/* nag_ode_ivp_bdf_gen (d02ejc) Example Program.
 *
 * Copyright 1992 Numerical Algorithms Group.
 *
 * Mark 3, 1992.
 * Mark 7 revised, 2001.
 * Mark 8 revised, 2004.
 *
 */

#include <nag.h>
#include <math.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <nagd02.h>


#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL fcn(Integer neq, double x, const double y[], double f[],
                         Nag_User *comm);
static void NAG_CALL pederv(Integer neq, double x, const double y[], double pw[],
                            Nag_User *comm);
static double NAG_CALL g(Integer neq, double x, const double y[], Nag_User *comm);
static void NAG_CALL out(Integer neq, double *tsol, const double y[],
                         Nag_User *comm);
#ifdef __cplusplus
}
#endif

struct user
{
  double  xend, h;
  Integer k;
};

#define NEQ 3
int main(void)
{
  Integer     exit_status = 0, i, j, neq;
  NagError    fail;
  Nag_User    comm;
  double      tol, x, *y = 0;
  struct user s;

  INIT_FAIL(fail);

  printf("nag_ode_ivp_bdf_gen (d02ejc) Example Program Results\n");

  /* For communication with function out()
   * assign address of user defined structure
   * to comm.p.
   */
  comm.p = (Pointer)&s;

  neq = NEQ;
  if (neq >= 1)
    {
      if (!(y = NAG_ALLOC(neq, double)))
        {
          printf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
    }
  else
    {
      exit_status = 1;
      return exit_status;
    }
  s.xend = 10.0;
  printf("\nCase 1: calculating Jacobian internally\n");
  printf(" intermediate output, root-finding\n\n");

  for (j = 3; j <= 4; ++j)
    {
      tol = pow(10.0, -(double) j);
      printf("\n Calculation with tol = %10.1e\n", tol);
      x = 0.0;
      y[0] = 1.0;
      y[1] = 0.0;
      y[2] = 0.0;
      s.k = 4;
      s.h = (s.xend-x) /(double)(s.k+1);
      printf("     X         Y(1)         Y(2)         Y(3)\n");
      /* nag_ode_ivp_bdf_gen (d02ejc).
       * Ordinary differential equations solver, stiff, initial
       * value problems using the Backward Differentiation
       * Formulae
       */
      nag_ode_ivp_bdf_gen(neq, fcn, NULLFN, &x, y, s.xend, tol, Nag_Relative,
                          out, g, &comm, &fail);
      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_ode_ivp_bdf_gen (d02ejc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }
      printf("  Root of Y(1)-0.9 at %5.3f\n", x);
      printf("  Solution is ");
      for (i = 0; i < 3; ++i)
        printf("%7.5f ", y[i]);
      printf("\n");
    }
  printf("\nCase 2: calculating Jacobian by pederv\n");
  printf(" intermediate output, root-finding\n\n");

  for (j = 3; j <= 4; ++j)
    {
      tol = pow(10.0, -(double) j);
      printf("\n Calculation with tol = %10.1e\n", tol);
      x = 0.0;
      y[0] = 1.0;
      y[1] = 0.0;
      y[2] = 0.0;
      s.k = 4;
      s.h = (s.xend-x) /(double)(s.k+1);
      printf("     X         Y(1)         Y(2)         Y(3)\n");
      /* nag_ode_ivp_bdf_gen (d02ejc), see above. */
      nag_ode_ivp_bdf_gen(neq, fcn, pederv, &x, y, s.xend, tol, Nag_Relative,
                          out, g, &comm, &fail);
      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_ode_ivp_bdf_gen (d02ejc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }
      printf("  Root of Y(1)-0.9 at %5.3f\n", x);
      printf("  Solution is ");
      for (i = 0; i < 3; ++i)
        printf("%7.5f ", y[i]);
      printf("\n");
    }
  printf("\nCase 3: calculating Jacobian internally\n");
  printf(" no intermediate output, root-finding\n\n");
  for (j = 3; j <= 4; ++j)
    {
      tol = pow(10.0, -(double) j);
      printf("\n Calculation with tol = %10.1e\n", tol);
      x = 0.0;
      y[0] = 1.0;
      y[1] = 0.0;
      y[2] = 0.0;

