/* nag_complex_sparse_eigensystem_sol (f12aqc) Example Program.
 *
 * Copyright 2005 Numerical Algorithms Group.
 *
 * Mark 8, 2005.
 */

#include <math.h>
#include <nag.h>
#include <nagx04.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 rho = { 10., 0. };


static void av(Integer, Complex *, Complex *);
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(int argc, char *argv[])
{
  FILE     *fpin, *fpout;

  /* Constants */
  Integer  licomm = 140, imon = 0;

  /* Scalars */
  Complex  h, h4, sigma;
  double   estnrm, hr;
  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;

  /* Assign to Complex type using nag_complex (a02bac) */
  sigma = nag_complex(0.0, 0.0);
  exit_status = 0;
  INIT_FAIL(fail);

  /* Check for command-line IO options */
  fpin = nag_example_file_io(argc, argv, "-data", NULL);
  fpout = nag_example_file_io(argc, argv, "-results", NULL);

  fprintf(fpout, "nag_complex_sparse_eigensystem_sol (f12aqc) Example "
          "Program Results\n");
  /* Skip heading in data file */
  fscanf(fpin, "%*[^\n] ");

  fscanf(fpin, "%ld%ld%ld%*[^\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)))
    {
      fprintf(fpout, "Allocation failure\n");
      exit_status = -1;
      goto END;
    }
  /* Initialise 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)
    {
      fprintf(fpout, "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("REGULAR INVERSE",
                                        icomm, comm, &fail);
  /* Select the problem type using
     nag_complex_sparse_eigensystem_option (f12arc). */
  nag_complex_sparse_eigensystem_option("GENERALIZED", icomm,
                                        comm, &fail);
  hr = 1.0/(double)(n+1);
  /* Assign to Complex type using nag_complex (a02bac) */
  h = nag_complex(hr, 0.0);
  h4 = nag_complex(4.0 * hr, 0.0);

  for (j = 0; j <= n - 2; ++j)
    {
      dl[j] = h;
      dd[j] = h4;
      du[j] = h;
    }
  dd[n - 1] = h4;

  my_zgttrf(n, dl, dd, du, du2, ipiv, &info);
  if (fail.code != NE_NOERROR)
    {
      fprintf(fpout, " Error from nag_zgttrf.\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  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 || irevcm == 1)
        {
          /* Perform  y <--- OP*x = inv[M]*A*x      | */
          av(nx, x, y);
          my_zgttrs(n, dl, dd, du, du2, ipiv, y);
          if (fail.code != NE_NOERROR)
            {
              fprintf(fpout, " Error from nag_zgttrs.\n%s\n", fail.message);
              exit_status = 1;
              goto END;
            }
        }
      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);
          fprintf(fpout, " Iteration %3ld, ", niter);
          fprintf(fpout, " No. converged = %3ld,", nconv);
          fprintf(fpout, " 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. */
      nag_complex_sparse_eigensystem_sol(&nconv, eigv, v, sigma,
                                         resid, v, comm, icomm,
                                         &fail);

      fprintf(fpout, "\n");
      fprintf(fpout, " The %4ld", nconv);
      fprintf(fpout, " Ritz values of largest magnitude are:\n\n");
      for (j = 0; j <= nconv-1; ++j)
        {
          fprintf(fpout, "%8ld%5s( %12.4f , %12.4f )\n", j+1, "",
                  eigv[j].re, eigv[j].im);
        }
    }
  else
    {
      fprintf(fpout, " Error from nag_complex_sparse_eigensystem_iter "
              "(f12apc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
 END:
  if (fpin != stdin) fclose(fpin);
  if (fpout != stdout) fclose(fpout);
  if (comm) NAG_FREE(comm);
  if (eigv) NAG_FREE(eigv);
  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);
  return exit_status;
}

static void av(Integer nx, Complex *v, Complex *y)
{
  /* Scalars */
  Complex dd, dl, du, z1, z2, z3;
  double  hr1, sr;
  Integer j, n;

