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adjust tests and remove semiclassical dep
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‎Project.toml

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Original file line numberDiff line numberDiff line change
@@ -22,7 +22,6 @@ LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
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LazyBandedMatrices = "d7e5e226-e90b-4449-9968-0f923699bf6f"
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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QuasiArrays = "c4ea9172-b204-11e9-377d-29865faadc5c"
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SemiclassicalOrthogonalPolynomials = "291c01f3-23f6-4eb6-aeb0-063a639b53f2"
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SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
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[compat]

‎test/test_decompOPs.jl

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@@ -4,120 +4,34 @@ import LazyArrays: AbstractCachedMatrix
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import LazyBandedMatrices: SymTridiagonal
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@testset "Basic properties" begin
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@testset "Test the Q&D conversion to BandedMatrix format" begin
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# Legendre
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P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
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x = axes(P,1)
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J = jacobimatrix(P)
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Jx = symmjacobim(J)
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@test J[1:100,1:100] == Jx[1:100,1:100]
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# Jacobi
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P = Normalized(Jacobi(1,2)[affine(0..1,Inclusion(-1..1)),:])
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x = axes(P,1)
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J = jacobimatrix(P)
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Jx = symmjacobim(J)
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@test J[1:100,1:100] == Jx[1:100,1:100]
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end
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@testset "Basic types and getindex variants" begin
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# basis
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P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
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x = axes(P,1)
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J = jacobimatrix(P)
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Jx = symmjacobim(J)
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# example weight
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w = (I - Jx^2)
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# banded cholesky for symmetric-tagged W
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@test cholesky(w).U isa UpperTriangular
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# compute Jacobi matrix via cholesky
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Jchol = cholesky_jacobimatrix(w)
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@test Jchol isa LazyBandedMatrices.SymTridiagonal
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# CholeskyJacobiBands object
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Cbands = CholeskyJacobiBands(w)
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@test Cbands isa CholeskyJacobiBands
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@test Cbands isa AbstractCachedMatrix
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@test getindex(Cbands,1,100) == getindex(Cbands,1,1:100)[100]
40-
end
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# basis
8+
P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
9+
x = axes(P,1)
10+
J = jacobimatrix(P)
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# example weight
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w(x) = (1 - x^2)
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W = Symmetric(P \ (w.(x) .* P))
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# banded cholesky for symmetric-tagged W
15+
@test cholesky(W).U isa UpperTriangular
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# compute Jacobi matrix via cholesky
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Jchol = cholesky_jacobimatrix(w,P)
18+
@test Jchol isa SymTridiagonal
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# CholeskyJacobiBands object
20+
Cbands = CholeskyJacobiBands(W,P)
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@test Cbands isa CholeskyJacobiBands
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@test Cbands isa AbstractCachedMatrix
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@test getindex(Cbands,1,100) == getindex(Cbands,1,1:100)[100]
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end
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@testset "Comparison with Lanczos and Classical" begin
44-
@testset "Not using Clenshaw" begin
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@testset "w(x) = x^2*(1-x)" begin
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P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
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x = axes(P,1)
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J = jacobimatrix(P)
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Jx = symmjacobim(J)
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w = (Jx^2 - Jx^3)
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# compute Jacobi matrix via cholesky
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Jchol = cholesky_jacobimatrix(w)
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# compute Jacobi matrix via classical recurrence
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Q = Normalized(Jacobi(1,2)[affine(0..1,Inclusion(-1..1)),:])
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Jclass = jacobimatrix(Q)
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# compute Jacobi matrix via Lanczos
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wf = x.^2 .* (1 .- x)
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Jlanc = jacobimatrix(LanczosPolynomial(@.(wf),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
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# Comparison with Lanczos
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@test Jchol[1:500,1:500] ≈ Jlanc[1:500,1:500]
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# Comparison with Classical
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@test Jchol[1:500,1:500] ≈ Jclass[1:500,1:500]
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end
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65-
@testset "w(x) = (1-x^2)" begin
66-
P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
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x = axes(P,1)
