/* nag_sparseig_real_proc (f12acc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.0, 2024.
*/
#include <nag.h>
#include <stdio.h>
static void av(Integer, double, double *, double *);
static void mv(Integer, double *, double *);
static void my_dpttrf(Integer, double *, double *, Integer *);
static void my_dpttrs(Integer, double *, double *, double *);
int main(void) {
/* Constants */
Integer licomm = 140, imon = 0;
/* Scalars */
double estnrm, h, rho, sigmai = 0.0, sigmar = 0.0;
Integer exit_status, info, irevcm, j, lcomm, n, nconv, ncv;
Integer nev, niter, nshift, nx;
/* Nag types */
NagError fail;
/* Arrays */
double *comm = 0, *eigvr = 0, *eigvi = 0, *eigest = 0, *md = 0, *me = 0;
double *resid = 0, *v = 0;
Integer *icomm = 0;
/* Pointers */
double *mx = 0, *x = 0, *y = 0;
exit_status = 0;
INIT_FAIL(fail);
printf("nag_sparseig_real_proc (f12acc) Example Program Results\n");
/* Skip heading in data file */
scanf("%*[^\n] ");
/* Read problem parameter values from data file. */
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%lf%*[^\n] ", &nx, &nev, &ncv,
&rho);
n = nx * nx;
lcomm = 3 * n + 3 * ncv * ncv + 6 * ncv + 60;
/* Allocate memory */
if (!(comm = NAG_ALLOC(lcomm, double)) || !(eigvr = NAG_ALLOC(ncv, double)) ||
!(eigvi = NAG_ALLOC(ncv, double)) || !(eigest = NAG_ALLOC(ncv, double)) ||
!(md = NAG_ALLOC(n, double)) || !(me = NAG_ALLOC(n, double)) ||
!(resid = NAG_ALLOC(n, double)) || !(v = NAG_ALLOC(n * ncv, double)) ||
!(icomm = NAG_ALLOC(licomm, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Initialize communication arrays for problem using
nag_sparseig_real_init (f12aac). */
nag_sparseig_real_init(n, nev, ncv, icomm, licomm, comm, lcomm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_real_init (f12aac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Set the mode. */
/* Select the mode using
nag_sparseig_real_option (f12adc). */
nag_sparseig_real_option("REGULAR INVERSE", icomm, comm, &fail);
/* Select the problem type using
nag_sparseig_real_option (f12adc). */
nag_sparseig_real_option("GENERALIZED", icomm, comm, &fail);
/* Construct M, and factorize using my_dpttrf. */
h = 1.0 / (double)(n + 1);
for (j = 0; j <= n - 2; ++j) {
md[j] = h * 4.0;
me[j] = h;
}
md[n - 1] = h * 4.0;
my_dpttrf(n, md, me, &info);
irevcm = 0;
REVCOMLOOP:
/* repeated calls to reverse communication routine
nag_sparseig_real_iter (f12abc). */
nag_sparseig_real_iter(&irevcm, resid, v, &x, &y, &mx, &nshift, comm, icomm,
&fail);
if (irevcm != 5) {
if (irevcm == -1 || irevcm == 1) {
/* Perform y <--- OP*x = inv[M]*A*x using my_dpttrs. */
av(nx, rho, x, y);
my_dpttrs(n, md, me, y);
} else if (irevcm == 2) {
/* Perform y <--- M*x. */
mv(nx, x, y);
} else if (irevcm == 4 && imon == 1) {
/* If imon=1, get monitoring information using
nag_sparseig_real_monit (f12aec). */
nag_sparseig_real_monit(&niter, &nconv, eigvr, eigvi, eigest, icomm,
comm);
/* Compute 2-norm of Ritz estimates using
nag_blast_dge_norm (f16rac). */
nag_blast_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_sparseig_real_proc (f12acc)
to compute eigenvalues/vectors. */
nag_sparseig_real_proc(&nconv, eigvr, eigvi, v, sigmar, sigmai, resid, v,
comm, icomm, &fail);
/* Print computed eigenvalues. */
printf("\n The %4" NAG_IFMT " generalized", nconv);
printf(" Ritz values of largest 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_sparseig_real_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(md);
NAG_FREE(me);
NAG_FREE(resid);
NAG_FREE(v);
NAG_FREE(icomm);
return exit_status;
}
static void av(Integer nx, double rho, double *v, double *y) {
/* Scalars */
double dd, dl, du, h, s;
Integer j, n;
/* Function Body */
n = nx * nx;
h = 1.0 / (double)(n + 1);
s = rho / 2.0;
dd = 2.0 / h;
dl = -1.0 / h - s;
du = -1.0 / h + s;
y[0] = dd * v[0] + du * v[1];
for (j = 1; j <= n - 2; ++j) {
y[j] = dl * v[j - 1] + dd * v[j] + du * v[j + 1];
}
y[n - 1] = dl * v[n - 2] + dd * v[n - 1];
return;
} /* av */
static void mv(Integer nx, double *v, double *y) {
/* Scalars */
double h;
Integer j, n;
/* Function Body */
n = nx * nx;
h = 1. / (double)(n + 1);
y[0] = h * (v[0] * 4. + v[1]);
for (j = 1; j <= n - 2; ++j) {
y[j] = h * (v[j - 1] + v[j] * 4. + v[j + 1]);
}
y[n - 1] = h * (v[n - 2] + v[n - 1] * 4.);
return;
} /* mv */
static void my_dpttrf(Integer n, double d[], double e[], Integer *info) {
/* A simple C version of the Lapack routine dpttrf with argument
checking removed */
/* Scalars */
double ei;
Integer i;
/* Function Body */
*info = 0;
for (i = 0; i < n - 1; ++i) {
if (d[i] <= 0.0) {
*info = i + 1;
goto END_DPTTRF;
}
ei = e[i];
e[i] = ei / d[i];
d[i + 1] = d[i + 1] - e[i] * ei;
}
if (d[n - 1] <= 0.0) {
*info = n;
}
END_DPTTRF:
return;
}
static void my_dpttrs(Integer n, double d[], double e[], double b[]) {
/* A simple C version of the Lapack routine dpttrs with argument
checking removed and nrhs=1 */
/* Scalars */
Integer i;
/* Function Body */
for (i = 1; i < n; ++i) {
b[i] = b[i] - b[i - 1] * e[i - 1];
}
b[n - 1] = b[n - 1] / d[n - 1];
for (i = n - 2; i >= 0; --i) {
b[i] = b[i] / d[i] - b[i + 1] * e[i];
}
return;
}