      /* nag_ode_ivp_bdf_gen (d02ejc), see above. */
      nag_ode_ivp_bdf_gen(neq, fcn, NULLFN, &x, y, s.xend, tol, Nag_Relative,
                          NULLFN, g, &comm, &fail);
      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_ode_ivp_bdf_gen (d02ejc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }

      printf("  Root of Y(1)-0.9 at %5.3f\n", x);
      printf("  Solution is ");
      for (i = 0; i < 3; ++i)
        printf("%7.5f ", y[i]);
      printf("\n");
    }
  printf("\nCase 4: calculating Jacobian internally\n");
  printf(" intermediate output, no root-finding\n\n");

  for (j = 3; j <= 4; ++j)
    {
      tol = pow(10.0, -(double) j);
      printf("\n Calculation with tol = %10.1e\n", tol);
      x = 0.0;
      y[0] = 1.0;
      y[1] = 0.0;
      y[2] = 0.0;
      s.k = 4;
      s.h = (s.xend-x) /(double)(s.k+1);
      printf("     X         Y(1)         Y(2)         Y(3)\n");
      /* nag_ode_ivp_bdf_gen (d02ejc), see above. */
      nag_ode_ivp_bdf_gen(neq, fcn, NULLFN, &x, y, s.xend, tol, Nag_Relative,
                          out, NULLDFN, &comm, &fail);
      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_ode_ivp_bdf_gen (d02ejc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }
      printf("%8.2f", x);
      for (i = 0; i < 3; ++i)
        printf("%13.5f", y[i]);
      printf("\n");
    }

  printf("\nCase 5: calculating Jacobian internally\n");
  printf(
          " no intermediate output, no root-finding (integrate to xend)\n\n");

  for (j = 3; j <= 4; ++j)
    {
      tol = pow(10.0, -(double) j);
      printf("\n Calculation with tol = %10.1e\n", tol);
      x = 0.0;
      y[0] = 1.0;
      y[1] = 0.0;
      y[2] = 0.0;
      printf("     X         Y(1)         Y(2)         Y(3)\n");
      printf("%8.2f", x);
      for (i = 0; i < 3; ++i)
        printf("%13.5f", y[i]);
      printf("\n");
      /* nag_ode_ivp_bdf_gen (d02ejc), see above. */
      nag_ode_ivp_bdf_gen(neq, fcn, NULLFN, &x, y, s.xend, tol, Nag_Relative,
                          NULLFN, NULLDFN, &comm, &fail);
      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_ode_ivp_bdf_gen (d02ejc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }
      printf("%8.2f", x);
      for (i = 0; i < 3; ++i)
        printf("%13.5f", y[i]);
      printf("\n");
    }
 END:
  if (y) NAG_FREE(y);
  return exit_status;
}

static void NAG_CALL fcn(Integer neq, double x, const double y[], double f[],
                         Nag_User *comm)
{
  f[0] = y[0] * -0.04 + y[1] * 1e4 * y[2];
  f[1] = y[0] * 0.04 - y[1] * 1e4 * y[2] - y[1] * 3e7 * y[1];
  f[2] = y[1] * 3e7 * y[1];
}

static void NAG_CALL pederv(Integer neq, double x, const double y[], double pw[],
                            Nag_User *comm)
{
#define PW(I, J) pw[((I) -1)*neq + (J) -1]

  PW(1, 1) = -0.04;
  PW(1, 2) = y[2] * 1e4;
  PW(1, 3) = y[1] * 1e4;
  PW(2, 1) = 0.04;
  PW(2, 2) = y[2] * -1e4 - y[1] * 6e7;
  PW(2, 3) = y[1] * -1e4;
  PW(3, 1) = 0.0;
  PW(3, 2) = y[1] * 6e7;
  PW(3, 3) = 0.0;
}

static double NAG_CALL g(Integer neq, double x, const double y[], Nag_User *comm)
{
  return y[0]-0.9;
}

static void NAG_CALL out(Integer neq, double *xsol, const double y[],
                         Nag_User *comm)
{
  Integer     j;
  struct user *s = (struct user *) comm->p;

  printf("%8.2f", *xsol);
  for (j = 0; j < 3; ++j)
    printf("%13.5f", y[j]);
  printf("\n");

  *xsol = s->xend - (double) s->k * s->h;
  s->k--;
}