' atom that is a dummy, which means that it - # has no scattering power. It is only used as a reference point for - # our bond length. We don't want to constrain it. - if not atom.isDummy(): - recipe.constrain(atom.Biso, Biso) - - # We need to let the molecule expand. If we were modeling it as a crystal, - # we could let the unit cell expand. For instruction purposes, we use a - # Molecule to model C60, and molecules have different modeling options than - # crystals. To make the molecule expand from a central point, we will - # constrain the distance from each atom to a dummy center atom that was - # created with the molecule, and allow that distance to vary. (We could - # also let the nearest-neighbor bond lengths vary, but that would be much - # more difficult to set up.) - center = c60.center - # Create a new Parameter that represents the radius of the molecule. Note - # that we don't give it an initial value. Since the variable is being - # directly constrained to further below, its initial value will be inferred - # from the constraint. - radius = recipe.newVar("radius") - for i, atom in enumerate(c60.getScatterers()): - - if atom.isDummy(): - continue - - # This creates a Parameter that moves the second atom according to the - # bond length. Note that each Parameter needs a unique name. - par = c60.addBondLengthParameter("rad%i" % i, center, atom) - recipe.constrain(par, radius) - - # Add the correlation term, scale. The scale is too short to effectively - # determine qdamp. - recipe.addVar(generator.delta2, 2) - recipe.addVar(generator.scale, 1.3e4) - - # Give the recipe away so it can be used! - return recipe - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # Plot this. - r = recipe.bucky.profile.x - g = recipe.bucky.profile.y - gcalc = recipe.bucky.profile.ycalc - diffzero = -0.8 * max(g) * numpy.ones_like(g) - diff = g - gcalc + diffzero - - import pylab - - pylab.plot(r, g, "ob", label="G(r) Data") - pylab.plot(r, gcalc, "-r", label="G(r) Fit") - pylab.plot(r, diff, "-g", label="G(r) diff") - pylab.plot(r, diffzero, "-k") - pylab.xlabel(r"$r (\AA)$") - pylab.ylabel(r"$G (\AA^{-2})$") - pylab.legend(loc=1) - - pylab.show() - return - - -def main(): - - molecule = makeC60() - # Make the data and the recipe - recipe = makeRecipe(molecule, "data/C60.gr") - # Tell the fithook that we want very verbose output. - recipe.fithooks[0].verbose = 3 - - # Optimize - from scipy.optimize import leastsq - - leastsq(recipe.residual, recipe.getValues()) - - # Print results - res = FitResults(recipe) - res.printResults() - - # Plot results - plotResults(recipe) - - return - - -c60xyz = """ -3.451266498 0.685000000 0.000000000 -3.451266498 -0.685000000 0.000000000 --3.451266498 0.685000000 0.000000000 --3.451266498 -0.685000000 0.000000000 -0.685000000 0.000000000 3.451266498 --0.685000000 0.000000000 3.451266498 -0.685000000 0.000000000 -3.451266498 --0.685000000 0.000000000 -3.451266498 -0.000000000 3.451266498 0.685000000 -0.000000000 3.451266498 -0.685000000 -0.000000000 -3.451266498 0.685000000 -0.000000000 -3.451266498 -0.685000000 -3.003809890 1.409000000 1.171456608 -3.003809890 1.409000000 -1.171456608 -3.003809890 -1.409000000 1.171456608 -3.003809890 -1.409000000 -1.171456608 --3.003809890 1.409000000 1.171456608 --3.003809890 1.409000000 -1.171456608 --3.003809890 -1.409000000 1.171456608 --3.003809890 -1.409000000 -1.171456608 -1.409000000 1.171456608 3.003809890 -1.409000000 -1.171456608 3.003809890 --1.409000000 1.171456608 3.003809890 --1.409000000 -1.171456608 3.003809890 -1.409000000 1.171456608 -3.003809890 -1.409000000 -1.171456608 -3.003809890 --1.409000000 1.171456608 -3.003809890 --1.409000000 -1.171456608 -3.003809890 -1.171456608 3.003809890 1.409000000 --1.171456608 3.003809890 1.409000000 -1.171456608 3.003809890 -1.409000000 --1.171456608 3.003809890 -1.409000000 -1.171456608 -3.003809890 1.409000000 --1.171456608 -3.003809890 1.409000000 -1.171456608 -3.003809890 -1.409000000 --1.171456608 -3.003809890 -1.409000000 -2.580456608 0.724000000 2.279809890 -2.580456608 0.724000000 -2.279809890 -2.580456608 -0.724000000 2.279809890 -2.580456608 -0.724000000 -2.279809890 --2.580456608 0.724000000 2.279809890 --2.580456608 0.724000000 -2.279809890 --2.580456608 -0.724000000 2.279809890 --2.580456608 -0.724000000 -2.279809890 -0.724000000 2.279809890 2.580456608 -0.724000000 -2.279809890 2.580456608 --0.724000000 2.279809890 2.580456608 --0.724000000 -2.279809890 2.580456608 -0.724000000 2.279809890 -2.580456608 -0.724000000 -2.279809890 -2.580456608 --0.724000000 2.279809890 -2.580456608 --0.724000000 -2.279809890 -2.580456608 -2.279809890 2.580456608 0.724000000 --2.279809890 2.580456608 0.724000000 -2.279809890 2.580456608 -0.724000000 --2.279809890 2.580456608 -0.724000000 -2.279809890 -2.580456608 0.724000000 --2.279809890 -2.580456608 0.724000000 -2.279809890 -2.580456608 -0.724000000 --2.279809890 -2.580456608 -0.724000000 -""" - - -def makeC60(): - """Make the C60 molecule using pyobjcryst.""" - - from pyobjcryst.crystal import Crystal - from pyobjcryst.molecule import Molecule - from pyobjcryst.scatteringpower import ScatteringPowerAtom - - # make a crystal box to put the molecule in - c = Crystal(1, 1, 1, "P1") - c.SetName("c60frame") - - # put a molecule inside the box - m = Molecule(c, "c60") - c.AddScatterer(m) - - # Create a dummy atom at the center. - m.AddAtom(0, 0, 0, None, "center") - - # Create the scattering power object for the carbon atoms - sp = ScatteringPowerAtom("C", "C") - c.AddScatteringPower(sp) - sp.SetBiso(0.25) - - # Add the other atoms. They will be named C1, C2, ..., C60. - for i, l in enumerate(c60xyz.strip().splitlines()): - x, y, z = map(float, l.split()) - m.AddAtom(x, y, z, sp, "C%i" % (i + 1)) - - return m - - -if __name__ == "__main__": - - main() - -# End of file diff --git a/docs/examples/srfit_ex/nppdfsas.py b/docs/examples/srfit_ex/nppdfsas.py deleted file mode 100644 index 493d299..0000000 --- a/docs/examples/srfit_ex/nppdfsas.py +++ /dev/null @@ -1,196 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of combining PDF and SAS nanoparticles data. - -This is an example of using both PDF and SAS data in the same fit. This -fits a crystal model to the PDF while fitting a shape model to both the -SAS profile and the PDF data. Using the same shape for the PDF and SAS -provides a feedback mechanism into the fit that allows the PDF and SAS -portions of the fit to guide one another, and in the end gives the shape -of the nanoparticle that agrees best with both the PDF and SAS data. -""" - -import numpy -from gaussianrecipe import scipyOptimize -from pyobjcryst import loadCrystal - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) -from diffpy.srfit.pdf import PDFGenerator, PDFParser -from diffpy.srfit.pdf.characteristicfunctions import SASCF -from diffpy.srfit.sas import SASGenerator, SASParser - - -def makeRecipe(ciffile, grdata, iqdata): - """Make complex-modeling recipe where I(q) and G(r) are fit - simultaneously. - - The fit I(q) is fed into the calculation of G(r), which provides - feedback for the fit parameters of both. - """ - - # Create a PDF contribution as before - pdfprofile = Profile() - pdfparser = PDFParser() - pdfparser.parseFile(grdata) - pdfprofile.loadParsedData(pdfparser) - pdfprofile.setCalculationRange(xmin=0.1, xmax=20) - - pdfcontribution = FitContribution("pdf") - pdfcontribution.setProfile(pdfprofile, xname="r") - - pdfgenerator = PDFGenerator("G") - pdfgenerator.setQmax(30.0) - stru = loadCrystal(ciffile) - pdfgenerator.setStructure(stru) - pdfcontribution.addProfileGenerator(pdfgenerator) - pdfcontribution.setResidualEquation("resv") - - # Create a SAS contribution as well. We assume the nanoparticle is roughly - # elliptical. - sasprofile = Profile() - sasparser = SASParser() - sasparser.parseFile(iqdata) - sasprofile.loadParsedData(sasparser) - if all(sasprofile.dy == 0): - sasprofile.dy[:] = 1 - - sascontribution = FitContribution("sas") - sascontribution.setProfile(sasprofile) - - from sas.models.EllipsoidModel import EllipsoidModel - - model = EllipsoidModel() - sasgenerator = SASGenerator("generator", model) - sascontribution.addProfileGenerator(sasgenerator) - sascontribution.setResidualEquation("resv") - - # Now we set up a characteristic function calculator that depends on the - # sas model. - cfcalculator = SASCF("f", model) - - # Register the calculator with the pdf contribution and define the fitting - # equation. - pdfcontribution.registerCalculator(cfcalculator) - # The PDF for a nanoscale crystalline is approximated by - # Gnano = f * Gcryst - pdfcontribution.setEquation("f * G") - - # Moving on - recipe = FitRecipe() - recipe.addContribution(pdfcontribution) - recipe.addContribution(sascontribution) - - # PDF - phase = pdfgenerator.phase - for par in phase.sgpars: - recipe.addVar(par) - - recipe.addVar(pdfgenerator.scale, 1) - recipe.addVar(pdfgenerator.delta2, 0) - - # SAS - recipe.addVar(sasgenerator.scale, 1, name="iqscale") - recipe.addVar(sasgenerator.radius_a, 10) - recipe.addVar(sasgenerator.radius_b, 10) - - # Even though the cfcalculator and sasgenerator depend on the same sas - # model, we must still constrain the cfcalculator Parameters so that it is - # informed of changes in the refined parameters. - recipe.constrain(cfcalculator.radius_a, "radius_a") - recipe.constrain(cfcalculator.radius_b, "radius_b") - - return recipe - - -def fitRecipe(recipe): - """We refine in stages to help the refinement converge.""" - - # Tune SAS. - recipe.setWeight(recipe.pdf, 0) - recipe.fix("all") - recipe.free("radius_a", "radius_b", iqscale=1e8) - recipe.constrain("radius_b", "radius_a") - scipyOptimize(recipe) - recipe.unconstrain("radius_b") - - # Tune PDF - recipe.setWeight(recipe.pdf, 1) - recipe.setWeight(recipe.sas, 0) - recipe.fix("all") - recipe.free("a", "Biso_0", "scale", "delta2") - scipyOptimize(recipe) - - # Tune all - recipe.setWeight(recipe.pdf, 1) - recipe.setWeight(recipe.sas, 1) - recipe.free("all") - scipyOptimize(recipe) - - return - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # All this should be pretty familiar by now. - r = recipe.pdf.profile.x - g = recipe.pdf.profile.y - gcalc = recipe.pdf.profile.ycalc - diffzero = -0.8 * max(g) * numpy.ones_like(g) - diff = g - gcalc + diffzero - - gcryst = recipe.pdf.evaluateEquation("G") - gcryst /= recipe.scale.value - - fr = recipe.pdf.evaluateEquation("f") - fr *= max(g) / fr[0] - - import pylab - - pylab.plot(r, g, "bo", label="G(r) Data") - pylab.plot(r, gcryst, "y--", label="G(r) Crystal") - pylab.plot(r, fr, "k--", label="f(r) calculated (scaled)") - pylab.plot(r, gcalc, "r-", label="G(r) Fit") - pylab.plot(r, diff, "g-", label="G(r) diff") - pylab.plot(r, diffzero, "k-") - pylab.xlabel(r"$r (\AA)$") - pylab.ylabel(r"$G (\AA^{-2})$") - pylab.legend(loc=1) - - pylab.show() - return - - -if __name__ == "__main__": - - ciffile = "data/pb.cif" - grdata = "data/pb_100_qmin1.gr" - iqdata = "data/pb_100_qmax1.iq" - - recipe = makeRecipe(ciffile, grdata, iqdata) - recipe.fithooks[0].verbose = 3 - fitRecipe(recipe) - - res = FitResults(recipe) - res.printResults() - - plotResults(recipe) - -# End of file diff --git a/docs/examples/srfit_ex/simplepdf.py b/docs/examples/srfit_ex/simplepdf.py deleted file mode 100644 index 027a6d7..0000000 --- a/docs/examples/srfit_ex/simplepdf.py +++ /dev/null @@ -1,91 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2010 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of a PDF using the PDFContribution helper class. - -This is example of fitting the fcc nickel structure to measured PDF -data. It uses the PDFContribution class to simplify fit setup. -""" - -from crystalpdf import plotResults -from gaussianrecipe import scipyOptimize - -from diffpy.srfit.fitbase import FitRecipe, FitResults -from diffpy.srfit.pdf import PDFContribution -from diffpy.structure import Structure - -###### -# Example Code - - -def makeRecipe(ciffile, datname): - """Create a fitting recipe for crystalline PDF data.""" - - # Work directly with a custom PDFContribution to load the data - contribution = PDFContribution("nickel") - contribution.loadData(datname) - contribution.setCalculationRange(xmin=1, xmax=20, dx=0.1) - - # and the phase - stru = Structure() - stru.read(ciffile) - contribution.addStructure("nickel", stru) - - # Make the FitRecipe and add the FitContribution. - recipe = FitRecipe() - recipe.addContribution(contribution) - - # Configure the fit variables - phase = contribution.nickel.phase - - from diffpy.srfit.structure import constrainAsSpaceGroup - - sgpars = constrainAsSpaceGroup(phase, "Fm-3m") - - for par in sgpars.latpars: - recipe.addVar(par) - for par in sgpars.adppars: - recipe.addVar(par, 0.005) - - recipe.addVar(contribution.scale, 1) - recipe.addVar(contribution.qdamp, 0.03, fixed=True) - recipe.addVar(contribution.nickel.delta2, 5) - - # Give the recipe away so it can be used! - return recipe - - -if __name__ == "__main__": - - # Make the data and the recipe - ciffile = "data/ni.cif" - data = "data/ni-q27r100-neutron.gr" - - # Make the recipe - recipe = makeRecipe(ciffile, data) - - # Optimize - scipyOptimize(recipe) - # Save the file - recipe.nickel.savetxt("nickel_example.fit") - - # Generate, print and save the FitResults - res = FitResults(recipe) - res.printResults() - res.saveResults("nickel_example.res") - - # Plot! - plotResults(recipe) - -# End of file diff --git a/docs/examples/srfit_ex/simplepdftwophase.py b/docs/examples/srfit_ex/simplepdftwophase.py deleted file mode 100644 index a8017c2..0000000 --- a/docs/examples/srfit_ex/simplepdftwophase.py +++ /dev/null @@ -1,122 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2010 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of a simplified PDF refinement of two-phase structure.""" - -from crystalpdftwophase import plotResults -from gaussianrecipe import scipyOptimize -from pyobjcryst import loadCrystal - -from diffpy.srfit.fitbase import FitRecipe, FitResults -from diffpy.srfit.pdf import PDFContribution - -###### -# Example Code - - -def makeRecipe(niciffile, siciffile, datname): - """Create a fitting recipe for crystalline PDF data.""" - - # Load data and add it to the profile - contribution = PDFContribution("nisi") - contribution.loadData(datname) - contribution.setCalculationRange(xmax=20) - - stru = loadCrystal(niciffile) - contribution.addStructure("ni", stru) - - stru = loadCrystal(siciffile) - contribution.addStructure("si", stru) - - # Make the FitRecipe and add the FitContribution. - recipe = FitRecipe() - recipe.addContribution(contribution) - - # Configure the fit variables - # Start by configuring the scale factor and resolution factors. - # We want the sum of the phase scale factors to be 1. - recipe.newVar("scale_ni", 0.1) - recipe.constrain(contribution.ni.scale, "scale_ni") - recipe.constrain(contribution.si.scale, "1 - scale_ni") - # We also want the resolution factor to be the same on each. This is done - # for free by the PDFContribution. We simply need to add it to the recipe. - recipe.addVar(contribution.qdamp, 0.03) - - # Vary the global scale as well. - recipe.addVar(contribution.scale, 1) - - # Now we can configure the structural parameters. Since we're using - # ObjCrystCrystalParSets, the