Hello,

I know that's such a dumb question but I am quite new to Eigen.

I am trying to solve Ax=x for x but I couldn't get it done in Eigen.

A is ~50,000x50,000 real, non-negative sparse matrix.

I need to efficiently solve either for the null space of (A-I)x=0 or base eigenvector of the equation, Ax=lambda*x where eigenvalue=lambda would have to be 1.

However, I really don't know how to translate these two methods into Eigen :s
Any help to efficiently solve the equation above will be highly appreciated!

Thanks in advance.

Looking at the documentation brings up this:
http://eigen.tuxfamily.org/dox-devel/cl ... b0f0c1c3fa

His problem is sparse, not dense. He wants a sparse solver here. say sparse LU for general matrices.

bjacob wrote:His problem is sparse, not dense. He wants a sparse solver here. say sparse LU for general matrices.

Thanks bjacob.

I checked out the other threads but couldn't find a sol'n for sparse solvers yet.

This one seems particularly enlightening:
viewtopic.php?f=74&t=83060

I guess, it talks about external modules like cholmod, umfpack but doesn't detail a lot(or such a newbie I am). Now I need to figure out a way to plug these modules into Eigen.

I will appreciate your help if you have any idea on how to manage that.

For sparse stuff, I strongly encourage you to use eigen 3 (the development version).

There you have this tutorial:
http://eigen.tuxfamily.org/dox-devel/Tu ... parse.html

Thanks bjacob! I read the tutorial now I am trying to use SuperLU support module to solve the problem. I've downloaded the SuperLU package from here: http://crd.lbl.gov/~xiaoye/SuperLU/ and placed it under Eigen directory as SuperLU is not built-in in Eigen.

ref: viewtopic.php?f=74&t=84904

Code: Select all

#define EIGEN_SUPERLU_SUPPORT

#include "Eigen/Sparse"
#include "Eigen/LU"

using namespace std;
using namespace Eigen;

int main(int, char *[])
{
   MatrixXf A(4,4);// will use dynamic sparse matrix soon
   A << 0, 0, 1, 0.5, 0.333, 0, 0, 0, 0.333, 0.5, 0, 0.5, 0.333, 0.5, 0, 0;
   cout << "A:\n" << A << endl;

   SparseLU<MatrixXf, SuperLU> lu(A);
   return 1;
}



Now that, when I compile the following I got this weird error:

Eigen/src/Sparse/SuperLUSupport.h:45: error: 'mem_usage_t' is not a member of 'SuperLU_S'

I don't know what's happening there - maybe I am linking the wrong version of SuperLU?

Regards.

Hi invisibleink,

what you need here is a sparse eigen decomposition algorithm that we don't have yet in Eigen. For instance there exist ARPACK++ and SLEPc. I'd recommend the later.

Gael, all he was asking for was computing the kernel of A-I, shouldn't some form of LU be enough here? Or do you mean that pivoting would be required (to handle singularness) and sparse LU is non-pivoting? Or is it just a matter of accuracy?