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‎src/decompOPs.jl

Lines changed: 0 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -52,7 +52,6 @@ function cache_filldata!(J::CholeskyJacobiBands, inds)
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end
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end
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55-
# Need to check which of these are actually useful in practice with tests
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function getindex(K::CholeskyJacobiBands, k::Integer, j::Integer)
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resizedata!(K, max(k,j))
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K.data[k, j]

‎test/test_decompOPs.jl

Lines changed: 100 additions & 87 deletions
Original file line numberDiff line numberDiff line change
@@ -1,96 +1,109 @@
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using Test, ClassicalOrthogonalPolynomials, BandedMatrices, LinearAlgebra, LazyArrays, ContinuumArrays, LazyBandedMatrices
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import ClassicalOrthogonalPolynomials: symmjacobim
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import ClassicalOrthogonalPolynomials: symmjacobim, CholeskyJacobiBands
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import LazyArrays: AbstractCachedMatrix
34

4-
@testset begin "Test the Q&D conversion to BandedMatrix format"
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# Legendre
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P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
7-
x = axes(P,1)
8-
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]
17-
end
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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
8+
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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19-
@testset begin "Basic properties of Cholesky based Jacobi operators"
20-
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 = (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)
29-
@test Jchol isa LazyBandedMatrices.SymTridiagonal
21+
@testset "Basic types and getindex variants" begin
22+
# basis
23+
P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
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x = axes(P,1)
25+
J = jacobimatrix(P)
26+
Jx = symmjacobim(J)
27+
# example weight
28+
w = (I - Jx^2)
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# banded cholesky for symmetric-tagged W
30+
@test cholesky(w).U isa UpperTriangular
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# compute Jacobi matrix via cholesky
32+
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 Cbands[1,100] == (Cbands[1,1:100])[100]
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@test Cbands[:,50] == [Cbands[1,50],Cbands[2,50]]
40+
end
3041
end
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32-
@testset begin "Comparison with Lanczos and Classical for w(x) = x^2*(1-x)"
33-
P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
34-
x = axes(P,1)
35-
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
39-
Jchol = cholesky_jacobimatrix(w)
40-
# compute Jacobi matrix via classical recurrence
41-
Q = Normalized(Jacobi(1,2)[affine(0..1,Inclusion(-1..1)),:])
42-
Jclass = jacobimatrix(Q)
43-
# compute Jacobi matrix via Lanczos
44-
wf = x.^2 .* (1 .- x)
45-
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
46-
# Comparison with Lanczos
47-
@test Jchol[1:500,1:500] ≈ Jlanc[1:500,1:500]
48-
# Comparison with Classical
49-
@test Jchol[1:500,1:500] ≈ Jclass[1:500,1:500]
50-
end
43+
@testset "Comparison with Lanczos and Classical" begin
44+
@testset "w(x) = x^2*(1-x)" begin
45+
P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
46+
x = axes(P,1)
47+
J = jacobimatrix(P)
48+
Jx = symmjacobim(J)
49+
w = (Jx^2 - Jx^3)
50+
# compute Jacobi matrix via cholesky
51+
Jchol = cholesky_jacobimatrix(w)
52+
# compute Jacobi matrix via classical recurrence
53+
Q = Normalized(Jacobi(1,2)[affine(0..1,Inclusion(-1..1)),:])
54+
Jclass = jacobimatrix(Q)
55+
# compute Jacobi matrix via Lanczos
56+
wf = x.^2 .* (1 .- x)
57+
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
58+
# Comparison with Lanczos
59+
@test Jchol[1:500,1:500] ≈ Jlanc[1:500,1:500]
60+
# Comparison with Classical
61+
@test Jchol[1:500,1:500] ≈ Jclass[1:500,1:500]
62+
end
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52-
@testset begin "Comparison with Lanczos for w(x) = (1-x^2)"
53-
P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
54-
x = axes(P,1)
55-
J = jacobimatrix(P)
56-
Jx = symmjacobim(J)
57-
w = (I - Jx^2)
58-
# compute Jacobi matrix via cholesky
59-
Jchol = cholesky_jacobimatrix(w)
60-
# compute Jacobi matrix via Lanczos
61-
wf = (1 .- x.^2)
62-
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
63-
# Comparison
64-
@test Jchol[1:500,1:500] ≈ Jlanc[1:500,1:500]
65-
end
64+
@testset "w(x) = (1-x^2)" begin
65+
P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
66+
x = axes(P,1)
67+
J = jacobimatrix(P)
68+
Jx = symmjacobim(J)
69+
w = (I - Jx^2)
70+
# compute Jacobi matrix via cholesky
71+
Jchol = cholesky_jacobimatrix(w)
72+
# compute Jacobi matrix via Lanczos
73+
wf = (1 .- x.^2)
74+
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
75+
# Comparison
76+
@test Jchol[1:500,1:500] ≈ Jlanc[1:500,1:500]
77+
end
6678

67-
@testset begin "Comparison with Lanczos for w(x) = (1-x^4)"
68-
P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
69-
x = axes(P,1)
70-
J = jacobimatrix(P)
71-
Jx = symmjacobim(J)
72-
w = (I - Jx^4)
73-
# compute Jacobi matrix via cholesky
74-
Jchol = cholesky_jacobimatrix(w)
75-
# compute Jacobi matrix via Lanczos
76-
wf = (1 .- x.^4)
77-
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
78-
# Comparison
79-
@test Jchol[1:500,1:500] ≈ Jlanc[1:500,1:500]
80-
end
79+
@testset "w(x) = (1-x^4)" begin
80+
P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
81+
x = axes(P,1)
82+
J = jacobimatrix(P)
83+
Jx = symmjacobim(J)
84+
w = (I - Jx^4)
85+
# compute Jacobi matrix via cholesky
86+
Jchol = cholesky_jacobimatrix(w)
87+
# compute Jacobi matrix via Lanczos
88+
wf = (1 .- x.^4)
89+
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
90+
# Comparison
91+
@test Jchol[1:500,1:500] ≈ Jlanc[1:500,1:500]
92+
end
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82-
@testset begin "Comparison with Lanczos for w(x) = (1.014-x^3)"
83-
P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
84-
x = axes(P,1)
85-
J = jacobimatrix(P)
86-
Jx = symmjacobim(J)
87-
t = 1.014
88-
w = (t*I - Jx^3)
89-
# compute Jacobi matrix via cholesky
90-
Jchol = cholesky_jacobimatrix(w)
91-
# compute Jacobi matrix via Lanczos
92-
wf = (t .- x.^3)
93-
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
94-
# Comparison
95-
@test Jchol[1:500,1:500] ≈ Jlanc[1:500,1:500]
94+
@testset "w(x) = (1.014-x^3)" begin
95+
P = Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])
96+
x = axes(P,1)
97+
J = jacobimatrix(P)
98+
Jx = symmjacobim(J)
99+
t = 1.014
100+
w = (t*I - Jx^3)
101+
# compute Jacobi matrix via cholesky
102+
Jchol = cholesky_jacobimatrix(w)
103+
# compute Jacobi matrix via Lanczos
104+
wf = (t .- x.^3)
105+
Jlanc = jacobimatrix(LanczosPolynomial(@.(wf),Normalized(Legendre()[affine(0..1,Inclusion(-1..1)),:])))
106+
# Comparison
107+
@test Jchol[1:500,1:500] ≈ Jlanc[1:500,1:500]
108+
end
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end

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