NAG Library Manual, Mark 28.5
```/* nag_lapacklin_dpbrfs (f07hhc) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.5, 2022.
*/

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

int main(void) {
/* Scalars */
Integer i, j, k, kd, n, nrhs, pdab, pdafb, pdb, pdx;
Integer ferr_len, berr_len;
Integer exit_status = 0;
Nag_UploType uplo;
NagError fail;
Nag_OrderType order;
/* Arrays */
char nag_enum_arg;
double *ab = 0, *afb = 0, *b = 0, *berr = 0, *ferr = 0, *x = 0;

#ifdef NAG_COLUMN_MAJOR
#define AB_UPPER(I, J) ab[(J - 1) * pdab + k + I - J - 1]
#define AB_LOWER(I, J) ab[(J - 1) * pdab + I - J]
#define AFB_UPPER(I, J) afb[(J - 1) * pdafb + k + I - J - 1]
#define AFB_LOWER(I, J) afb[(J - 1) * pdafb + 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_UPPER(I, J) ab[(I - 1) * pdab + J - I]
#define AB_LOWER(I, J) ab[(I - 1) * pdab + k + J - I - 1]
#define AFB_UPPER(I, J) afb[(I - 1) * pdafb + J - I]
#define AFB_LOWER(I, J) afb[(I - 1) * pdafb + k + J - I - 1]
#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_dpbrfs (f07hhc) Example Program Results\n\n");

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

ferr_len = nrhs;
berr_len = nrhs;

/* Allocate memory */
if (!(berr = NAG_ALLOC(berr_len, double)) ||
!(ferr = NAG_ALLOC(ferr_len, double)) ||
!(ab = NAG_ALLOC((kd + 1) * n, double)) ||
!(afb = NAG_ALLOC((kd + 1) * n, double)) ||
!(b = NAG_ALLOC(n * nrhs, double)) ||
!(x = NAG_ALLOC(n * nrhs, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read A from data file */
scanf(" %39s%*[^\n] ", nag_enum_arg);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
uplo = (Nag_UploType)nag_enum_name_to_value(nag_enum_arg);

k = kd + 1;
if (uplo == Nag_Upper) {
for (i = 1; i <= n; ++i) {
for (j = i; j <= MIN(i + kd, n); ++j)
scanf("%lf", &AB_UPPER(i, j));
}
scanf("%*[^\n] ");
} else {
for (i = 1; i <= n; ++i) {
for (j = MAX(1, i - kd); j <= i; ++j)
scanf("%lf", &AB_LOWER(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 AF and B to X */
if (uplo == Nag_Upper) {
for (i = 1; i <= n; ++i) {
for (j = i; j <= MIN(i + kd, n); ++j)
AFB_UPPER(i, j) = AB_UPPER(i, j);
}
} else {
for (i = 1; i <= n; ++i) {
for (j = MAX(1, i - kd); j <= i; ++j)
AFB_LOWER(i, j) = AB_LOWER(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 AFP */
/* nag_lapacklin_dpbtrf (f07hdc).
* Cholesky factorization of real symmetric
* positive-definite band matrix
*/
nag_lapacklin_dpbtrf(order, uplo, n, kd, afb, pdafb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_dpbtrf (f07hdc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Compute solution in the array X */
/* nag_lapacklin_dpbtrs (f07hec).
* Solution of real symmetric positive-definite band system
* of linear equations, multiple right-hand sides, matrix
* already factorized by nag_lapacklin_dpbtrf (f07hdc)
*/
nag_lapacklin_dpbtrs(order, uplo, n, kd, nrhs, afb, pdafb, x, pdx, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_dpbtrs (f07hec).\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_dpbrfs (f07hhc).
* Refined solution with error bounds of real symmetric
* positive-definite band system of linear equations,
* multiple right-hand sides
*/
nag_lapacklin_dpbrfs(order, uplo, n, kd, nrhs, ab, pdab, afb, pdafb, b, pdb,
x, pdx, ferr, berr, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_dpbrfs (f07hhc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Print details of 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;
}
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(berr);
NAG_FREE(ferr);
NAG_FREE(ab);
NAG_FREE(afb);
NAG_FREE(b);
NAG_FREE(x);
return exit_status;
}
```