@@ -19,7 +19,6 @@ synonyms are listed.
1919
2020Additional functionality is provided when these optional packages are installed:
2121- Symbolic manipulation of Haar matrices with [ GSL.jl] ( https://github.com/jiahao/GSL.jl )
22- - Invariant ensembles with [ ApproxFun.jl] ( https://github.com/dlfivefifty/ApproxFun.jl )
2322
2423# Gaussian matrix ensembles
2524
@@ -44,7 +43,6 @@ The hierarchy of dense matrices provided are
4443 - Circular symplectic ensemble (CSE, ` beta=4 ` )
4544- Laguerre matrices = white Wishart matrices
4645- Jacobi matrices = MANOVA matrices
47- - Unitary invariant ensembles
4846
4947Unless otherwise specified, ` beta=1,2,4 ` are supported. For the symplectic matrices ` beta=4 ` ,
5048the 2x2 outer block-diagonal complex representation ` USp(2N) ` is used.
@@ -89,11 +87,6 @@ Hermite, Laguerre(m) and Jacobi(m1, m2) ensembles.
8987 used. Other valid values are ` 0 ` (no correction) and ` 2 ` (Mezzadri's correction).
9088 - ` NeedsPiecewiseCorrection() ` implements a simple test to see if a correction is necessary.
9189
92- - ` InvariantEnsemble(str,n) `
93- Generates a unitary invariant ensemble, where str determines the
94- potential of the ensemble, see below.
95- Only available if ApproxFun package is installed.
96-
9790The parameters ` m ` , ` m1 ` , ` m2 ` refer to the number to independent "data" degrees of freedom.
9891For the dense samples these must be ` Integer ` s but can be ` Real ` s for the rest.
9992
@@ -168,21 +161,7 @@ The available `StochasticProcess`es are
168161# Invariant ensembles
169162
170163` InvariantEnsemble(str,n) ` supports n x n unitary invariant ensemble
171- with distribution
172-
173- ` exp(- Tr Q(M)) dM `
174-
175- ` str ` specifies an ensemble with precomputed recurrence coefficients.
176- The currently include ensembles are
177-
178- | | Q(M) |
179- | ----------------- | ----- |
180- | ` Quartic ` | n M^4 |
181- | ` Eighth ` | n M^8 |
182- | ` HODecay ` | n (M^4/20 - 4/15M^3 +M^2/5 + 8/5M) |
183- | ` CoshUnscaled ` | cosh(M) |
184- | ` QuarticUnscaled ` | M^4 |
185- | ` EightUnscaled ` | M^8 |
164+ with distribution. This has been moved to separate package [ InvariantEnsembles.jl] ( https://github.com/dlfivefifty/InvariantEnsembles.jl )
186165
187166# References
188167- James Albrecht, Cy Chan, and Alan Edelman,
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