space group constraints are automatically - # applied to each phase. We must selectively vary the free parameters. - # - # First the nickel parameters. - # Note that ni is the name of the PDFGenerator that was automatically - # created by the PDFContribution. We selected this name in addStructure - # above. - phase_ni = contribution.ni.phase - for par in phase_ni.sgpars: - recipe.addVar(par, name=par.name + "_ni") - recipe.addVar(contribution.ni.delta2, name="delta2_ni") - # Next the silicon parameters - phase_si = contribution.si.phase - for par in phase_si.sgpars: - recipe.addVar(par, name=par.name + "_si") - recipe.addVar(contribution.si.delta2, name="delta2_si") - - # We have prior information from the earlier examples so we'll use it here - # in the form of restraints. - # - # The nickel lattice parameter was measured to be 3.527. The uncertainty - # values are invalid for that measurement, since the data from which it is - # derived has no uncertainty. Thus, we will tell the recipe to scale the - # residual, which means that it will be weighted as much as the average - # data point during the fit. - recipe.restrain("a_ni", lb=3.527, ub=3.527, scaled=True) - # Now we do the same with the delta2 and Biso parameters (remember that - # Biso = 8*pi**2*Uiso) - recipe.restrain("delta2_ni", lb=2.22, ub=2.22, scaled=True) - recipe.restrain("Biso_0_ni", lb=0.454, ub=0.454, scaled=True) - # - # We can do the same with the silicon values. We haven't done a thorough - # job of measuring the uncertainties in the results, so we'll scale these - # as well. - recipe.restrain("a_si", lb=5.430, ub=5.430, scaled=True) - recipe.restrain("delta2_si", lb=3.54, ub=3.54, scaled=True) - recipe.restrain("Biso_0_si", lb=0.645, ub=0.645, scaled=True) - - # Give the recipe away so it can be used! - return recipe - - -if __name__ == "__main__": - - # Make the data and the recipe - niciffile = "data/ni.cif" - siciffile = "data/si.cif" - data = "data/si90ni10-q27r60-xray.gr" - - # Make the recipe - recipe = makeRecipe(niciffile, siciffile, data) - - # Optimize - scipyOptimize(recipe) - - # Generate and print the FitResults - res = FitResults(recipe) - res.printResults() - - # Plot! - plotResults(recipe) - -# End of file diff --git a/docs/examples/srfit_ex/simplerecipe.py b/docs/examples/srfit_ex/simplerecipe.py deleted file mode 100644 index 0ec297a..0000000 --- a/docs/examples/srfit_ex/simplerecipe.py +++ /dev/null @@ -1,63 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of simplified fitting. - -This is like gaussianrecipe.py, but it uses the SimpleRecipe, which -integrates the FitContribution and Profile objects for simple recipe -creation. -""" - -from diffpy.srfit.fitbase import SimpleRecipe - -###### -# Example Code - - -def main(): - """Set up a simple recipe in a few lines.""" - - # The SimpleRecipe class is a type of FitRecipe. It provides attribute-like - # access to variables and a residual function that can be minimized. - recipe = SimpleRecipe() - - # Load text from file. - recipe.loadtxt("data/gaussian.dat") - - # Set the equation. The variable "x" is taken from the data that was just - # loaded. The other variables, "A", "x0" and "sigma" are turned into - # attributes with an initial value of 0. - recipe.setEquation("A * exp(-0.5*(x-x0)**2/sigma**2)") - - # We can give them other values here. - recipe.A = 1 - recipe.x0 = 5 - recipe.sigma = 1 - - # We explicitly optimize the residual method of the SimpleRecipe - from scipy.optimize import leastsq - - leastsq(recipe.residual, recipe.values) - - # Print the results - recipe.printResults() - - return - - -if __name__ == "__main__": - - main() - -# End of file diff --git a/docs/examples/srfit_ex/threedoublepeaks.py b/docs/examples/srfit_ex/threedoublepeaks.py deleted file mode 100644 index 97fd4d5..0000000 --- a/docs/examples/srfit_ex/threedoublepeaks.py +++ /dev/null @@ -1,261 +0,0 @@ -#!/usr/bin/env python -######################################################################## -# -# diffpy.srfit by DANSE Diffraction group -# Simon J. L. Billinge -# (c) 2009 The Trustees of Columbia University -# in the City of New York. All rights reserved. -# -# File coded by: Chris Farrow -# -# See AUTHORS.txt for a list of people who contributed. -# See LICENSE_DANSE.txt for license information. -# -######################################################################## -"""Example of fitting a three double peaks to simulated data.""" - -from __future__ import print_function - -import numpy - -from diffpy.srfit.fitbase import ( - FitContribution, - FitRecipe, - FitResults, - Profile, -) - -###### -# Example Code - - -def makeRecipe(): - """Make a FitRecipe for fitting three double-gaussian curves to - data. - - The separation and amplitude ratio of the double peaks follows a - specific relationship. The peaks are broadend according to their - position and they sit on top of a background. We are seeking the - absolute locations of the peaks as well as their amplitudes. - - The independent variable is t. The relationship between the double - peaks is sin(t2) / l2 = sin(t1) / l1 amplitude(peak2) = r * - amplitude(peak1) The values of l1, l2 and r come from experiment. - For this example, we use l1 = 1.012, l2 = 1.0 and r = 0.23. - """ - - # The Profile - # Create a Profile to hold the experimental and calculated signal. - profile = Profile() - x, y, dy = profile.loadtxt("data/threedoublepeaks.dat") - - # Create the contribution - contribution = FitContribution("peaks") - contribution.setProfile(profile, xname="t") - pi = numpy.pi - exp = numpy.exp - - # This is a building-block of our profile function - def gaussian(t, mu, sig): - return 1 / (2 * pi * sig**2) ** 0.5 * exp(-0.5 * ((t - mu) / sig) ** 2) - - contribution.registerFunction(gaussian, name="peakshape") - - def delta(t, mu): - """Calculate a delta-function. - - We don't have perfect precision, so we must make this a very - thin Gaussian. - """ - sig = t[1] - t[0] - return gaussian(t, mu, sig) - - contribution.registerFunction(delta) - - # Here is another one - bkgdstr = "b0 + b1*t + b2*t**2 + b3*t**3 + b4*t**4 + b5*t**5 + b6*t**6" - - contribution.registerStringFunction(bkgdstr, "bkgd") - - # Now define our fitting equation. We will hardcode the peak ratios. - contribution.setEquation( - "A1 * ( convolve( delta(t, mu11), peakshape(t, c, sig11) ) \ - + 0.23*convolve( delta(t, mu12), peakshape(t, c, sig12) ) ) + \ - A2 * ( convolve( delta(t, mu21), peakshape(t, c, sig21) ) \ - + 0.23*convolve( delta(t, mu22), peakshape(t, c, sig22) ) ) + \ - A3 * ( convolve( delta(t, mu31), peakshape(t, c, sig31) ) \ - + 0.23*convolve( delta(t, mu32), peakshape(t, c, sig32) ) ) + \ - bkgd" - ) - - # c is the center of the gaussian. - contribution.c.value = x[len(x) // 2] - - # The FitRecipe - # The FitRecipe lets us define what we want to fit. It is where we can - # create variables, constraints and restraints. - recipe = FitRecipe() - - # Here we tell the FitRecipe to use our FitContribution. When the FitRecipe - # calculates its residual function, it will call on the FitContribution to - # do part of the work. - recipe.addContribution(contribution) - - # Vary the amplitudes for each double peak - recipe.addVar(contribution.A1, 100) - recipe.addVar(contribution.A2, 100) - recipe.addVar(contribution.A3, 100) - - # Vary the position of the first of the double peaks - recipe.addVar(contribution.mu11, 13.0) - recipe.addVar(contribution.mu21, 24.0) - recipe.addVar(contribution.mu31, 33.0) - - # Constrain the position of the second double peak - from numpy import arcsin, sin - - def peakloc(mu): - """Calculate the location of the second peak given the first.""" - l1 = 1.012 - l2 = 1.0 - return 180 / pi * arcsin(pi / 180 * l2 * sin(mu) / l1) - - recipe.registerFunction(peakloc) - recipe.constrain(contribution.mu12, "peakloc(mu11)") - recipe.constrain(contribution.mu22, "peakloc(mu21)") - recipe.constrain(contribution.mu32, "peakloc(mu31)") - - # Vary the width of the peaks. We know the functional form of the peak - # broadening. - recipe.newVar("sig0", 0.001) - recipe.newVar("dsig", 4) - - def sig(sig0, dsig, mu): - """Calculate the peak broadening with respect to position.""" - return sig0 * (1 - dsig * mu**2) - - recipe.registerFunction(sig) - recipe.fix("mu") - # Now constrain the peak widths to this - recipe.sig0.value = 0.001 - recipe.dsig.value = 4.0 - recipe.constrain(contribution.sig11, "sig(sig0, dsig, mu11)") - recipe.constrain( - contribution.sig12, - "sig(sig0, dsig, mu12)", - ns={"mu12": contribution.mu12}, - ) - recipe.constrain(contribution.sig21, "sig(sig0, dsig, mu21)") - recipe.constrain( - contribution.sig22, - "sig(sig0, dsig, mu22)", - ns={"mu22": contribution.mu22}, - ) - recipe.constrain(contribution.sig31, "sig(sig0, dsig, mu31)") - recipe.constrain( - contribution.sig32, - "sig(sig0, dsig, mu32)", - ns={"mu32": contribution.mu32}, - ) - - # Also the background - recipe.addVar(contribution.b0, 0, tag="bkgd") - recipe.addVar(contribution.b1, 0, tag="bkgd") - recipe.addVar(contribution.b2, 0, tag="bkgd") - recipe.addVar(contribution.b3, 0, tag="bkgd") - recipe.addVar(contribution.b4, 0, tag="bkgd") - recipe.addVar(contribution.b5, 0, tag="bkgd") - recipe.addVar(contribution.b6, 0, tag="bkgd") - return recipe - - -def scipyOptimize(recipe): - """Optimize the recipe created above using scipy. - - The FitRecipe we created in makeRecipe has a 'residual' method that - we can be minimized using a scipy optimizer. The details are - described in the source. - """ - - # We're going to use the least-squares (Levenberg-Marquardt) optimizer from - # scipy. We simply have to give it the function to minimize - # (recipe.residual) and the starting values of the Variables - # (recipe.getValues()). - from scipy.optimize.minpack import leastsq - - print("Fit using scipy's LM optimizer") - leastsq(recipe.residual, recipe.getValues()) - - return - - -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # We can access the data and fit profile through the Profile we created - # above. We get to it through our FitContribution, which we named "g1". - # - # The independent variable. This is always under the "x" attribute. - x = recipe.peaks.profile.x - # The observed profile that we loaded earlier, the "y" attribute. - y = recipe.peaks.profile.y - # The calculated profile, the "ycalc" attribute. - ycalc = recipe.peaks.profile.ycalc - - # This stuff is specific to pylab from the matplotlib distribution. - import pylab - - pylab.plot(x, y, "b.", label="observed profile") - pylab.plot(x, ycalc, "r-", label="calculated profile") - pylab.plot(x, y - ycalc - 0.1 * max(y), "g-", label="difference") - pylab.legend(loc=(0.0, 0.8)) - pylab.xlabel("x") - pylab.ylabel("y") - - pylab.show() - return - - -def steerFit(recipe): - """Steer the fit for this problem. - - This is a complex fit, it requires some steering. - """ - recipe.fix("all") - - recipe.free("bkgd") - scipyOptimize(recipe) - - recipe.free("all") - recipe.fix("mu11", "mu21", "mu31") - scipyOptimize(recipe) - - recipe.free("all") - scipyOptimize(recipe) - - return - - -if __name__ == "__main__": - - # Create the recipe - recipe = makeRecipe() - - # Refine - steerFit(recipe) - - # Get the results in a FitResults object. The FitResults object stores the - # current state of the recipe, and uses it to calculate useful statistics - # about the fit. If you later modify the recipe, the FitResults object - # will hold the recipe values from when it was created. You can tell it to - # update its values by calling its 'update' method. - res = FitResults(recipe) - - # Print the results - res.printResults() - - # Plot the results - plotResults(recipe) - - -# End of file From 5aab0930af35902a01d845a2c98beb1cba978e17 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Thu, 20 Nov 2025 10:58:55 -0500 Subject: [PATCH 17/23] update plotting appearance --- docs/examples/core/debye-waller/debyemodel.py | 31 ++++--------------- .../core/debye-waller/debyemodelII.py | 6 ++-- .../core/gaussianfit/gaussiangenerator.py | 5 ++- .../core/gaussianfit/gaussianrecipe.py | 15 +++++---- .../examples/core/intensityfit/npintensity.py | 4 +-- .../core/intensityfit/npintensityII.py | 4 +-- 6 files changed, 26 insertions(+), 39 deletions(-) diff --git a/docs/examples/core/debye-waller/debyemodel.py b/docs/examples/core/debye-waller/debyemodel.py index 26fdaea..3ca50a9 100644 --- a/docs/examples/core/debye-waller/debyemodel.py +++ b/docs/examples/core/debye-waller/debyemodel.py @@ -35,7 +35,7 @@ import numpy -from diffpy.cmi.fit_tools import optimize_recipe +from diffpy.cmi.fit_tools import optimize_recipe, plot_results from diffpy.srfit.fitbase import ( FitContribution, FitRecipe, @@ -158,29 +158,6 @@ def make_recipe(): return recipe -def plotResults(recipe): - """Plot the results contained within a refined FitRecipe.""" - - # Plot this. - # Note that since the contribution was given the name "pb", it is - # accessible from the recipe with this name. This is a useful way to - # organize multiple contributions to a fit. - T = recipe.pb.profile.x - U = recipe.pb.profile.y - Ucalc = recipe.pb.profile.ycalc - - import pylab - - pylab.plot(T, U, "o", label="Pb $U_{iso}$ Data") - pylab.plot(T, Ucalc) - pylab.xlabel("T (K)") - pylab.ylabel(r"$U_{iso} (\AA^2)$") - pylab.legend(loc=(0.0, 0.8)) - - pylab.show() - return - - def main(): """The workflow of creating, running and inspecting a fit.""" @@ -197,7 +174,11 @@ def main(): res.printResults() # Plot the results - plotResults(recipe) + x = recipe.pb.profile.x + yobs = recipe.pb.profile.y + ycalc = recipe.pb.profile.ycalc + + plot_results(x, yobs, ycalc) return diff --git a/docs/examples/core/debye-waller/debyemodelII.py b/docs/examples/core/debye-waller/debyemodelII.py index 0aa565b..875d8f7 100644 --- a/docs/examples/core/debye-waller/debyemodelII.py +++ b/docs/examples/core/debye-waller/debyemodelII.py @@ -95,7 +95,7 @@ def make_recipeII(): return recipe -def plotResults(recipe): +def plot_results(recipe): """Display the results contained within a refined FitRecipe.""" # The variable values are returned in the order in which the variables were @@ -130,7 +130,7 @@ def plotResults(recipe): pylab.plot(T, highU, label=lbl2) pylab.xlabel("T (K)") pylab.ylabel(r"$U_{iso} (\AA^2)$") - pylab.legend(loc=(0.0, 0.8)) + pylab.legend() pylab.show() return @@ -151,7 +151,7 @@ def main(): res.printResults() # Plot the results - plotResults(recipe) + plot_results(recipe) return diff --git a/docs/examples/core/gaussianfit/gaussiangenerator.py b/docs/examples/core/gaussianfit/gaussiangenerator.py index 15ff292..5c98f6d 100644 --- a/docs/examples/core/gaussianfit/gaussiangenerator.py +++ b/docs/examples/core/gaussianfit/gaussiangenerator.py @@ -38,6 +38,8 @@ GaussianGenerator will be accessible by its name, "g". """ +from pathlib import Path + from numpy import exp from diffpy.srfit.fitbase import ( @@ -131,7 +133,8 @@ def make_recipe(): # Load data and add it to the profile. This uses the loadtxt function from # numpy. - profile.loadtxt("data/gaussian.dat") + gaussian_data = str(Path(__file__).parent / "gaussian.dat") + profile.loadtxt(gaussian_data) # The ProfileGenerator # Create a GaussianGenerator named "g". This will be the name we use to diff --git