NAG Library Manual, Mark 29.2
```/* nag_sparseig_complex_init (f12anc) Example Program.
*
* Copyright 2023 Numerical Algorithms Group.
*
* Mark 29.2, 2023.
*/

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

static void av(Integer, Complex *, Complex *);
static void tv(Integer, Complex *, Complex *);

int main(void) {
/* Constants */
Integer imon = 0;
/* Scalars */
Complex sigma;
double estnrm;
Integer exit_status, i, irevcm, lcomm, licomm, n, nconv, ncv;
Integer nev, niter, nshift, nx;
/* Nag types */
NagError fail;

/* Arrays */
Complex *comm = 0, *eigest = 0, *eigv = 0, *resid = 0, *v = 0;
Integer *icomm = 0;
/* Ponters */
Complex *mx = 0, *x = 0, *y = 0;

/* Assign to Complex type using nag_complex_create (a02bac) */
sigma = nag_complex_create(0.0, 0.0);
exit_status = 0;
INIT_FAIL(fail);

printf("nag_sparseig_complex_init (f12anc) Example "
"Program Results\n");
/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &nx, &nev, &ncv);
n = nx * nx;
/* Allocate memory */
if (!(eigv = NAG_ALLOC(ncv, Complex)) ||
!(eigest = NAG_ALLOC(ncv, Complex)) || !(resid = NAG_ALLOC(n, Complex)) ||
!(v = NAG_ALLOC(n * ncv, Complex))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Initialize communication arrays for problem using
nag_sparseig_complex_init (f12anc).
The first call sets lcomm = licomm = -1 to perform a workspace
query. */
lcomm = licomm = -1;
if (!(comm = NAG_ALLOC(1, Complex)) || !(icomm = NAG_ALLOC(1, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
nag_sparseig_complex_init(n, nev, ncv, icomm, licomm, comm, lcomm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_complex_init (f12anc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
lcomm = (Integer)comm[0].re;
licomm = icomm[0];
NAG_FREE(comm);
NAG_FREE(icomm);
if (!(comm = NAG_ALLOC(lcomm, Complex)) ||
!(icomm = NAG_ALLOC(licomm, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
nag_sparseig_complex_init(n, nev, ncv, icomm, licomm, comm, lcomm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_complex_init (f12anc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
irevcm = 0;
REVCOMLOOP:
/* repeated calls to reverse communication routine
nag_sparseig_complex_iter (f12apc). */
nag_sparseig_complex_iter(&irevcm, resid, v, &x, &y, &mx, &nshift, comm,
icomm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_complex_iter (f12apc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
if (irevcm != 5 && irevcm != 0) {
if (irevcm == -1 || irevcm == 1) {
/* Perform matrix vector multiplication y <--- Op*x */
av(nx, x, y);
} else if (irevcm == 4 && imon == 1) {
/* If imon=1, get monitoring information using
nag_sparseig_complex_monit (f12asc). */
nag_sparseig_complex_monit(&niter, &nconv, eigv, eigest, icomm, comm);
/* Compute 2-norm of Ritz estimates using
nag_blast_zge_norm (f16uac). */
nag_blast_zge_norm(Nag_ColMajor, Nag_FrobeniusNorm, nev, 1, eigest, nev,
&estnrm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_complex_monit"
" (f12asc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
printf("Iteration %3" NAG_IFMT ", ", niter);
printf(" No. converged = %3" NAG_IFMT ",", nconv);
printf(" norm of estimates = %17.8e\n", estnrm);
}
goto REVCOMLOOP;
}
if (fail.code == NE_NOERROR) {
/* Post-Process using nag_sparseig_complex_proc
(f12aqc) to compute eigenvalues/vectors. */
nag_sparseig_complex_proc(&nconv, eigv, v, sigma, resid, v, comm, icomm,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_complex_proc "
"(f12aqc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

printf("\n The %" NAG_IFMT " Ritz values", nconv);
printf(" of largest magnitude are:\n\n");
for (i = 0; i <= nconv - 1; ++i) {
printf("%8" NAG_IFMT "%5s(%12.4f, %12.4f)\n", i + 1, "", eigv[i].re,
eigv[i].im);
}
} else {
printf("Error from nag_sparseig_complex_iter "
"(f12apc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
END:
NAG_FREE(comm);
NAG_FREE(eigv);
NAG_FREE(eigest);
NAG_FREE(resid);
NAG_FREE(v);
NAG_FREE(icomm);
return exit_status;
}

static void av(Integer nx, Complex *x, Complex *y) {
/* Scalars */
double hr;
Integer i, j, lo;
/* Function Body */

/* Allocate memory */
hr = (double)-(nx + 1) * (nx + 1);
tv(nx, x, y);
for (j = 0; j <= nx - 1; ++j) {
y[j].re = y[j].re + hr * x[nx + j].re;
y[j].im = y[j].im + hr * x[nx + j].im;
}
for (j = 2; j <= nx - 1; ++j) {
lo = (j - 1) * nx;
tv(nx, &x[lo], &y[lo]);
for (i = 0; i <= nx - 1; ++i) {
y[lo + i].re =
y[lo + i].re + hr * (x[lo - nx + i].re + x[lo + nx + i].re);
y[lo + i].im =
y[lo + i].im + hr * (x[lo - nx + i].im + x[lo + nx + i].im);
}
}
lo = (nx - 1) * nx;
tv(nx, &x[lo], &y[lo]);
for (j = 0; j <= nx - 1; ++j) {
y[lo + j].re = y[lo + j].re + hr * x[lo - nx + j].re;
y[lo + j].im = y[lo + j].im + hr * x[lo - nx + j].im;
}
} /* av */

static void tv(Integer nx, Complex *x, Complex *y) {
/* Compute the matrix vector multiplication y<---T*x where T is a */
/* nx by nx tridiagonal matrix. */

/* Scalars */
Complex dd, dl, du, h2, h, rho, z1, z2, z3;
Integer j;

/* Function Body */
/* Assign to Complex type using nag_complex_create (a02bac) */
h = nag_complex_create((double)(nx + 1), 0.);
/* Compute Complex multiply using nag_complex_multiply (a02ccc). */
h2 = nag_complex_multiply(h, h);
dd = nag_complex_multiply(nag_complex_create(4.0, 0.0), h2);
z1 = nag_complex_multiply(nag_complex_create(-1.0, 0.0), h2);
/* Assign to Complex type using nag_complex_create (a02bac) */
rho = nag_complex_create(1.0e2, 0.0);
z2 = nag_complex_multiply(rho, h);
z3 = nag_complex_multiply(nag_complex_create(5.0e-1, 0.0), z2);
/* Compute Complex subtraction using nag_complex_subtract
(a02cbc). */
dl = nag_complex_subtract(z1, z3);

/* Compute Complex multiply using nag_complex_multiply (a02ccc). */
z1 = nag_complex_multiply(dd, x[0]);
z2 = nag_complex_multiply(du, x[1]);
for (j = 1; j <= nx - 2; ++j) {
/* Compute Complex multiply using nag_complex_multiply
(a02ccc). */
z1 = nag_complex_multiply(dl, x[j - 1]);
z2 = nag_complex_multiply(dd, x[j]);
z3 = nag_complex_multiply(du, x[j + 1]);