is there any equivalent to scipy.sparse.linalg.spsolve in Julia? Here's the description of the function in Python.
In [59]: ?spsolve
Signature: spsolve(A, b, permc_spec=None, use_umfpack=True)
Docstring:
Solve the sparse linear system Ax=b, where b may be a vector or a matrix.
I couldn't find this in Julia's LinearAlgebra and SparseArrays. Is there anything I miss or any alternatives?
Thanks
EDIT
For example:
In [71]: A = sparse.csc_matrix([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
In [72]: B = sparse.csc_matrix([[2, 0], [-1, 0], [2, 0]], dtype=float)
In [73]: spsolve(A, B).data
Out[73]: array([ 1., -3.])
In [74]: spsolve(A, B).toarray()
Out[74]:
array([[ 0., 0.],
[ 1., 0.],
[-3., 0.]])
In Julia, with \ operator
julia> A = Float64.(sparse([3 2 0; 1 -1 0; 0 5 1]))
3×3 SparseMatrixCSC{Float64,Int64} with 6 stored entries:
[1, 1] = 3.0
[2, 1] = 1.0
[1, 2] = 2.0
[2, 2] = -1.0
[3, 2] = 5.0
[3, 3] = 1.0
julia> B = Float64.(sparse([2 0; -1 0; 2 0]))
3×2 SparseMatrixCSC{Float64,Int64} with 3 stored entries:
[1, 1] = 2.0
[2, 1] = -1.0
[3, 1] = 2.0
julia> A \ B
ERROR: MethodError: no method matching ldiv!(::SuiteSparse.UMFPACK.UmfpackLU{Float64,Int64}, ::SparseMatrixCSC{Float64,Int64})
Closest candidates are:
ldiv!(::Number, ::AbstractArray) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.3/LinearAlgebra/src/generic.jl:236
ldiv!(::SymTridiagonal, ::Union{AbstractArray{T,1}, AbstractArray{T,2}} where T; shift) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.3/LinearAlgebra/src/tridiag.jl:208
ldiv!(::LU{T,Tridiagonal{T,V}}, ::Union{AbstractArray{T,1}, AbstractArray{T,2}} where T) where {T, V} at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.3/LinearAlgebra/src/lu.jl:588
...
Stacktrace:
[1] \(::SuiteSparse.UMFPACK.UmfpackLU{Float64,Int64}, ::SparseMatrixCSC{Float64,Int64}) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.3/LinearAlgebra/src/factorization.jl:99
[2] \(::SparseMatrixCSC{Float64,Int64}, ::SparseMatrixCSC{Float64,Int64}) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.3/SparseArrays/src/linalg.jl:1430
[3] top-level scope at REPL[81]:1
Yes, it's the \ function.
julia> using SparseArrays, LinearAlgebra
julia> A = sprand(Float64, 20, 20, 0.01) + I # just adding the identity matrix so A is non-singular.
julia> typeof(A)
SparseMatrixCSC{Float64,Int64}
julia> v = rand(20);
julia> A \ v
20-element Array{Float64,1}:
0.5930744938331236
0.8726507741810358
0.6846427450637211
0.3135234897986168
0.8366321472466727
0.11338490488638651
0.3679058951515244
0.4931583108292607
0.3057947282994271
0.27481281228206955
0.888942874188458
0.905356044150361
0.17546911165214607
0.13636389619386557
0.9607381212005248
0.2518153541168824
0.6237205353883974
0.6588050295549153
0.14748809413104935
0.9806131247053784
Edit in response to question edit:
If you want v here to instead be a sparse matrix B, then we can proceed by using the QR decomposition of B (note that cases where B is truly sparse are rare:
function myspsolve(A, B)
qrB = qr(B)
Q, R = qrB.Q, qrB.R
R = [R; zeros(size(Q, 2) - size(R, 1), size(R, 2))]
A\Q * R
end
now:
julia> A = Float64.(sparse([3 2 0; 1 -1 0; 0 5 1]))
3×3 SparseMatrixCSC{Float64,Int64} with 6 stored entries:
[1, 1] = 3.0
[2, 1] = 1.0
[1, 2] = 2.0
[2, 2] = -1.0
[3, 2] = 5.0
[3, 3] = 1.0
julia> B = Float64.(sparse([2 0; -1 0; 2 0]))
3×2 SparseMatrixCSC{Float64,Int64} with 3 stored entries:
[1, 1] = 2.0
[2, 1] = -1.0
[3, 1] = 2.0
julia> mysolve(A, B)
3×2 Array{Float64,2}:
0.0 0.0
1.0 0.0
-3.0 0.0
and we can test to make sure we did it right:
julia> mysolve(A, B) ≈ A \ collect(B)
true
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