/* nag_real_sparse_eigensystem_monit (f12aec) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 8, 2005.
*/
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <stdio.h>
#include <naga02.h>
#include <nagf12.h>
#include <nagf16.h>
static void mv(Integer, double *, double *);
static void av(Integer, double *, double *);
static int ytax(Integer, double *, double *, double *);
static int ytmx(Integer, double *, double *, double *);
static void my_zgttrf(Integer, Complex *, Complex *, Complex *,
Complex *, Integer *, Integer *);
static void my_zgttrs(Integer, Complex *, Complex *, Complex *,
Complex *, Integer *, Complex *);
int main(void)
{
/* Constants */
Integer licomm = 140, imon = 1;
/* Scalars */
Complex c1, c2, c3, eigv, num, den;
double estnrm, deni, denr, i2, numi, numr, r2;
double sigmai, sigmar;
Integer exit_status, info, irevcm, j, k, lcomm, n;
Integer nconv, ncv, nev, niter, nshift;
/* Nag types */
Nag_Boolean first;
NagError fail;
/* Arrays */
Complex *cdd = 0, *cdl = 0, *cdu = 0, *cdu2 = 0, *ctemp = 0;
double *comm = 0, *eigvr = 0, *eigvi = 0, *eigest = 0;
double *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_real_sparse_eigensystem_monit (f12aec) Example Program "
"Results\n");
/* Skip heading in data file */
scanf("%*[^\n] ");
/* Read problem parameter values from data file. */
scanf("%ld%ld%ld%lf%lf%*[^\n] ", &n, &nev, &ncv,
&sigmar, &sigmai);
/* Allocate memory */
lcomm = 3*n + 3*ncv*ncv + 6*ncv + 60;
if (!(cdd = NAG_ALLOC(n, Complex)) ||
!(cdl = NAG_ALLOC(n, Complex)) ||
!(cdu = NAG_ALLOC(n, Complex)) ||
!(cdu2 = NAG_ALLOC(n, Complex)) ||
!(ctemp = NAG_ALLOC(n, Complex)) ||
!(comm = NAG_ALLOC(lcomm, double)) ||
!(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)) ||
!(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_sparse_eigensystem_init (f12aac). */
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 (f12adc). */
nag_real_sparse_eigensystem_option("SHIFTED REAL", icomm, comm,
&fail);
/* Select the problem type using
nag_real_sparse_eigensystem_option (f12adc). */
nag_real_sparse_eigensystem_option("GENERALIZED", icomm, comm,
&fail);
/* Solve A*x = lambda*B*x in shift-invert mode. */
/* The shift, sigma, is a complex number (sigmar, sigmai). */
/* OP = Real_Part{inv[A-(sigmar,sigmai)*M]*M and B = M. */
c1 = nag_complex(-2. - sigmar, -sigmai);
c2 = nag_complex(2. - sigmar * 4., sigmai * -4.);
c3 = nag_complex(3. - sigmar, -sigmai);
for (j = 0; j <= n - 2; ++j)
{
cdl[j] = c1;
cdd[j] = c2;
cdu[j] = c3;
}
cdd[n-1] = c2;
my_zgttrf(n, cdl, cdd, cdu, cdu2, ipiv, &info);
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)
{
/* Perform x <--- OP*x = inv[A-SIGMA*M]*M*x */
mv(n, x, y);
for (j = 0; j <= n-1; ++j)
{
ctemp[j].re = y[j], ctemp[j].im = 0.;
}
my_zgttrs(n, cdl, cdd, cdu, cdu2, ipiv, ctemp);
for (j = 0; j <= n-1; ++j)
{
y[j] = ctemp[j].re;
}
}
else if (irevcm == 1)
{
/* Perform x <--- OP*x = inv[A-SIGMA*M]*M*x, */
/* M*X stored in MX. */
for (j = 0; j <= n-1; ++j)
{
ctemp[j].re = mx[j], ctemp[j].im = 0.;
}
my_zgttrs(n, cdl, cdd, cdu, cdu2, ipiv, ctemp);
for (j = 0; j <= n-1; ++j)
{
y[j] = ctemp[j].re;
}
}
else if (irevcm == 2)
{
/* Perform y <--- M*x */
mv(n, 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 %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_sparse_eigensystem_sol
(f12acc) to compute eigenvalues/vectors. */
nag_real_sparse_eigensystem_sol(&nconv, eigvr, eigvi, v, sigmar,
sigmai, resid, v, comm, icomm,
&fail);
first = Nag_TRUE;
k = 0;
for (j = 0; j <= nconv-1; ++j)
{
/* Use Rayleigh Quotient to recover eigenvalues of the */
/* original problem. */
if (eigvi[j] == 0.)
