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Fix performance bug for * with AbstractQ #44615

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Mar 22, 2022
Merged

Fix performance bug for * with AbstractQ #44615

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4785167
Fix performance bug for `*` with `AbstractQ`
dkarrasch Mar 14, 2022
7a87a27
Merge branch 'master' into dk/fixq
ViralBShah Mar 17, 2022
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10 changes: 4 additions & 6 deletions stdlib/LinearAlgebra/src/bidiag.jl
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Expand Up @@ -168,15 +168,13 @@ end
function Matrix{T}(A::Bidiagonal) where T
n = size(A, 1)
B = zeros(T, n, n)
if n == 0
return B
end
for i = 1:n - 1
n == 0 && return B
@inbounds for i = 1:n - 1
B[i,i] = A.dv[i]
if A.uplo == 'U'
B[i, i + 1] = A.ev[i]
B[i,i+1] = A.ev[i]
else
B[i + 1, i] = A.ev[i]
B[i+1,i] = A.ev[i]
end
end
B[n,n] = A.dv[n]
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12 changes: 10 additions & 2 deletions stdlib/LinearAlgebra/src/diagonal.jl
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Expand Up @@ -77,8 +77,16 @@ Diagonal{T}(D::Diagonal{T}) where {T} = D
Diagonal{T}(D::Diagonal) where {T} = Diagonal{T}(D.diag)

AbstractMatrix{T}(D::Diagonal) where {T} = Diagonal{T}(D)
Matrix(D::Diagonal) = diagm(0 => D.diag)
Array(D::Diagonal) = Matrix(D)
Matrix(D::Diagonal{T}) where {T} = Matrix{T}(D)
Array(D::Diagonal{T}) where {T} = Matrix{T}(D)
function Matrix{T}(D::Diagonal) where {T}
n = size(D, 1)
B = zeros(T, n, n)
@inbounds for i in 1:n
B[i,i] = D.diag[i]
end
return B
end

"""
Diagonal{T}(undef, n)
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69 changes: 59 additions & 10 deletions stdlib/LinearAlgebra/src/special.jl
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Expand Up @@ -292,16 +292,65 @@ function (-)(A::UniformScaling, B::Diagonal{<:Number})
Diagonal(A.λ .- B.diag)
end

rmul!(A::AbstractTriangular, adjB::Adjoint{<:Any,<:Union{QRCompactWYQ,QRPackedQ}}) =
rmul!(full!(A), adjB)
*(A::AbstractTriangular, adjB::Adjoint{<:Any,<:Union{QRCompactWYQ,QRPackedQ}}) =
*(copyto!(similar(parent(A)), A), adjB)
*(A::BiTriSym, adjB::Adjoint{<:Any,<:Union{QRCompactWYQ, QRPackedQ}}) =
rmul!(copyto!(Array{promote_type(eltype(A), eltype(adjB))}(undef, size(A)...), A), adjB)
*(adjA::Adjoint{<:Any,<:Union{QRCompactWYQ, QRPackedQ}}, B::Diagonal) =
lmul!(adjA, copyto!(Array{promote_type(eltype(adjA), eltype(B))}(undef, size(B)...), B))
*(adjA::Adjoint{<:Any,<:Union{QRCompactWYQ, QRPackedQ}}, B::BiTriSym) =
lmul!(adjA, copyto!(Array{promote_type(eltype(adjA), eltype(B))}(undef, size(B)...), B))
lmul!(Q::AbstractQ, B::AbstractTriangular) = lmul!(Q, full!(B))
lmul!(Q::QRPackedQ, B::AbstractTriangular) = lmul!(Q, full!(B)) # disambiguation
lmul!(Q::Adjoint{<:Any,<:AbstractQ}, B::AbstractTriangular) = lmul!(Q, full!(B))
lmul!(Q::Adjoint{<:Any,<:QRPackedQ}, B::AbstractTriangular) = lmul!(Q, full!(B)) # disambiguation