  /* Function Body */
  n = nx * nx;
  hr1 = (double)(n+1);
  sr = 0.5*rho.re;
  /* Assign to Complex type using nag_complex (a02bac) */
  dd = nag_complex(2.0*hr1, 0.0); /* dd = 2.0/h */
  dl = nag_complex(-hr1-sr, 0.0); /* dl = -1.0/h - rho/2 */
  du = nag_complex(-hr1+sr, 0.0); /* du = -1.0/h + rho/2 */
  /* w[0] = dd*v[0] + du*v[1] */
  /* Compute Complex multiply using nag_complex_multiply (a02ccc). */
  z1 = nag_complex_multiply(dd, v[0]);
  z2 = nag_complex_multiply(du, v[1]);
  /* Compute Complex addition using nag_complex_add (a02cac). */
  y[0] = nag_complex_add(z1, z2);
  for (j = 1; j <= n - 2; ++j)
    {
      /* y[j] = dl*V[j-1] + dd*V[j] + du*v[j+1] */
      /* Compute Complex multiply using nag_complex_multiply
         (a02ccc). */
      z1 = nag_complex_multiply(dl, v[j-1]);
      z2 = nag_complex_multiply(dd, v[j]);
      z3 = nag_complex_multiply(du, v[j+1]);
      /* Compute Complex addition using nag_complex_add
         (a02cac). */
      z1 = nag_complex_add(z1, z2);
      y[j] = nag_complex_add(z1, z3);
    }
  /* y[n-1] = dl*v[n-2] + dd*v[n-1] */
  /* Compute Complex multiply using nag_complex_multiply (a02ccc). */
  z1 = nag_complex_multiply(dl, v[n-2]);
  z2 = nag_complex_multiply(dd, v[n-1]);
  /* Compute Complex addition using nag_complex_add (a02cac). */
  y[n-1] = nag_complex_add(z1, z2);
  return;
} /* av */


static void mv(Integer nx, Complex *v, Complex *y)
{
  /* Scalars */
  Complex oneh, fourh, z1, z2;
  double  hr;
  Integer j, n;

  /* Function Body */
  n = nx * nx;
  hr = 1.0/(double)(n+1);
  /* Assign to Complex type using nag_complex (a02bac) */
  oneh = nag_complex(hr, 0.0);
  fourh = nag_complex(4.0*hr, 0.0);
  /* y[0] = h*(four*v[0] + one*v[1]) */
  /* Compute Complex multiply using nag_complex_multiply
     (a02ccc). */
  z1 = nag_complex_multiply(fourh, v[0]);
  z2 = nag_complex_multiply(oneh, v[1]);
  /* Compute Complex addition using nag_complex_add (a02cac). */
  y[0] = nag_complex_add(z1, z2);
  for (j = 1; j <= n - 2; ++j)
    {
      /* y[j] = h*(one*v[j-1] + four*v[j] + one*v[j+1]) */
      /* Compute Complex multiply using nag_complex_multiply
         (a02ccc). */
      z1 = nag_complex_multiply(fourh, v[j]);
      /* Compute Complex addition using nag_complex_add
         (a02cac). */
      z2 = nag_complex_add(v[j-1], v[j+1]);
      z2 = nag_complex_multiply(oneh, z2);
      y[j] = nag_complex_add(z1, z2);
    }
  /* y[n-1] = h*(one*v[n-2] + four*v[n-1]) */
  /* Compute Complex multiply using nag_complex_multiply
     (a02ccc). */
  z1 = nag_complex_multiply(fourh, v[n-1]);
  z2 = nag_complex_multiply(oneh, v[n-2]);
  /* Compute Complex addition using nag_complex_add (a02cac). */
  y[n-1] = nag_complex_add(z1, z2);
  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]);
      /* 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;
}