{
/* Ritz value is real. */
/* Numerator = Vj . AVj where Vj is jth Ritz vector */
if (ytax(n, &v[k], &v[k], &numr))
{
goto END;
}
/* Denominator = Vj . MVj */
if (ytmx(n, &v[k], &v[k], &denr))
{
goto END;
}
eigvr[j] = numr / denr;
}
else if (first)
{
/* Ritz value is complex: (x,y). */
/* Compute x'(Ax) and y'(Ax). */
if (ytax(n, &v[k], &v[k], &numr))
{
goto END;
}
if (ytax(n, &v[k], &v[k+n], &numi))
{
goto END;
}
/* Compute y'(Ay) and x'(Ay). */
if (ytax(n, &v[k+n], &v[k+n], &r2))
{
goto END;
}
if (ytax(n, &v[k+n], &v[k], &i2))
{
goto END;
}
numr += r2;
numi = i2 - numi;
/* Assign to Complex type using nag_complex (a02bac). */
num = nag_complex(numr, numi);
/* Compute x'(Mx) and y'(Mx). */
if (ytmx(n, &v[k], &v[k], &denr))
{
goto END;
}
if (ytmx(n, &v[k], &v[k+n], &deni))
{
goto END;
}
/* Compute y'(Ay) and x'(Ay). */
if (ytmx(n, &v[k+n], &v[k+n], &r2))
{
goto END;
}
if (ytmx(n, &v[k+n], &v[k], &i2))
{
goto END;
}
denr += r2;
deni = i2 - deni;
/* Assign to Complex type using nag_complex (a02bac). */
den = nag_complex(denr, deni);
/* eigv = x'(Ax)/x'(Mx) */
/* Compute Complex division using nag_complex_divide
(a02cdc). */
eigv = nag_complex_divide(num, den);
eigvr[j] = eigv.re;
eigvi[j] = eigv.im;
first = Nag_FALSE;
}
else
{
/* Second of complex conjugate pair. */
eigvr[j] = eigvr[j-1];
eigvi[j] = -eigvi[j-1];
first = Nag_TRUE;
}
k = k + n;
}
/* Print computed eigenvalues. */
printf("\n The %4ld generalized Ritz values closest", nconv);
printf(" to ( %8.4f , %8.4f ) are:\n\n", sigmar, sigmai);
for (j = 0; j <= nconv-1; ++j)
{
printf("%8ld%5s( %7.4f, %7.4f )\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(cdd);
NAG_FREE(cdl);
NAG_FREE(cdu);
NAG_FREE(cdu2);
NAG_FREE(ctemp);
NAG_FREE(comm);
NAG_FREE(eigvr);
NAG_FREE(eigvi);
NAG_FREE(eigest);
NAG_FREE(resid);
NAG_FREE(v);
NAG_FREE(icomm);
NAG_FREE(ipiv);
return exit_status;
}
static void mv(Integer n, double *v, double *y)
{
/* Compute the matrix vector multiplication y<---M*x, */
/* where M is mass matrix formed by using piecewise linear elements */
/* on [0,1]. */
/* Scalars */
Integer j;
/* Function Body */
y[0] = v[0] * 4. + v[1];
for (j = 1; j <= n - 2; ++j)
{
y[j] = v[j-1] + v[j] * 4. + v[j+1];
}
y[n-1] = v[n-2] + v[n-1] * 4.;
return;
} /* mv */
static void av(Integer n, double *v, double *w)
{
/* Scalars */
Integer j;
/* Function Body */
w[0] = v[0] * 2. + v[1] * 3.;
for (j = 1; j <= n - 2; ++j)
{
w[j] = v[j-1] * -2. + v[j] * 2. + v[j+1] * 3.;
}
w[n-1] = v[n-2] * -2. + v[n-1] * 2.;
return;
} /* av */
static int ytax(Integer n, double x[], double y[], double *r)
{
/* Given the vectors x and y, Performs the operation */
/* y'Ax and returns the scalar value. */
/* Scalars */
Integer exit_status, j;
/* Arrays */
