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Merged
merged 4 commits into from
Apr 17, 2024
Merged

Test periodic Schrodinger with QL #168

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ab0f7f9
Test periodic Schrodinger with QL
dlfivefifty Apr 16, 2024
6eef685
Merge branch 'master' into dl/periodictests
dlfivefifty Apr 16, 2024
28b4e5a
Update infql.jl
dlfivefifty Apr 17, 2024
e1850a9
ql for b-∞ periodic
dlfivefifty Apr 17, 2024
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21 changes: 14 additions & 7 deletions src/infql.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -165,15 +165,16 @@ end

function blocktailiterate(c,a,b, d=c, e=a)
z = zero(c)
n = size(c,1)
for _=1:1_000_000
X = [c a b; z d e]
F = ql!(X)
d̃,ẽ = F.L[1:2,1:2], F.L[1:2,3:4]
d̃,ẽ = F.L[1:n,1:n], F.L[1:n,n+1:2n]

d̃,ẽ = QLPackedQ(F.factors[1:2,3:4],F.τ[1:2])*d̃,QLPackedQ(F.factors[1:2,3:4],F.τ[1:2])*ẽ # undo last rotation
d̃,ẽ = QLPackedQ(F.factors[1:n,n+1:2n],F.τ[1:n])*d̃,QLPackedQ(F.factors[1:n,n+1:2n],F.τ[1:n])*ẽ # undo last rotation
if ≈(d̃, d; atol=1E-10) && ≈(ẽ, e; atol=1E-10)
X[1:2,1:2] = d̃; X[1:2,3:4] = ẽ
return PseudoBlockArray(X,fill(2,2), fill(2,3)), F.τ[3:end]
X[1:n,1:n] = d̃; X[1:n,n+1:2n] = ẽ
return PseudoBlockArray(X,fill(n,2), fill(n,3)), F.τ[n+1:2n]
end
d,e = d̃,ẽ
end
Expand All @@ -191,8 +192,8 @@ function _blocktripert_ql(A, d, e)
P,τ = blocktailiterate(c,a,b,d,e)
B = BlockBandedMatrix(A,(2,1))


BB = _BlockBandedMatrix(B.data.args[1], fill(2,N+2), fill(2,N), (2,1))
n = size(c,1)
BB = _BlockBandedMatrix(B.data.args[1], fill(n,N+2), fill(n,N), (2,1))
BB[Block(N),Block.(N-1:N)] .= P[Block(1), Block.(1:2)]
F = ql!(view(BB, Block.(1:N), Block.(1:N)))
BB[Block(N+1),Block.(N-1:N)] .= P[Block(2), Block.(1:2)]
Expand Down Expand Up @@ -241,7 +242,7 @@ function lmul!(adjA::AdjointQtype{<:Any,<:QLPackedQ{<:Any,<:InfBlockBandedMatrix
B
end

getindex(Q::QLPackedQ{T,<:InfBlockBandedMatrix{T}}, i::Integer, j::Integer) where T =
getindex(Q::QLPackedQ{T,<:InfBlockBandedMatrix{T}}, i::Int, j::Int) where T =
(Q'*Vcat(Zeros{T}(i-1), one(T), Zeros{T}(∞)))[j]'
getindex(Q::QLPackedQ{<:Any,<:InfBlockBandedMatrix}, I::AbstractVector{Int}, J::AbstractVector{Int}) =
[Q[i,j] for i in I, j in J]
Expand All @@ -256,6 +257,12 @@ function (*)(A::AdjointQtype{T,<:QLPackedQ{T,<:InfBlockBandedMatrix}}, x::Abstra
lmul!(A, cache(convert(AbstractVector{TS},x)))
end

function (*)(A::AdjointQtype{T,<:QLPackedQ{T,<:InfBlockBandedMatrix}}, x::LayoutVector{S}) where {T,S}
TS = promote_op(matprod, T, S)
lmul!(A, cache(convert(AbstractVector{TS},x)))
end


ldiv!(F::QLProduct, b::AbstractVector) = ldiv!(F.L, lmul!(F.Q',b))
ldiv!(F::QLProduct, b::LayoutVector) = ldiv!(F.L, lmul!(F.Q',b))

Expand Down
3 changes: 2 additions & 1 deletion test/runtests.jl
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Expand Up @@ -472,4 +472,5 @@ include("test_infql.jl")
include("test_infqr.jl")
include("test_inful.jl")
include("test_infcholesky.jl")
include("test_infreversecholesky.jl")
include("test_periodic.jl")
include("test_infreversecholesky.jl")
95 changes: 60 additions & 35 deletions test/test_periodic.jl
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Original file line number Diff line number Diff line change
@@ -1,37 +1,62 @@
using InfiniteLinearAlgebra, BlockBandedMatrices, LinearAlgebra, Test

