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Improve src/matrixlu.jl to optimize arrlu #49

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Merged
shinaoka merged 5 commits into from
Nov 11, 2024
Merged

Improve src/matrixlu.jl to optimize arrlu #49

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d6b869c
Optimize swaprow! and swapcol!
terasakisatoshi Nov 11, 2024
4d8e1e3
Use view macro to avoid memory allocation
terasakisatoshi Nov 11, 2024
d823e41
Optimize cols2Lmatrix! and rows2Umatrix!
terasakisatoshi Nov 11, 2024
492368d
Minor fix
terasakisatoshi Nov 11, 2024
0650adb
Use append! rather than push!
terasakisatoshi Nov 11, 2024
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60 changes: 42 additions & 18 deletions src/matrixlu.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -96,13 +96,19 @@ function rrLU{T}(A::AbstractMatrix{T}; leftorthogonal::Bool=true) where {T}
end

function swaprow!(lu::rrLU{T}, A::AbstractMatrix{T}, a, b) where {T}
lu.rowpermutation[[a, b]] = lu.rowpermutation[[b, a]]
A[[a, b], :] = A[[b, a], :]
lurp = lu.rowpermutation
lurp[a], lurp[b] = lurp[b], lurp[a]
@inbounds for j in axes(A, 2)
A[a, j], A[b, j] = A[b, j], A[a, j]
end
end

function swapcol!(lu::rrLU{T}, A::AbstractMatrix{T}, a, b) where {T}
lu.colpermutation[[a, b]] = lu.colpermutation[[b, a]]
A[:, [a, b]] = A[:, [b, a]]
lucp = lu.colpermutation
lucp[a], lucp[b] = lucp[b], lucp[a]
@inbounds for i in axes(A, 1)
A[i, a], A[i, b] = A[i, b], A[i, a]
end
end

function addpivot!(lu::rrLU{T}, A::AbstractMatrix{T}, newpivot) where {T}
Expand All @@ -111,9 +117,9 @@ function addpivot!(lu::rrLU{T}, A::AbstractMatrix{T}, newpivot) where {T}
swapcol!(lu, A, k, newpivot[2])

if lu.leftorthogonal
A[k+1:end, k] /= A[k, k]
A[k+1:end, k] ./= A[k, k]
else
A[k, k+1:end] /= A[k, k]
A[k, k+1:end] ./= A[k, k]
end

# perform BLAS subroutine manually: A <- -x * transpose(y) + A
Expand All @@ -139,12 +145,12 @@ function _optimizerrlu!(
reltol::Number=1e-14,
abstol::Number=0.0
) where {T}
maxrank = min(maxrank, size(A)...)
maxrank = min(maxrank, size(A, 1), size(A, 2))
maxerror = 0.0
while lu.npivot < maxrank
k = lu.npivot + 1
newpivot = submatrixargmax(abs2, A, k)
lu.error = abs(A[newpivot...])
lu.error = abs(A[newpivot[1], newpivot[2]])
# Add at least 1 pivot to get a well-defined L * U
if (abs(lu.error) < reltol * maxerror || abs(lu.error) < abstol) && lu.npivot > 0
break
Expand All @@ -153,8 +159,8 @@ function _optimizerrlu!(
addpivot!(lu, A, newpivot)
end

lu.L = tril(A[:, 1:lu.npivot])
lu.U = triu(A[1:lu.npivot, :])
lu.L = tril(@view A[:, 1:lu.npivot])
lu.U = triu(@view A[1:lu.npivot, :])
if any(isnan.(lu.L))
error("lu.L contains NaNs")
end
Expand Down Expand Up @@ -271,16 +277,16 @@ function arrlu(
I2 = setdiff(1:matrixsize[1], I0)
lu.rowpermutation = vcat(I0, I2)
L2 = _batchf(I2, J0)
cols2Lmatrix!(L2, lu.U[1:lu.npivot, 1:lu.npivot], leftorthogonal)
lu.L = vcat(lu.L[1:lu.npivot, 1:lu.npivot], L2)
cols2Lmatrix!(L2, (@view lu.U[1:lu.npivot, 1:lu.npivot]), leftorthogonal)
lu.L = vcat((@view lu.L[1:lu.npivot, 1:lu.npivot]), L2)
end

if size(lu.U, 2) < matrixsize[2]
J2 = setdiff(1:matrixsize[2], J0)
lu.colpermutation = vcat(J0, J2)
U2 = _batchf(I0, J2)
rows2Umatrix!(U2, lu.L[1:lu.npivot, 1:lu.npivot], leftorthogonal)
lu.U = hcat(lu.U[1:lu.npivot, 1:lu.npivot], U2)
rows2Umatrix!(U2, (@view lu.L[1:lu.npivot, 1:lu.npivot]), leftorthogonal)
lu.U = hcat((@view lu.U[1:lu.npivot, 1:lu.npivot]), U2)
end

return lu
Expand Down Expand Up @@ -313,8 +319,17 @@ function cols2Lmatrix!(C::AbstractMatrix, P::AbstractMatrix, leftorthogonal::Boo
end

for k in axes(P, 1)
C[:, k] /= P[k, k]
C[:, k+1:end] -= C[:, k] * transpose(P[k, k+1:end])
C[:, k] ./= P[k, k]
# C[:, k+1:end] .-= C[:, k] * transpose(P[k, k+1:end])
x = @view C[:, k]
y = @view P[k, k+1:end]
C̃ = @view C[:, k+1:end]
@inbounds for j in eachindex(axes(C̃, 2), y)
for i in eachindex(axes(C̃, 1), x)
# update `C[:, k+1:end]`
C̃[i, j] -= x[i] * y[j]
end
end
end
return C
end
Expand All @@ -327,8 +342,17 @@ function rows2Umatrix!(R::AbstractMatrix, P::AbstractMatrix, leftorthogonal::Boo
end

for k in axes(P, 1)
R[k, :] /= P[k, k]
R[k+1:end, :] -= P[k+1:end, k] * transpose(R[k, :])
R[k, :] ./= P[k, k]
# R[k+1:end, :] -= P[k+1:end, k] * transpose(R[k, :])
x = @view P[k+1:end, k]
y = @view R[k, :]
R̃ = @view R[k+1:end, :]
@inbounds for j in eachindex(axes(R̃, 2), y)
for i in eachindex(axes(R̃, 1), x)
# update R[k+1:end, :]
R̃[i, j] -= x[i] * y[j]
end
end
end
return R
end
Expand Down
2 changes: 1 addition & 1 deletion src/util.jl
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Expand Up @@ -53,7 +53,7 @@ end

function pushrandomsubset!(subset, set, n::Int)
topush = randomsubset(setdiff(set, subset), n)
push!(subset, topush...)
append!(subset, topush)
nothing
end

Expand Down