double *ax = 0;
/* Function Body */
exit_status = 0;
/* Allocate memory */
if (!(ax = NAG_ALLOC(n, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto YTAXEND;
}
av(n, x, ax);
*r = 0.0;
for (j = 0; j <= n - 1; ++j)
{
*r = *r + y[j] * ax[j];
}
YTAXEND:
NAG_FREE(ax);
return exit_status;
} /* ytax */
static int ytmx(Integer n, double x[], double y[], double *r)
{
/* Given the vectors x and y, Performs the operation */
/* y'Mx and returns the scalar value. */
/* Scalars */
Integer exit_status, j;
/* Arrays */
double *mx = 0;
/* Function Body */
exit_status = 0;
/* Allocate memory */
if (!(mx = NAG_ALLOC(n, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto YTMXEND;
}
mv(n, x, mx);
*r = 0.0;
for (j = 0; j <= n - 1; ++j)
{
*r = *r + y[j] * mx[j];
}
YTMXEND:
NAG_FREE(mx);
return exit_status;
} /* ytmx */
static void my_zgttrf(Integer n, Complex dl[], Complex d[],
Complex du[], Complex du2[], Integer ipiv[],
Integer *info)
{
/* A simple C version of the Lapack routine zgttrf with argument
checking removed */
/* Scalars */
Complex temp, fact, z1;
Integer i;
/* Function Body */
*info = 0;
for (i = 0; i < n; ++i)
{
ipiv[i] = i;
}
for (i = 0; i < n - 2; ++i)
{
du2[i] = nag_complex(0.0, 0.0);
}
for (i = 0; i < n - 2; ++i)
{
if (fabs(d[i].re)+fabs(d[i].im) >= fabs(dl[i].re)+fabs(dl[i].im))
{
/* No row interchange required, eliminate dl[i]. */
if (fabs(d[i].re)+fabs(d[i].im) != 0.0)
{
/* Compute Complex division using nag_complex_divide
(a02cdc). */
fact = nag_complex_divide(dl[i], d[i]);
dl[i] = fact;
/* Compute Complex multiply using nag_complex_multiply
(a02ccc). */
fact = nag_complex_multiply(fact, du[i]);
/* Compute Complex subtraction using
nag_complex_subtract (a02cbc). */
d[i+1] = nag_complex_subtract(d[i+1], fact);
}
}
else
{
/* Interchange rows I and I+1, eliminate dl[I] */
/* Compute Complex division using nag_complex_divide
(a02cdc). */
fact = nag_complex_divide(d[i], dl[i]);
d[i] = dl[i];
dl[i] = fact;
temp = du[i];
du[i] = d[i+1];
/* Compute Complex multiply using nag_complex_multiply
(a02ccc). */
z1 = nag_complex_multiply(fact, d[i+1]);
/* Compute Complex subtraction using nag_complex_subtract
(a02cbc). */
d[i+1] = nag_complex_subtract(temp, z1);
du2[i] = du[i+1];
/* Compute Complex multiply using nag_complex_multiply
(a02ccc). */
du[i+1] = nag_complex_multiply(fact, du[i+1]);
/* Perform Complex negation using nag_complex_negate
(a02cec). */
du[i+1] = nag_complex_negate(du[i+1]);
ipiv[i] = i + 1;
}
}
if (n > 1)
{
i = n - 2;
if (fabs(d[i].re)+fabs(d[i].im) >= fabs(dl[i].re)+fabs(dl[i].im))
{
if (fabs(d[i].re)+fabs(d[i].im) != 0.0)
{
/* Compute Complex division using nag_complex_divide
(a02cdc). */
fact = nag_complex_divide(dl[i], d[i]);
dl[i] = fact;
