Problems with dgeqrf and dorgqr

Hello,

I'm having some unexpected results with the function LAPACKE_dgeqrf. Apparently I'm unable to get the appropriate QR decomposition at some cases, I'm rather obtaining a QR decomposition with some unexpected vector orientations for the orthogonal matrix Q.

Here is a MWE of the problem:

#include <stdio.h>
#include <stdlib.h>
#include "mkl.h"

#define N 2

int main()
{
    double *x   = (double *) malloc( sizeof(double) * N * N );
    double *tau = (double *) malloc( sizeof(double) * N );
    int i, j;

    /* Pathological example */
    x[0] = 4.0, x[1] = 1.0, x[2] = 3.0, x[3] = 1.0;

    printf("\n INITIAL MATRIX\n\n");
    for (i = 0; i < N; i++) {
        for (j = 0; j < N; j++) {
            printf(" %3.2lf\t", x[i*N+j]);
        }
        printf("\n");
    }

    LAPACKE_dgeqrf ( LAPACK_ROW_MAJOR, N, N, x, N, tau);

    printf("\n R MATRIX\n\n");
    for (i = 0; i < N; i++) {
        for (j = 0; j < N; j++) {
            if ( j >= i ){
                printf(" %3.2lf\t", x[i*N+j]);
            }else{
                printf(" %3.2lf\t", 0.0);
            }
        }
        printf("\n");
    }

    LAPACKE_dorgqr ( LAPACK_ROW_MAJOR, N, N, N, x, N, tau);

    printf("\n Q MATRIX\n\n");
    for (i = 0; i < N; i++) {
        for (j = 0; j < N; j++) {
            printf(" %3.2lf\t", x[i*N+j]);
        }
        printf("\n");
    }

    printf("\n");

    return 0;
}

With this example, the output I get is:

 INITIAL MATRIX

 4.00     1.00    
 3.00     1.00    

 R MATRIX

 -5.00     -1.40    
 0.00     0.20    

 Q MATRIX

 -0.80     -0.60    
 -0.60     0.80   

However, the expected QR decomposition would be:

 R MATRIX

 5.00     1.40    
 0.00     0.20    

 Q MATRIX

 0.80     -0.60    
 0.60     0.80  

I have found this problem with other Initial matrices as well.

Thanks in advance,

Paulo