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Specialize isdiag for certain ConversionWrappers (#287)
* Specialize isdiag for certain ConversionWrappers * isdiag for Jacobi ConversionWrapper * Bump version to v0.6.42 * Conversions between Jacobi and Ultraspherical * Specialize israggedbelow, fix Ultraspheriacl ConcreteConversion indexing * Specialize ConcreteConversion indexing for Union{Integer, HalfOddInteger} * Fix ambiguity
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‎Project.toml‎

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -1,6 +1,6 @@
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name = "ApproxFunOrthogonalPolynomials"
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uuid = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
3-
version = "0.6.41"
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version = "0.6.42"
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[deps]
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ApproxFunBase = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"

‎src/ApproxFunOrthogonalPolynomials.jl‎

Lines changed: 2 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -56,7 +56,8 @@ import ApproxFunBase: Fun, SubSpace, WeightSpace, NoSpace, HeavisideSpace,
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isleftendpoint, isrightendpoint, evaluation_point, boundaryfn, ldiffbc, rdiffbc,
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LeftEndPoint, RightEndPoint, normalizedspace, promotedomainspace,
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bandmatrices_eigen, SymmetricEigensystem, SkewSymmetricEigensystem,
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mean # differs from Statistics.mean after https://github.com/JuliaApproximation/ApproxFunBase.jl/pull/506
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mean, # differs from Statistics.mean after https://github.com/JuliaApproximation/ApproxFunBase.jl/pull/506
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israggedbelow
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import DomainSets: Domain, indomain, UnionDomain, FullSpace, Point,
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Interval, ChebyshevInterval, boundary, rightendpoint, leftendpoint,

‎src/Spaces/Jacobi/JacobiOperators.jl‎

Lines changed: 8 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -192,7 +192,14 @@ end
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193193
bandwidths(::ConcreteConversion{<:Jacobi,<:Jacobi}) = (0,1)
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195-
195+
# These methods help with constant propagating the bandwidths of a KroneckerOperator
196+
isdiag(::ConversionWrapper{<:Chebyshev,<:Jacobi}) = false
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isdiag(::ConversionWrapper{<:Jacobi,<:Jacobi,<:Any,<:ConstantOperator}) = true
198+
isdiag(::ConversionWrapper{<:Union{Ultraspherical,Jacobi},<:Union{Ultraspherical,Jacobi}}) = false
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200+
# These operators are banded and UpperTriangular
201+
israggedbelow(::ConversionWrapper{<:Chebyshev,<:Jacobi}) = true
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israggedbelow(::ConversionWrapper{<:Union{Ultraspherical,Jacobi},<:Union{Ultraspherical,Jacobi}}) = true
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197204
function getindex(C::ConcreteConversion{<:Jacobi,<:Jacobi,T},k::Integer,j::Integer) where {T}
198205
L=C.domainspace

‎src/Spaces/Ultraspherical/UltrasphericalOperators.jl‎

Lines changed: 23 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -213,10 +213,10 @@ function getindex(M::ConcreteConversion{<:Chebyshev,U,T},
213213
end
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215215

216-
function getindex(M::ConcreteConversion{U1,U2,T},
217-
k::Integer,j::Integer) where {DD,RR,
218-
U1<:Ultraspherical{<:Integer,DD,RR},
219-
U2<:Ultraspherical{<:Integer,DD,RR},T}
216+
function _getindex(M::ConcreteConversion{U1,U2,T}, k, j) where {DD,RR,
217+
OT<:Union{Integer, HalfOddInteger},
218+
U1<:Ultraspherical{<:OT,DD,RR},
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U2<:Ultraspherical{<:OT,DD,RR},T}
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# we can assume that λ==m+1
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λ=order(rangespace(M))
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c=λ-one(T) # this supports big types
@@ -229,6 +229,17 @@ function getindex(M::ConcreteConversion{U1,U2,T},
229229
end
230230
end
231231