a/docs/examples/core/gaussianfit/gaussianrecipe.py b/docs/examples/core/gaussianfit/gaussianrecipe.py index 3d84e46..9634a92 100644 --- a/docs/examples/core/gaussianfit/gaussianrecipe.py +++ b/docs/examples/core/gaussianfit/gaussianrecipe.py @@ -26,8 +26,8 @@ to get an understanding of how a fit recipe can be used once created. After that, read the 'make_recipe' code to see what goes into a fit recipe. After that, read the 'optimize_recipe' code to see how the refinement is executed. -Finally, read the 'plotResults' code to see how to extracts the refined profile -and plot it. +Finally, read the 'plot_results' code to see how to extracts the refined +profile and plot it. Extensions @@ -44,6 +44,8 @@ """ +from pathlib import Path + from diffpy.srfit.fitbase import ( FitContribution, FitRecipe, @@ -75,7 +77,7 @@ def main(): res.printResults() # Plot the results. - plotResults(recipe) + plot_results(recipe) return @@ -101,7 +103,8 @@ def make_recipe(): # Load data and add it to the profile. This uses the loadtxt function from # numpy. - profile.loadtxt("data/gaussian.dat") + gaussian_data = str(Path(__file__).parent / "gaussian.dat") + profile.loadtxt(gaussian_data) # The FitContribution # The FitContribution associates the Profile with a fitting equation. The @@ -180,7 +183,7 @@ def optimize_recipe(recipe): return -def plotResults(recipe): +def plot_results(recipe): """Plot the results contained within a refined FitRecipe.""" # We can access the data and fit profile through the Profile we created @@ -198,7 +201,7 @@ def plotResults(recipe): pylab.plot(x, y, "b.", label="observed Gaussian") pylab.plot(x, ycalc, "g-", label="calculated Gaussian") - pylab.legend(loc=(0.0, 0.8)) + pylab.legend() pylab.xlabel("x") pylab.ylabel("y") diff --git a/docs/examples/core/intensityfit/npintensity.py b/docs/examples/core/intensityfit/npintensity.py index 7e6aa87..464f56f 100644 --- a/docs/examples/core/intensityfit/npintensity.py +++ b/docs/examples/core/intensityfit/npintensity.py @@ -331,12 +331,12 @@ def main(): res.printResults(footer=footer) # Plot! - plotResults(recipe) + plot_results(recipe) return -def plotResults(recipe): +def plot_results(recipe): """Plot the results contained within a refined FitRecipe.""" # All this should be pretty familiar by now. diff --git a/docs/examples/core/intensityfit/npintensityII.py b/docs/examples/core/intensityfit/npintensityII.py index 287d826..32508c2 100644 --- a/docs/examples/core/intensityfit/npintensityII.py +++ b/docs/examples/core/intensityfit/npintensityII.py @@ -187,7 +187,7 @@ def gaussian(q, q0, width): return recipe -def plotResults(recipe): +def plot_results(recipe): """Plot the results contained within a refined FitRecipe.""" # plotting song and dance @@ -271,7 +271,7 @@ def main(): res.printResults() # Plot! - plotResults(recipe) + plot_results(recipe) return From a45d32abd344ac1a892a3be687da6886f55a65d4 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Thu, 20 Nov 2025 10:59:44 -0500 Subject: [PATCH 18/23] news --- news/srfit_examples.rst | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) create mode 100644 news/srfit_examples.rst diff --git a/news/srfit_examples.rst b/news/srfit_examples.rst new file mode 100644 index 0000000..e45189a --- /dev/null +++ b/news/srfit_examples.rst @@ -0,0 +1,23 @@ +**Added:** + +* Add ``diffpy.srfit`` examples to ``core`` pack. + +**Changed:** + +* + +**Deprecated:** + +* + +**Removed:** + +* + +**Fixed:** + +* + +**Security:** + +* From 38e4423f87f885fb771e960f41fc03eeefd4f3cd Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Thu, 20 Nov 2025 11:04:02 -0500 Subject: [PATCH 19/23] change example name --- docs/examples/pdf/{core-shell-NP => nanoparticle-fit}/CdS.cif | 0 .../pdf/{core-shell-NP => nanoparticle-fit}/CdS_ZnS_nano.gr | 0 docs/examples/pdf/{core-shell-NP => nanoparticle-fit}/ZnS.cif | 0 .../pdf/{core-shell-NP => nanoparticle-fit}/coreshellnp.py | 0 4 files changed, 0 insertions(+), 0 deletions(-) rename docs/examples/pdf/{core-shell-NP => nanoparticle-fit}/CdS.cif (100%) rename docs/examples/pdf/{core-shell-NP => nanoparticle-fit}/CdS_ZnS_nano.gr (100%) rename docs/examples/pdf/{core-shell-NP => nanoparticle-fit}/ZnS.cif (100%) rename docs/examples/pdf/{core-shell-NP => nanoparticle-fit}/coreshellnp.py (100%) diff --git a/docs/examples/pdf/core-shell-NP/CdS.cif b/docs/examples/pdf/nanoparticle-fit/CdS.cif similarity index 100% rename from docs/examples/pdf/core-shell-NP/CdS.cif rename to docs/examples/pdf/nanoparticle-fit/CdS.cif diff --git a/docs/examples/pdf/core-shell-NP/CdS_ZnS_nano.gr b/docs/examples/pdf/nanoparticle-fit/CdS_ZnS_nano.gr similarity index 100% rename from docs/examples/pdf/core-shell-NP/CdS_ZnS_nano.gr rename to docs/examples/pdf/nanoparticle-fit/CdS_ZnS_nano.gr diff --git a/docs/examples/pdf/core-shell-NP/ZnS.cif b/docs/examples/pdf/nanoparticle-fit/ZnS.cif similarity index 100% rename from docs/examples/pdf/core-shell-NP/ZnS.cif rename to docs/examples/pdf/nanoparticle-fit/ZnS.cif diff --git a/docs/examples/pdf/core-shell-NP/coreshellnp.py b/docs/examples/pdf/nanoparticle-fit/coreshellnp.py similarity