NAG Library Manual, Mark 27.2
Interfaces:  FL   CL   CPP   AD
```/* nag_lapackeig_dgeqlf (f08cec) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.2, 2021.
*/

#include <nag.h>
#include <stdio.h>

int main(void) {
/* Scalars */
Integer i, j, m, n, nrhs, pda, pdb;
Integer exit_status = 0;
/* Arrays */
double *a = 0, *b = 0, *rnorm = 0, *tau = 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_dgeqlf (f08cec) Example Program Results\n\n");

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

/* Allocate memory */
if (!(a = NAG_ALLOC(m * n, double)) || !(b = NAG_ALLOC(m * nrhs, double)) ||
!(rnorm = NAG_ALLOC(nrhs, double)) || !(tau = NAG_ALLOC(n, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

#ifdef NAG_COLUMN_MAJOR
pda = m;
pdb = m;
#else
pda = n;
pdb = nrhs;
#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_dgeqlf (f08cec).
* Compute the QL factorization of A.
*/
nag_lapackeig_dgeqlf(order, m, n, a, pda, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dgeqlf (f08cec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_lapackeig_dormql (f08cgc).
* Compute C = (C1) = (Q^T)*B, storing the result in B.
*             (C2)
*/
nag_lapackeig_dormql(order, Nag_LeftSide, Nag_Trans, m, nrhs, n, a, pda, tau,
b, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dormql (f08cgc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_lapacklin_dtrtrs (f07tec).
* Compute least squares solutions by back-substitution in
* L*X = C2.
*/
nag_lapacklin_dtrtrs(order, Nag_Lower, Nag_NoTrans, Nag_NonUnitDiag, n, nrhs,
&A(m - n + 1, 1), pda, &B(m - n + 1, 1), pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_dtrtrs (f07tec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_file_print_matrix_real_gen (x04cac).
* Print least squares solution(s).
*/
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
nrhs, &B(m - n + 1, 1), 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;
}

/* nag_blast_dge_norm (f16rac).
* Compute and print estimates of the square roots of the residual
* sums of squares.
*/
for (j = 1; j <= nrhs; ++j) {
nag_blast_dge_norm(order, Nag_FrobeniusNorm, m - n, 1, &B(1, j), pdb,
&rnorm[j - 1], &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dge_norm (f16rac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
}

printf("\nSquare root(s) of the residual sum(s) of squares\n");
for (j = 0; j < nrhs; ++j)
printf("%11.2e%s", rnorm[j],
(j + 1) % 7 == 0 || j == nrhs - 1 ? "\n" : " ");

END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(rnorm);
NAG_FREE(tau);

return exit_status;
}

#undef A
#undef B
```