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Merge pull request #99 from SciML/genericlu
add GenericLUFactorizations
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| MIT License | ||
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| Copyright (c) 2021 Jonathan <[email protected]> and contributors | ||
| Copyright (c) 2021 SciML and contributors | ||
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| Permission is hereby granted, free of charge, to any person obtaining a copy | ||
| of this software and associated documentation files (the "Software"), to deal | ||
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@@ -19,3 +19,6 @@ AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | |
| LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | ||
| OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE | ||
| SOFTWARE. | ||
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| SimpleLU.jl is derived from https://github.com/JuliaGNI/SimpleSolvers.jl under | ||
| an MIT license. | ||
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| ## From https://github.com/JuliaGNI/SimpleSolvers.jl/blob/master/src/linear/lu_solver.jl | ||
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| mutable struct LUSolver{T} | ||
| n::Int | ||
| A::Matrix{T} | ||
| b::Vector{T} | ||
| x::Vector{T} | ||
| pivots::Vector{Int} | ||
| perms::Vector{Int} | ||
| info::Int | ||
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| LUSolver{T}(n) where {T} = new(n, zeros(T, n, n), zeros(T, n), zeros(T, n), zeros(Int, n), zeros(Int, n), 0) | ||
| end | ||
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| function LUSolver(A::Matrix{T}) where {T} | ||
| n = LinearAlgebra.checksquare(A) | ||
| lu = LUSolver{eltype(A)}(n) | ||
| lu.A .= A | ||
| lu | ||
| end | ||
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| function LUSolver(A::Matrix{T}, b::Vector{T}) where {T} | ||
| n = LinearAlgebra.checksquare(A) | ||
| @assert n == length(b) | ||
| lu = LUSolver{eltype(A)}(n) | ||
| lu.A .= A | ||
| lu.b .= b | ||
| lu | ||
| end | ||
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| function simplelu_factorize!(lu::LUSolver{T}, pivot=true) where {T} | ||
| A = lu.A | ||
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| begin | ||
| @inbounds for i in eachindex(lu.perms) | ||
| lu.perms[i] = i | ||
| end | ||
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| @inbounds for k = 1:lu.n | ||
| # find index max | ||
| kp = k | ||
| if pivot | ||
| amax = real(zero(T)) | ||
| for i = k:lu.n | ||
| absi = abs(A[i,k]) | ||
| if absi > amax | ||
| kp = i | ||
| amax = absi | ||
| end | ||
| end | ||
| end | ||
| lu.pivots[k] = kp | ||
| lu.perms[k], lu.perms[kp] = lu.perms[kp], lu.perms[k] | ||
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| if A[kp,k] != 0 | ||
| if k != kp | ||
| # Interchange | ||
| for i = 1:lu.n | ||
| tmp = A[k,i] | ||
| A[k,i] = A[kp,i] | ||
| A[kp,i] = tmp | ||
| end | ||
| end | ||
| # Scale first column | ||
| Akkinv = inv(A[k,k]) | ||
| for i = k+1:lu.n | ||
| A[i,k] *= Akkinv | ||
| end | ||
| elseif lu.info == 0 | ||
| lu.info = k | ||
| end | ||
| # Update the rest | ||
| for j = k+1:lu.n | ||
| for i = k+1:lu.n | ||
| A[i,j] -= A[i,k]*A[k,j] | ||
| end | ||
| end | ||
| end | ||
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| lu.info | ||
| end | ||
| end | ||
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| function simplelu_solve!(lu::LUSolver{T}) where {T} | ||
| @inbounds for i = 1:lu.n | ||
| lu.x[i] = lu.b[lu.perms[i]] | ||
| end | ||
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| @inbounds for i = 2:lu.n | ||
| s = zero(T) | ||
| for j = 1:i-1 | ||
| s += lu.A[i,j] * lu.x[j] | ||
| end | ||
| lu.x[i] -= s | ||
| end | ||
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| lu.x[lu.n] /= lu.A[lu.n,lu.n] | ||
| @inbounds for i = lu.n-1:-1:1 | ||
| s = zero(T) | ||
| for j = i+1:lu.n | ||
| s += lu.A[i,j] * lu.x[j] | ||
| end | ||
| lu.x[i] -= s | ||
| lu.x[i] /= lu.A[i,i] | ||
| end | ||
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| copyto!(lu.b,lu.x) | ||
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| lu.x | ||
| end | ||
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| ### Wrapper | ||
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| struct SimpleLUFactorization <: AbstractFactorization | ||
| pivot::Bool | ||
| SimpleLUFactorization(pivot=true) = new(pivot) | ||
| end | ||
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| function SciMLBase.solve(cache::LinearCache, alg::SimpleLUFactorization; kwargs...) | ||
| if cache.isfresh | ||
| cache.cacheval.A = cache.A | ||
| simplelu_factorize!(cache.cacheval, alg.pivot) | ||
| end | ||
| cache.cacheval.b = cache.b | ||
| cache.cacheval.x = cache.u | ||
| y = simplelu_solve!(cache.cacheval) | ||
| SciMLBase.build_linear_solution(alg,y,nothing,cache) | ||
| end | ||
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| init_cacheval(alg::SimpleLUFactorization, A, b, u, Pl, Pr, maxiters, abstol, reltol, verbose) = LUSolver(convert(AbstractMatrix,A)) |