```/* nag_complex_sparse_eigensystem_option (f12arc) Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
*
* Mark 26.1, 2017.
*/

#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nag_string.h>
#include <stdio.h>
#include <naga02.h>
#include <nagf12.h>
#include <nagf16.h>

/* Table of constant values */
static Complex four = { 4., 0. };

static void mv(Integer, Complex *, Complex *);
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 = 0;

/* Scalars */
Complex rho, s1, s2, s3, sigma;
double estnrm, hr, hr1, sr, shs;
Integer exit_status, info, irevcm, j, lcomm, n, nconv, ncv;
Integer nev, niter, nshift, nx;
/* Nag types */
NagError fail;
/* Arrays */
Complex *comm = 0, *eigv = 0, *eigest = 0, *dd = 0, *dl = 0, *du = 0;
Complex *du2 = 0, *resid = 0, *v = 0;
Integer *icomm = 0, *ipiv = 0;
/* Ponters */
Complex *mx = 0, *x = 0, *y = 0;

exit_status = 0;
INIT_FAIL(fail);

printf("nag_complex_sparse_eigensystem_option (f12arc) Example "
"Program Results\n");
/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &nx, &nev, &ncv);
n = nx * nx;
lcomm = 3 * n + 3 * ncv * ncv + 5 * ncv + 60;
/* Allocate memory */
if (!(comm = NAG_ALLOC(lcomm, Complex)) ||
!(eigv = NAG_ALLOC(ncv, Complex)) ||
!(eigest = NAG_ALLOC(ncv, Complex)) ||
!(dd = NAG_ALLOC(n, Complex)) ||
!(dl = NAG_ALLOC(n, Complex)) ||
!(du = NAG_ALLOC(n, Complex)) ||
!(du2 = NAG_ALLOC(n, Complex)) ||
!(resid = NAG_ALLOC(n, Complex)) ||
!(v = NAG_ALLOC(n * ncv, Complex)) ||
!(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_complex_sparse_eigensystem_init (f12anc). */
nag_complex_sparse_eigensystem_init(n, nev, ncv, icomm, licomm,
comm, lcomm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_complex_sparse_eigensystem_init (f12anc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
/* Select the required mode using
nag_complex_sparse_eigensystem_option (f12arc). */
nag_complex_sparse_eigensystem_option("SHIFTED INVERSE", icomm,
comm, &fail);
/* Select the problem type using
nag_complex_sparse_eigensystem_option (f12arc). */
nag_complex_sparse_eigensystem_option("GENERALIZED", icomm, comm, &fail);
/* Set values for sigma and rho */
/* Assign to Complex type using nag_complex (a02bac) */
sigma = nag_complex(500.0, 0.0);
rho = nag_complex(10.0, 0.0);
hr1 = (double) (n + 1); /* one/h */
hr = 1.0 / hr1; /* h */
sr = 0.5 * rho.re; /* s */
shs = sigma.re * hr / 6.0; /* sigma*h/6 */
/* Assign to Complex type using nag_complex (a02bac) */
s1 = nag_complex(-hr1 - sr - shs, 0.0); /* -one/h - s -sigma*h/six */
s3 = nag_complex(-hr1 + sr - shs, 0.0); /* -one/h + s -sigma*h/six */
s2 = nag_complex(2.0 * hr1 - 4.0 * shs, 0.0); /* two/h - four*sigma*h/six */

for (j = 0; j <= n - 2; ++j) {
dl[j] = s1;
dd[j] = s2;
du[j] = s3;
}
dd[n - 1] = s2;

my_zgttrf(n, dl, dd, du, du2, ipiv, &info);
irevcm = 0;
REVCOMLOOP:
/* repeated calls to reverse communication routine
nag_complex_sparse_eigensystem_iter (f12apc). */
nag_complex_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(nx, x, y);
my_zgttrs(n, dl, dd, du, du2, ipiv, y);
}
else if (irevcm == 1) {
/* Perform  x <--- OP*x = inv[A-SIGMA*M]*M*x, */
/* MX stored in mx */
for (j = 0; j < n; ++j) {
y[j] = mx[j];
}
my_zgttrs(n, dl, dd, du, du2, ipiv, 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_complex_sparse_eigensystem_monit (f12asc). */
nag_complex_sparse_eigensystem_monit(&niter, &nconv, eigv,
eigest, icomm, comm);
/* Compute 2-norm of Ritz estimates using
nag_zge_norm (f16uac). */
nag_zge_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_complex_sparse_eigensystem_sol
(f12aqc) to compute eigenvalues/vectors. */
nag_complex_sparse_eigensystem_sol(&nconv, eigv, v, sigma, resid, v,
comm, icomm, &fail);
printf("\n The %4" NAG_IFMT " generalized Ritz values closest to "
"( %7.3f , %7.3f ) are:\n\n", nconv, sigma.re, sigma.im);
for (j = 0; j <= nconv - 1; ++j) {
printf("%8" NAG_IFMT "%5s( %12.4f , %12.4f )\n", j + 1, "",
eigv[j].re, eigv[j].im);
}
}
else {
printf(" Error from nag_complex_sparse_eigensystem_iter (f12apc)."
"\n%s\n", fail.message);
exit_status = 1;
goto END;
}
END:
NAG_FREE(comm);
NAG_FREE(eigv);
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 mv(Integer nx, Complex *v, Complex *y)
{
/* Compute the out-of--place matrix vector multiplication Y<---M*X, */
/* where M is mass matrix formed by using piecewise linear elements */
/* on [0,1]. */

/* Scalars */
Complex hsix, z1;
Integer j, n;
/* Function Body */
n = nx * nx;
/* Assign to Complex type using nag_complex (a02bac) */
hsix = nag_complex(1.0 / (6.0 * (double) (n + 1)), 0.0);
/* y[0] = (four*v[0]+v[1])*(h/six) */
/* Compute Complex multiply using nag_complex_multiply
(a02ccc). */
z1 = nag_complex_multiply(four, v[0]);
y[0] = nag_complex_multiply(z1, hsix);
for (j = 1; j <= n - 2; ++j) {
/* y[j] = (v[j-1] + four*v[j] + V[j+1])*(h/six) */
/* Compute Complex multiply using nag_complex_multiply
(a02ccc). */
z1 = nag_complex_multiply(four, v[j]);
z1 = nag_complex_add(v[j - 1], z1);
z1 = nag_complex_add(z1, v[j + 1]);
y[j] = nag_complex_multiply(z1, hsix);
}
/* y[n-1] = (v[n-2] + four*v[n-1])*(h/six) */
/* Compute Complex multiply using nag_complex_multiply (a02ccc). */
z1 = nag_complex_multiply(four, v[n - 1]);
z1 = nag_complex_add(v[n - 2], z1);
y[n - 1] = nag_complex_multiply(z1, hsix);
return;
} /* mv */

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]);