NAG Library Manual, Mark 30.1
```/* nag_lapackeig_zgelqf (f08avc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.1, 2024.
*/

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

int main(void) {
/* Scalars */
Integer i, j, m, n, nrhs, pda, pdb, tau_len;
Integer exit_status = 0;
NagError fail;
Nag_OrderType order;
/* Arrays */
Complex *a = 0, *b = 0, *tau = 0;

#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_zgelqf (f08avc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &m, &n, &nrhs);

#ifdef NAG_COLUMN_MAJOR
pda = m;
pdb = n;
#else
pda = n;
pdb = nrhs;
#endif

tau_len = MIN(m, n);

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

/* 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] ");

/* Compute the LQ factorization of A */
/* nag_lapackeig_zgelqf (f08avc).
* LQ factorization of complex general rectangular matrix
*/
nag_lapackeig_zgelqf(order, m, n, a, pda, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgelqf (f08avc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Solve L*Y = B, storing the result in B */
/* nag_lapacklin_ztrtrs (f07tsc).
* Solution of complex triangular system of linear
* equations, multiple right-hand sides
*/
nag_lapacklin_ztrtrs(order, Nag_Lower, Nag_NoTrans, Nag_NonUnitDiag, m, nrhs,
a, pda, b, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_ztrtrs (f07tsc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Set rows (M+1) to N of B to zero */
if (m < n) {
for (i = m + 1; i <= n; ++i) {
for (j = 1; j <= nrhs; ++j) {
B(i, j).re = 0.0;
B(i, j).im = 0.0;
}
}
}

/* Compute minimum-norm solution X = (Q^H)*B in B */
/* nag_lapackeig_zunmlq (f08axc).
* Apply unitary transformation determined by nag_lapackeig_zgelqf (f08avc)
*/
nag_lapackeig_zunmlq(order, Nag_LeftSide, Nag_ConjTrans, n, nrhs, m, a, pda,
tau, b, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zunmlq (f08axc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print minimum-norm solution(s) */
/* nag_file_print_matrix_complex_gen_comp (x04dbc).
* Print complex general matrix (comprehensive)
*/
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b, pdb,
Nag_BracketForm, "%7.4f", "Minimum-norm solution(s)", Nag_IntegerLabels,
0, Nag_IntegerLabels, 0, 80, 0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(tau);
return exit_status;
}
```