NAG Library Manual, Mark 29.3
```/* nag_lapackeig_dsbtrd (f08hec) Example Program.
*
* Copyright 2023 Numerical Algorithms Group.
*
* Mark 29.3, 2023.
*/

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

int main(void) {
/* Scalars */
Integer i, j, k, kd, n, pdab, pdz, d_len, e_len;
Integer exit_status = 0;
NagError fail;
Nag_UploType uplo;
Nag_OrderType order;
/* Arrays */
char nag_enum_arg[40];
double *ab = 0, *d = 0, *e = 0, *z = 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 Z(I, J) z[(J - 1) * pdz + 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 Z(I, J) z[(I - 1) * pdz + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_dsbtrd (f08hec) Example Program Results\n\n");

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

/* Allocate memory */
if (!(ab = NAG_ALLOC(pdab * n, double)) || !(d = NAG_ALLOC(d_len, double)) ||
!(e = NAG_ALLOC(e_len, double)) || !(z = NAG_ALLOC(pdz * n, 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] ");
}

/* Reduce A to tridiagonal form */
/* nag_lapackeig_dsbtrd (f08hec).
* Orthogonal reduction of real symmetric band matrix to
* symmetric tridiagonal form
*/
nag_lapackeig_dsbtrd(order, Nag_FormQ, uplo, n, kd, ab, pdab, d, e, z, pdz,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dsbtrd (f08hec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Calculate all the eigenvalues and eigenvectors of A */
/* nag_lapackeig_dsteqr (f08jec).
* All eigenvalues and eigenvectors of real symmetric
* tridiagonal matrix, reduced from real symmetric matrix
* using implicit QL or QR
*/
nag_lapackeig_dsteqr(order, Nag_UpdateZ, n, d, e, z, pdz, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dsteqr (f08jec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Normalize the eigenvectors */
for (j = 1; j <= n; j++) {
for (i = n; i >= 1; i--) {
Z(i, j) = Z(i, j) / Z(1, j);
}
}
/* Print eigenvalues and eigenvectors */
printf("Eigenvalues\n");
for (i = 1; i <= n; ++i)
printf("%8.4f%s", d[i - 1], i % 8 == 0 ? "\n" : " ");
printf("\n\n");
/* 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,
n, z, pdz, "Eigenvectors", 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;
}
END:
NAG_FREE(ab);
NAG_FREE(d);
NAG_FREE(e);
NAG_FREE(z);

return exit_status;
}
```