function _qlmul(Q::AbstractQ, B)
TQB = promote_type(eltype(Q), eltype(B))
if size(Q.factors, 1) == size(B, 1)
Bnew = Matrix{TQB}(B)
elseif size(Q.factors, 2) == size(B, 1)
Bnew = [Matrix{TQB}(B); zeros(TQB, size(Q.factors, 1) - size(B,1), size(B, 2))]
else
throw(DimensionMismatch("first dimension of matrix must have size either $(size(Q.factors, 1)) or $(size(Q.factors, 2))"))
end
lmul!(convert(AbstractMatrix{TQB}, Q), Bnew)
end
function _qlmul(adjQ::Adjoint{<:Any,<:AbstractQ}, B)
TQB = promote_type(eltype(adjQ), eltype(B))
lmul!(adjoint(convert(AbstractMatrix{TQB}, parent(adjQ))), Matrix{TQB}(B))
end

*(Q::AbstractQ, B::AbstractTriangular) = _qlmul(Q, B)
*(Q::Adjoint{<:Any,<:AbstractQ}, B::AbstractTriangular) = _qlmul(Q, B)
*(Q::AbstractQ, B::BiTriSym) = _qlmul(Q, B)
*(Q::Adjoint{<:Any,<:AbstractQ}, B::BiTriSym) = _qlmul(Q, B)
*(Q::AbstractQ, B::Diagonal) = _qlmul(Q, B)
*(Q::Adjoint{<:Any,<:AbstractQ}, B::Diagonal) = _qlmul(Q, B)

rmul!(A::AbstractTriangular, Q::AbstractQ) = rmul!(full!(A), Q)
rmul!(A::AbstractTriangular, Q::Adjoint{<:Any,<:AbstractQ}) = rmul!(full!(A), Q)

function _qrmul(A, Q::AbstractQ)
TAQ = promote_type(eltype(A), eltype(Q))
return rmul!(Matrix{TAQ}(A), convert(AbstractMatrix{TAQ}, Q))
end
function _qrmul(A, adjQ::Adjoint{<:Any,<:AbstractQ})
Q = adjQ.parent
TAQ = promote_type(eltype(A), eltype(Q))
if size(A,2) == size(Q.factors, 1)
Anew = Matrix{TAQ}(A)
elseif size(A,2) == size(Q.factors,2)
Anew = [Matrix{TAQ}(A) zeros(TAQ, size(A, 1), size(Q.factors, 1) - size(Q.factors, 2))]
else
throw(DimensionMismatch("matrix A has dimensions $(size(A)) but matrix B has dimensions $(size(Q))"))
end
return rmul!(Anew, adjoint(convert(AbstractMatrix{TAQ}, Q)))
end

*(A::AbstractTriangular, Q::AbstractQ) = _qrmul(A, Q)
*(A::AbstractTriangular, Q::Adjoint{<:Any,<:AbstractQ}) = _qrmul(A, Q)
*(A::BiTriSym, Q::AbstractQ) = _qrmul(A, Q)
*(A::BiTriSym, Q::Adjoint{<:Any,<:AbstractQ}) = _qrmul(A, Q)
*(A::Diagonal, Q::AbstractQ) = _qrmul(A, Q)
*(A::Diagonal, Q::Adjoint{<:Any,<:AbstractQ}) = _qrmul(A, Q)

*(Q::AbstractQ, B::AbstractQ) = _qlmul(Q, B)
*(Q::Adjoint{<:Any,<:AbstractQ}, B::AbstractQ) = _qrmul(Q, B)
*(Q::AbstractQ, B::Adjoint{<:Any,<:AbstractQ}) = _qlmul(Q, B)
*(Q::Adjoint{<:Any,<:AbstractQ}, B::Adjoint{<:Any,<:AbstractQ}) = _qrmul(Q, B)

