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Fix LU factorization in-place operations #22774

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merged 4 commits into from
Aug 24, 2017
Merged

Fix LU factorization in-place operations #22774

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8775d66
Add tests for in-place operations of A_ldiv_B!(y, LU, x) for LU facto…
haampie Jul 12, 2017
d08467c
Do Ax_ldiv_B! for LU factorizations in-place
haampie Jul 12, 2017
5f2350a
Remove incorrect condition in LU test. The transpose should be tested…
haampie Jul 12, 2017
944f02a
Get rid of allocations, apply the (inverse) permutation in-place
haampie Aug 22, 2017
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Get rid of allocations, apply the (inverse) permutation in-place
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@haampie
haampie committed Aug 23, 2017
commit 944f02af900bd3b0d722d999564497de78e9b7ce
59 changes: 31 additions & 28 deletions base/linalg/lu.jl
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Expand Up @@ -241,51 +241,54 @@ function show(io::IO, F::LU)
print(io, "\nsuccessful: $(issuccess(F))")
end

A_ldiv_B!(A::LU{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:BlasFloat} =
@assertnonsingular LAPACK.getrs!('N', A.factors, A.ipiv, B) A.info
_apply_ipiv!(A::LU, B::StridedVecOrMat) = _ipiv!(A, 1 : length(A.ipiv), B)
_apply_inverse_ipiv!(A::LU, B::StridedVecOrMat) = _ipiv!(A, length(A.ipiv) : -1 : 1, B)

function A_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, b::StridedVector)
b_permuted = b[ipiv2perm(A.ipiv, length(b))]
A_ldiv_B!(UpperTriangular(A.factors), A_ldiv_B!(UnitLowerTriangular(A.factors), b_permuted))
copy!(b, b_permuted)
function _ipiv!(A::LU, order::OrdinalRange, B::StridedVecOrMat)
for i = order
if i != A.ipiv[i]
_swap_rows!(B, i, A.ipiv[i])
end
end
B
end

function A_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, B::StridedMatrix)
B_permuted = B[ipiv2perm(A.ipiv, size(B, 1)), :]
A_ldiv_B!(UpperTriangular(A.factors), A_ldiv_B!(UnitLowerTriangular(A.factors), B_permuted))
copy!(B, B_permuted)
function _swap_rows!(B::StridedVector, i::Integer, j::Integer)
B[i], B[j] = B[j], B[i]
B
end
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Not necessary in this pull request, but DRYing out these and the similar method definitions below might be nice. For example, as a first step perhaps something along the lines of

function A_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, B::StridedVecOrMat)
    B_permuted = _ipivpermute(B, A.ipiv)
    A_ldiv_B!(UpperTriangular(A.factors), A_ldiv_B!(UnitLowerTriangular(A.factors), B_permuted))
    copy!(B, B_permuted)
end
_ipivpermute(b::StridedVector, ipiv) = b[ipiv2perm(ipiv, length(b))]
_ipivpermute(B::StridedMatrix, ipiv) = B[ipiv2perm(ipiv, size(B, 1)), :]

would do the trick? :)


At_ldiv_B!(A::LU{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:BlasFloat} =
@assertnonsingular LAPACK.getrs!('T', A.factors, A.ipiv, B) A.info
function _swap_rows!(B::StridedMatrix, i::Integer, j::Integer)
for col = 1 : size(B, 2)
B[i,col], B[j,col] = B[j,col], B[i,col]
end
B
end

function At_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, b::StridedVector)
At_ldiv_B!(UnitLowerTriangular(A.factors), At_ldiv_B!(UpperTriangular(A.factors), b))
b_permuted = b[invperm(ipiv2perm(A.ipiv, length(b)))]
copy!(b, b_permuted)
A_ldiv_B!(A::LU{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:BlasFloat} =
@assertnonsingular LAPACK.getrs!('N', A.factors, A.ipiv, B) A.info

function A_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, B::StridedVecOrMat)
_apply_ipiv!(A, B)
A_ldiv_B!(UpperTriangular(A.factors), A_ldiv_B!(UnitLowerTriangular(A.factors), B))
end

function At_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, B::StridedMatrix)
At_ldiv_B!(A::LU{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:BlasFloat} =
@assertnonsingular LAPACK.getrs!('T', A.factors, A.ipiv, B) A.info

function At_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, B::StridedVecOrMat)
At_ldiv_B!(UnitLowerTriangular(A.factors), At_ldiv_B!(UpperTriangular(A.factors), B))
B_permuted = B[invperm(ipiv2perm(A.ipiv, size(B,1))), :]
copy!(B, B_permuted)
_apply_inverse_ipiv!(A, B)
end

Ac_ldiv_B!(F::LU{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:Real} =
At_ldiv_B!(F, B)
Ac_ldiv_B!(A::LU{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:BlasComplex} =
@assertnonsingular LAPACK.getrs!('C', A.factors, A.ipiv, B) A.info

function Ac_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, b::StridedVector)
Ac_ldiv_B!(UnitLowerTriangular(A.factors), Ac_ldiv_B!(UpperTriangular(A.factors), b))
b_permuted = b[invperm(ipiv2perm(A.ipiv, length(b)))]
copy!(b, b_permuted)
end

function Ac_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, B::StridedMatrix)
function Ac_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, B::StridedVecOrMat)
Ac_ldiv_B!(UnitLowerTriangular(A.factors), Ac_ldiv_B!(UpperTriangular(A.factors), B))
B_permuted = B[invperm(ipiv2perm(A.ipiv, size(B,1))), :]
copy!(B, B_permuted)
_apply_inverse_ipiv!(A, B)
end

At_ldiv_Bt(A::LU{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:BlasFloat} =
Expand Down