NAG Library Manual, Mark 27.2
```/* nag_lapackeig_dspgvx (f08tbc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.2, 2021.
*/

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

int main(void) {
/* Scalars */
double abstol, vl, vu;
Integer i, il = 0, iu = 0, j, m, n, pdz;
Integer exit_status = 0;
/* Arrays */
double *ap = 0, *bp = 0, *w = 0, *z = 0;
Integer *index = 0;
char nag_enum_arg[40];

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

#ifdef NAG_COLUMN_MAJOR
#define A_UPPER(I, J) ap[J * (J - 1) / 2 + I - 1]
#define A_LOWER(I, J) ap[(2 * n - J) * (J - 1) / 2 + I - 1]
#define B_UPPER(I, J) bp[J * (J - 1) / 2 + I - 1]
#define B_LOWER(I, J) bp[(2 * n - J) * (J - 1) / 2 + I - 1]
#define Z(I, J) z[(J - 1) * pdz + I - 1]
order = Nag_ColMajor;
#else
#define A_UPPER(I, J) ap[(2 * n - I) * (I - 1) / 2 + J - 1]
#define A_LOWER(I, J) ap[I * (I - 1) / 2 + J - 1]
#define B_UPPER(I, J) bp[(2 * n - I) * (I - 1) / 2 + J - 1]
#define B_LOWER(I, J) bp[I * (I - 1) / 2 + J - 1]
#define Z(I, J) z[(I - 1) * pdz + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_dspgvx (f08tbc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%*[^\n]", &n);
if (n < 0) {
printf("Invalid n\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);

m = n;
pdz = n;
/* Allocate memory */
if (!(ap = NAG_ALLOC(n * (n + 1) / 2, double)) ||
!(bp = NAG_ALLOC(n * (n + 1) / 2, double)) ||
!(w = NAG_ALLOC(n, double)) || !(z = NAG_ALLOC(n * m, 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 <= n; ++j)
scanf("%lf", &A_UPPER(i, j));
scanf("%*[^\n]");
for (i = 1; i <= n; ++i)
for (j = i; j <= n; ++j)
scanf("%lf", &B_UPPER(i, j));
} else if (uplo == Nag_Lower) {
for (i = 1; i <= n; ++i)
for (j = 1; j <= i; ++j)
scanf("%lf", &A_LOWER(i, j));
scanf("%*[^\n]");
for (i = 1; i <= n; ++i)
for (j = 1; j <= i; ++j)
scanf("%lf", &B_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_dspgvx (f08tbc).
*/
nag_lapackeig_dspgvx(order, 1, Nag_DoBoth, Nag_Interval, uplo, n, ap, bp, vl,
vu, il, iu, abstol, &m, w, z, pdz, index, &fail);

if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dspgvx (f08tbc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Normalize the eigenvectors */
for (j = 1; j <= m; j++)
for (i = n; i >= 1; i--)
Z(i, j) = Z(i, j) / Z(1, j);

/* Print eigensolution */
printf("Number of eigenvalues found =%5" NAG_IFMT "\n\n", m);
printf(" Eigenvalues\n   ");
for (j = 0; j < m; ++j)
printf(" %8.4f%s", w[j], j % 8 == 7 ? "\n" : "");
printf("\n");

/* Print normalized vectors using nag_file_print_matrix_real_gen (x04cac). */
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;
}

END:
NAG_FREE(ap);
NAG_FREE(bp);
NAG_FREE(w);
NAG_FREE(z);
NAG_FREE(index);

return exit_status;
}
```