Computing the reciprocal condition number with lapack (i.e. rcond(x))

Question

I wish to do exactly what rcond does in MATLAB/Octave using LAPACK from C. The MATLAB manual tells me dgecon is used, and that is uses a 1-based norm.

I wrote a simple test program for an extremely simple case; [1,1; 1,0] For this input matlab and octave gives me 0.25 using rcond and 1/cond(x,1), but in the case using LAPACK, this sample program prints 0.0. For other cases, such as identity, it prints the correct value.

Since MATLAB is supposely actually using this routine with success, what am I doing wrong? I'm trying to decipher what Octave does, with little success as its wrapped in

#include <stdio.h>

extern void dgecon_(const char *norm, const int *n, const double *a, 
     const int *lda, const double *anorm, double *rcond, double *work, 
     int *iwork, int *info, int len_norm);

int main()
{
    int i, info, n, lda;
    double anorm, rcond;

    double w[8] = { 0,0,0,0,0,0,0,0 };

    int iw[2] = { 0,0 };

    double x[4] = { 1, 1, 1, 0 };
    anorm = 2.0; /* maximum column sum, computed manually */
    n = 2;
    lda = 2;

    dgecon_("1", &n, x, &lda, &anorm, &rcond, w, iw, &info, 1);

    if (info != 0) fprintf(stderr, "failure with error %d\n", info);
    printf("%.5e\n", rcond);
    return 0;
}

Compiled with cc testdgecon.c -o testdgecon -llapack; ./testdgecon

Answer 1

I found the answer to me own question.

The matrix is must be LU-decomposed before it is sent to dgecon. This seems very logical since one often wants to solve the system after checking the condition, in which case there is no need to decompose the matrix twice. The same idea goes for the norm which is computed separately.

The following code is all the necessary parts the compute the reciprocal condition number with LAPACK.

#include "stdio.h"

extern int dgecon_(const char *norm, const int *n, double *a, const int *lda, const double *anorm, double *rcond, double *work, int *iwork, int *info, int len);
extern int dgetrf_(const int *m, const int *n, double *a, const int *lda, int *lpiv, int *info);
extern double dlange_(const char *norm, const int *m, const int *n, const double *a, const int *lda, double *work, const int norm_len);

int main()
{
    int i, info, n, lda;
    double anorm, rcond;

    int iw[2];
    double w[8];
    double x[4] = {7,3,-9,2 };
    n = 2;
    lda = 2;

    /* Computes the norm of x */
    anorm = dlange_("1", &n, &n, x, &lda, w, 1);

    /* Modifies x in place with a LU decomposition */
    dgetrf_(&n, &n, x, &lda, iw, &info);
    if (info != 0) fprintf(stderr, "failure with error %d\n", info);

    /* Computes the reciprocal norm */
    dgecon_("1", &n, x, &lda, &anorm, &rcond, w, iw, &info, 1);
    if (info != 0) fprintf(stderr, "failure with error %d\n", info);

    printf("%.5e\n", rcond);
    return 0;
}