```/* nag_dgeqrt (f08abc) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 24, 2013.
*/

#include <nag.h>
#include <nag_stdlib.h>
#include <nagf07.h>
#include <nagf08.h>
#include <nagf16.h>
#include <nagx04.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]
#define T(I,J) t[(J-1)*pdt + 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 T(I,J) t[(I-1)*pdt + J-1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_dgeqrt (f08abc) Example Program Results\n\n");
fflush(stdout);

/* Skip heading in data file*/
scanf("%*[^\n]");
scanf("%ld%ld%ld%*[^\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_dgeqrt (f08abc).
* Compute the QR factorization of A by recursive algorithm.
*/
nag_dgeqrt(order, m, n, nb, a, pda, t, pdt, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgeqrt (f08abc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_dgemqrt (f08acc).
* Compute C = (C1) = (Q^T)*B, storing the result in B
*             (C2)
* by applying Q^T from left.
*/
nag_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_dgemqrt (f08acc).\n%s\n", fail.message);
exit_status = 2;
goto END;
}

/* nag_dtrtrs (f07tec).
* Compute least-squares solutions by backsubstitution in R*X = C1.
*/
nag_dtrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n, nrhs, a, pda,
b, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dtrtrs (f07tec).\n%s\n", fail.message);
exit_status = 3;
goto END;
}

/* nag_gen_real_mat_print (x04cac).
* Print least-squares solutions.
*/
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b,
pdb, "Least-squares solution(s)", 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_real_mat_print (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_dge_norm (f16rac).
* Compute and print estimate of the square root of the residual
* sum of squares.
*/
nag_dge_norm(order, Nag_FrobeniusNorm, m - n, 1, &B(n + 1,j), pdb, &rnorm,
&fail);
if (fail.code != NE_NOERROR) {
printf("\nError from nag_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;
}
```