[HectorRedal]

Hi,


I would like to know if there exists a mathematical library that can be used for computing the inverse of a matrix (or the solution to a A . x = b linear system) leveraging in paralelism.


Currently I am using Eigen library, but the obtained paralelism is not very high.


Thanks in advance for your support.


Best regards,

[sbaffini]

Computing the inverse is quite different from computing the solution to the system, for a number of reasons. In practice, the inverse is almost never looked for, especially for large parallel systems.

Try giving a look at PETSc and Hypre. PETSc is basically targeted toward giving you the solution but, maybe, among the different third party libraries it can link to, you may find also something for the inverse.

[praveen]

As sbaffini wrote, do you really need the inverse matrix ?

Anyway,

MUMPS is a direct solver that works in parallel. It can solve Ax=b but I dont know if it can compute the inverse. You can do this yourself as follows.

First compute the LU decomposition using MUMPS. Then solve a sequence of problems with varying right hand side

A x_i = e_i, for i=1,2,...,n

where e_i has zeros except it has 1 at i'th location. Then the matrix

X = [x_1, x_2, ..., x_n]

is the inverse of A. Solving these problems is cheap (O(n^2) in general) as compare to computing the LU decomposition which costs O(n^3).

There is also superlu_dist. Both of these can be used via PETSc I think. If you already have your matrices setup in PETSc, then it is easy.

[HectorRedal]

Hi,


I don't really need the computation of the inverse matrix.
Indeed, in my current implementation, I am solving the linear system A . x = b without computing the inverse of the sparse matrix. I have implemented the BiGSTAB method for sparse matrices.


I was just looking for a more efficient manner, since I have spotted the bottleneck of the computation in this part of the software.



Thanks for the references, I will take a look at them.


Best regards,

[praveen]

If your goal is to solve large problems, then I would recommend learning to use petsc. PETSc has its own solvers and it can also call many other solvers. So advantage is if you build your matrix/rhs in petsc, you can experiment with many solvers easily, and you dont have to learn to use all of them, since each one will have its own interface/data structures.

[FMDenaro]

Originally Posted by HectorRedal

Hi,


I don't really need the computation of the inverse matrix.
Indeed, in my current implementation, I am solving the linear system A . x = b without computing the inverse of the sparse matrix. I have implemented the BiGSTAB method for sparse matrices.


I was just looking for a more efficient manner, since I have spotted the bottleneck of the computation in this part of the software.



Thanks for the references, I will take a look at them.


Best regards,

An answer depends also on the shape of your matrix, sparse or not. If it is a matrix obtained by the discretization of elliptic equations on structured grids, you can find surprising that a black/white-marked SOR method will be the most efficient in terms of computational time and memory cost.

[HectorRedal]

Originally Posted by praveen

If your goal is to solve large problems, then I would recommend learning to use petsc. PETSc has its own solvers and it can also call many other solvers. So advantage is if you build your matrix/rhs in petsc, you can experiment with many solvers easily, and you dont have to learn to use all of them, since each one will have its own interface/data structures.

I will give it a try to petsc.

Thanks.

[HectorRedal]

Originally Posted by FMDenaro

An answer depends also on the shape of your matrix, sparse or not. If it is a matrix obtained by the discretization of elliptic equations on structured grids, you can find surprising that a black/white-marked SOR method will be the most efficient in terms of computational time and memory cost.

The matrix is obtained from unstructured grids (no structured grid). That's the reason why I am using sparse matrices.
Thanks.