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Optimizing some structured matrix multiply methods #32521

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Optimizing some structured matrix multiply methods #32521

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d8cdd9d
adding new matrix fallback
mcognetta Jul 8, 2019
56af7ce
adding tests and fixing bidiag*bidiag
mcognetta Jul 8, 2019
10469cf
remove ambiguity
mcognetta Jul 8, 2019
be35d9b
change to strided array
mcognetta Jul 25, 2019
f6150dc
Merge branch 'master' into dense_times_structured
mcognetta Jul 26, 2019
0b48d6c
readding methods
mcognetta Aug 5, 2019
b862c59
merge conflict
mcognetta Aug 5, 2019
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14 changes: 14 additions & 0 deletions stdlib/LinearAlgebra/src/bidiag.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -632,6 +632,20 @@ function *(A::SymTridiagonal, B::Diagonal)
A_mul_B_td!(Tridiagonal(zeros(TS, size(A, 1)-1), zeros(TS, size(A, 1)), zeros(TS, size(A, 1)-1)), A, B)
end

function *(A::Bidiagonal, B::Bidiagonal)
TS = promote_op(matprod, eltype(A), eltype(B))
if A.uplo == B.uplo
A_mul_B_td!(similar(B, TS, size(B, 1), size(B, 2)), A, B)
else
A_mul_B_td!(Tridiagonal(zeros(TS, size(A, 1)-1), zeros(TS, size(A, 1)), zeros(TS, size(A, 1)-1)), A, B)
end
end

function *(A::StridedMatrix, B::BiTriSym)
TS = promote_op(matprod, eltype(A), eltype(B))
A_mul_B_td!(similar(A, TS), A, B)
end

#Linear solvers
ldiv!(A::Union{Bidiagonal, AbstractTriangular}, b::AbstractVector) = naivesub!(A, b)
ldiv!(A::Transpose{<:Any,<:Bidiagonal}, b::AbstractVector) = ldiv!(copy(A), b)
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35 changes: 29 additions & 6 deletions stdlib/LinearAlgebra/test/bidiag.jl
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Expand Up @@ -317,6 +317,7 @@ Random.seed!(1)

# Issue #31870
# Bi/Tri/Sym times Diagonal
Dense = rand(elty, 10, 10)
Diag = Diagonal(rand(elty, 10))
BidiagU = Bidiagonal(rand(elty, 10), rand(elty, 9), 'U')
BidiagL = Bidiagonal(rand(elty, 10), rand(elty, 9), 'L')
Expand All @@ -325,20 +326,42 @@ Random.seed!(1)

mats = [Diag, BidiagU, BidiagL, Tridiag, SymTri]
for a in mats
@test typeof(Dense*a) <: Array
@test typeof(a*Dense) <: Array
for b in mats
@test a*b ≈ Matrix(a)*Matrix(b)
end
end

@test typeof(BidiagU*Diag) <: Bidiagonal
@test typeof(Diag*Diag) <: Diagonal
@test typeof(Diag*BidiagL) <: Bidiagonal
@test typeof(Diag*BidiagU) <: Bidiagonal
@test typeof(Diag*Tridiag) <: Tridiagonal
@test typeof(Diag*SymTri) <: Tridiagonal

@test typeof(BidiagL*Diag) <: Bidiagonal
@test typeof(Tridiag*Diag) <: Tridiagonal
@test typeof(SymTri*Diag) <: Tridiagonal
@test typeof(BidiagL*BidiagL) <: SparseMatrixCSC
@test typeof(BidiagL*BidiagU) <: Tridiagonal
@test typeof(BidiagL*Tridiag) <: SparseMatrixCSC
@test typeof(BidiagL*SymTri) <: SparseMatrixCSC

@test typeof(BidiagU*Diag) <: Bidiagonal
@test typeof(Diag*BidiagL) <: Bidiagonal
@test typeof(Diag*Tridiag) <: Tridiagonal
@test typeof(Diag*SymTri) <: Tridiagonal
@test typeof(BidiagU*BidiagL) <: Tridiagonal
@test typeof(BidiagU*BidiagU) <: SparseMatrixCSC
@test typeof(BidiagU*Tridiag) <: SparseMatrixCSC
@test typeof(BidiagU*SymTri) <: SparseMatrixCSC

@test typeof(Tridiag*Diag) <: Tridiagonal
@test typeof(Tridiag*BidiagL) <: SparseMatrixCSC
@test typeof(Tridiag*BidiagU) <: SparseMatrixCSC
@test typeof(Tridiag*Tridiag) <: SparseMatrixCSC
@test typeof(Tridiag*SymTri) <: SparseMatrixCSC

@test typeof(SymTri*Diag) <: Tridiagonal
@test typeof(SymTri*BidiagL) <: SparseMatrixCSC
@test typeof(SymTri*BidiagU) <: SparseMatrixCSC
@test typeof(SymTri*Tridiag) <: SparseMatrixCSC
@test typeof(SymTri*SymTri) <: SparseMatrixCSC
end

@test inv(T)*Tfull ≈ Matrix(I, n, n)
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