NAG Library Manual, Mark 30
```/* nag_lapackeig_dgeqrf (f08aec) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.0, 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 */
double *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_dgeqrf (f08aec) 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;
#else
pda = n;
pdb = nrhs;
#endif
tau_len = MIN(m, n);

/* Allocate memory */
if (!(a = NAG_ALLOC(m * n, double)) || !(b = NAG_ALLOC(m * nrhs, double)) ||
!(tau = NAG_ALLOC(tau_len, double))) {
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] ");

/* Compute the QR factorization of A */
/* nag_lapackeig_dgeqrf (f08aec).
* QR factorization of real general rectangular matrix
*/
nag_lapackeig_dgeqrf(order, m, n, a, pda, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dgeqrf (f08aec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* 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*X = 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, n, 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;
}
/* Print least squares solution(s) */
/* 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, b, pdb, "Least squares solution(s)", 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);
return exit_status;
}
```