@testset "periodic" begin
A = BlockTridiagonal(Vcat([[0. 1.; 0. 0.]],Fill([0. 1.; 0. 0.], ∞)),
Vcat([[-1. 1.; 1. 1.]], Fill([-1. 1.; 1. 1.], ∞)),
Vcat([[0. 0.; 1. 0.]], Fill([0. 0.; 1. 0.], ∞)))


Q,L = ql(A);
@test Q.factors isa InfiniteLinearAlgebra.InfBlockBandedMatrix
Q̃,L̃ = ql(BlockBandedMatrix(A)[Block.(1:100),Block.(1:100)])

@test Q̃.factors[1:100,1:100] ≈ Q.factors[1:100,1:100]
@test Q̃.τ[1:100] ≈ Q.τ[1:100]
@test L[1:100,1:100] ≈ L̃[1:100,1:100]
@test Q[1:10,1:10] ≈ Q̃[1:10,1:10]
@test Q[1:10,1:12]*L[1:12,1:10] ≈ A[1:10,1:10]

# complex non-selfadjoint
c,a,b = [0 0.5; 0 0],[0 2.0; 0.5 0],[0 0.0; 2.0 0];
A = BlockTridiagonal(Vcat([c], Fill(c,∞)),
Vcat([a], Fill(a,∞)),
Vcat([b], Fill(b,∞))) - 5im*I
Q,L = ql(A)
@test Q[1:10,1:12]*L[1:12,1:10] ≈ A[1:10,1:10]

c,a,b = [0 0.5; 0 0],[0 2.0; 0.5 0],[0 0.0; 2.0 0];
A = BlockTridiagonal(Vcat([c], Fill(c,∞)),
Vcat([a], Fill(a,∞)),
Vcat([b], Fill(b,∞)))
Q,L = ql(A)
@test Q[1:10,1:12]*L[1:12,1:10] ≈ A[1:10,1:10]
@test L[1,1] == 0 # degenerate


Q,L = ql(A')
@test Q[1:10,1:12]*L[1:12,1:10] ≈ A[1:10,1:10]'
@test L[1,1] ≠ 0 # non-degenerate
@testset "single-∞" begin
A = BlockTridiagonal(Vcat([[0. 1.; 0. 0.]],Fill([0. 1.; 0. 0.], ∞)),
Vcat([[-1. 1.; 1. 1.]], Fill([-1. 1.; 1. 1.], ∞)),
Vcat([[0. 0.; 1. 0.]], Fill([0. 0.; 1. 0.], ∞)))


Q,L = ql(A);
@test Q.factors isa InfiniteLinearAlgebra.InfBlockBandedMatrix
Q̃,L̃ = ql(BlockBandedMatrix(A)[Block.(1:100),Block.(1:100)])

@test Q̃.factors[1:100,1:100] ≈ Q.factors[1:100,1:100]
@test Q̃.τ[1:100] ≈ Q.τ[1:100]
@test L[1:100,1:100] ≈ L̃[1:100,1:100]
@test Q[1:10,1:10] ≈ Q̃[1:10,1:10]
@test Q[1:10,1:12]*L[1:12,1:10] ≈ A[1:10,1:10]

# complex non-selfadjoint
c,a,b = [0 0.5; 0 0],[0 2.0; 0.5 0],[0 0.0; 2.0 0];
A = BlockTridiagonal(Vcat([c], Fill(c,∞)),
Vcat([a], Fill(a,∞)),
Vcat([b], Fill(b,∞))) - 5im*I
Q,L = ql(A)
@test Q[1:10,1:12]*L[1:12,1:10] ≈ A[1:10,1:10]

c,a,b = [0 0.5; 0 0],[0 2.0; 0.5 0],[0 0.0; 2.0 0];
A = BlockTridiagonal(Vcat([c], Fill(c,∞)),
Vcat([a], Fill(a,∞)),
Vcat([b], Fill(b,∞)))
Q,L = ql(A)
@test Q[1:10,1:12]*L[1:12,1:10] ≈ A[1:10,1:10]
@test abs(L[1,1] ) ≤ 1E-11 # degenerate


Q,L = ql(A')
@test Q[1:10,1:12]*L[1:12,1:10] ≈ A[1:10,1:10]'
@test L[1,1] ≠ 0 # non-degenerate
end

@testset "bi" begin
B = [ 0 0 1 0;
0 0 0 1;
0 0 0 0;
0 0 0 0]/2
A₀ = [ 1 1/2 1/2 0 ;
1/2 -1 0 1/2;
1/2 0 -1 0 ;
0 1/2 0 1]
A = [ 1 0 1/2 0 ;
0 -1 0 1/2 ;
1/2 0 -1 0 ;
0 1/2 0 1 ]

A = BlockTridiagonal(Vcat([B],Fill(B, ∞)),
Vcat([A₀], Fill(A, ∞)),
Vcat([copy(B')], Fill(copy(B'), ∞)))
Q,L = ql(A)
@test Q[1:10,1:12]*L[1:12,1:10] ≈ A[1:10,1:10]
end
end