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minor fixes in multiplication with Diagonals #31443

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Apr 4, 2019
Merged

minor fixes in multiplication with Diagonals #31443

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ca1b555
minor fixes in multiplication with Diagonals
dkarrasch Mar 22, 2019
a7b7a6e
correct rmul!(A,D), revert changes in AdjTrans(x)*D
dkarrasch Mar 25, 2019
5d1bcc8
[r/l]mul!: replace conj by adjoint, add transpose
dkarrasch Mar 25, 2019
fc1f32b
add tests
dkarrasch Mar 25, 2019
2fcfd2e
fix typo
dkarrasch Mar 25, 2019
562412e
relax some tests, added more tests
dkarrasch Apr 2, 2019
e215f89
simplify tests, strict equality
dkarrasch Apr 3, 2019
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13 changes: 6 additions & 7 deletions stdlib/LinearAlgebra/src/diagonal.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -172,7 +172,7 @@ end

function rmul!(A::AbstractMatrix, D::Diagonal)
require_one_based_indexing(A)
A .= A .* transpose(D.diag)
A .= A .* permutedims(D.diag)
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return A
end

Expand Down Expand Up @@ -260,20 +260,20 @@ lmul!(A::Diagonal, B::Diagonal) = Diagonal(B.diag .= A.diag .* B.diag)

function lmul!(adjA::Adjoint{<:Any,<:Diagonal}, B::AbstractMatrix)
A = adjA.parent
return lmul!(conj(A.diag), B)
return lmul!(adjoint(A), B)
end
function lmul!(transA::Transpose{<:Any,<:Diagonal}, B::AbstractMatrix)
A = transA.parent
return lmul!(A.diag, B)
return lmul!(transpose(A), B)
end

function rmul!(A::AbstractMatrix, adjB::Adjoint{<:Any,<:Diagonal})
B = adjB.parent
return rmul!(A, conj(B.diag))
return rmul!(A, adjoint(B))
end
function rmul!(A::AbstractMatrix, transB::Transpose{<:Any,<:Diagonal})
B = transB.parent
return rmul!(A, B.diag)
return rmul!(A, transpose(B))
end

# Get ambiguous method if try to unify AbstractVector/AbstractMatrix here using AbstractVecOrMat
Expand Down Expand Up @@ -552,10 +552,9 @@ end
*(x::Adjoint{<:Any,<:AbstractVector}, D::Diagonal) = Adjoint(map((t,s) -> t'*s, D.diag, parent(x)))
*(x::Adjoint{<:Any,<:AbstractVector}, D::Diagonal, y::AbstractVector) =
mapreduce(t -> t[1]*t[2]*t[3], +, zip(x, D.diag, y))
*(x::Transpose{<:Any,<:AbstractVector}, D::Diagonal) = Transpose(map(*, D.diag, parent(x)))
*(x::Transpose{<:Any,<:AbstractVector}, D::Diagonal) = Transpose(map((t,s) -> transpose(t)*s, D.diag, parent(x)))
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Does this change the behavior? Was this previously non-recursive?

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For Number eltypes this does not change behaviour, since transpose doesn't do anything to them. For block matrices, this is a bugfix. It makes this Transpose line consistent with the Adjoint line 552 above. Both these are now also covered by tests, testing Complex numbers (where the adjoint boils down to conjugation on the element level) and 2x2 matrices (where both adjoint and transpose have an effect).

