/* nag_sparseig_real_symm_iter (f12fbc) Example Program.
*
* Copyright 2023 Numerical Algorithms Group.
*
* Mark 29.2, 2023.
*/
#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 *);
static void av(Integer, Integer, double *, double *);
static void atv(Integer, Integer, double *, double *);
static int ex1(void), ex2(void);
int main(void) {
Integer exit_status_ex1 = 0;
Integer exit_status_ex2 = 0;
printf("nag_sparseig_real_symm_iter (f12fbc) Example "
"Program Results\n");
exit_status_ex1 = ex1();
exit_status_ex2 = ex2();
return (exit_status_ex1 == 0 && exit_status_ex2 == 0) ? 0 : 1;
}
int ex1(void) {
/* Constants */
Integer licomm = 140, imon = 0;
/* Scalars */
double estnrm, h2, sigma;
Integer exit_status = 0, info, irevcm, j, lcomm, n, nconv, ncv;
Integer nev, niter, nshift;
/* Nag types */
NagError fail;
/* Arrays */
double *dd = 0, *dl = 0, *du = 0, *du2 = 0, *comm = 0, *eigest = 0;
double *eigv = 0, *resid = 0, *v = 0;
Integer *icomm = 0, *ipiv = 0;
/* Pointers */
double *mx = 0, *x = 0, *y = 0;
INIT_FAIL(fail);
printf("\nExample 1\n");
/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%*[^\n] ");
/* Read values for nx, nev and cnv from data file. */
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &n, &nev, &ncv);
/* Allocate memory */
lcomm = 3 * n + ncv * ncv + 8 * ncv + 60;
if (!(dd = NAG_ALLOC(n, double)) || !(dl = NAG_ALLOC(n, double)) ||
!(du = NAG_ALLOC(n, double)) || !(du2 = NAG_ALLOC(n, double)) ||
!(comm = NAG_ALLOC(lcomm, double)) || !(eigv = NAG_ALLOC(ncv, double)) ||
!(eigest = NAG_ALLOC(ncv, 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_symm_init (f12fac). */
nag_sparseig_real_symm_init(n, nev, ncv, icomm, licomm, comm, lcomm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_real_symm_init "
"(f12fac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
/* Select the required spectrum using
nag_sparseig_real_symm_option (f12fdc). */
nag_sparseig_real_symm_option("largest magnitude", icomm, comm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_real_symm_option "
"(f12fdc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
/* Select the required mode */
nag_sparseig_real_symm_option("shifted inverse", icomm, comm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_real_symm_option "
"(f12fdc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
h2 = 1.0 / (double)((n + 1) * (n + 1));
sigma = 0.0;
for (j = 0; j <= n - 1; ++j) {
dd[j] = 2.0 / h2 - sigma;
dl[j] = -1.0 / h2;
du[j] = dl[j];
}
my_dgttrf(n, dl, dd, du, du2, ipiv, &info);
irevcm = 0;
REVCOMLOOP:
/* Repeated calls to reverse communication routine
nag_sparseig_real_symm_iter (f12fbc). */
nag_sparseig_real_symm_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_symm_monit (f12fec). */
nag_sparseig_real_symm_monit(&niter, &nconv, eigv, 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_symm_proc
(f12fcc) to compute eigenvalues/vectors. */
nag_sparseig_real_symm_proc(&nconv, eigv, v, sigma, resid, v, comm, icomm,
&fail);
printf("\n The %4" NAG_IFMT " Ritz values", nconv);
printf(" closest to %8.4f are:\n\n", sigma);
for (j = 0; j <= nconv - 1; ++j) {
printf("%8" NAG_IFMT "%5s%12.4f\n", j + 1, "", eigv[j]);
}
} else {
printf(" Error from "
"nag_sparseig_real_symm_iter (f12fbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
END:
NAG_FREE(dd);
NAG_FREE(dl);
NAG_FREE(du);
NAG_FREE(du2);
NAG_FREE(comm);
NAG_FREE(eigv);
NAG_FREE(eigest);
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;
