```/* nag_matop_real_nmf (f01sac) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/
#include <nag.h>

#define A(I,J) a[(J - 1)*pda + I - 1]

int main(void)
{
/* Scalars */
Integer exit_status = 0;
Integer i, j, m, n, k, pda, pdw, pdh, seed, maxit;
double errtol, norm, norma;
/* Arrays */
double *a = 0, *w = 0, *h = 0;
/* Nag Types */
Nag_OrderType order = Nag_ColMajor;
NagError fail;

INIT_FAIL(fail);

/* Output preamble */
printf("nag_matop_real_nmf (f01sac) ");
printf("Example Program Results\n\n");
fflush(stdout);

/* Skip heading in data file */
scanf("%*[^\n] ");

/* Read in the matrix size and the required rank */
scanf("%" NAG_IFMT "", &m);
scanf("%" NAG_IFMT "", &n);
scanf("%" NAG_IFMT "", &k);
scanf("%*[^\n]");

pda = m;
if (!(a = NAG_ALLOC(pda * n, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
pdw = m;
if (!(w = NAG_ALLOC(pdw * k, double)))
{
printf("Allocation failure\n");
exit_status = -2;
goto END;
}
pdh = k;
if (!(h = NAG_ALLOC(pda * n, double)))
{
printf("Allocation failure\n");
exit_status = -3;
goto END;
}

/* Read in the matrix A from data file */
for (i = 1; i <= m; i++)
for (j = 1; j <= n; j++)
scanf("%lf", &A(i, j));
scanf("%*[^\n] ");

/* Choose the values of seed and errtol */
seed = 23;
errtol = 1.0e-6;

/* Use the default value of maxit */
maxit = -1;

/* Find a non-negative matrix factorization using
* nag_matop_real_nmf (f01sac)
* Non-negative matrix factorization of real non-negative matrix
*/
nag_matop_real_nmf(m, n, k, a, pda, w, pdw, h, pdh, seed, errtol,
maxit, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_matop_real_nmf (f01sac)\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Print matrix W using nag_file_print_matrix_real_gen (x04cac)
* Print real general matrix (easy-to-use)
*/
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
m, k, w, pdw, "W", NULL, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac)\n%s\n",
fail.message);
exit_status = 2;
goto END;
}

printf("\n");

/* Print matrix H using nag_file_print_matrix_real_gen (x04cac)
* Print real general matrix (easy-to-use)
*/
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
k, n, h, pdh, "H", NULL, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac)\n%s\n",
fail.message);
exit_status = 3;
goto END;
}

/* Compute ||A||_F using
* nag_blast_dge_norm (f16rac)
*/
nag_blast_dge_norm(order, Nag_FrobeniusNorm, m, n, a, pda, &norma, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dge_norm (f16yac)\n%s\n", fail.message);
exit_status = 4;
goto END;
}

/* Compute residual A-WH using nag_blast_dgemm (f16yac)
* Matrix-matrix product, two rectangular matrices
*/
nag_blast_dgemm(order, Nag_NoTrans, Nag_NoTrans, m, n, k, -1.0, w, pdw, h, pdh,
1.0, a, pda, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dgemm (f16yac)\n%s\n", fail.message);
exit_status = 5;
goto END;
}

/* Compute ||A-WH||_F using
* nag_blast_dge_norm (f16rac)
*/
nag_blast_dge_norm(order, Nag_FrobeniusNorm, m, n, a, pda, &norm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dge_norm (f16yac)\n%s\n", fail.message);
exit_status = 6;
goto END;
}

/* Print relative residual norm */
printf("\nThe relative residual norm, ||A-WH||/||A||, is: %9.2e\n",
norm/norma);

END:
NAG_FREE(a);
NAG_FREE(w);
NAG_FREE(h);
return exit_status;
}
```