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Here's why I call this a bugfix and think it's worthy of a backport:

julia> A = reshape([[1 2; 3 4], zeros(Int,2,2), zeros(Int, 2, 2), [5 6; 7 8]], 2, 2)
2×2 Array{Array{Int64,2},2}:
 [1 2; 3 4]  [0 0; 0 0]
 [0 0; 0 0]  [5 6; 7 8]

julia> adjoint(1:2) * A
1×2 Adjoint{Adjoint{Int64,Array{Int64,2}},Array{Array{Int64,2},1}}:
 [1 2; 3 4]  [10 12; 14 16]

julia> transpose(1:2) * A
1×2 Transpose{Transpose{Int64,Array{Int64,2}},Array{Array{Int64,2},1}}:
 [1 2; 3 4]  [10 12; 14 16]

julia> adjoint(1:2) * Diagonal(A)
1×2 Adjoint{Adjoint{Int64,Array{Int64,2}},Array{Array{Int64,2},1}}:
 [1 2; 3 4]  [10 12; 14 16]

julia> transpose(1:2) * Diagonal(A)
1×2 Transpose{Transpose{Int64,Array{Int64,2}},Array{Array{Int64,2},1}}:
 [1 3; 2 4]  [10 14; 12 16]

*(x::Transpose{<:Any,<:AbstractVector}, D::Diagonal, y::AbstractVector) =
mapreduce(t -> t[1]*t[2]*t[3], +, zip(x, D.diag, y))
# TODO: these methods will yield row matrices, rather than adjoint/transpose vectors

function cholesky!(A::Diagonal, ::Val{false} = Val(false); check::Bool = true)
info = 0
Expand Down
30 changes: 25 additions & 5 deletions stdlib/LinearAlgebra/test/diagonal.jl
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Expand Up @@ -468,10 +468,20 @@ end
fullBB = copyto!(Matrix{Matrix{T}}(undef, 2, 2), BB)
for (transform1, transform2) in ((identity, identity),
(identity, adjoint ), (adjoint, identity ), (adjoint, adjoint ),
(identity, transpose), (transpose, identity ), (transpose, transpose) )
(identity, transpose), (transpose, identity ), (transpose, transpose),
(identity, Adjoint ), (Adjoint, identity ), (Adjoint, Adjoint ),
(identity, Transpose), (Transpose, identity ), (Transpose, Transpose))
@test *(transform1(D), transform2(B))::typeof(D) ≈ *(transform1(Matrix(D)), transform2(Matrix(B))) atol=2 * eps()
@test *(transform1(DD), transform2(BB))::typeof(DD) == *(transform1(fullDD), transform2(fullBB))
end
M = randn(T, 5, 5)
MM = [randn(T, 2, 2) for _ in 1:2, _ in 1:2]
for transform in (identity, adjoint, transpose, Adjoint, Transpose)
@test lmul!(transform(D), copy(M)) == *(transform(Matrix(D)), M)
@test rmul!(copy(M), transform(D)) == *(M, transform(Matrix(D)))
@test lmul!(transform(DD), copy(MM)) == *(transform(fullDD), MM)
@test rmul!(copy(MM), transform(DD)) == *(MM, transform(fullDD))
end
end
end

Expand All @@ -481,10 +491,20 @@ end
end

@testset "Multiplication with Adjoint and Transpose vectors (#26863)" begin
x = rand(5)
D = Diagonal(rand(5))
@test x'*D*x == (x'*D)*x == (x'*Array(D))*x
@test Transpose(x)*D*x == (Transpose(x)*D)*x == (Transpose(x)*Array(D))*x
K = 5
x = rand(ComplexF64, K)
D = Diagonal(rand(ComplexF64, K))
@test x'*D == x'*Array(D) == copy(x')*D == copy(x')*Array(D)
@test x'*D*x ≈ (x'*D)*x ≈ (x'*Array(D))*x
@test transpose(x)*D*x ≈ (transpose(x)*D)*x ≈ (transpose(x)*Array(D))*x
# non-commutative eltype
x = [rand(2) for _ in 1:K]
dd = [rand(2,2) for _ in 1:K]
D = Diagonal(dd)
DM = fill(zeros(2,2), K, K); DM[diagind(DM)] .= dd
@test x'*D == x'*DM == copy(x')*D == copy(x')*DM
@test x'*D*x == (x'*D)*x == (x'*DM)*x
@test transpose(x)*D*x == (transpose(x)*D)*x == (transpose(x)*DM)*x
end

@testset "Triangular division by Diagonal #27989" begin
Expand Down