232+
function getindex(M::ConcreteConversion{U1,U2,T}, k::Integer, j::Integer) where {DD,RR,
233+
U1<:Ultraspherical{<:Integer,DD,RR},
234+
U2<:Ultraspherical{<:Integer,DD,RR},T}
235+
_getindex(M, k, j)
236+
end
237+
function getindex(M::ConcreteConversion{U1,U2,T}, k::Integer, j::Integer) where {DD,RR,
238+
U1<:Ultraspherical{<:HalfOddInteger,DD,RR},
239+
U2<:Ultraspherical{<:HalfOddInteger,DD,RR},T}
240+
_getindex(M, k, j)
241+
end
242+
232243
function getindex(M::ConcreteConversion{U1,U2,T},
233244
k::Integer,j::Integer) where {DD,RR,
234245
U1<:Ultraspherical{<:Any,DD,RR},
@@ -273,6 +284,13 @@ isdiag(::ConcreteConversion{<:Chebyshev,<:Ultraspherical}) = false
273284
isdiag(::ConcreteConversion{<:Ultraspherical,<:Chebyshev}) = false
274285
isdiag(::ConcreteConversion{<:Ultraspherical,<:Ultraspherical}) = false
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287+
# These methods help with constant propagating the bandwidths of a KroneckerOperator
288+
isdiag(::ConversionWrapper{<:Chebyshev,<:Ultraspherical}) = false
289+
isdiag(::ConversionWrapper{<:Ultraspherical,<:Ultraspherical, <:Any, <:ConstantOperator}) = true
290+
291+
# These operators are banded and UpperTriangular
292+
israggedbelow(::ConversionWrapper{<:Chebyshev,<:Ultraspherical}) = true
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## coefficients
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278296
# return the space that has banded Conversion to the other
@@ -381,7 +399,7 @@ function getindex(M::ConcreteConversion{Ultraspherical{LT,DD,RR},
381399
zero(T)
382400
end
383401
else
384-
error("Not implemented")
402+
error("Not implemented for $M")
385403
end
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end
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‎test/JacobiTest.jl‎

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Original file line numberDiff line numberDiff line change
@@ -791,6 +791,63 @@ include("testutils.jl")
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@test ApproxFunBase.hasconversion(NormalizedChebyshev()*Legendre(), Chebyshev()*Legendre())
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@test ApproxFunBase.hasconversion(NormalizedChebyshev()*NormalizedLegendre(), Chebyshev()*Legendre())
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@test ApproxFunBase.hasconversion(Chebyshev()*Legendre(), NormalizedChebyshev()*NormalizedLegendre())
794+
795+
@testset "isbanded and israggedbelow for KroneckerOperator" begin
796+
function testspaces(d1, d2, r1, r2, res = Val(false))
797+
K = (Operator(I, d1) ⊗ Operator(I, d2)) → (r1 * r2)
798+
@test (@inferred (K -> Val(isbanded(K)))(K)) == res
799+
@test (@inferred (K -> Val(ApproxFunBase.israggedbelow(K)))(K)) == Val(true)
800+
f = Fun((x,y)->x*y, d1*d2)
801+
g = Fun((x,y)->x*y, r1*r2)
802+
@test K * f ≈ g
803+
end
804+
805+
d1, r1 = Chebyshev(), Legendre()
806+
d2, r2 = Chebyshev(), Chebyshev()
807+
testspaces(d1, d2, r1, r2)
808+
809+
d1, r1 = Legendre(), Chebyshev()
810+
testspaces(d1, d2, r1, r2)
811+
812+
d1, r1 = Chebyshev(), Jacobi(1,1)
813+
testspaces(d1, d2, r1, r2)
814+
815+
d1, r1 = Chebyshev(), Jacobi(Ultraspherical(1))
816+
d2, r2 = Chebyshev(), Chebyshev()
817+
testspaces(d1, d2, r1, r2)
818+
819+
d1, r1 = Chebyshev(), Jacobi(Ultraspherical(2))
820+
testspaces(d1, d2, r1, r2)
821+
822+
d1, r1 = Jacobi(Ultraspherical(1)), Jacobi(Ultraspherical(1))
823+
testspaces(d1, d2, r1, r2, Val(true))
824+
825+
d1, r1 = Jacobi(Ultraspherical(1)), Jacobi(Ultraspherical(2))
826+
testspaces(d1, d2, r1, r2)
827+
828+
d1, r1 = Jacobi(Ultraspherical(1)), Ultraspherical(2)
829+
testspaces(d1, d2, r1, r2)
830+
831+
d1, r1 = Ultraspherical(1), Jacobi(Ultraspherical(2))
832+
testspaces(d1, d2, r1, r2)
833+
834+
d1, r1 = Jacobi(Ultraspherical(1)), Jacobi(Ultraspherical(3))
835+
testspaces(d1, d2, r1, r2)
836+
837+
d1, r1 = Jacobi(Ultraspherical(1)), Jacobi(2,2)
838+
testspaces(d1, d2, r1, r2)
839+
840+
d1, r1 = Ultraspherical(1), Jacobi(2,2)
841+
testspaces(d1, d2, r1, r2)
842+
end
843+
844+
d1, r1 = Legendre(), Jacobi(2,2)
845+
d2, r2 = Chebyshev(), Chebyshev()
846+
K = (Operator(I, d1) ⊗ Operator(I, d2)) → (r1 ⊗ r2)
847+
M = K[1:20, 1:20]
848+
for ind in CartesianIndices(M)
849+
@test K[ind] ≈ M[ind]
850+
end
794851
end
795852
end
796853

