/* nag_ode_bvp_fd_nonlin_gen (d02rac) Example Program.
 *
 * Copyright 1992 Numerical Algorithms Group.
 *
 * Mark 3, 1992.
 * Mark 7 revised, 2001.
 * Mark 8 revised, 2004.
 *
 */

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

#ifdef __cplusplus
extern "C" {
#endif
  static void fcn(Integer neq, double x, double eps, double y[], double f[],
                  Nag_User *comm);
  static void g(Integer neq, double eps, double ya[], double yb[],
                double bc[], Nag_User *comm);
  static void jaceps(Integer neq, double x, double eps, double y[], double f[],
                     Nag_User *comm);
  static void jacgep(Integer neq, double eps, double ya[], double yb[],
                     double bcep[], Nag_User *comm);
  static void jacobf(Integer neq, double x, double eps, double y[],
                     double f[], Nag_User *comm);
  static void jacobg(Integer neq, double eps, double ya[], double yb[],
                     double aj[], double bj[], Nag_User *comm);
#ifdef __cplusplus
}
#endif

#define NEQ 3
#define MNP 40

#define Y(I,J) y[(I)*tdy + J]
int main(void)
{

  double *abt=0;
  double deleps;
  double tol;
  double *x=0, *y=0;
  Integer exit_status=0;
  Integer i, j;
  Integer np;
  Integer numbeg, nummix;
  Integer neq, mnp, tdy;
  Nag_User comm;
  NagError fail;

  INIT_FAIL(fail);

  Vprintf("nag_ode_bvp_fd_nonlin_gen (d02rac) Example Program Results\n");
  Vprintf("\nCalculation using analytic Jacobians\n\n");
  neq = NEQ;
  mnp = MNP;
  if (neq>=1)
    {
      if ( !( abt = NAG_ALLOC(neq, double)) ||
           !( x = NAG_ALLOC(mnp, double)) ||
           !( y = NAG_ALLOC(neq*mnp, double)) )
        {
          Vprintf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
      tdy = mnp;
    }
  else
    {
      exit_status = 1;
      return exit_status;
    }
  tol = 1.0e-4;
  np = 17;
  numbeg = 2;
  nummix = 0;
  x[0] = 0.0;
  x[np-1] = 10.0;
  deleps = 0.1;

  /* nag_ode_bvp_fd_nonlin_gen (d02rac).
   * Ordinary differential equations solver, for general
   * nonlinear two-point boundary value problems, using a
   * finite difference technique with deferred correction
   */
  nag_ode_bvp_fd_nonlin_gen(neq, &deleps, fcn, numbeg, nummix, g,
                            Nag_DefInitMesh, mnp, &np, x, y, tol, abt, jacobf,
                            jacobg, jaceps, jacgep, &comm, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_ode_bvp_fd_nonlin_gen (d02rac).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

  Vprintf("Solution on final mesh of %ld points \n", np);
  Vprintf("      X           Y(1)        Y(2)        Y(3)\n");

  for (j=0; j< np; ++j)
    {
      Vprintf(" %9.3f ", x[j]);
      for (i=0; i<neq; ++i)
        Vprintf("   %9.4f", Y(i,j));
      Vprintf("\n");
    }

  Vprintf("\n\nMaximum estimated error by components \n");

  for (i=1; i<=3; ++i)
    Vprintf(" %9.2e", abt[i-1]);
  Vprintf(" \n");

 END:
  if (abt) NAG_FREE(abt);
  if (x) NAG_FREE(x);
  if (y) NAG_FREE(y);
  return exit_status;
}
#undef Y
static void fcn(Integer neq, double x, double eps, double y[], double f[],
                Nag_User *comm)
{
  f[0] = y[1];
  f[1] = y[2];
  f[2] = -y[0] * y[2] - (1.0 - y[1]*y[1])*2.0*eps;

}
static void g(Integer neq, double eps, double ya[], double yb[],
              double bc[], Nag_User *comm)
{
  bc[0] = ya[0];
  bc[1] = ya[1];
  bc[2] = yb[1] - 1.0;
}                               /* g */
static void jaceps(Integer neq, double x, double eps, double y[],
                   double f[], Nag_User *comm)
{
  f[0] = 0.0;
  f[1] = 0.0;
  f[2] = (1.0 - y[1]*y[1]) * -2.0;
}
static void jacgep(Integer neq, double eps, double ya[], double yb[],
                   double bcep[], Nag_User *comm)
{
  Integer i;

  for (i=0; i< neq; ++i)
    bcep[i] = 0.0;

}
static void jacobf(Integer neq, double x, double eps, double y[],
                   double f[], Nag_User *comm)
{

  Integer i, j;

#define Y(I) y[(I)-1]
#define F(I,J) f[((I)-1)*neq+(J)-1]

  for (i=1; i<= neq; ++i)
    {
      for (j=1; j<= neq; ++j)
        F(i, j) = 0.0;
    }
  F(1,2) = 1.0;
  F(2,3) = 1.0;
  F(3,1) = -Y(3);
  F(3,2) = Y(2) * 4.0 * eps;
  F(3,3) = -Y(1);
}
static void jacobg(Integer neq, double eps, double ya[], double yb[],
                   double aj[], double bj[], Nag_User *comm)
{
  Integer i, j;
#define YA(I) ya[(I)-1]
#define YB(I) yb[(I)-1]
#define AJ(I,J) aj[((I)-1)*neq+(J)-1]
#define BJ(I,J) bj[((I)-1)*neq+(J)-1]

  for (i=1; i<= neq; ++i)
    for (j=1; j<= neq; ++j)
      {
        AJ(i,j) = 0.0;
        BJ(i,j) = 0.0;
      }
  AJ(1,1) = 1.0;
  AJ(2,2) = 1.0;
  BJ(3,2) = 1.0;
}