```/* nag_lapackeig_dgbbrd (f08lec) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/

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

int main(void)
{
/* Scalars */
double alpha, beta, norm;
Integer i, j, kl, ku, m, n, ncc, pdab, pdaw, pdc, pdf, pdq;
Integer pdpt, d_len, e_len;
Integer exit_status = 0;
NagError fail;
Nag_OrderType order;
/* Arrays */
double *ab = 0, *aw = 0, *c = 0, *d = 0, *e = 0, *f = 0, *pt = 0, *q = 0;

#ifdef NAG_COLUMN_MAJOR
#define AB(I, J) ab[(J - 1) * pdab + ku + I - J]
#define AW(I, J) aw[(J - 1) * pdaw + I - 1]
#define F(I, J) f[(J - 1) * pdf + I - 1]
#define Q(I, J) q[(J - 1) * pdq + I - 1]
order = Nag_ColMajor;
#else
#define AB(I, J) ab[(I - 1) * pdab + kl + J - I]
#define AW(I, J) aw[(I - 1) * pdaw + J - 1]
#define F(I, J) f[(I - 1) * pdf + J - 1]
#define Q(I, J) q[(I - 1) * pdq + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_dgbbrd (f08lec) Example Program Results\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT
"%*[^\n] ", &m, &n, &kl, &ku, &ncc);
#ifdef NAG_COLUMN_MAJOR
pdab = kl + ku + 1;
pdaw = m;
pdf = m;
pdq = m;
pdpt = n;
pdc = m;
#else
pdab = kl + ku + 1;
pdaw = n;
pdf = n;
pdq = m;
pdpt = n;
pdc = MAX(1, ncc);
#endif
d_len = MIN(m, n);
e_len = MIN(m, n) - 1;

/* Allocate memory */
if (!(ab = NAG_ALLOC((kl + ku + 1) * m, double)) ||
!(aw = NAG_ALLOC(m * n, double)) ||
!(f = NAG_ALLOC(m * n, double)) ||
!(c = NAG_ALLOC(m * MAX(1, ncc), double)) ||
!(d = NAG_ALLOC(d_len, double)) ||
!(e = NAG_ALLOC(e_len, double)) ||
!(pt = NAG_ALLOC(n * n, double)) || !(q = NAG_ALLOC(m * m, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read A from data file */
for (i = 1; i <= m; ++i) {
for (j = MAX(1, i - kl); j <= MIN(n, i + ku); ++j)
scanf("%lf", &AB(i, j));
}
scanf("%*[^\n] ");

/* Copy AB into AW */
for (i = 1; i <= m; ++i) {
for (j = 1; j <= n; ++j) {
if (j >= MAX(1, i - kl) && j <= MIN(n, i + ku))
AW(i, j) = AB(i, j);
else
AW(i, j) = 0;
}
}

/* nag_file_print_matrix_real_gen (x04cac): Print Matrix A. */
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n,
aw, pdaw, "Matrix A", 0, &fail);
printf("\n");
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;
}

/* Reduce A to bidiagonal form */
/* nag_lapackeig_dgbbrd (f08lec).
* Reduction of real rectangular band matrix to upper
* bidiagonal form
*/
nag_lapackeig_dgbbrd(order, Nag_FormBoth, m, n, ncc, kl, ku, ab,
pdab, d, e, q, pdq, pt, pdpt, c, pdc, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dgbbrd (f08lec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* F = Q*B */
for (i = 1; i <= m; i++) {
F(i, 1) = Q(i, 1) * d;
for (j = 2; j <= n; j++) {
F(i, j) = (Q(i, j) * d[j - 1]) + (Q(i, j - 1) * e[j - 2]);
}
}

/* nag_blast_dgemm (f16yac): Compute A - Q*B*P^T from the factorization of A */
/* and store in matrix AW */
alpha = -1.0;
beta = 1.0;
nag_blast_dgemm(order, Nag_NoTrans, Nag_NoTrans, m, n, n, alpha, f, pdf,
pt, pdpt, beta, aw, pdaw, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dgemm (f16yac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_blast_dge_norm (f16rac): Find norm of matrix AW and print warning if */
/* it is too large */
nag_blast_dge_norm(order, Nag_OneNorm, m, n, aw, pdaw, &norm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dge_norm (f16rac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
if (norm > pow(x02ajc(), 0.8)) {
printf("%s\n%s\n", "Norm of A-(Q*B*P^T) is much greater than 0.",
"Schur factorization has failed.");
}

END:
NAG_FREE(ab);
NAG_FREE(aw);
NAG_FREE(c);
NAG_FREE(d);
NAG_FREE(e);
NAG_FREE(f);
NAG_FREE(pt);
NAG_FREE(q);

return exit_status;
}
```