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Add lmul! and rmul! for Bidiagonal #51777

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merged 7 commits into from
Nov 19, 2023
Merged

Add lmul! and rmul! for Bidiagonal #51777

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1a785c4
Add `lmul!` and `rmul!` for `Bidiagonal`
dkarrasch Oct 19, 2023
149f8db
make `rmul!` aliasing-ready
dkarrasch Oct 25, 2023
7409293
resolve ambiguity
dkarrasch Oct 25, 2023
ae67df4
more disambiguation
dkarrasch Oct 30, 2023
e937c6d
revert size check change
dkarrasch Oct 30, 2023
63b1009
add more tests
dkarrasch Nov 18, 2023
e9b3ac2
Merge branch 'master' into dk/bidiagmul!
dkarrasch Nov 18, 2023
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44 changes: 41 additions & 3 deletions stdlib/LinearAlgebra/src/bidiag.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -426,13 +426,17 @@ end

const BandedMatrix = Union{Bidiagonal,Diagonal,Tridiagonal,SymTridiagonal} # or BiDiTriSym
const BiTriSym = Union{Bidiagonal,Tridiagonal,SymTridiagonal}
const TriSym = Union{Tridiagonal,SymTridiagonal}
const BiTri = Union{Bidiagonal,Tridiagonal}
@inline mul!(C::AbstractVector, A::BandedMatrix, B::AbstractVector, alpha::Number, beta::Number) = _mul!(C, A, B, MulAddMul(alpha, beta))
@inline mul!(C::AbstractMatrix, A::BandedMatrix, B::AbstractVector, alpha::Number, beta::Number) = _mul!(C, A, B, MulAddMul(alpha, beta))
@inline mul!(C::AbstractMatrix, A::BandedMatrix, B::AbstractMatrix, alpha::Number, beta::Number) = _mul!(C, A, B, MulAddMul(alpha, beta))
@inline mul!(C::AbstractMatrix, A::AbstractMatrix, B::BandedMatrix, alpha::Number, beta::Number) = _mul!(C, A, B, MulAddMul(alpha, beta))
@inline mul!(C::AbstractMatrix, A::BandedMatrix, B::BandedMatrix, alpha::Number, beta::Number) = _mul!(C, A, B, MulAddMul(alpha, beta))

lmul!(A::Bidiagonal, B::AbstractVecOrMat) = @inline _mul!(B, A, B, MulAddMul())
rmul!(B::AbstractMatrix, A::Bidiagonal) = @inline _mul!(B, B, A, MulAddMul())

function check_A_mul_B!_sizes(C, A, B)
mA, nA = size(A)
mB, nB = size(B)
Expand Down Expand Up @@ -460,7 +464,11 @@ function _diag(A::Bidiagonal, k)
end
end

function _mul!(C::AbstractMatrix, A::BiTriSym, B::BiTriSym, _add::MulAddMul = MulAddMul())
_mul!(C::AbstractMatrix, A::BiTriSym, B::TriSym, _add::MulAddMul = MulAddMul()) =
_bibimul!(C, A, B, _add)
_mul!(C::AbstractMatrix, A::BiTriSym, B::Bidiagonal, _add::MulAddMul = MulAddMul()) =
_bibimul!(C, A, B, _add)
function _bibimul!(C, A, B, _add)
check_A_mul_B!_sizes(C, A, B)
n = size(A,1)
n <= 3 && return mul!(C, Array(A), Array(B), _add.alpha, _add.beta)
Expand Down Expand Up @@ -583,7 +591,7 @@ function _mul!(C::AbstractVecOrMat, A::BiTriSym, B::AbstractVecOrMat, _add::MulA
C
end

