/* nag_dae_ivp_dassl_gen (d02nec) Example Program.
 *
 * Copyright 2009, Numerical Algorithms Group.
 *
 * Mark 9, 2009.
 *
 */

/* Pre-processor includes */
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <nag.h>
#include <nagx04.h>
#include <nag_stdlib.h>
#include <nagd02.h>

#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL res(Integer neq, double t, const double y[],
                         const double ydot[], double r[], Integer *ires,
                         Nag_Comm *comm);
static void NAG_CALL jac(Integer neq, double t, const double y[],
                         const double ydot[], double *pd, double cj,
                         Nag_Comm *comm);
static void NAG_CALL myjac(Integer neq, Integer ml, Integer mu, double t,
                           const double y[], const double ydot[], double *pd,
                           double cj);
#ifdef __cplusplus
}
#endif
int main(int argc, char *argv[])
{
  FILE        *fpout;
  /*Integer scalar and array declarations */
  Integer     exit_status = 0, maxord = 5;
  Nag_Comm    comm;
  Integer     neq, licom, mu, ml, lcom;
  Integer     i, itask, j;
  Nag_Boolean vector_tol;
  Integer     *icom = 0;
  NagError    fail;
  /*Double scalar and array declarations */
  double      dt, h0, hmax, t, tout;
  double      *atol = 0, *com = 0, *rtol = 0, *y = 0, *ydot = 0;

  INIT_FAIL(fail);

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

  fprintf(fpout, "nag_dae_ivp_dassl_gen (d02nec) Example Program Results\n\n");

  /* Set problem parameters required to allocate arrays */
  neq = 3;
  ml = 1;
  mu = 2;
  licom = 50+neq;
  lcom = 40+(maxord+4)*neq+(2*ml+mu+1)*neq+2*(neq/(ml+mu+1)+1);
  if (
    !(atol = NAG_ALLOC(neq, double)) ||
    !(com = NAG_ALLOC(lcom, double)) ||
    !(rtol = NAG_ALLOC(neq, double)) ||
    !(y = NAG_ALLOC(neq, double)) ||
    !(ydot = NAG_ALLOC(neq, double)) ||
    !(comm.iuser = NAG_ALLOC(2, Integer)) ||
    !(icom = NAG_ALLOC(licom, Integer)))
    {
      fprintf(fpout, "Allocation failure\n");
      exit_status = -1;
      goto END;
    }
  /* Initialize the problem, specifying that the Jacobian is to be */
  /* evaluated analytically using the provided routine jac.        */
  h0 = 0.0;
  hmax = 0.0;
  vector_tol = Nag_TRUE;
  /*
   * nag_dae_ivp_dassl_setup (d02mwc)
   * Implicit DAE/ODEs, stiff ivp, setup for nag_dae_ivp_dassl_gen (d02nec)
   */
  nag_dae_ivp_dassl_setup(neq, maxord, Nag_AnalyticalJacobian, hmax, h0,
                          vector_tol, icom, licom, com, lcom, &fail);
  if (fail.code != NE_NOERROR)
    {
      fprintf(fpout, "Error from nag_dae_ivp_dassl_setup (d02mwc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }
  /* Specify that the Jacobian is banded.
   *
   * nag_dae_ivp_dassl_linalg (d02npc)
   * ODE/DAEs, ivp, linear algebra setup routine for
   * nag_dae_ivp_dassl_gen (d02nec)
   */
  nag_dae_ivp_dassl_linalg(neq, ml, mu, icom, licom, &fail);
  if (fail.code != NE_NOERROR)
    {
      fprintf(fpout, "Error from nag_dae_ivp_dassl_linalg (d02npc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

