```/* nag_det_real_band_sym (f03bhc) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/
#include <math.h>
#include <nag.h>

int main(void)
{
/* Scalars */
Integer exit_status = 0;
Integer i, id, j, kd, kl, ku, k, n, pdab;
double d;
/* Arrays */
char nag_enum_arg[40];
double *ab = 0;
/* NAG types */
NagError fail;
Nag_UploType uplo;
Nag_OrderType order;

printf("nag_det_real_band_sym (f03bhc) Example Program Results\n\n");

/* Skip heading in data file  */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &n, &kd);
k = kd + 1;
pdab = k;

if (!(ab = NAG_ALLOC(k * n, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
scanf("%39s %*[^\n] ", nag_enum_arg);
uplo = (Nag_UploType) nag_enum_name_to_value(nag_enum_arg);

/* Define matrix element A_ij in terms of elements of array ab[] */
#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]
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]
order = Nag_RowMajor;
#endif
if (uplo == Nag_Upper) {
/* Read in upper triangular banded matrix  */
ku = kd;
kl = 0;
for (i = 1; i <= n; i++)
for (j = i; j <= MIN(i + kd, n); j++)
scanf("%lf", &AB_UPPER(i, j));
scanf("%*[^\n] ");
}
else if (uplo == Nag_Lower) {
/* Read in lower triangular banded matrix  */
ku = 0;
kl = kd;
for (i = 1; i <= n; i++)
for (j = MAX(1, i - kd); j <= i; j++)
scanf("%lf", &AB_LOWER(i, j));
scanf("%*[^\n] ");
}
else {
printf("Illegal value read for uplo\n");
exit_status = -4;
goto END;
}

INIT_FAIL(fail);
/* Factorize A using nag_lapacklin_dpbtrf (f07hdc)
* Cholesky factorization of real symmetric positive definite band matrix
*/
nag_lapacklin_dpbtrf(order, uplo, n, kd, ab, pdab, &fail);
if (fail.code != NE_NOERROR) {
printf("%s\n", fail.message);
exit_status = 1;
goto END;
}

/* 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, ku, ab, pdab,
"Array ab after factorization", NULL, &fail);
if (fail.code != NE_NOERROR) {
printf("%s\n", fail.message);
exit_status = 2;
goto END;
}

/* nag_det_real_band_sym (f03bhc)
* Determinant of real symmetric positive definite banded matrix
*/
nag_det_real_band_sym(order, uplo, n, kd, ab, pdab, &d, &id, &fail);
if (fail.code != NE_NOERROR) {
printf("%s\n", fail.message);
exit_status = 3;
goto END;
}

printf("\nd = %12.5f  id = %10" NAG_IFMT "\n", d, id);
printf("Value of determinant = %13.5e\n", d * pow(2.0, id));

END:
NAG_FREE(ab);

return exit_status;
}
```