NAG Library Manual, Mark 27.3
/* nag_linsys_real_band_solve (f04bbc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.3, 2021.
*/

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

int main(void) {

/* Scalars */
double errbnd, rcond;
Integer exit_status, i, j, kl, ku, n, nrhs, pdab, pdb;

/* Arrays */
double *ab = 0, *b = 0;
Integer *ipiv = 0;

/* Nag Types */
NagError fail;
Nag_OrderType order;

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

exit_status = 0;
INIT_FAIL(fail);

printf("nag_linsys_real_band_solve (f04bbc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &n, &kl,
&ku, &nrhs);
if (n >= 0 && kl >= 0 && ku >= 0 && nrhs >= 0) {
/* Allocate memory */
if (!(ab = NAG_ALLOC((2 * kl + ku + 1) * n, double)) ||
!(b = NAG_ALLOC(n * nrhs, double)) || !(ipiv = NAG_ALLOC(n, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
pdab = 2 * kl + ku + 1;
#ifdef NAG_COLUMN_MAJOR
pdb = n;
#else
pdb = nrhs;
#endif
} else {
printf("%s\n", "One or more of nmax, kl, ku or nrhs is"
" too small");
exit_status = 1;
return exit_status;
}
/* Read A and B 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] ");

for (i = 1; i <= n; ++i) {
for (j = 1; j <= nrhs; ++j) {
scanf("%lf", &B(i, j));
}
}
scanf("%*[^\n] ");

/* Solve the equations AX = B for X */
/* nag_linsys_real_band_solve (f04bbc).
* Computes the solution and error-bound to a real banded
* system of linear equations
*/
nag_linsys_real_band_solve(order, n, kl, ku, nrhs, ab, pdab, ipiv, b, pdb,
&rcond, &errbnd, &fail);
if (fail.code == NE_NOERROR) {
/* Print solution, estimate of condition number and approximate */
/* error bound */

/* 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, b, pdb, "Solution", 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("\n%s\n%6s%10.1e\n\n\n", "Estimate of condition number", "",
1.0 / rcond);

printf("%s\n%6s%10.1e\n\n",
"Estimate of error bound for computed solutions", "", errbnd);
} else if (fail.code == NE_RCOND) {
/* Matrix A is numerically singular.  Print estimate of */
/* reciprocal of condition number and solution */
printf("\n");
printf("%s\n%6s%10.1e\n\n\n", "Estimate of reciprocal of condition number",
"", rcond);
/* nag_file_print_matrix_real_gen (x04cac), see above. */
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
nrhs, b, pdb, "Solution", 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;
}
} else if (fail.code == NE_SINGULAR) {
/* The upper triangular matrix U is exactly singular.  Print */
/* details of factorization */
printf("\n");
/* nag_file_print_matrix_real_band (x04cec).
* Print real packed banded matrix (easy-to-use)
*/
fflush(stdout);
nag_file_print_matrix_real_band(order, n, n, kl, kl + ku, ab, pdab,
"Details of factorization", 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_band (x04cec).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Print pivot indices */
printf("\n%s\n", "Pivot indices");
for (i = 1; i <= n; ++i) {
printf("%11" NAG_IFMT "%s", ipiv[i - 1],
i % 7 == 0 || i == n ? "\n" : " ");
}
printf("\n");
} else {
printf("Error from nag_linsys_real_band_solve (f04bbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

END:
NAG_FREE(ab);
NAG_FREE(b);
NAG_FREE(ipiv);

return exit_status;
}