```/* nag_dtpqrt (f08bbc) Example Program.
*
* NAGPRODCODE Version.
*
* Copyright 2016 Numerical Algorithms Group.
*
* Mark 26, 2016.
*/

#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, *c = 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 C(I,J) c[(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]
#define C(I,J) c[(I-1)*pdb + J-1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_dtpqrt (f08bbc) 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)) ||
!(c = 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]");

for (i = 1; i <= m; ++i)
for (j = 1; j <= nrhs; ++j)
C(i, j) = B(i, j);

/* nag_dgeqrt (f08abc).
* Compute the QR factorization of first n rows of A by recursive algorithm.
*/
nag_dgeqrt(order, n, 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 C
*             (C2)
* by applying Q^T from left.
*/
nag_dgemqrt(order, Nag_LeftSide, Nag_Trans, n, nrhs, n, nb, a, pda, t, pdt,
c, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgemqrt (f08acc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

for (i = 1; i <= n; ++i)
for (j = 1; j <= nrhs; ++j)
B(i, j) = C(i, j);

/* nag_dtrtrs (f07tec).
* Compute least squares solutions for first n rows
* by back-substitution in R*X = C1.
*/
nag_dtrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n, nrhs, a, pda,
c, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dtrtrs (f07tec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_gen_real_mat_print (x04cac).
* Print least squares solutions using first n rows.
*/
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs,
c, pdb, "Solution(s) for n rows", 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_dtpqrt (f08bbc).
* Now add the remaining rows and perform QR update.
*/
nag_dtpqrt(order, m - n, n, 0, nb, a, pda, &A(n + 1, 1), pda, t, pdt,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dtpqrt (f08bbc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_dtpmqrt (f08bcc).
* Apply orthogonal transformations to C.
*/
nag_dtpmqrt(order, Nag_LeftSide, Nag_Trans, m - n, nrhs, n, 0, nb,
&A(n + 1, 1), pda, t, pdt, b, pdb, &B(5, 1), pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dtpmqrt (f08bcc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_dtrtrs (f07tec).
* Compute least squares solutions for first n rows
* by back-substitution 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 = 1;
goto END;
}

/* nag_gen_real_mat_print (x04cac).
* Print least squares solutions.
*/
printf("\n");
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs,
b, pdb, "Least squares solution(s) for all rows", 0,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message);
exit_status = 1;
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 = 1;
goto END;
}
printf("  %11.2e ", rnorm);
}
printf("\n");

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

return exit_status;
}
```