```/* nag_dgelqf (f08ahc) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 7, 2001.
*/

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf07.h>
#include <nagf08.h>
#include <nagx04.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_dgelqf (f08ahc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%ld%ld%ld%*[^\n] ", &m, &n, &nrhs);

#ifdef NAG_COLUMN_MAJOR
pda = m;
pdb = n;
#else
pda = n;
pdb = nrhs;
#endif

tau_len = MIN(m, n);

/* Allocate memory */
if (!(a = NAG_ALLOC(m * n, double)) ||
!(b = NAG_ALLOC(n * 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 LQ factorization of A */
/* nag_dgelqf (f08ahc).
* LQ factorization of real general rectangular matrix
*/
nag_dgelqf(order, m, n, a, pda, tau, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_dgelqf (f08ahc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Solve L*Y = B, storing the result in B */
/* nag_dtrtrs (f07tec).
* Solution of real triangular system of linear equations,
* multiple right-hand sides
*/
nag_dtrtrs(order, Nag_Lower, Nag_NoTrans, Nag_NonUnitDiag, m,
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;
}
/* Set rows (M+1) to N of B to zero */
if (m < n)
{
for (i = m + 1; i <= n; ++i)
{
for (j = 1; j <= nrhs; ++j)
B(i, j) = 0.0;
}
}

/* Compute minimum-norm solution X = (Q**T)*B in B */
/* nag_dormlq (f08akc).
* Apply orthogonal transformation determined by nag_dgelqf (f08ahc)
*/
nag_dormlq(order, Nag_LeftSide, Nag_Trans, n, nrhs, m, a, pda,
tau, b, pdb, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_dormlq (f08akc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print minimum-norm solution(s) */
/* nag_gen_real_mat_print (x04cac).
* Print real general matrix (easy-to-use)
*/
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, b,
pdb, "Minimum-norm 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 = 1;
goto END;
}
END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(tau);
return exit_status;
}
```