NAG Library Manual, Mark 28.5
Interfaces:  FL   CL   CPP   AD
```/* nag_sparseig_feast_complex_symm_solve (f12jsc) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.5, 2022.
*/
#include <nag.h>

#define A(I, J) a[(J - 1) * pda + I - 1]
#define AZ(I, J) az[(J - 1) * n + I - 1]
#define B(I, J) b[(J - 1) * pdb + I - 1]

int main(void) {
/* Scalars */
Integer exit_status = 0;
Integer i, j, n, pda, pdb, pdx, pdy, pdz, m0, iter, nconv, irevcm, exit_loop;
double r, eps;
Complex ze, emid, cone, czero;
/* Arrays */
Complex *a = 0, *x = 0, *z = 0, *d = 0, *b = 0;
double *resid = 0;
Complex *y = 0, *az = 0;
Integer *ipiv = 0;
void *handle = 0;
/* Nag Types */
Nag_OrderType order = Nag_ColMajor;
NagError fail;

INIT_FAIL(fail);

/* Output preamble */
printf("nag_sparseig_feast_complex_symm_solve (f12jsc) ");
printf("Example Program Results\n\n");
fflush(stdout);

/* Skip heading in data file */
scanf("%*[^\n] ");

/* Read in the matrix size and the required rank */
scanf("%" NAG_IFMT "%*[^\n]", &n);

pda = n;
pdb = n;
pdx = n;
pdy = n;
pdz = n;
m0 = n;

cone = nag_complex_create(1.0, 0.0);
czero = nag_complex_create(0.0, 0.0);

if (!(a = NAG_ALLOC(pda * n, Complex)) ||
!(b = NAG_ALLOC(pdb * n, Complex)) ||
!(x = NAG_ALLOC(pdx * m0, Complex)) ||
!(y = NAG_ALLOC(pdy * m0, Complex)) ||
!(z = NAG_ALLOC(pdz * m0, Complex)) || !(resid = NAG_ALLOC(m0, double)) ||
!(d = NAG_ALLOC(m0, Complex)) || !(az = NAG_ALLOC(n * n, Complex)) ||
!(ipiv = NAG_ALLOC(n, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read in the matrix A from data file */
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] ");

/* Read in the matrix B from data file */
for (i = 1; i <= n; i++)
for (j = i; j <= n; j++)
scanf(" ( %lf , %lf ) ", &B(i, j).re, &B(i, j).im);

/* Initialize the data handle using nag_sparseig_feast_init (f12jac) */
nag_sparseig_feast_init(&handle, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_feast_init (f12jac)\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Set options using nag_sparseig_feast_option (f12jbc) */
nag_sparseig_feast_option(handle, "Ellipse Contour Ratio = 10", &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_feast_option (f12jbc)\n%s\n", fail.message);
exit_status = 2;
goto END;
}
nag_sparseig_feast_option(handle, "Ellipse Rotation = 45", &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_feast_option (f12jbc)\n%s\n", fail.message);
exit_status = 3;
goto END;
}

emid = nag_complex_create(0.0, 0.0);
r = 1.0;
/* Generate the contour using nag_sparseig_feast_gen_contour (f12jfc) */
nag_sparseig_feast_gen_contour(handle, emid, r, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_feast_gen_contour (f12jfc)\n%s\n",
fail.message);
exit_status = 4;
goto END;
}

exit_loop = 0;
irevcm = 0;

do {
/* Call solver nag_sparseig_feast_complex_symm_solve (f12jsc) */
nag_sparseig_feast_complex_symm_solve(handle, &irevcm, &ze, n, x, pdx, y,
pdy, &m0, &nconv, d, z, pdz, &eps,
&iter, resid, &fail);
switch (irevcm) {
case 1:
/* Form the matrix ze B-A */
for (j = 1; j <= n; j++) {
for (i = 1; i <= n; i++) {
AZ(i, j) =
nag_complex_subtract(nag_complex_multiply(ze, B(i, j)), A(i, j));
}
}
/* Compute Bunch Kaufman factorization of ze B - A */
nag_lapacklin_zsytrf(Nag_ColMajor, Nag_Upper, n, az, n, ipiv, &fail);
if (fail.code != NE_NOERROR) {
exit_loop = 1;
}
break;
case 2:
/* Solve the linear system (ze B -A)w = y, overwriting y with w */
nag_lapacklin_zsytrs(Nag_ColMajor, Nag_Upper, n, m0, az, n, ipiv, y, pdy,
&fail);
if (fail.code != NE_NOERROR) {
exit_loop = 1;
}
break;
case 3:
/* Compute x <- Az */
nag_zsymm(Nag_ColMajor, Nag_LeftSide, Nag_Upper, n, m0, cone, a, pda, z,
pdz, czero, x, pdx, &fail);
if (fail.code != NE_NOERROR) {
exit_loop = 1;
}
break;
case 4:
/* Compute x <- Bz */
nag_zsymm(Nag_ColMajor, Nag_LeftSide, Nag_Upper, n, m0, cone, b, pdb, z,
pdz, czero, x, pdx, &fail);
if (fail.code != NE_NOERROR) {
exit_loop = 1;
}
break;
}
} while (irevcm != 0 && exit_loop == 0);

if (fail.code != NE_NOERROR) {
printf("Error during reverse communication solve\n%s\n", fail.message);
exit_status = 5;
goto END;
}

/* Print solution */
printf(" Eigenvalues\n");
for (i = 0; i < nconv; ++i) {
if (d[i].im == 0.0)
printf("%13.4e%s", d[i].re, (i + 1) % 4 == 0 ? "\n" : " ");
else
printf(" (%13.4e, %13.4e)%s", d[i].re, d[i].im,
(i + 1) % 4 == 0 ? "\n" : " ");
}
printf("\n\n");

/* Print eigenvectors using nag_file_print_matrix_complex_gen (x04dac) */
nag_file_print_matrix_complex_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
n, nconv, z, pdz, "Eigenvectors", NULL,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_complex_gen (x04dac)\n%s\n",
fail.message);
exit_status = 6;
goto END;
}

END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(az);
NAG_FREE(x);
NAG_FREE(y);
NAG_FREE(z);
NAG_FREE(resid);
NAG_FREE(d);
NAG_FREE(ipiv);

/* Destroy the data handle using nag_sparseig_feast_free (f12jzc) */
nag_sparseig_feast_free(&handle, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_feast_free (f12jzc)\n%s\n", fail.message);
exit_status = 7;
}

return exit_status;
}
```