index 100% rename from docs/examples/pdf/core-shell-NP/coreshellnp.py rename to docs/examples/pdf/nanoparticle-fit/coreshellnp.py From 4acb1ff5fb15a1c1c71b72a989c1ae670f67a65d Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Thu, 20 Nov 2025 12:59:10 -0500 Subject: [PATCH 20/23] add examples to docs --- docs/source/tutorials/core.rst | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/docs/source/tutorials/core.rst b/docs/source/tutorials/core.rst index 7afaf42..62da432 100644 --- a/docs/source/tutorials/core.rst +++ b/docs/source/tutorials/core.rst @@ -6,4 +6,8 @@ To copy an example to your current working directory, use the command ``cmi copy Available Examples ------------------ +- debye-waller +- gaussianfit +- intensityfit - linefit +- readme From dadf17e2c453fd701c0e76d8063710ff0288a78f Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Thu, 20 Nov 2025 13:03:12 -0500 Subject: [PATCH 21/23] add necessary instructions to release checklist and pack proposal --- .github/ISSUE_TEMPLATE/new_pack_proposal.md | 1 + .github/ISSUE_TEMPLATE/release_checklist.md | 3 ++- 2 files changed, 3 insertions(+), 1 deletion(-) diff --git a/.github/ISSUE_TEMPLATE/new_pack_proposal.md b/.github/ISSUE_TEMPLATE/new_pack_proposal.md index 3d4328d..c1f7404 100644 --- a/.github/ISSUE_TEMPLATE/new_pack_proposal.md +++ b/.github/ISSUE_TEMPLATE/new_pack_proposal.md @@ -16,6 +16,7 @@ assignees: "" - [ ] Create a requirements file by running `touch requirements/packs/.txt`. List all dependencies for your pack. - [ ] (OPTIONAL) Create a directory to place your examples, if applicable, by running `mkdir docs/examples//`. - [ ] (OPTIONAL) Copy your example scripts and data under the directory you just made. If you have multiple examples, house them under their own separate directory (i.e. `...//example1` and `...//example2`). +- [ ] (OPTIONAL) Make a file under `docs/source/tutorial/` call `.rst` with `cp docs/source/tutorial/core.rst docs/source/tutorial/.rst`. Add your examples to the file in the same format as listed. - [ ] List your pack and its dependencies under `docs/source/available-packs.rst` using the same format as the other packs. In this same file, add a description of your pack (1-2 sentences is recommended). - [ ] Give yourself credit by listing your name and contributors to the pack you've created! diff --git a/.github/ISSUE_TEMPLATE/release_checklist.md b/.github/ISSUE_TEMPLATE/release_checklist.md index 5be9636..873b0eb 100644 --- a/.github/ISSUE_TEMPLATE/release_checklist.md +++ b/.github/ISSUE_TEMPLATE/release_checklist.md @@ -6,9 +6,10 @@ labels: "release" assignees: "" --- -### Run diffpy.cmi example scripts +### checklist for diffpy.cmi - [ ] Manually trigger the `validate-examples.yml` workflow to run all example scripts. +- [ ] Make sure available examples, packs, and profiles are listed in the docs. Check this by installing locally with `pip install .`, building the docs with `cmi install docs && cd docs && make html && open build/html/index.html`, running `cmi info`, and comparing the output to what is listed under "Examples" in the docs. ### PyPI/GitHub rc-release preparation checklist: From d845c8e7a1755bbd7b52c90704d86e222af48177 Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Thu, 20 Nov 2025 13:11:26 -0500 Subject: [PATCH 22/23] add segue to more complex fitting in cmi --- docs/source/writing-script.rst | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) diff --git a/docs/source/writing-script.rst b/docs/source/writing-script.rst index 4b92ace..568aae8 100644 --- a/docs/source/writing-script.rst +++ b/docs/source/writing-script.rst @@ -423,3 +423,22 @@ Words of Encouragement Remember, all the computer knows how to do is minimize a value. It has no understanding of the physical meaning of the parameters. That is why we need smart people like yourself to guide the fitting process! + +What's Next? +------------ + +Now that you have a basic understanding of how to write a script using ``diffpy.cmi``, +you can explore more advanced examples such as fitting a gaussian (``gaussianfit`` example) or fitting intensity (``intensityfit`` example) data with ``diffpy.cmi``. +To see available examples, run + +.. code-block:: bash + + cmi info examples + +To copy an example to your current working directory, use the command + +.. code-block:: bash + + cmi copy + +Happy fitting! From 1eb0de52047eaed32ed822e70ce386da112a04ef Mon Sep 17 00:00:00 2001 From: Caden Myers Date: Thu, 20 Nov 2025 15:28:57 -0500 Subject: [PATCH 23/23] add fit_tools to api docs --- docs/source/api/diffpy.cmi.rst | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/docs/source/api/diffpy.cmi.rst b/docs/source/api/diffpy.cmi.rst index 9365832..bd41f2c 100644 --- a/docs/source/api/diffpy.cmi.rst +++ b/docs/source/api/diffpy.cmi.rst @@ -43,6 +43,14 @@ diffpy.cmi.installer module :undoc-members: :show-inheritance: +diffpy.cmi.fit_tools module +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. automodule:: diffpy.cmi.fit_tools + :members: + :undoc-members: + :show-inheritance: + diffpy.cmi.cli module ^^^^^^^^^^^^^^^^^^^^^