NAG Library Manual, Mark 27.3
Interfaces:  FL   CL   CPP   AD 

NAG CL Interface Introduction
Example description
/* nag_sparseig_real_proc (f12acc) Example Program.
 *
 * Copyright 2021 Numerical Algorithms Group.
 *
 * Mark 27.3, 2021.
 */

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

static void av(Integer, double, double *, double *);
static void mv(Integer, double *, double *);
static void my_dpttrf(Integer, double *, double *, Integer *);
static void my_dpttrs(Integer, double *, double *, double *);

int main(void) {
  /* Constants */
  Integer licomm = 140, imon = 0;
  /* Scalars */
  double estnrm, h, rho, sigmai = 0.0, sigmar = 0.0;
  Integer exit_status, info, irevcm, j, lcomm, n, nconv, ncv;
  Integer nev, niter, nshift, nx;
  /* Nag types */
  NagError fail;
  /* Arrays */
  double *comm = 0, *eigvr = 0, *eigvi = 0, *eigest = 0, *md = 0, *me = 0;
  double *resid = 0, *v = 0;
  Integer *icomm = 0;
  /* Pointers */
  double *mx = 0, *x = 0, *y = 0;

  exit_status = 0;
  INIT_FAIL(fail);

  printf("nag_sparseig_real_proc (f12acc) 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%*[^\n] ", &nx, &nev, &ncv,
        &rho);
  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)) ||
      !(md = NAG_ALLOC(n, double)) || !(me = NAG_ALLOC(n, double)) ||
      !(resid = NAG_ALLOC(n, 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_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;
  }
  /* Set the mode. */
  /* Select the mode using
     nag_sparseig_real_option (f12adc). */
  nag_sparseig_real_option("REGULAR INVERSE", icomm, comm, &fail);
  /* Select the problem type using
     nag_sparseig_real_option (f12adc). */
  nag_sparseig_real_option("GENERALIZED", icomm, comm, &fail);

  /* Construct M, and factorize using my_dpttrf. */
  h = 1.0 / (double)(n + 1);
  for (j = 0; j <= n - 2; ++j) {
    md[j] = h * 4.0;
    me[j] = h;
  }
  md[n - 1] = h * 4.0;

  my_dpttrf(n, md, me, &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[M]*A*x using my_dpttrs. */
      av(nx, rho, x, y);
      my_dpttrs(n, md, me, 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_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  The %4" NAG_IFMT " generalized", nconv);
    printf(" Ritz values of largest magnitude 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(md);
  NAG_FREE(me);
  NAG_FREE(resid);
  NAG_FREE(v);
  NAG_FREE(icomm);
  return exit_status;
}

static void av(Integer nx, double rho, double *v, double *y) {
  /* Scalars */
  double dd, dl, du, h, s;
  Integer j, n;
  /* Function Body */
  n = nx * nx;
  h = 1.0 / (double)(n + 1);
  s = rho / 2.0;
  dd = 2.0 / h;
  dl = -1.0 / h - s;
  du = -1.0 / h + s;
  y[0] = dd * v[0] + du * v[1];
  for (j = 1; j <= n - 2; ++j) {
    y[j] = dl * v[j - 1] + dd * v[j] + du * v[j + 1];
  }
  y[n - 1] = dl * v[n - 2] + dd * v[n - 1];
  return;
} /* av */

static void mv(Integer nx, double *v, double *y) {
  /* Scalars */
  double h;
  Integer j, n;
  /* Function Body */
  n = nx * nx;
  h = 1. / (double)(n + 1);
  y[0] = h * (v[0] * 4. + v[1]);
  for (j = 1; j <= n - 2; ++j) {
    y[j] = h * (v[j - 1] + v[j] * 4. + v[j + 1]);
  }
  y[n - 1] = h * (v[n - 2] + v[n - 1] * 4.);
  return;
} /* mv */

static void my_dpttrf(Integer n, double d[], double e[], Integer *info) {
  /* A simple C version of the Lapack routine dpttrf with argument
     checking removed */
  /* Scalars */
  double ei;
  Integer i;
  /* Function Body */
  *info = 0;
  for (i = 0; i < n - 1; ++i) {
    if (d[i] <= 0.0) {
      *info = i + 1;
      goto END_DPTTRF;
    }
    ei = e[i];
    e[i] = ei / d[i];
    d[i + 1] = d[i + 1] - e[i] * ei;
  }
  if (d[n - 1] <= 0.0) {
    *info = n;
  }
END_DPTTRF:
  return;
}

static void my_dpttrs(Integer n, double d[], double e[], double b[]) {
  /* A simple C version of the Lapack routine dpttrs with argument
     checking removed and nrhs=1 */
  /* Scalars */
  Integer i;
  /* Function Body */
  for (i = 1; i < n; ++i) {
    b[i] = b[i] - b[i - 1] * e[i - 1];
  }
  b[n - 1] = b[n - 1] / d[n - 1];
  for (i = n - 2; i >= 0; --i) {
    b[i] = b[i] / d[i] - b[i + 1] * e[i];
  }
  return;
}