```/* nag_real_sparse_eigensystem_init (f12aac) Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
*
* Mark 26.2, 2017.
*/

#include <nag.h>
#include <nag_stdlib.h>
#include <nag_string.h>
#include <stdio.h>
#include <nagf12.h>
#include <nagf16.h>

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

int main(void)
{
/* Constants */
Integer imon = 0;
/* Scalars */
double sigmai = 0, sigmar = 0, estnrm;
Integer exit_status, irevcm, j, lcomm, licomm, n, nconv, ncv, nev;
Integer niter, nshift, nx;
/* Arrays */
double *comm = 0, *eigvr = 0, *eigvi = 0, *eigest = 0;
double *resid = 0, *v = 0;
Integer *icomm = 0;
/* Pointers */
double *mx = 0, *x = 0, *y = 0;
/* Nag types */
NagError fail;

exit_status = 0;
INIT_FAIL(fail);

printf("nag_real_sparse_eigensystem_init (f12aac) Example Program "
"Results\n");
/* Skip heading in data file. */
scanf("%*[^\n] ");

/* Read values for nx, nev and cnv from data file. */
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &nx, &nev, &ncv);

/* Allocate memory */
n = nx * nx;
if (!(eigvr = NAG_ALLOC(ncv, double)) ||
!(eigvi = NAG_ALLOC(ncv, double)) ||
!(eigest = NAG_ALLOC(ncv, double)) ||
!(resid = NAG_ALLOC(n, double)) || !(v = NAG_ALLOC(n * ncv, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Initialize communication arrays for problem using
nag_real_sparse_eigensystem_init (f12aac).
The first call sets lcomm = licomm = -1 to perform a workspace
query. */
lcomm = licomm = -1;
if (!(comm = NAG_ALLOC(1, double)) || !(icomm = NAG_ALLOC(1, Integer)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
nag_real_sparse_eigensystem_init(n, nev, ncv, icomm, licomm,
comm, lcomm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_real_sparse_eigensystem_init (f12aac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
lcomm = (Integer) comm[0];
licomm = icomm[0];
NAG_FREE(comm);
NAG_FREE(icomm);
if (!(comm = NAG_ALLOC(lcomm, double)) ||
!(icomm = NAG_ALLOC(licomm, Integer)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
nag_real_sparse_eigensystem_init(n, nev, ncv, icomm, licomm,
comm, lcomm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_real_sparse_eigensystem_init (f12aac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
/* Select the required spectrum using
nag_real_sparse_eigensystem_option("SMALLEST MAG", icomm, comm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_real_sparse_eigensystem_option (f12adc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
irevcm = 0;
REVCOMLOOP:
/* Repeated calls to reverse communication routine
nag_real_sparse_eigensystem_iter (f12abc). */
nag_real_sparse_eigensystem_iter(&irevcm, resid, v, &x, &y, &mx,
&nshift, comm, icomm, &fail);
if (irevcm != 5) {
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_real_sparse_eigensystem_monit (f12aec). */
nag_real_sparse_eigensystem_monit(&niter, &nconv, eigvr,
eigvi, eigest, icomm, comm);
/* Compute 2-norm of Ritz estimates using
nag_dge_norm (f16rac). */
nag_dge_norm(Nag_ColMajor, Nag_FrobeniusNorm, nev, 1, eigest,
nev, &estnrm, &fail);
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_real_sparse_eigensystem_sol
(f12acc) to compute eigenvalues/vectors. */
nag_real_sparse_eigensystem_sol(&nconv, eigvr, eigvi, v, sigmar,
sigmai, resid, v, comm, icomm, &fail);
printf("\n\n The %4" NAG_IFMT " Ritz values", nconv);
printf(" of smallest magnitude are:\n\n");
for (j = 0; j <= nconv - 1; ++j) {
printf("%8" NAG_IFMT "%5s( %12.4f , %12.4f )\n", j + 1, "",
eigvr[j], eigvi[j]);
}
}
else {
printf("Error from nag_real_sparse_eigensystem_iter (f12abc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
END:
NAG_FREE(comm);
NAG_FREE(eigvr);
NAG_FREE(eigvi);
NAG_FREE(eigest);
NAG_FREE(resid);
NAG_FREE(v);
NAG_FREE(icomm);
return exit_status;
}

static void av(Integer nx, double *v, double *w)
{
/* Constants */
const double beta = 1.0;
/* Scalars */
double nx2;
Integer j, lo;
/* Nag types */
NagError fail;

/* Function Body */
INIT_FAIL(fail);
nx2 = -((double) ((nx + 1) * (nx + 1)));
tv(nx, v, w);
nag_daxpby(nx, nx2, &v[nx], 1, beta, w, 1, &fail);
for (j = 2; j <= nx - 1; ++j) {
lo = (j - 1) * nx;
tv(nx, &v[lo], &w[lo]);
nag_daxpby(nx, nx2, &v[lo - nx], 1, beta, &w[lo], 1, &fail);
nag_daxpby(nx, nx2, &v[lo + nx], 1, beta, &w[lo], 1, &fail);
}
lo = (nx - 1) * nx;
tv(nx, &v[lo], &w[lo]);
nag_daxpby(nx, nx2, &v[lo - nx], 1, beta, &w[lo], 1, &fail);
return;
} /* av */

static void tv(Integer nx, double *x, double *y)
{
/* Compute the matrix vector multiplication y<---T*x where T is a nx */
/* by nx tridiagonal matrix with constant diagonals (dd, dl and du). */
/* Scalars */
double dd, dl, du, nx1, nx2;
Integer j;
/* Function Body */
nx1 = (double) (nx + 1);
nx2 = nx1 * nx1;
dd = nx2 * 4.;
dl = -nx2 - nx1 * 50.;
du = -nx2 + nx1 * 50.;
y[0] = dd * x[0] + du * x[1];
for (j = 1; j <= nx - 2; ++j) {
y[j] = dl * x[j - 1] + dd * x[j] + du * x[j + 1];
}
y[nx - 1] = dl * x[nx - 2] + dd * x[nx - 1];
return;
} /* tv */
```