# fill[stored]! methods
fillstored!(A::Diagonal, x) = (fill!(A.diag, x); A)
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9 changes: 5 additions & 4 deletions stdlib/LinearAlgebra/src/tridiag.jl
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Expand Up @@ -571,15 +571,16 @@ function size(M::Tridiagonal, d::Integer)
end
end

function Matrix{T}(M::Tridiagonal{T}) where T
function Matrix{T}(M::Tridiagonal) where {T}
A = zeros(T, size(M))
for i = 1:length(M.d)
n = length(M.d)
n == 0 && return A
for i in 1:n-1
A[i,i] = M.d[i]
end
for i = 1:length(M.d)-1
A[i+1,i] = M.dl[i]
A[i,i+1] = M.du[i]
end
A[n,n] = M.d[n]
A
end
Matrix(M::Tridiagonal{T}) where {T} = Matrix{T}(M)
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32 changes: 18 additions & 14 deletions stdlib/LinearAlgebra/test/special.jl
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Expand Up @@ -188,16 +188,21 @@ end


@testset "Triangular Types and QR" begin
for typ in [UpperTriangular,LowerTriangular,LinearAlgebra.UnitUpperTriangular,LinearAlgebra.UnitLowerTriangular]
for typ in (UpperTriangular, LowerTriangular, UnitUpperTriangular, UnitLowerTriangular)
a = rand(n,n)
atri = typ(a)
matri = Matrix(atri)
b = rand(n,n)
qrb = qr(b, ColumnNorm())
@test *(atri, adjoint(qrb.Q)) ≈ Matrix(atri) * qrb.Q'
@test rmul!(copy(atri), adjoint(qrb.Q)) ≈ Matrix(atri) * qrb.Q'
@test atri * qrb.Q ≈ matri * qrb.Q ≈ rmul!(copy(atri), qrb.Q)
@test atri * qrb.Q' ≈ matri * qrb.Q' ≈ rmul!(copy(atri), qrb.Q')
@test qrb.Q * atri ≈ qrb.Q * matri ≈ lmul!(qrb.Q, copy(atri))
@test qrb.Q' * atri ≈ qrb.Q' * matri ≈ lmul!(qrb.Q', copy(atri))
qrb = qr(b, NoPivot())
@test *(atri, adjoint(qrb.Q)) ≈ Matrix(atri) * qrb.Q'
@test rmul!(copy(atri), adjoint(qrb.Q)) ≈ Matrix(atri) * qrb.Q'
@test atri * qrb.Q ≈ matri * qrb.Q ≈ rmul!(copy(atri), qrb.Q)
@test atri * qrb.Q' ≈ matri * qrb.Q' ≈ rmul!(copy(atri), qrb.Q')
@test qrb.Q * atri ≈ qrb.Q * matri ≈ lmul!(qrb.Q, copy(atri))
@test qrb.Q' * atri ≈ qrb.Q' * matri ≈ lmul!(qrb.Q', copy(atri))
end
end

Expand Down Expand Up @@ -421,19 +426,18 @@ end
end

@testset "BiTriSym*Q' and Q'*BiTriSym" begin
dl = [1, 1, 1];
d = [1, 1, 1, 1];
Tri = Tridiagonal(dl, d, dl)
dl = [1, 1, 1]
d = [1, 1, 1, 1]
D = Diagonal(d)
Bi = Bidiagonal(d, dl, :L)
Tri = Tridiagonal(dl, d, dl)
Sym = SymTridiagonal(d, dl)
F = qr(ones(4, 1))
A = F.Q'
@test Tri*A ≈ Matrix(Tri)*A
@test A*Tri ≈ A*Matrix(Tri)
@test Bi*A ≈ Matrix(Bi)*A
@test A*Bi ≈ A*Matrix(Bi)
@test Sym*A ≈ Matrix(Sym)*A
@test A*Sym ≈ A*Matrix(Sym)
for A in (F.Q, F.Q'), B in (D, Bi, Tri, Sym)
@test B*A ≈ Matrix(B)*A
@test A*B ≈ A*Matrix(B)
end
end

@testset "Ops on SymTridiagonal ev has the same length as dv" begin
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