/* nag_real_sparse_eigensystem_option (f12adc) Example Program.
 *
 * Copyright 2005 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 mv(Integer, double *, double *);
static void my_dgttrf(Integer, double *, double *, double *,
                      double *, Integer *, Integer *);
static void my_dgttrs(Integer, double *, double *, double *,
                      double *, Integer *, double *, double *);

int main(void)
{
  /* Constants */
  Integer  licomm = 140, imon = 0;
  /* Scalars */
  double   estnrm, h, rho, s, s1, s2, s3, sigmai, sigmar;
  Integer  exit_status, info, irevcm, j, lcomm, n, nconv, ncv;
  Integer  nev, niter, nshift, nx;
  /* Nag types */
  NagError fail;

  /* Arrays */
  double   *comm = 0, *dd = 0, *dl = 0, *du = 0, *du2 = 0, *eigvr = 0;
  double   *eigvi = 0, *eigest = 0, *resid = 0, *x2 = 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_option (f12adc) Example "
          "Program Results\n");
  /* Skip heading in data file */
  scanf("%*[^\n] ");
  /* Read problem parameter values from data file. */
  scanf("%ld%ld%ld%lf%lf%lf%*[^\n] ", &nx, &nev, &ncv,
         &rho, &sigmar, &sigmai);
  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)) ||
      !(dd = NAG_ALLOC(n, double)) ||
      !(dl = NAG_ALLOC(n, double)) ||
      !(du = NAG_ALLOC(n, double)) ||
      !(du2 = NAG_ALLOC(n, double)) ||
      !(resid = NAG_ALLOC(n, double)) ||
      !(v = NAG_ALLOC(n * ncv, double)) ||
      !(x2 = NAG_ALLOC(n, 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);
  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 problem type using
     nag_real_sparse_eigensystem_option (f12adc). */
  nag_real_sparse_eigensystem_option("GENERALIZED", icomm, comm, &fail);
  /* Construct C = A - SIGMA*I, and factor C using my_dgttrf. */
  h = 1.0 / (double)(n + 1);
  s = rho / 2.0;
  s1 = -1.0 / h - s - sigmar * h / 6.0;
  s2 = 2.0 / h - sigmar * 4.0 * h / 6.0;
  s3 = -1.0 / h + s - sigmar * h / 6.0;
  for (j = 0; j <= n - 2; ++j)
    {
      dl[j] = s1;
      dd[j] = s2;
      du[j] = s3;
    }
  dd[n - 1] = s2;

  my_dgttrf(n, dl, dd, du, du2, 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  y <--- OP*x = inv[A-SIGMA*M]*M*x using
             my_dggtrs */
          mv(n, x, x2);
          my_dgttrs(n, dl, dd, du, du2, ipiv, x2, y);
        }
      else if (irevcm == 1)
        {
          /* Perform  y <--- OP*x = inv[A-SIGMA*M]*M*x where
             mx is available. */
          my_dgttrs(n, dl, dd, du, du2, ipiv, mx, y);
        }
      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);
      /* Print computed eigenvalues. */

      printf("\n The %4ld generalized Ritz values closest", nconv);
      printf(" to  unity are:\n\n");
      for (j = 0; j <= nconv-1; ++j)
        {
          printf("%8ld%5s( %12.4f ,%12.4f )\n", j+1, "",
                  sigmar + 1.0/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:
  if (comm) NAG_FREE(comm);
  if (eigvr) NAG_FREE(eigvr);
  if (eigvi) NAG_FREE(eigvi);
  if (eigest) NAG_FREE(eigest);
  if (dd) NAG_FREE(dd);
  if (dl) NAG_FREE(dl);
  if (du) NAG_FREE(du);
  if (du2) NAG_FREE(du2);
  if (resid) NAG_FREE(resid);
  if (v) NAG_FREE(v);
  if (icomm) NAG_FREE(icomm);
  if (ipiv) NAG_FREE(ipiv);
  if (x2) NAG_FREE(x2);
  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 */
  double  h;
  Integer j;

  /* Function Body */
  h = 1.0 / (double)(6*(n + 1));
  y[0] = h*(v[0] * 4.0 + v[1]);
  for (j = 1; j <= n - 2; ++j)
    {
      y[j] = h*(v[j-1] + v[j] * 4.0 + v[j+1]);
    }
  y[n-1] = h*(v[n-2] + v[n-1] * 4.0);
  return;
} /* mv */

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;
}