In matlab, we calculate inv(A)* B by A\B. How about Julia? note that A&B are two large sparse matrices

New to Julia
1

Does anybody have experience with the calculation of inv(A)*B in Julia, where A and B are large sparse matrices?

When I used zz = A\B in Julia. It shows the following error in Julia

MethodError: no method matching ldiv!(::SuiteSparse.UMFPACK.UmfpackLU{Float64,Int64}, ::SparseArrays.SparseMatrixCSC{Float64,Int64})
Closest candidates are:
  ldiv!(!Matched::Number, ::AbstractArray) at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.2\LinearAlgebra\src\generic.jl:152
  ldiv!(!Matched::LinearAlgebra.LU{T,LinearAlgebra.Tridiagonal{T,V}}, ::Union{AbstractArray{T,2}, AbstractArray{T,1}} where T) where {T, V} at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.2\LinearAlgebra\src\lu.jl:523
  ldiv!(!Matched::LinearAlgebra.Transpose{#s617,#s616} where #s616<:LinearAlgebra.LU{T,LinearAlgebra.Tridiagonal{T,V}} where #s617, ::Union{AbstractArray{T,2}, AbstractArray{T,1}} where T) where {T, V} at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.2\LinearAlgebra\src\lu.jl:555
  ...

Stacktrace:
 [1] \(::SuiteSparse.UMFPACK.UmfpackLU{Float64,Int64}, ::SparseArrays.SparseMatrixCSC{Float64,Int64}) at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.2\LinearAlgebra\src\factorization.jl:87
 [2] \(::SparseArrays.SparseMatrixCSC{Float64,Int64}, ::SparseArrays.SparseMatrixCSC{Float64,Int64}) at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.2\SparseArrays\src\linalg.jl:1374
 [3] top-level scope at In[5]:1
```![wktBM|592x499](upload://pFiCUnwBi5tsGuciDEaMhO8sxqw.png)![wktBM|592x499](upload://pFiCUnwBi5tsGuciDEaMhO8sxqw.png)
2

Just make B dense? The result will be a dense matrix of that size anyway.

3 Likes
3

Thank you :slight_smile: I’ll try. Wondering if full() command is not supported in Julia 1.2?

4

You can just do Matrix(B).

1 Like
5

Unfortunately, Same error.

MethodError: no method matching ldiv!(::SuiteSparse.UMFPACK.UmfpackLU{Float64,Int64}, ::SparseArrays.SparseMatrixCSC{Float64,Int64})
Closest candidates are:
ldiv!(!Matched::Number, ::AbstractArray) at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.2\LinearAlgebra\src\generic.jl:152
ldiv!(!Matched::LinearAlgebra.LU{T,LinearAlgebra.Tridiagonal{T,V}}, ::Union{AbstractArray{T,2}, AbstractArray{T,1}} where T) where {T, V} at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.2\LinearAlgebra\src\lu.jl:523
ldiv!(!Matched::LinearAlgebra.Transpose{#s617,#s616} where #s616<:LinearAlgebra.LU{T,LinearAlgebra.Tridiagonal{T,V}} where #s617, ::Union{AbstractArray{T,2}, AbstractArray{T,1}} where T) where {T, V} at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.2\LinearAlgebra\src\lu.jl:555
…

Stacktrace:
[1] (::SuiteSparse.UMFPACK.UmfpackLU{Float64,Int64}, ::SparseArrays.SparseMatrixCSC{Float64,Int64}) at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.2\LinearAlgebra\src\factorization.jl:87
[2] (::SparseArrays.SparseMatrixCSC{Float64,Int64}, ::SparseArrays.SparseMatrixCSC{Float64,Int64}) at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.2\SparseArrays\src\linalg.jl:1374
[3] top-level scope at In[5]:1

6

Looks like you’re stll calling ldiv! with the sparse matrix :thinking:

Can you show the code that produces this error?

7

Can you give an example of what you are doing?

julia> A = lu(sprand(5,5,0.5) + I)
UMFPACK LU Factorization of a (5, 5) sparse matrix
Ptr{Nothing} @0x00007fbedec06620

julia> B = sprand(5,5,0.4);

julia> A \ Matrix(B)
5Ă—5 Array{Float64,2}:
 -0.247253  -0.458155    0.331186   -0.179299   0.222382
 -0.812489  -2.25484     1.4221     -0.251258   1.58024
  1.17403    2.29645    -0.930615    0.164422  -1.03411
  0.338484   0.0         0.0         0.0        0.0
 -0.18574   -0.0906186   0.0367224   0.660449   0.844956
8

image
image1085Ă—791 42 KB

I tried with another problem, it worked. However, stucked with the memory issue.

9

Yes, it would require a lot of memory to store that. What is the reason for doing this computation though? If this is some type of discretized problem where K is a “stiffness matrix” and M a “mass matrix” then I don’t see why you are doing K \ M.

10

Developing formulation for modal reduction in Multiphysics problems. It works in matlab if I consider both matrix as sparse and implement K \ M .