NAG Library Manual, Mark 27.2
Interfaces:  FL   CL   CPP   AD
```/* nag_sparseig_real_iter (f12abc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.2, 2021.
*/

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

static void my_dgttrf(Integer, double *, double *, double *, double *,
Integer *, Integer *);
static void my_dgttrs(Integer, double *, double *, double *, double *,
Integer *, double *, double *);

int main(void) {
/* Constants */
Integer licomm = 140, imon = 0;
/* Scalars */
double h, rho, s, s1, s2, s3, estnrm, sigmai, sigmar;
Integer exit_status, info, irevcm, j, lcomm, n, nconv, ncv;
Integer nev, niter, nshift, nx;
/* Nag types */
NagError fail;
/* Arrays */
double *comm = 0, *dd = 0, *dl = 0, *du = 0, *du2 = 0, *eigvr = 0;
double *eigvi = 0, *eigest = 0, *resid = 0, *v = 0;
Integer *icomm = 0, *ipiv = 0;
/* Pointers */
double *mx = 0, *x = 0, *y = 0;

exit_status = 0;
INIT_FAIL(fail);

printf("nag_sparseig_real_iter (f12abc) 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%lf%lf%*[^\n] ", &nx, &nev,
&ncv, &rho, &sigmar, &sigmai);
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)) ||
!(dd = NAG_ALLOC(n, double)) || !(dl = NAG_ALLOC(n, double)) ||
!(du = NAG_ALLOC(n, double)) || !(du2 = NAG_ALLOC(n, double)) ||
!(resid = NAG_ALLOC(n, double)) || !(v = NAG_ALLOC(n * ncv, double)) ||
!(icomm = NAG_ALLOC(licomm, Integer)) ||
!(ipiv = NAG_ALLOC(n, 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;
}
/* Select the required mode using
nag_sparseig_real_option (f12adc). */
nag_sparseig_real_option("SHIFTED INVERSE REAL", icomm, comm, &fail);
/* Construct C = A - sigma*I, and factorize using my_dgttrf. */
h = 1.0 / (double)(n + 1);
s = rho * h / 2.0;
s1 = -1.0 - s;
s2 = 2.0 - sigmar;
s3 = s - 1.0;
for (j = 0; j <= n - 2; ++j) {
dl[j] = s1;
dd[j] = s2;
du[j] = s3;
}
dd[n - 1] = s2;

my_dgttrf(n, dl, dd, du, du2, ipiv, &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[A-SIGMA*I]*x. */
/* Use my_dgttrs, a cut down C version of Lapack's dgttrs. */
my_dgttrs(n, dl, dd, du, du2, ipiv, 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");
printf(" The %4" NAG_IFMT " Ritz values of closest", nconv);
printf(" to unity 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(dd);
NAG_FREE(dl);
NAG_FREE(du);
NAG_FREE(du2);
NAG_FREE(resid);
NAG_FREE(v);
NAG_FREE(icomm);
NAG_FREE(ipiv);
return exit_status;
}

static void my_dgttrf(Integer n, double dl[], double d[], double du[],
double du2[], Integer ipiv[], Integer *info) {
/* A simple C version of the Lapack routine dgttrf with argument
checking removed */
/* Scalars */
double temp, fact;
Integer i;
/* Function Body */
*info = 0;
for (i = 0; i < n; ++i) {
ipiv[i] = i;
}
for (i = 0; i < n - 2; ++i) {
du2[i] = 0.0;
}
for (i = 0; i < n - 2; i++) {
if (fabs(d[i]) >= fabs(dl[i])) {
/* No row interchange required, eliminate dl[i]. */
if (d[i] != 0.0) {
fact = dl[i] / d[i];
dl[i] = fact;
d[i + 1] = d[i + 1] - fact * du[i];
}
} else {
/* Interchange rows I and I+1, eliminate dl[I] */
fact = d[i] / dl[i];
d[i] = dl[i];
dl[i] = fact;
temp = du[i];
du[i] = d[i + 1];
d[i + 1] = temp - fact * d[i + 1];
du2[i] = du[i + 1];
du[i + 1] = -fact * du[i + 1];
ipiv[i] = i + 1;
}
}
if (n > 1) {
i = n - 2;
if (fabs(d[i]) >= fabs(dl[i])) {
if (d[i] != 0.0) {
fact = dl[i] / d[i];
dl[i] = fact;
d[i + 1] = d[i + 1] - fact * du[i];
}
} else {
fact = d[i] / dl[i];
d[i] = dl[i];
dl[i] = fact;
temp = du[i];
du[i] = d[i + 1];
d[i + 1] = temp - fact * d[i + 1];
ipiv[i] = i + 1;
}
}
/* Check for a zero on the diagonal of U. */
for (i = 0; i < n; ++i) {
if (d[i] == 0.0) {
*info = i;
goto END;
}
}
END:
return;
}

static void my_dgttrs(Integer n, double dl[], double d[], double du[],
double du2[], Integer ipiv[], double b[], double y[]) {
/* A simple C version of the Lapack routine dgttrs with argument
checking removed, the number of right-hand-sides=1, Trans='N' */
/* Scalars */
Integer i, ip;
double temp;
/* Solve L*x = b. */
for (i = 0; i <= n - 1; ++i) {
y[i] = b[i];
}
for (i = 0; i < n - 1; ++i) {
ip = ipiv[i];
temp = y[i + 1 - ip + i] - dl[i] * y[ip];
y[i] = y[ip];
y[i + 1] = temp;
}
/* Solve U*x = b. */
y[n - 1] = y[n - 1] / d[n - 1];
if (n > 1) {
y[n - 2] = (y[n - 2] - du[n - 2] * y[n - 1]) / d[n - 2];
}
for (i = n - 3; i >= 0; --i) {
y[i] = (y[i] - du[i] * y[i + 1] - du2[i] * y[i + 2]) / d[i];
}
return;
}
```