/* nag_real_sparse_eigensystem_monit (f12aec) Example Program.
 *
 * Copyright 2005 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);

  Vprintf("nag_real_sparse_eigensystem_monit (f12aec) Example Program Results"
          "\n");
  /* Skip heading in data file */
  Vscanf("%*[^\n] ");

  /* Read problem parameter values from data file. */
  Vscanf("%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)) )
    {
      Vprintf("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);
  /* 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);
          Vprintf("Iteration %3ld, ", niter);
          Vprintf(" No. converged = %3ld,", nconv);
          Vprintf(" norm of estimates = %16.8e\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. */
      Vprintf("\n The %4ld generalized Ritz values closest", nconv);
      Vprintf(" to ( %8.4f ,  %8.4f ) are:\n\n", sigmar, sigmai);
      for (j = 0; j <= nconv-1; ++j)
        {
          Vprintf("%8ld%5s( %7.4f, %7.4f )\n", j+1, "",
                  eigvr[j],eigvi[j]);
        }
    }
  else
    {
      Vprintf(" Error from nag_real_sparse_eigensystem_iter (f12abc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }
 END:
  if (cdd) NAG_FREE(cdd);
  if (cdl) NAG_FREE(cdl);
  if (cdu) NAG_FREE(cdu);
  if (cdu2) NAG_FREE(cdu2);
  if (ctemp) NAG_FREE(ctemp);
  if (comm) NAG_FREE(comm);
  if (eigvr) NAG_FREE(eigvr);
  if (eigvi) NAG_FREE(eigvi);
  if (eigest) NAG_FREE(eigest);
  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 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)) )
    {
      Vprintf("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:
  if (ax) 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)) )
    {
      Vprintf("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:
  if (mx) 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;
}