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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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73 changes: 36 additions & 37 deletions stdlib/LinearAlgebra/src/symmetric.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -453,47 +453,46 @@ function triu(A::Symmetric, k::Integer=0)
end
end

for (T, trans, real) in [(:Symmetric, :transpose, :identity), (:(Hermitian{<:Union{Real,Complex}}), :adjoint, :real)]
@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
dot(A::Symmetric, B::Symmetric) = _dot_hermsym(A, B, transpose, identity)
dot(A::Hermitian{<:Union{Real,Complex}}, B::Hermitian{<:Union{Real,Complex}}) = _dot_hermsym(A, B, conj, real)

dotprod = 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])
end
elseif A.uplo == 'L' && B.uplo == 'L'
for j in 1:n
dotprod += 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
end
elseif A.uplo == 'U' && B.uplo == 'L'
for j in 1:n
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])
end
else
for j in 1:n
dotprod += 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
end
function _dot_hermsym(A, B, trans, real)
n = size(A, 2)
if n != size(B, 2)
throw(DimensionMismatch("A has dimensions $(size(A)) but B has dimensions $(size(B))"))
end

dotprod = real(zero(dot(first(A), first(B))))
@inbounds if A.uplo == 'U' && B.uplo == 'U'
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Can we stop using this? This function assumes but does not enforce 1-based indexing.

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The parents of Symmetric and Hermitian are required to be one-based at construction (see the very top of this file), so this is safe.

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 += real(dot(A[j, j], B[j, j]))
end
elseif A.uplo == 'L' && B.uplo == 'L'
for j in 1:n
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
end
elseif A.uplo == 'U' && B.uplo == 'L'
for j in 1:n
for i in 1:(j-1)
dotprod += 2 * real(dot(A.data[i, j], trans(B.data[j, i])))
end
dotprod += real(dot(A[j, j], B[j, j]))
end
else
for j in 1:n
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
return dotprod
end
end
return dotprod
end

(-)(A::Symmetric) = Symmetric(-A.data, sym_uplo(A.uplo))
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