Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Solve systems with multiple rhs #81

Merged
merged 2 commits into from
Oct 18, 2023
Merged

Solve systems with multiple rhs #81

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
6112cee
fix #80 (multiple rhs)
geoffroyleconte Mar 9, 2023
2df725d
fix type solve function
geoffroyleconte Mar 9, 2023
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
66 changes: 55 additions & 11 deletions src/LimitedLDLFactorizations.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -769,7 +769,7 @@ function abspermute!(
end
end

function lldl_lsolve!(n, x, Lp, Li, Lx)
function lldl_lsolve!(n, x::AbstractVector, Lp, Li, Lx)
@inbounds for j = 1:n
xj = x[j]
@inbounds for p = Lp[j]:(Lp[j + 1] - 1)
Expand All @@ -779,14 +779,14 @@ function lldl_lsolve!(n, x, Lp, Li, Lx)
return x
end

function lldl_dsolve!(n, x, D)
function lldl_dsolve!(n, x::AbstractVector, D)
@inbounds for j = 1:n
x[j] /= D[j]
end
return x
end

function lldl_ltsolve!(n, x, Lp, Li, Lx)
function lldl_ltsolve!(n, x::AbstractVector, Lp, Li, Lx)
@inbounds for j = n:-1:1
xj = x[j]
@inbounds for p = Lp[j]:(Lp[j + 1] - 1)
Expand All @@ -797,31 +797,75 @@ function lldl_ltsolve!(n, x, Lp, Li, Lx)
return x
end

function lldl_solve!(n, b, Lp, Li, Lx, D, P)
function lldl_solve!(n, b::AbstractVector, Lp, Li, Lx, D, P)
@views y = b[P]
lldl_lsolve!(n, y, Lp, Li, Lx)
lldl_dsolve!(n, y, D)
lldl_ltsolve!(n, y, Lp, Li, Lx)
return b
end

import Base.(\)
function (\)(LLDL::LimitedLDLFactorization, b::AbstractVector)
y = copy(b)
factorized(LLDL) || throw(LLDLException(error_string))
lldl_solve!(LLDL.n, y, LLDL.colptr, LLDL.Lrowind, LLDL.Lnzvals, LLDL.D, LLDL.P)
# solve functions for multiple rhs
function lldl_lsolve!(n, X::AbstractMatrix, Lp, Li, Lx)
@inbounds for j = 1:n
@inbounds for p = Lp[j]:(Lp[j + 1] - 1)
for k ∈ axes(X, 2)
X[Li[p], k] -= Lx[p] * X[j, k]
end
end
end
return X
end

function lldl_dsolve!(n, X::AbstractMatrix, D)
@inbounds for j = 1:n
for k ∈ axes(X, 2)
X[j, k] /= D[j]
end
end
return X
end

function lldl_ltsolve!(n, X::AbstractMatrix, Lp, Li, Lx)
@inbounds for j = n:-1:1
@inbounds for p = Lp[j]:(Lp[j + 1] - 1)
for k ∈ axes(X, 2)
X[j, k] -= conj(Lx[p]) * X[Li[p], k]
end
end
end
return X
end

function lldl_solve!(n, B::AbstractMatrix, Lp, Li, Lx, D, P)
@views Y = B[P, :]
lldl_lsolve!(n, Y, Lp, Li, Lx)
lldl_dsolve!(n, Y, D)
lldl_ltsolve!(n, Y, Lp, Li, Lx)
return B
end

import Base.(\)
(\)(LLDL::LimitedLDLFactorization, b::AbstractVector) = ldiv!(LLDL, copy(b))
(\)(LLDL::LimitedLDLFactorization, B::AbstractMatrix) = ldiv!(LLDL, copy(B))

import LinearAlgebra.ldiv!
function ldiv!(LLDL::LimitedLDLFactorization, b::AbstractVector)
factorized(LLDL) || throw(LLDLException(error_string))
lldl_solve!(LLDL.n, b, LLDL.colptr, LLDL.Lrowind, LLDL.Lnzvals, LLDL.D, LLDL.P)
end
function ldiv!(LLDL::LimitedLDLFactorization, B::AbstractMatrix)
factorized(LLDL) || throw(LLDLException(error_string))
lldl_solve!(LLDL.n, B, LLDL.colptr, LLDL.Lrowind, LLDL.Lnzvals, LLDL.D, LLDL.P)
end

function ldiv!(y::AbstractVector, LLDL::LimitedLDLFactorization, b::AbstractVector)
factorized(LLDL) || throw(LLDLException(error_string))
y .= b
lldl_solve!(LLDL.n, y, LLDL.colptr, LLDL.Lrowind, LLDL.Lnzvals, LLDL.D, LLDL.P)
ldiv!(LLDL, y)
end
function ldiv!(Y::AbstractMatrix, LLDL::LimitedLDLFactorization, B::AbstractMatrix)
Y .= B
ldiv!(LLDL, Y)
end

import SparseArrays.nnz
Expand Down
23 changes: 19 additions & 4 deletions test/runtests.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -82,36 +82,45 @@ end
0 0.01 0 0 0.53 0 0.56 0 0 3.1
]
A = sparse(A)
B = tril(A)
Al = tril(A)

for perm ∈ (1:(A.n), amd(A), Metis.permutation(A)[1])
LLDL = lldl(B, P = perm, memory = 0)
LLDL = lldl(Al, P = perm, memory = 0)
nnzl0 = nnz(LLDL)
@test nnzl0 == nnz(tril(A))
@test LLDL.α_out == 0

LLDL = lldl(B, P = perm, memory = 5)
LLDL = lldl(Al, P = perm, memory = 5)
nnzl5 = nnz(LLDL)
@test nnzl5 ≥ nnzl0
@test LLDL.α_out == 0

LLDL = lldl(B, P = perm, memory = 10)
LLDL = lldl(Al, P = perm, memory = 10)
@test nnz(LLDL) ≥ nnzl5
@test LLDL.α_out == 0
L = LLDL.L + I
@test norm(L * diagm(0 => LLDL.D) * L' - A[perm, perm]) ≤ sqrt(eps()) * norm(A)

sol = ones(A.n)
Sol = rand(A.n, 4)
b = A * sol
B = A * Sol # test matrix rhs
x = LLDL \ b
X = LLDL \ B
@test x ≈ sol
@test isapprox(X, Sol, atol = sqrt(eps()))

y = similar(b)
Y = similar(B)
ldiv!(y, LLDL, b)
ldiv!(Y, LLDL, B)
@test y ≈ sol
@test isapprox(Y, Sol, atol = sqrt(eps()))

ldiv!(LLDL, b)
ldiv!(LLDL, B)
@test b ≈ sol
@test isapprox(B, Sol, atol = sqrt(eps()))
end
end

Expand Down Expand Up @@ -184,8 +193,14 @@ end
ldiv!(y, LLDL, b)
@test y ≈ sol

allocs = @allocated ldiv!(y, LLDL, b)
@test allocs == 0

ldiv!(LLDL, b)
@test b ≈ sol

allocs = @allocated ldiv!(LLDL, b)
@test allocs == 0
end

@testset "with shift lower triangle" begin
Expand Down
Loading