Solving a linear system with dpotrs (Cholesky factorization)

Question

I am trying to solve a linear system of equations with clapack.

My code is as follows:

//ATTENTION: matrix in column-major
double A[3*3]={  2.0, -1.0,  0.0,
                0.0,  2.0, -1.0,
                0.0,  0.0,  2.0},
b[3]={1.0,2.0,3.0};

integer n=3,info,nrhs=1; char uplo='L';

dpotrf_("L", &n, A, &n, &info);
dpotrs_("L", &n, &nrhs, A, &n, b, &n, &info);

printf("Solution: %10.4f %10.4f %10.4f",b[0], b[1], b[2]);

As asked in this question , it is necessary to first factorize the matrix. dpotrf is supposed to factorize, dpotrs solves the system using the factorized matrix.

However, my result

2.5   4.0   3.5

is clearly wrong, I checked it here with WolframAlpha

Where is my mistake?

Answer 1

Curiously, 2.5 4.0 3.5 is the solution of rhs 1 2 3 ...if the matrix is

 2   -1  0
 -1  2   -1
 0   -1  2

dpotrf and dpotrs are made for symetric positive definite matrices...

I would suggest to use dgetrf and dgetrs instead. In your case :

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <lapacke.h>

int main()
{
    //ATTENTION: matrix in column-major
    double A[3*3]={  2.0, -1.0,  0.0,
            0,  2.0, -1.0,
            0.0,  0,  2.0},
            b[3]={1.0,2,3.0};

    int n=3,info,nrhs=1; char uplo='L';
    int ipvs[3];
    dgetrf_(&n, &n, A, &n,ipvs, &info);
    printf("info %d\n",info);
    dgetrs_("T", &n, &nrhs, A, &n,ipvs, b, &n, &info);
    printf("info %d\n",info);
    printf("Solution: %10.4f %10.4f %10.4f\n",b[0], b[1], b[2]);

    return 0;
}

The solution i got is 1.3750 1.75 1.5 . If it is not the column major order, switch to "N" instead of "T" . Then, the solution becomes 0.5 1.25 2.125

Choose your favorite !

Bye,

Francis