NAG Library Manual, Mark 30.1
/* nag_lapackeig_zgelss (f08knc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.1, 2024.
*/

#include <nag.h>
#include <stdio.h>

int main(void) {

/* Scalars */
double rcond, rnorm;
Integer exit_status = 0, i, j, m, n, nrhs, rank, pda, pdb;

/* Arrays */
Complex *a = 0, *b = 0;
double *s = 0;

/* Nag Types */
NagError fail;
Nag_OrderType order;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define B(I, J) b[(J - 1) * pdb + I - 1]
order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define B(I, J) b[(I - 1) * pdb + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_zgelss (f08knc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &m, &n, &nrhs);
if (m < 0 || n < 0 || nrhs < 0) {
printf("Invalid m, n or nrhs\n");
exit_status = 1;
goto END;
}

/* Allocate memory */
if (!(a = NAG_ALLOC(m * n, Complex)) ||
!(b = NAG_ALLOC(MAX(m, n) * nrhs, Complex)) ||
!(s = NAG_ALLOC(MIN(m, n), double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

#ifdef NAG_COLUMN_MAJOR
pda = m;
pdb = MAX(m, n);
#else
pda = n;
pdb = nrhs;
#endif

/* Read A and B from data file */
for (i = 1; i <= m; ++i)
for (j = 1; j <= n; ++j)
scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im);
scanf("%*[^\n]");
for (i = 1; i <= m; ++i)
for (j = 1; j <= nrhs; ++j)
scanf(" ( %lf , %lf )", &B(i, j).re, &B(i, j).im);
scanf("%*[^\n]");

/* Choose rcond to reflect the relative accuracy of the input data */
rcond = 0.01;

/* Solve the least squares problem min( norm2(b - Ax) ) for the x
* of minimum norm.
* nag_lapackeig_zgelss (f08knc).
*/
nag_lapackeig_zgelss(order, m, n, nrhs, a, pda, b, pdb, s, rcond, &rank,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgelss (f08knc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print solution */
printf("Least squares solution\n");
for (i = 1; i <= n; ++i) {
for (j = 1; j <= nrhs; ++j)
printf("(%7.4f, %7.4f)%s", B(i, j).re, B(i, j).im,
j % 4 == 0 ? "\n" : " ");
printf("\n");
}

/* Print the effective rank of A */
printf("\nTolerance used to estimate the rank of A\n%11.2e\n", rcond);

printf("Estimated rank of A\n%6" NAG_IFMT "\n", rank);

/* Print singular values of A */
printf("\nSingular values of A\n");
for (i = 0; i < n; ++i)
printf(" %10.4f%s", s[i], i % 7 == 6 ? "\n" : "");
printf("\n");

/* Compute and print estimate of the square root of the residual sum of
* squares using nag_blast_zge_norm (f16uac) with Frobenius norm.*/
if (rank == n) {
nag_blast_zge_norm(order, Nag_FrobeniusNorm, m - n, 1, &B(n + 1, 1), pdb,
&rnorm, &fail);
printf("\nSquare root of the residual sum of squares\n%11.2e\n", rnorm);
}

END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(s);

return exit_status;
}

#undef A
#undef B