function _mul!(C::AbstractMatrix, A::AbstractMatrix, B::BiTriSym, _add::MulAddMul = MulAddMul())
function _mul!(C::AbstractMatrix, A::AbstractMatrix, B::TriSym, _add::MulAddMul = MulAddMul())
require_one_based_indexing(C, A)
check_A_mul_B!_sizes(C, A, B)
iszero(_add.alpha) && return _rmul_or_fill!(C, _add.beta)
Expand Down Expand Up @@ -618,7 +626,37 @@ function _mul!(C::AbstractMatrix, A::AbstractMatrix, B::BiTriSym, _add::MulAddMu
C
end

function _mul!(C::AbstractMatrix, A::Diagonal, B::BiTriSym, _add::MulAddMul = MulAddMul())
function _mul!(C::AbstractMatrix, A::AbstractMatrix, B::Bidiagonal, _add::MulAddMul = MulAddMul())
require_one_based_indexing(C, A)
check_A_mul_B!_sizes(C, A, B)
iszero(_add.alpha) && return _rmul_or_fill!(C, _add.beta)
if size(A, 1) <= 3 || size(B, 2) <= 1
return mul!(C, Array(A), Array(B), _add.alpha, _add.beta)
end
m, n = size(A)
@inbounds if B.uplo == 'U'
for i in 1:m
for j in n:-1:2
_modify!(_add, A[i,j] * B.dv[j] + A[i,j-1] * B.ev[j-1], C, (i, j))
end
_modify!(_add, A[i,1] * B.dv[1], C, (i, 1))
end
else # uplo == 'L'
for i in 1:m
for j in 1:n-1
_modify!(_add, A[i,j] * B.dv[j] + A[i,j+1] * B.ev[j], C, (i, j))
end
_modify!(_add, A[i,n] * B.dv[n], C, (i, n))
end
end
C
end

_mul!(C::AbstractMatrix, A::Diagonal, B::Bidiagonal, _add::MulAddMul = MulAddMul()) =
_dibimul!(C, A, B, _add)
_mul!(C::AbstractMatrix, A::Diagonal, B::TriSym, _add::MulAddMul = MulAddMul()) =
_dibimul!(C, A, B, _add)
function _dibimul!(C, A, B, _add)
require_one_based_indexing(C)
check_A_mul_B!_sizes(C, A, B)
n = size(A,1)
Expand Down
12 changes: 9 additions & 3 deletions stdlib/LinearAlgebra/test/bidiag.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -439,14 +439,18 @@ Random.seed!(1)
for op in (+, -, *)
@test Array(op(T, T2)) ≈ op(Tfull, Tfull2)
end
A = kron(T.dv, T.dv')
@test T * A ≈ lmul!(T, copy(A))
@test A * T ≈ rmul!(copy(A), T)
end
# test pass-through of mul! for SymTridiagonal*Bidiagonal
TriSym = SymTridiagonal(T.dv, T.ev)
@test Array(TriSym*T) ≈ Array(TriSym)*Array(T)
# test pass-through of mul! for AbstractTriangular*Bidiagonal
Tri = UpperTriangular(diagm(1 => T.ev))
Dia = Diagonal(T.dv)
@test Array(Tri*T) ≈ Array(Tri)*Array(T)
@test Array(Tri*T) ≈ Array(Tri)*Array(T) ≈ rmul!(copy(Tri), T)
@test Array(T*Tri) ≈ Array(T)*Array(Tri) ≈ lmul!(T, copy(Tri))
# test mul! itself for these types
for AA in (Tri, Dia)
for f in (identity, transpose, adjoint)
Expand All @@ -459,8 +463,10 @@ Random.seed!(1)
for f in (identity, transpose, adjoint)
C = relty == Int ? rand(float(elty), n, n) : rand(elty, n, n)
B = rand(elty, n, n)
D = copy(C) + 2.0 * Array(T*f(B))
mul!(C, T, f(B), 2.0, 1.0) ≈ D
D = C + 2.0 * Array(T*f(B))
@test mul!(C, T, f(B), 2.0, 1.0) ≈ D
@test lmul!(T, copy(f(B))) ≈ T * f(B)
@test rmul!(copy(f(B)), T) ≈ f(B) * T
end

# Issue #31870
Expand Down