}
int ex2(void) {
/* Constants */
Integer licomm = 140;
/* Scalars */
double sigma = 0, axnorm;
Integer exit_status = 0, irevcm, j, lcomm, m, n, nconv, ncv;
Integer nev, nshift;
NagError fail;
/* Arrays */
double *comm = 0, *eigv = 0, *eigest = 0;
double *resid = 0, *v = 0, *ax = 0;
Integer *icomm = 0;
/* Ponters */
double *mx = 0, *x = 0, *y = 0;
INIT_FAIL(fail);
printf("\nExample 2\n");
/* Skip heading in data file. */
scanf("%*[^\n] ");
/* Read values for m, n, nev and cnv from data file. */
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "*[^\n] ", &m, &n,
&nev, &ncv);
/* Allocate memory */
lcomm = 3 * n + ncv * ncv + 8 * ncv + 60;
if (!(comm = NAG_ALLOC(lcomm, double)) || !(eigv = NAG_ALLOC(ncv, double)) ||
!(eigest = NAG_ALLOC(ncv, double)) || !(resid = NAG_ALLOC(n, double)) ||
!(ax = NAG_ALLOC(m, 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_symm_init (f12fac). */
nag_sparseig_real_symm_init(n, nev, ncv, icomm, licomm, comm, lcomm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sparseig_real_symm_init "
"(f12fac).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
irevcm = 0;
REVCOMLOOP:
/* Repeated calls to reverse communication routine
nag_sparseig_real_symm_iter (f12fbc). */
nag_sparseig_real_symm_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(m, n, x, ax);
atv(m, n, ax, y);
}
goto REVCOMLOOP;
}
if (fail.code == NE_NOERROR) {
/* Post-Process using nag_sparseig_real_symm_proc
(f12fcc) to compute singular values/vectors. */
nag_sparseig_real_symm_proc(&nconv, eigv, v, sigma, resid, v, comm, icomm,
&fail);
/* Singular values (squared) are returned in eigv and the
corresponding right singular vectors are returned in the first
nev n-length vectors in v. */
printf("\n The %4" NAG_IFMT " leading Singular values and", nconv);
printf(" direct residuals are:\n\n");
for (j = 0; j <= nconv - 1; ++j) {
eigv[j] = sqrt(eigv[j]);
/* Compute the left singular vectors from the formula
u = Av/sigma
u should have norm 1 so divide by norm(Av). */
av(m, n, &v[j * n], ax);
/* Compute 2-norm of Av using nag_blast_dge_norm (f16rac). */
nag_blast_dge_norm(Nag_ColMajor, Nag_FrobeniusNorm, m, 1, ax, m, &axnorm,
&fail);
resid[j] = axnorm * fabs(1.0 - eigv[j] / axnorm);
printf("%8" NAG_IFMT "%5s%12.4f%5s%12.7f\n", j + 1, "", eigv[j], "",
resid[j]);
}
} else {
printf(" Error from "
"nag_sparseig_real_symm_iter (f12fbc).\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(ax);
NAG_FREE(icomm);
return exit_status;
}
static void av(Integer m, Integer n, double *x, double *w) {
/* Computes w <- A*x. */
/* Local Scalars */
double h, k, s, t;
Integer i, j;
h = 1.0 / (double)(m + 1);
k = 1.0 / (double)(n + 1);
for (i = 0; i < m; ++i) {
w[i] = 0.0;
}
t = 0.0;
for (j = 0; j < n; ++j) {
t = t + k;
s = 0.0;
for (i = 0; i < j + 1; i++) {
s = s + h;
w[i] = w[i] + k * s * (t - 1.0) * x[j];
}
for (i = j + 1; i < m; ++i) {
s = s + h;
w[i] = w[i] + k * t * (s - 1.0) * x[j];
}
}
return;
} /* av */
static void atv(Integer m, Integer n, double *x, double *y) {
/* Computes y <- A'*w. */
/* Local Scalars */
double h, k, s, t;
Integer i, j;
h = 1.0 / (double)(m + 1);
k = 1.0 / (double)(n + 1);
for (i = 0; i < n; ++i) {
y[i] = 0.0;
}
t = 0.0;
for (j = 0; j < n; ++j) {
t = t + k;
s = 0.0;
for (i = 0; i < j + 1; ++i) {
s = s + h;
y[j] = y[j] + k * s * (t - 1.0) * x[i];
}
for (i = j + 1; i < m; ++i) {
s = s + h;
y[j] = y[j] + k * t * (s - 1.0) * x[i];
}
}
return;
} /* atv */