NAG Library Manual, Mark 28.4
/* nag_lapackeig_zhegv (f08snc) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.4, 2022.
*/

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

int main(void) {
/* Scalars */
Complex scal;
double anorm, bnorm, eps, r, rcond, rcondb, t1, t2, t3;
Integer i, j, k, n, pda, pdb;
Integer exit_status = 0, inc = 1;
/* Arrays */
Complex *a = 0, *b = 0;
double *eerbnd = 0, *rcondz = 0, *w = 0, *zerbnd = 0, *temp = 0;
char nag_enum_arg[40];

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

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define B(I, J) b[(J - 1) * pdb + I - 1]
order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define B(I, J) b[(I - 1) * pdb + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_zhegv (f08snc) 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);

pda = n;
pdb = n;
/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, Complex)) || !(b = NAG_ALLOC(n * n, Complex)) ||
!(eerbnd = NAG_ALLOC(n, double)) || !(rcondz = NAG_ALLOC(n, double)) ||
!(temp = NAG_ALLOC(n, double)) || !(w = NAG_ALLOC(n, double)) ||
!(zerbnd = NAG_ALLOC(n, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read the triangular parts of the matrices A and B */
if (uplo == Nag_Upper) {
for (i = 1; i <= n; ++i)
for (j = i; j <= n; ++j)
scanf(" ( %lf , %lf ) ", &A(i, j).re, &A(i, j).im);
scanf("%*[^\n]");
for (i = 1; i <= n; ++i)
for (j = i; j <= n; ++j)
scanf(" ( %lf , %lf ) ", &B(i, j).re, &B(i, j).im);
} else {
for (i = 1; i <= n; ++i)
for (j = 1; j <= i; ++j)
scanf(" ( %lf , %lf ) ", &A(i, j).re, &A(i, j).im);
scanf("%*[^\n]");
for (i = 1; i <= n; ++i)
for (j = 1; j <= i; ++j)
scanf(" ( %lf , %lf ) ", &B(i, j).re, &B(i, j).im);
}
scanf("%*[^\n]");

/* Compute the one-norms of the symmetric matrices A and B
* using nag_blast_zhe_norm (f16ucc).
*/
nag_blast_zhe_norm(order, Nag_OneNorm, uplo, n, a, pda, &anorm, &fail);
nag_blast_zhe_norm(order, Nag_OneNorm, uplo, n, b, pdb, &bnorm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_zhe_norm (f16ucc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Solve the generalized Hermitian eigenvalue problem A*x = lambda*B*x
* using nag_lapackeig_zhegv (f08snc).
*/
nag_lapackeig_zhegv(order, 1, Nag_DoBoth, uplo, n, a, pda, b, pdb, w, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zhegv (f08snc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print eigensolution */
printf(" Eigenvalues\n  ");
for (j = 0; j < n; ++j)
printf(" %11.4f%s", w[j], j % 6 == 5 ? "\n" : "");
printf("\n");

/* Normalize the eigenvectors, largest element real
* (normalization w.r.t B unaffected: Z^HBZ = I).
*/
for (j = 1; j <= n; j++) {
for (i = 1; i <= n; i++) {
/* nag_complex_abs (a02dbc).
* Modulus of a complex number
*/
temp[i - 1] = nag_complex_abs(A(i, j));
}
/* nag_blast_dmax_val (f16jnc).
* Get maximum value (r) and location of that value (k) of double array.
*/
nag_blast_dmax_val(n, temp, inc, &k, &r, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dmax_val (f16jnc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
k = k + 1;
scal.re = A(k, j).re / r;
scal.im = -A(k, j).im / r;
for (i = 1; i <= n; i++)
A(i, j) = nag_complex_multiply(A(i, j), scal);
A(k, j).im = 0.0;
}
/* Print normalized vectors using nag_file_print_matrix_complex_gen (x04dac).
*/
fflush(stdout);
nag_file_print_matrix_complex_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
n, n, a, pda, "Eigenvectors", 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_complex_gen (x04dac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* Estimate the reciprocal condition number of the Cholesky factor of B.
* nag_lapacklin_ztrcon (f07tuc)
* Note that: cond(B) = 1/(rcond*rcond)
*/
nag_lapacklin_ztrcon(order, Nag_OneNorm, uplo, Nag_NonUnitDiag, n, b, pdb,
&rcond, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_ztrcon (f07tuc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print the reciprocal condition number of B */
rcondb = rcond * rcond;
printf("\nEstimate of reciprocal condition number for B\n    %11.1e\n",
rcondb);

/* Get the machine precision, using nag_machine_precision (x02ajc) */
eps = nag_machine_precision;
if (rcond < eps) {
printf("\nB is very ill-conditioned, error estimates have not been"
" computed\n");
goto END;
}

/* Call nag_lapackeig_ddisna (f08flc) to estimate reciprocal condition numbers
* for the eigenvectors of (A - lambda*B)
*/
nag_lapackeig_ddisna(Nag_EigVecs, n, n, w, rcondz, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_ddisna (f08flc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Compute the error estimates for the eigenvalues and  eigenvectors. */
t1 = eps / rcondb;
t2 = anorm / bnorm;
t3 = t2 / rcond;
for (i = 0; i < n; ++i) {
eerbnd[i] = t1 * (t2 + fabs(w[i]));
zerbnd[i] = t1 * (t3 + fabs(w[i])) / rcondz[i];
}

/* Print the approximate error bounds for the eigenvalues and vectors. */
printf("\nError estimates for the eigenvalues\n    ");
for (i = 0; i < n; ++i)
printf(" %10.1e%s", eerbnd[i], i % 6 == 5 ? "\n" : "");

printf("\n\nError estimates for the eigenvectors\n    ");
for (i = 0; i < n; ++i)
printf(" %10.1e%s", zerbnd[i], i % 6 == 5 ? "\n" : "");
printf("\n");

END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(eerbnd);
NAG_FREE(rcondz);
NAG_FREE(w);
NAG_FREE(zerbnd);
NAG_FREE(temp);

return exit_status;
}