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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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Do Ax_ldiv_B! for LU factorizations in-place
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@haampie
haampie committed Aug 23, 2017
commit d08467c92795549ee777f1e2e4450a831ee6f53f
54 changes: 36 additions & 18 deletions base/linalg/lu.jl
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Expand Up @@ -243,32 +243,50 @@ 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
A_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, b::StridedVector) =
A_ldiv_B!(UpperTriangular(A.factors),
A_ldiv_B!(UnitLowerTriangular(A.factors), b[ipiv2perm(A.ipiv, length(b))]))
A_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, B::StridedMatrix) =
A_ldiv_B!(UpperTriangular(A.factors),
A_ldiv_B!(UnitLowerTriangular(A.factors), B[ipiv2perm(A.ipiv, size(B, 1)),:]))

function A_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, b::StridedVector)
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I think it is sufficient to do A_ldiv_B!(UpperTriangular(A[:U]), A_ldiv_B!(LinAlg.UnitLowerTriangular(A[:L]), view(b, A[:p]))) here.

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I have tried exactly this, but the problem is that the user works with b itself after calling A_ldiv_B!(LU, b), and b has to be permuted. So whether you do the permutation during the backward & forward substitutions implicitly with a view doesn't really matter, the permutation has to be applied in the end anyway.

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I didn't know about A[:p] btw, thanks

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)
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)
end

At_ldiv_B!(A::LU{T,<:StridedMatrix}, B::StridedVecOrMat{T}) where {T<:BlasFloat} =
@assertnonsingular LAPACK.getrs!('T', A.factors, A.ipiv, B) A.info
At_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, b::StridedVector) =
At_ldiv_B!(UnitLowerTriangular(A.factors),
At_ldiv_B!(UpperTriangular(A.factors), b))[invperm(ipiv2perm(A.ipiv, length(b)))]
At_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, B::StridedMatrix) =
At_ldiv_B!(UnitLowerTriangular(A.factors),
At_ldiv_B!(UpperTriangular(A.factors), B))[invperm(ipiv2perm(A.ipiv, size(B,1))),:]

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)
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couldn't this permute in place?

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I was thinking the same, but permute! copies the permutation array, so a new allocation of roughly the same size is done anyway. Also the docs suggest using b[perm]. But if the array or number type is special, then permute! might be better.

end

function At_ldiv_B!(A::LU{<:Any,<:StridedMatrix}, B::StridedMatrix)
At_ldiv_B!(UnitLowerTriangular(A.factors), At_ldiv_B!(UpperTriangular(A.factors), B))
B_permuted = B[invperm(ipiv2perm(A.ipiv, size(B,1))), :]
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Perhaps space-separate the arguments to size as in the similar method above? :)

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

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)
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)
end

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