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stdlib: make dot product of Hermitian matrices real #52318

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merged 6 commits into from
Feb 3, 2024
Merged

stdlib: make dot product of Hermitian matrices real #52318

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525edb5
make dot product of Hermitian matrices real
araujoms Nov 27, 2023
9f1f5ea
restrict to real or complex Hermitian matrices
araujoms Nov 28, 2023
82cc8c5
Merge branch 'master' into patch-1
dkarrasch Dec 5, 2023
5097097
change into extensible version
araujoms Dec 7, 2023
58f5ed8
Revert "change into extensible version"
araujoms Dec 30, 2023
e7c27fb
Merge branch 'master' into patch-1
dkarrasch Feb 1, 2024
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15 changes: 9 additions & 6 deletions stdlib/LinearAlgebra/src/symmetric.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -453,25 +453,28 @@ function triu(A::Symmetric, k::Integer=0)
end
end

for (T, trans, real) in [(:Symmetric, :transpose, :identity), (:Hermitian, :adjoint, :real)]
for (T, trans, real) in [
(:Symmetric, :transpose, :identity),
(:(Hermitian{<:Union{Real,Complex}}), :adjoint, :real),
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@mikmoore mikmoore Nov 30, 2023 •
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It's slightly unfortunate that this specialization prevents this from being applicable to e.g. Hermitian{<:AbstractMatrix{<:Union{Real,Complex}}}. Although I'm not sure how we might engineer a definition that's robust through multiple levels of nested AbstractMatrix so it would probably be hard to do something about this right now.

I'll also remark that this specialization should also be suitable for dot(::Symmetric{<:Real},::Hermitian{<:Complex}}, although currently it appears we miss this case. Would LinearAlgebra.RealHermSymComplexHerm be suitable here?

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I think this is a design flaw of LinearAlgebra. Symmetric should have been defined as real symmetric, and should be made a subtype of Hermitian, as mathematically a real symmetric matrix is just a particular case of a complex Hermitian matrix, and we'd get for free all of these particular cases without having to write a method for each specifically. Then one could also have a GenericSymmetric to deal with the more exotic cases if anyone needed them.

FWIW I did think about mixing real symmetric and complex Hermitian, but I decided against adding additional methods that were going to be rarely used. Of course, I know my opinion counts for very little here.

]
@eval begin
function dot(A::$T, B::$T)
n = size(A, 2)
if n != size(B, 2)
throw(DimensionMismatch("A has dimensions $(size(A)) but B has dimensions $(size(B))"))
end

dotprod = zero(dot(first(A), first(B)))
dotprod = $real(zero(dot(first(A), first(B))))
@inbounds if A.uplo == 'U' && B.uplo == 'U'
for j in 1:n
for i in 1:(j - 1)
dotprod += 2 * $real(dot(A.data[i, j], B.data[i, j]))
end
dotprod += dot(A[j, j], B[j, j])
dotprod += $real(dot(A[j, j], B[j, j]))
end
elseif A.uplo == 'L' && B.uplo == 'L'
for j in 1:n
dotprod += dot(A[j, j], B[j, j])
dotprod += $real(dot(A[j, j], B[j, j]))
for i in (j + 1):n
dotprod += 2 * $real(dot(A.data[i, j], B.data[i, j]))
end
Expand All @@ -481,11 +484,11 @@ for (T, trans, real) in [(:Symmetric, :transpose, :identity), (:Hermitian, :adjo
for i in 1:(j - 1)
dotprod += 2 * $real(dot(A.data[i, j], $trans(B.data[j, i])))
end
dotprod += dot(A[j, j], B[j, j])
dotprod += $real(dot(A[j, j], B[j, j]))
end
else
for j in 1:n
dotprod += dot(A[j, j], B[j, j])
dotprod += $real(dot(A[j, j], B[j, j]))
for i in (j + 1):n
dotprod += 2 * $real(dot(A.data[i, j], $trans(B.data[j, i])))
end
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