NAG Library Manual, Mark 27.3
```/* nag_lapacklin_dgbrfs (f07bhc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.3, 2021.
*/

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

int main(void) {
/* Scalars */
Integer i, ipiv_len, j, kl, ku, n, nrhs, pdab, pdafb, pdb, pdx;
Integer exit_status = 0;
NagError fail;
Nag_OrderType order;

/* Arrays */
double *ab = 0, *afb = 0, *b = 0, *berr = 0, *ferr = 0, *x = 0;
Integer *ipiv = 0;

#ifdef NAG_COLUMN_MAJOR
#define AB(I, J) ab[(J - 1) * pdab + ku + I - J]
#define AFB(I, J) afb[(J - 1) * pdafb + kl + ku + I - J]
#define B(I, J) b[(J - 1) * pdb + I - 1]
#define X(I, J) x[(J - 1) * pdx + I - 1]
order = Nag_ColMajor;
#else
#define AB(I, J) ab[(I - 1) * pdab + kl + J - I]
#define AFB(I, J) afb[(I - 1) * pdafb + kl + J - I]
#define B(I, J) b[(I - 1) * pdb + J - 1]
#define X(I, J) x[(I - 1) * pdx + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapacklin_dgbrfs (f07bhc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &n,
&nrhs, &kl, &ku);
ipiv_len = n;
pdab = kl + ku + 1;
pdafb = 2 * kl + ku + 1;
#ifdef NAG_COLUMN_MAJOR
pdb = n;
pdx = n;
#else
pdb = nrhs;
pdx = nrhs;
#endif

/* Allocate memory */
if (!(ab = NAG_ALLOC((kl + ku + 1) * n, double)) ||
!(afb = NAG_ALLOC((2 * kl + ku + 1) * n, double)) ||
!(b = NAG_ALLOC(nrhs * n, double)) ||
!(x = NAG_ALLOC(nrhs * n, double)) || !(berr = NAG_ALLOC(nrhs, double)) ||
!(ferr = NAG_ALLOC(nrhs, double)) ||
!(ipiv = NAG_ALLOC(ipiv_len, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Set A to zero to avoid referencing unitialized elements */
for (i = 0; i < n * (kl + ku + 1); ++i)
ab[i] = 0.0;
/* Read A from data file */
for (i = 1; i <= n; ++i) {
for (j = MAX(i - kl, 1); j <= MIN(i + ku, n); ++j)
scanf("%lf", &AB(i, j));
}
scanf("%*[^\n] ");
/* Read B from data file */
for (i = 1; i <= n; ++i) {
for (j = 1; j <= nrhs; ++j)
scanf("%lf", &B(i, j));
}
scanf("%*[^\n] ");
/* Copy A to AFB and B to X */
for (i = 1; i <= n; ++i) {
for (j = MAX(i - kl, 1); j <= MIN(i + ku, n); ++j)
AFB(i, j) = AB(i, j);
}
for (i = 1; i <= n; ++i) {
for (j = 1; j <= nrhs; ++j)
X(i, j) = B(i, j);
}
/* Factorize A in the array AFB */
/* nag_lapacklin_dgbtrf (f07bdc).
* LU factorization of real m by n band matrix
*/
nag_lapacklin_dgbtrf(order, n, n, kl, ku, afb, pdafb, ipiv, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_dgbtrf (f07bdc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Compute solution in the array X */
/* nag_lapacklin_dgbtrs (f07bec).
* Solution of real band system of linear equations,
* multiple right-hand sides, matrix already factorized by
* nag_lapacklin_dgbtrf (f07bdc)
*/
nag_lapacklin_dgbtrs(order, Nag_NoTrans, n, kl, ku, nrhs, afb, pdafb, ipiv, x,
pdx, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_dgbtrs (f07bec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Improve solution, and compute backward errors and  */
/* estimated bounds on the forward errors */
/* nag_lapacklin_dgbrfs (f07bhc).
* Refined solution with error bounds of real band system of
* linear equations, multiple right-hand sides
*/
nag_lapacklin_dgbrfs(order, Nag_NoTrans, n, kl, ku, nrhs, ab, pdab, afb,
pdafb, ipiv, b, pdb, x, pdx, ferr, berr, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_dgbrfs (f07bhc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Print solution */
/* nag_file_print_matrix_real_gen (x04cac).
* Print real general matrix (easy-to-use)
*/
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
nrhs, x, pdx, "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;
}
/* Print forward and backward errors */
printf("\nBackward errors (machine-dependent)\n");

for (j = 1; j <= nrhs; ++j)
printf("%11.1e%s", berr[j - 1], j % 7 == 0 ? "\n" : " ");

printf("\nEstimated forward error bounds (machine-dependent)\n");

for (j = 1; j <= nrhs; ++j)
printf("%11.1e%s", ferr[j - 1], j % 7 == 0 ? "\n" : " ");
printf("\n");
END:
NAG_FREE(ab);
NAG_FREE(afb);
NAG_FREE(b);
NAG_FREE(x);
NAG_FREE(berr);
NAG_FREE(ferr);
NAG_FREE(ipiv);
return exit_status;
}
```