CUSP sparse library giving strange results

Question

I'm trying to do the following in CUSP:

A=[
    1,1,0,0;
    2,2,2,0;
    0,3,3,3;
    0,0,4,4];
B=[1,1,1,1]';
disp(mldivide(A,B));

which is

X=[0.9167,0.0833,-0.5000,0.7500]

On the other hand I get a strange answer from CUSP

#include <cusp/dia_matrix.h>
#include <cusp/krylov/cg.h>
#include <cusp/print.h>
int main()
{
    cusp::dia_matrix<int,float,cusp::host_memory> A(4,4,10,3);
    A.diagonal_offsets[0] = -1;
    A.diagonal_offsets[1] =  0;
    A.diagonal_offsets[2] =  1;
    for (int i = 0;i <3;i++)
    {
        for (int q = 0 ;q < A.num_cols;q++)
        {
            A.values(q,i)=q+1;
        }
    }
    //copy
    cusp::dia_matrix<int,float,cusp::device_memory> AA = A;
    cusp::array1d<float,cusp::device_memory> BB(A.num_rows,1);
    cusp::array1d<float,cusp::device_memory> XX(A.num_rows,0);
    cusp::print(AA);
    cusp::print(XX);
    cusp::print(BB);
    cusp::krylov::cg(AA,XX,BB);\
    cusp::print(XX);
    return 0;
}

The result looks like

sparse matrix <4, 4> with 10 entries
              0              0              1
              0              1              1
              1              0              2
              1              1              2
              1              2              2
              2              1              3
              2              2              3
              2              3              3
              3              2              4
              3              3              4
array1d <4>
             0
             0
             0
             0
array1d <4>
             1
             1
             1
             1
array1d <4>
      -39.9938
       -53.436
       87.9025
      -30.1429

The last one doesn't look quite right. Anybody know what I'm doing wrong? Am I using the code wrong or are we supposed to have a really good guessed solution + use a preconditioner?

Answer 1

The conjugate gradient method is only valid for use in symmetric positive definite matrices. Your matrix isn't symmetric. That is why it isn't (and cannot) producing a valid solution. Either use an appropriate, well conditioned SPD matrix, or use a different numerical method.