NAG Library Manual, Mark 30.1
```/* nag_lapackeig_dsbgvx (f08ubc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.1, 2024.
*/

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

int main(void) {
/* Scalars */
double abstol, vl, vu;
Integer exit_status = 0, il = 1, iu = 1;
Integer i, j, ka, kb, m, n, pdab, pdbb, pdq, pdz, zsize;

/* Arrays */
double *ab = 0, *bb = 0, *q = 0, *w = 0, *z = 0;
Integer *index = 0;
char nag_enum_arg[40];

/* Nag Types */
NagError fail;
Nag_OrderType order;
Nag_UploType uplo;
Nag_JobType job;

#ifdef NAG_COLUMN_MAJOR
#define AB_UPPER(I, J) ab[(J - 1) * pdab + ka + I - J]
#define AB_LOWER(I, J) ab[(J - 1) * pdab + I - J]
#define BB_UPPER(I, J) bb[(J - 1) * pdbb + kb + I - J]
#define BB_LOWER(I, J) bb[(J - 1) * pdbb + 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 + ka + J - I]
#define BB_UPPER(I, J) bb[(I - 1) * pdbb + J - I]
#define BB_LOWER(I, J) bb[(I - 1) * pdbb + kb + J - I]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_dsbgvx (f08ubc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &n, &ka, &kb);
if (n < 0 || ka < kb || kb < 0) {
printf("Invalid n, ka or kb\n");
exit_status = 1;
goto END;
}
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);
scanf(" %39s%*[^\n]", nag_enum_arg);
job = (Nag_JobType)nag_enum_name_to_value(nag_enum_arg);
if (job == Nag_EigVals) {
zsize = 1;
pdz = 1;
} else {
zsize = n * n;
pdz = n;
}

pdab = ka + 1;
pdbb = kb + 1;
pdq = n;
/* Allocate memory */
if (!(ab = NAG_ALLOC((ka + 1) * n, double)) ||
!(bb = NAG_ALLOC((kb + 1) * n, double)) ||
!(q = NAG_ALLOC(n * n, double)) || !(w = NAG_ALLOC(n, double)) ||
!(z = NAG_ALLOC(zsize, double)) || !(index = NAG_ALLOC(n, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read the lower and upper bounds of the interval to be searched. */
scanf("%lf%lf%*[^\n]", &vl, &vu);

/* Read the triangular parts of the matrices A and B from data file */
if (uplo == Nag_Upper) {
for (i = 1; i <= n; ++i)
for (j = i; j <= MIN(i + ka, n); ++j)
scanf("%lf", &AB_UPPER(i, j));
scanf("%*[^\n]");
for (i = 1; i <= n; ++i)
for (j = i; j <= MIN(i + kb, n); ++j)
scanf("%lf", &BB_UPPER(i, j));
} else {
for (i = 1; i <= n; ++i)
for (j = MAX(1, i - ka); j <= i; ++j)
scanf("%lf", &AB_LOWER(i, j));
scanf("%*[^\n]");
for (i = 1; i <= n; ++i)
for (j = MAX(1, i - kb); j <= i; ++j)
scanf("%lf", &BB_LOWER(i, j));
}
scanf("%*[^\n]");

/* Use the default absolute error tolerance for eigenvalues. */
abstol = 0.0;

/* Solve the generalized symmetric eigenvalue problem A*x = lambda*B*x
* using nag_lapackeig_dsbgvx (f08ubc).
*/
nag_lapackeig_dsbgvx(order, job, Nag_Interval, uplo, n, ka, kb, ab, pdab, bb,
pdbb, q, pdq, vl, vu, il, iu, abstol, &m, w, z, pdz,
index, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from in nag_lapackeig_dsbgvx (f08ubc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print eigensolution */
printf("Number of eigenvalues found = %8" NAG_IFMT "\n\n", m);
printf(" Eigenvalues\n   ");
for (j = 0; j < m; ++j)
printf(" %7.4f%s", w[j], j % 6 == 5 ? "\n" : " ");
printf("\n");

if (job == Nag_DoBoth) {
/* nag_file_print_matrix_real_gen (x04cac): Print Matrix of eigenvectors Z.
*/
printf("\n");
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
m, z, pdz, "Selected 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;
}
if (fail.code == NE_CONVERGENCE) {
printf("eigenvectors failed to converge\n");
printf("Indices of eigenvectors that did not converge\n   ");
for (j = 0; j < n; ++j)
printf("%8" NAG_IFMT "%s", index[j], j % 6 == 5 ? "\n" : "");
}
}

END:
NAG_FREE(ab);
NAG_FREE(bb);
NAG_FREE(q);
NAG_FREE(w);
NAG_FREE(z);
NAG_FREE(index);

return exit_status;
}
```