/* nag_real_symm_sparse_eigensystem_iter (f12fbc) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 8, 2005.
*/
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <stdio.h>
#include <nagf12.h>
#include <nagf16.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_real_symm_sparse_eigensystem_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("%ld%ld%ld%*[^\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;
}
/* Initialise communication arrays for problem using
nag_real_symm_sparse_eigensystem_init (f12fac). */
nag_real_symm_sparse_eigensystem_init(n, nev, ncv, icomm, licomm, comm,
lcomm, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_real_symm_sparse_eigensystem_init "
"(f12fac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Select the required spectrum using
nag_real_symm_sparse_eigensystem_option (f12fdc). */
nag_real_symm_sparse_eigensystem_option("largest magnitude", icomm, comm,
&fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_real_symm_sparse_eigensystem_option "
"(f12fdc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Select the required mode */
nag_real_symm_sparse_eigensystem_option("shifted inverse", icomm, comm,
&fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_real_symm_sparse_eigensystem_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_real_symm_sparse_eigensystem_iter (f12fbc). */
nag_real_symm_sparse_eigensystem_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_real_symm_sparse_eigensystem_monit (f12fec). */
nag_real_symm_sparse_eigensystem_monit(&niter, &nconv, eigv, 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 %3ld, ", niter);
printf(" No. converged = %3ld,", nconv);
printf(" norm of estimates = %17.8e\n", estnrm);
}
goto REVCOMLOOP;
}
if (fail.code == NE_NOERROR)
{
/* Post-Process using nag_real_symm_sparse_eigensystem_sol
(f12fcc) to compute eigenvalues/vectors. */
nag_real_symm_sparse_eigensystem_sol(&nconv, eigv, v, sigma, resid, v,
comm, icomm, &fail);
printf("\n The %4ld Ritz values", nconv);
printf(" closest to %8.4f are:\n\n", sigma);
for (j = 0; j <= nconv-1; ++j)
{
printf("%8ld%5s%12.4f\n", j+1, "", eigv[j]);
}
}
else
{
printf(" Error from "
"nag_real_symm_sparse_eigensystem_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("%ld%ld%ld%ld*[^\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;
}
/* Initialise communication arrays for problem using
nag_real_symm_sparse_eigensystem_init (f12fac). */
nag_real_symm_sparse_eigensystem_init(n, nev, ncv, icomm, licomm, comm,
lcomm, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_real_symm_sparse_eigensystem_init "
"(f12fac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
irevcm = 0;
REVCOMLOOP:
/* Repeated calls to reverse communication routine
nag_real_symm_sparse_eigensystem_iter (f12fbc). */
nag_real_symm_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(m, n, x, ax);
atv(m, n, ax, y);
}
goto REVCOMLOOP;
}
if (fail.code == NE_NOERROR)
{
/* Post-Process using nag_real_symm_sparse_eigensystem_sol
(f12fcc) to compute singular values/vectors. */
nag_real_symm_sparse_eigensystem_sol(&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 %4ld 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_dge_norm (f16rac).*/
nag_dge_norm(Nag_ColMajor, Nag_FrobeniusNorm, m, 1, ax,
m, &axnorm, &fail);
resid[j] = axnorm*fabs(1.0-eigv[j]/axnorm);
printf("%8ld%5s%12.4f%5s%12.7f\n", j+1, "", eigv[j], "",
resid[j]);
}
}
else
{
printf(" Error from "
"nag_real_symm_sparse_eigensystem_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 */