  /* Set initial values*/
  t = 0.00e0;
  tout = 0.00e0;
  dt = 0.020e0;
  for (i = 0; i < neq; i++)
    {
      rtol[i] = 1.00e-3;
      atol[i] = 1.00e-6;
      y[i] = 0.00e0;
      ydot[i] = 0.00e0;
    }
  y[0] = 1.00e0;
  /* Use the comm.iuser array to pass the band dimensions through to jac. */
  /* An alternative would be to hard code values for ml and mu in jac.    */
  comm.iuser[0] = ml;
  comm.iuser[1] = mu;
  fprintf(fpout, "    t          y(1)         y(2)         y(3)\n");
  fprintf(fpout, "%8.4f", t);
  for (i = 0; i < neq; i++)
    fprintf(fpout, "%12.6f%s", y[i], (i+1)%3?" ":"\n");
  itask = 0;
  /*     Obtain the solution at 5 equally spaced values of t.*/
  for (j = 0; j < 5; j++)
    {
      tout = tout + dt;
      /*
       * nag_dae_ivp_dassl_gen (d02nec)
       * dassl integrator
       */
      nag_dae_ivp_dassl_gen(neq, &t, tout, y, ydot, rtol, atol, &itask, res,
                            jac, icom, com, lcom, &comm, &fail);
      if (fail.code != NE_NOERROR)
        {
          fprintf(fpout, "Error from nag_dae_ivp_dassl_gen (d02nec).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }
      fprintf(fpout, "%8.4f", t);
      for (i = 0; i < neq; i++)
        fprintf(fpout, "%12.6f%s", y[i], (i+1)%3?" ":"\n");
      /*
       * nag_dae_ivp_dassl_cont (d02mcc)
       * dassl method continuation resetting function
       */
      nag_dae_ivp_dassl_cont(icom);
    }
  fprintf(fpout, "\n");
  fprintf(fpout, "  The integrator completed task, ITASK = %4ld\n", itask);

 END:
  if (fpout != stdout) fclose(fpout);
  if (atol) NAG_FREE(atol);
  if (com) NAG_FREE(com);
  if (rtol) NAG_FREE(rtol);
  if (y) NAG_FREE(y);
  if (ydot) NAG_FREE(ydot);
  if (comm.iuser) NAG_FREE(comm.iuser);
  if (icom) NAG_FREE(icom);

  return exit_status;
}

static void NAG_CALL res(Integer neq, double t, const double y[],
                         const double ydot[], double r[], Integer *ires,
                         Nag_Comm *comm)
{
  r[0] = (-(0.040e0*y[0])) + 1.00e4*y[1]*y[2] - ydot[0];
  r[1] = 0.040e0*y[0] - 1.00e4*y[1]*y[2]-3.00e7*y[1]*y[1] - ydot[1];
  r[2] = 3.00e7*y[1]*y[1] - ydot[2];
  return;
}
static void NAG_CALL jac(Integer neq, double t, const double y[],
                         const double ydot[], double *pd, double cj,
                         Nag_Comm *comm)
{
  Integer ml, mu;
  ml = comm->iuser[0];
  mu = comm->iuser[1];
  myjac(neq, ml, mu, t, y, ydot, pd, cj);
  return;
}
static void NAG_CALL myjac(Integer neq, Integer ml, Integer mu, double t,
                           const double y[], const double ydot[], double *pd,
                           double cj)
{
  Integer md, ms;
  Integer pdpd;
  pdpd = 2*ml+mu+1;
#define PD(I, J) pd[(J-1)*pdpd + I - 1]
  /*     Main diagonal PDFULL(i,i), i=1,neq*/
  md = mu + ml + 1;
  PD(md, 1) = -0.040e0 - cj;
  PD(md, 2) = -1.00e4*y[2] - 6.00e7*y[1] - cj;
  PD(md, 3) = -cj;
  /*     1 Sub-diagonal PDFULL(i+1:i), i=1,neq-1*/
  ms = md + ml;
  PD(ms, 1) = 0.040e0;
  PD(ms, 2) = 6.00e7*y[1];
  /*     First super-diagonal PDFULL(i-1,i), i=2, neq*/
  ms = md - 1;
  PD(ms, 2) = 1.00e4*y[2];
  PD(ms, 3) = -1.00e4*y[1];
  /*     Second super-diagonal PDFULL(i-2,i), i=3, neq*/
  ms = md-2;
  PD(ms, 3) = 1.00e4*y[1];
  return;
}