```/* nag_lapackeig_dgeqrt (f08abc) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/

#include <nag.h>

int main(void)
{
/* Scalars */
double rnorm;
Integer exit_status = 0;
Integer pda, pdb, pdt;
Integer i, j, m, n, nb, nrhs;
/* Arrays */
double *a = 0, *b = 0, *t = 0;
/* Nag Types */
Nag_OrderType order;
NagError fail;

#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_dgeqrt (f08abc) Example Program Results\n\n");
fflush(stdout);

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &m, &n, &nrhs);
nb = MIN(m, n);
if (!(a = NAG_ALLOC(m * n, double)) ||
!(b = NAG_ALLOC(m * nrhs, double)) ||
!(t = NAG_ALLOC(nb * MIN(m, n), double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
#ifdef NAG_COLUMN_MAJOR
pda = m;
pdb = m;
pdt = nb;
#else
pda = n;
pdb = nrhs;
pdt = MIN(m, n);
#endif

/* 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]");

/* nag_lapackeig_dgeqrt (f08abc).
* Compute the QR factorization of A by recursive algorithm.
*/
nag_lapackeig_dgeqrt(order, m, n, nb, a, pda, t, pdt, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dgeqrt (f08abc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_lapackeig_dgemqrt (f08acc).
* Compute C = (C1) = (Q^T)*B, storing the result in B
*             (C2)
* by applying Q^T from left.
*/
nag_lapackeig_dgemqrt(order, Nag_LeftSide, Nag_Trans, m, nrhs, n, nb, a, pda, t, pdt,
b, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dgemqrt (f08acc).\n%s\n", fail.message);
exit_status = 2;
goto END;
}

/* nag_lapacklin_dtrtrs (f07tec).
* Compute least squares solutions by back-substitution in R*X = C1.
*/
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 = 3;
goto END;
}

/* nag_file_print_matrix_real_gen (x04cac).
* Print least squares solutions.
*/
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 = 4;
goto END;
}

printf("\n Square root(s) of the residual sum(s) of squares\n");
for (j = 1; j <= nrhs; j++) {
/* nag_blast_dge_norm (f16rac).
* Compute and print estimate of the square root of the residual
* sum of squares.
*/
nag_blast_dge_norm(order, Nag_FrobeniusNorm, m - n, 1, &B(n + 1, j), pdb,
&rnorm, &fail);
if (fail.code != NE_NOERROR) {
printf("\nError from nag_blast_dge_norm (f16rac).\n%s\n", fail.message);
exit_status = 5;
goto END;
}
printf("  %11.2e ", rnorm);
}
printf("\n");

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

return exit_status;
}
```