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J = jacobimatrix(P)
69-
Jx = symmjacobim(J)
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w = (I - Jx^2)
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# compute Jacobi matrix via cholesky
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Jchol = cholesky_jacobimatrix(w)
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# compute Jacobi matrix via Lanczos
74-
wf = (1 .- x.^2)
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Jlanc = jacobimatrix(LanczosPolynomial(@.(wf),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
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# Comparison
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@test Jchol[1:500,1:500] ≈ Jlanc[1:500,1:500]
78-
end
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80-
@testset "w(x) = (1-x^4)" begin
81-
P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
82-
x = axes(P,1)
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J = jacobimatrix(P)
84-
Jx = symmjacobim(J)
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w = (I - Jx^4)
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# compute Jacobi matrix via cholesky
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Jchol = cholesky_jacobimatrix(w)
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# compute Jacobi matrix via Lanczos
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wf = (1 .- x.^4)
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Jlanc = jacobimatrix(LanczosPolynomial(@.(wf),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
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# Comparison
92-
@test Jchol[1:500,1:500] ≈ Jlanc[1:500,1:500]
93-
end
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95-
@testset "w(x) = (1.014-x^3)" begin
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P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
97-
x = axes(P,1)
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J = jacobimatrix(P)
99-
Jx = symmjacobim(J)
100-
t = 1.014
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w = (t*I - Jx^3)
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# compute Jacobi matrix via cholesky
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Jchol = cholesky_jacobimatrix(w)
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# compute Jacobi matrix via Lanczos
105-
wf = (t .- x.^3)
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Jlanc = jacobimatrix(LanczosPolynomial(@.(wf),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
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# Comparison
108-
@test Jchol[1:500,1:500] ≈ Jlanc[1:500,1:500]
109-
end
110-
end
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11227
@testset "Using Clenshaw for polynomial weights" begin
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@testset "w(x) = x^2*(1-x)" begin
11429
P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
11530
x = axes(P,1)
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J = jacobimatrix(P)
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wf(x) = x^2*(1-x)
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# compute Jacobi matrix via cholesky
119-
W = P \ (wf.(x) .* P)
120-
Jchol = cholesky_jacobimatrix(Symmetric(W))
34+
Jchol = cholesky_jacobimatrix(wf, P)
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# compute Jacobi matrix via classical recurrence
12236
Q = Normalized(Jacobi(1,2)[affine(0..1,Inclusion(-1..1)),:])
12337
Jclass = jacobimatrix(Q)
@@ -135,8 +49,7 @@ end
13549
J = jacobimatrix(P)
13650
wf(x) = (1-x^2)
13751
# compute Jacobi matrix via cholesky
138-
W = P \ (wf.(x) .* P)
139-
Jchol = cholesky_jacobimatrix(Symmetric(W))
52+
Jchol = cholesky_jacobimatrix(wf, P)
14053
# compute Jacobi matrix via Lanczos
14154
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf.(x)),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
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# Comparison with Lanczos
@@ -149,8 +62,7 @@ end
14962
J = jacobimatrix(P)
15063
wf(x) = (1-x^4)
15164
# compute Jacobi matrix via cholesky
152-
W = P \ (wf.(x) .* P)
153-
Jchol = cholesky_jacobimatrix(Symmetric(W))
65+
Jchol = cholesky_jacobimatrix(wf, P)
15466
# compute Jacobi matrix via Lanczos
15567
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf.(x)),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
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# Comparison with Lanczos
@@ -163,8 +75,7 @@ end
16375
J = jacobimatrix(P)
16476
wf(x) = 1.014-x^4
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# compute Jacobi matrix via cholesky
166-
W = P \ (wf.(x) .* P)
167-
Jchol = cholesky_jacobimatrix(Symmetric(W))
78+
Jchol = cholesky_jacobimatrix(wf, P)
16879
# compute Jacobi matrix via Lanczos
16980
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf.(x)),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
17081
# Comparison with Lanczos
@@ -179,8 +90,7 @@ end
17990
J = jacobimatrix(P)
18091
wf(x) = exp(x)
18192
# compute Jacobi matrix via cholesky
182-
W = P \ (wf.(x) .* P)
183-
Jchol = cholesky_jacobimatrix(Symmetric(W))
93+
Jchol = cholesky_jacobimatrix(wf, P)
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# compute Jacobi matrix via Lanczos
18595
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf.(x)),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
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# Comparison with Lanczos
@@ -193,8 +103,7 @@ end
193103
J = jacobimatrix(P)
194104
wf(x) = (1-x)*exp(x)
195105
# compute Jacobi matrix via cholesky
196-
W = P \ (wf.(x) .* P)
197-
Jchol = cholesky_jacobimatrix(Symmetric(W))
106+
Jchol = cholesky_jacobimatrix(wf, P)
198107
# compute Jacobi matrix via Lanczos
199108
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf.(x)),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
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# Comparison with Lanczos
@@ -207,8 +116,7 @@ end
207116
J = jacobimatrix(P)
208117
wf(x) = (1-x^2)*exp(x^2)
209118
# compute Jacobi matrix via cholesky
210-
W = P \ (wf.(x) .* P)
211-
Jchol = cholesky_jacobimatrix(Symmetric(W))
119+
Jchol = cholesky_jacobimatrix(wf, P)
212120
# compute Jacobi matrix via Lanczos
213121
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf.(x)),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
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# Comparison with Lanczos
@@ -221,12 +129,11 @@ end
221129
J = jacobimatrix(P)
222130
wf(x) = x*(1-x^2)*exp(-x^2)
223131
# compute Jacobi matrix via cholesky
224-
W = P \ (wf.(x) .* P)
225-
Jchol = cholesky_jacobimatrix(Symmetric(W))
132+
Jchol = cholesky_jacobimatrix(wf, P)
226133
# compute Jacobi matrix via Lanczos
227134
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf.(x)),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
228135
# Comparison with Lanczos
229136
@test Jchol[1:500,1:500] ≈ Jlanc[1:500,1:500]
230137
end
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end
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end
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end

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