/* Compute Complex multiply using nag_complex_multiply
(a02ccc). */
fact = nag_complex_multiply(fact, du[i]);
/* Compute Complex subtraction using
nag_complex_subtract (a02cbc). */
d[i+1] = nag_complex_subtract(d[i+1], fact);
}
}
else
{
/* Compute Complex division using nag_complex_divide
(a02cdc). */
fact = nag_complex_divide(d[i], dl[i]);
d[i] = dl[i];
dl[i] = fact;
temp = du[i];
du[i] = d[i+1];
/* Compute Complex multiply using nag_complex_multiply
(a02ccc). */
z1 = nag_complex_multiply(fact, d[i+1]);
/* Compute Complex subtraction using nag_complex_subtract
(a02cbc). */
d[i+1] = nag_complex_subtract(temp, z1);
ipiv[i] = i + 1;
}
}
/* Check for a zero on the diagonal of U. */
for (i = 0; i < n; ++i)
{
if (fabs(d[i].re)+fabs(d[i].im) == 0.0)
{
*info = i;
goto END;
}
}
END:
return;
}
static void my_zgttrs(Integer n, Complex dl[], Complex d[],
Complex du[], Complex du2[], Integer ipiv[],
Complex b[])
{
/* A simple C version of the Lapack routine zgttrs with argument
checking removed, the number of right-hand-sides=1, Trans='N' */
/* Scalars */
Complex temp, z1;
Integer i;
/* Solve L*x = b. */
for (i = 0; i < n - 1; ++i)
{
if (ipiv[i] == i)
{
/* b[i+1] = b[i+1] - dl[i]*b[i] */
/* Compute Complex multiply using nag_complex_multiply
(a02ccc). */
temp = nag_complex_multiply(dl[i], b[i]);
/* Compute Complex subtraction using nag_complex_subtract
(a02cbc). */
b[i+1] = nag_complex_subtract(b[i+1], temp);
}
else
{
temp = b[i];
b[i] = b[i+1];
/* Compute Complex multiply using nag_complex_multiply
(a02ccc). */
z1 = nag_complex_multiply(dl[i], b[i]);
/* Compute Complex subtraction using nag_complex_subtract
(a02cbc). */
b[i+1] = nag_complex_subtract(temp, z1);
}
}
/* Solve U*x = b. */
/* Compute Complex division using nag_complex_divide (a02cdc). */
b[n-1] = nag_complex_divide(b[n-1], d[n-1]);
if (n > 1)
{
/* Compute Complex multiply using nag_complex_multiply
(a02ccc). */
temp = nag_complex_multiply(du[n-2], b[n-1]);
/* Compute Complex subtraction using nag_complex_subtract
(a02cbc). */
z1 = nag_complex_subtract(b[n-2], temp);
/* Compute Complex division using nag_complex_divide (a02cdc). */
b[n-2] = nag_complex_divide(z1, d[n-2]);
}
for (i = n - 3; i >= 0; --i)
{
/* b[i] = (b[i]-du[i]*b[i+1]-du2[i]*b[i+2])/d[i]; */
/* Compute Complex multiply using nag_complex_multiply
(a02ccc). */
temp = nag_complex_multiply(du[i], b[i+1]);
z1 = nag_complex_multiply(du2[i], b[i+2]);
/* Compute Complex addition using nag_complex_add
(a02cac). */
temp = nag_complex_add(temp, z1);
/* Compute Complex subtraction using nag_complex_subtract
(a02cbc). */
z1 = nag_complex_subtract(b[i], temp);
/* Compute Complex division using nag_complex_divide
(a02cdc). */
b[i] = nag_complex_divide(z1, d[i]);
}
return;
}