‎test/UltrasphericalTest.jl‎

Lines changed: 44 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -2,12 +2,13 @@ module UltrasphericalTest
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33
using ApproxFunOrthogonalPolynomials
44
using ApproxFunBase
5-
using Test
6-
using SpecialFunctions
5+
using BandedMatrices
6+
using HalfIntegers
77
using LinearAlgebra
8-
using Static
98
using OddEvenIntegers
10-
using HalfIntegers
9+
using SpecialFunctions
10+
using Static
11+
using Test
1112

1213
include("testutils.jl")
1314

@@ -187,6 +188,45 @@ include("testutils.jl")
187188
end
188189
end
189190
end
191+
192+
@testset "isbanded for KroneckerOperator" begin
193+
function testspaces(d1, d2, r1, r2, res = Val(false))
194+
K = (Operator(I, d1) ⊗ Operator(I, d2)) → (r1 * r2)
195+
@test (@inferred (K -> Val(isbanded(K)))(K)) == res
196+
@test (@inferred (K -> Val(ApproxFunBase.israggedbelow(K)))(K)) == Val(true)
197+
f = Fun((x,y)->x*y, d1*d2)
198+
g = Fun((x,y)->x*y, r1*r2)
199+
@test K * f ≈ g
200+
end
201+
d1, r1 = Chebyshev(), Ultraspherical(1)
202+
d2, r2 = Chebyshev(), Chebyshev()
203+
testspaces(d1, d2, r1, r2)
204+
205+
d1, r1 = Chebyshev(), Ultraspherical(2)
206+
testspaces(d1, d2, r1, r2)
207+
208+
d1, r1 = Ultraspherical(1), Ultraspherical(1)
209+
testspaces(d1, d2, r1, r2, Val(true))
210+
211+
d1, r1 = Ultraspherical(1), Ultraspherical(2)
212+
testspaces(d1, d2, r1, r2)
213+
214+
d1, r1 = Ultraspherical(1), Ultraspherical(3)
215+
testspaces(d1, d2, r1, r2)
216+
end
217+
218+
@testset "ConcreteConversion indexing" begin
219+
for (s1, s2) in ((Ultraspherical(Legendre()), Ultraspherical(Jacobi(1,1))),
220+
(Ultraspherical(1), Ultraspherical(2)),
221+
(Ultraspherical(static(1)), Ultraspherical(static(2))),
222+
)
223+
C = Conversion(s1, s2)
224+
M = C[1:4, 1:4]
225+
for ind in CartesianIndices(M)
226+
@test C[ind] ≈ M[ind]
227+
end
228+
end
229+
end
190230
end
191231

192232
@testset "Normalized space" begin

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