NAG Library Manual, Mark 28.7
```/* nag_lapackeig_dgeqpf (f08bec) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.7, 2022.
*/

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

int main(void) {
/* Scalars */
double tol;
Integer i, j, jpvt_len, k, m, n, nrhs;
Integer pda, pdb, pdx, tau_len;
Integer exit_status = 0;
NagError fail;
Nag_OrderType order;
/* Arrays */
double *a = 0, *b = 0, *tau = 0, *x = 0;
Integer *jpvt = 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]
#define X(I, J) x[(J - 1) * pdx + 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]
#define X(I, J) x[(I - 1) * pdx + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_dgeqpf (f08bec) 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 = m;
pdx = m;
#else
pda = n;
pdb = nrhs;
pdx = nrhs;
#endif
tau_len = MIN(m, n);
jpvt_len = n;

/* Allocate memory */
if (!(a = NAG_ALLOC(m * n, double)) || !(b = NAG_ALLOC(m * nrhs, double)) ||
!(tau = NAG_ALLOC(tau_len, double)) ||
!(x = NAG_ALLOC(m * nrhs, double)) ||
!(jpvt = NAG_ALLOC(jpvt_len, Integer))) {
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", &A(i, j));
}
scanf("%*[^\n] ");
for (i = 1; i <= m; ++i) {
for (j = 1; j <= nrhs; ++j)
scanf("%lf", &B(i, j));
}
scanf("%*[^\n] ");

/* Initialize JPVT to be zero so that all columns are free */
* Broadcast scalar into integer vector
*/
/* Compute the QR factorization of A */
/* nag_lapackeig_dgeqpf (f08bec).
* QR factorization of real general rectangular matrix with
* column pivoting
*/
nag_lapackeig_dgeqpf(order, m, n, a, pda, jpvt, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dgeqpf (f08bec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

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

/* Determine which columns of R to use */
for (k = 1; k <= n; ++k) {
if (ABS(A(k, k)) <= tol * ABS(A(1, 1)))
break;
}
--k;

/* Compute C = (Q^T)*B, storing the result in B */

/* nag_lapackeig_dormqr (f08agc).
* Apply orthogonal transformation determined by nag_lapackeig_dgeqrf
* (f08aec) or nag_lapackeig_dgeqpf (f08bec)
*/
nag_lapackeig_dormqr(order, Nag_LeftSide, Nag_Trans, m, nrhs, n, a, pda, tau,
b, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dormqr (f08agc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Compute least squares solution by back-substitution in R*B = C */

/* nag_lapacklin_dtrtrs (f07tec).
* Solution of real triangular system of linear equations,
* multiple right-hand sides
*/
nag_lapacklin_dtrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, k, nrhs,
a, pda, b, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_dtrtrs (f07tec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
for (i = k + 1; i <= n; ++i) {
for (j = 1; j <= nrhs; ++j)
B(i, j) = 0.0;
}

/* Unscramble the least squares solution stored in B */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= nrhs; ++j)
X(jpvt[i - 1], j) = B(i, j);
}

/* Print least squares solution */
/* nag_file_print_matrix_real_gen (x04cac).
* Print real general matrix (easy-to-use)
*/
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
nrhs, x, pdx, "Least squares solution", 0,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(tau);
NAG_FREE(x);
NAG_FREE(jpvt);
return exit_status;
}
```