/* nag_ode_dae_dassl_setup (d02mwc) Example Program.
 *
 * Copyright 2019 Numerical Algorithms Group.
 *
 * Mark 27.0, 2019.
 *
 */

/* Pre-processor includes */
#include <stdio.h>
#include <math.h>
#include <nag.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);
#ifdef __cplusplus
}
#endif
int main(void)
{
  /* Scalars */
  Integer exit_status = 0;
  Integer i, itask, neq, maxord, licom, lcom;
  double h0, hmax, g1, g2, t, tout;
  /* Arrays */
  static double ruser[2] = { -1.0, -1.0 };
  Integer *icom = 0;
  double *atol = 0, *com = 0, *rtol = 0, *y = 0, *ydot = 0;
  /* NAG types */
  Nag_Boolean vector_tol;
  Nag_Comm comm;
  NagError fail;

  INIT_FAIL(fail);

  printf("nag_ode_dae_dassl_setup (d02mwc) Example Program Results\n\n");

  /* For communication with user-supplied functions: */
  comm.user = ruser;

  /* Set problem size and allocate accordingly */
  neq = 5;
  maxord = 5;
  licom = 50 + neq;
  lcom = 40 + (maxord + 4 + neq) * neq;
  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)) || !(icom = NAG_ALLOC(licom, Integer)))
  {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Use vector of tolerances */
  vector_tol = Nag_TRUE;
  for (i = 0; i < neq; i++) {
    rtol[i] = 1.00e-8;
    atol[i] = 1.00e-8;
  }
  /* Set up integrator to use supplied Jacobian, default step-sizes and
   * vector tolerances using nag_ode_dae_dassl_setup (d02mwc).
   */
  h0 = 0.0;
  hmax = 0.0;
  nag_ode_dae_dassl_setup(neq, maxord, Nag_AnalyticalJacobian, hmax, h0,
                          vector_tol, icom, licom, com, lcom, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_ode_dae_dassl_setup (d02mwc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Set initial values */
  y[0] = 1.0;
  y[1] = 0.0;
  y[2] = 0.0;
  y[3] = 1.0;
  y[4] = 1.0;
  for (i = 0; i < neq; i++)
    ydot[i] = 0.0;
  t = 0.0;
  tout = 1.0;

  /* Print header and initial values */
  printf("%7s%12s%12s%12s%12s%12s\n", "t", "y_1", "y_2", "y_3", "y_4", "y_5");
  printf("   %6.4f", t);
  for (i = 0; i < neq; i++)
    printf("%11.6f%s", y[i], (i + 1) % 5 ? " " : "\n");

  itask = 0;
  while ((itask >= 0) && (itask <= 3) && (t < tout)) {
    /* Integrate using  nag_ode_dae_dassl_gen (d02nec). */
    nag_ode_dae_dassl_gen(neq, &t, tout, y, ydot, rtol, atol, &itask, res,
                          jac, icom, com, lcom, &comm, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_ode_dae_dassl_gen (d02nec).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }
    else {
      printf("   %6.4f", t);
      for (i = 0; i < neq; i++)
        printf("%11.6f%s", y[i], (i + 1) % 5 ? " " : "\n");
      printf("\n  d02nec  returned with ITASK = %4" NAG_IFMT "\n\n", itask);
    }
  }
  if ((itask >= 0) && (itask <= 3)) {
    g1 = y[0] * y[0] + y[1] * y[1] - 1.0;
    g2 = y[0] * y[2] + y[1] * y[3];
    printf("  The position-level constraint G1 =  %13.4e\n", g1);
    printf("  The velocity-level constraint G2 =  %13.4e\n", g2);
  }

END:
  NAG_FREE(atol);
  NAG_FREE(com);
  NAG_FREE(rtol);
  NAG_FREE(y);
  NAG_FREE(ydot);
  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)
{
  if (comm->user[0] == -1.0) {
    printf("(User-supplied callback res, first invocation.)\n");
    comm->user[0] = 0.0;
  }
  r[0] = y[2] - ydot[0];
  r[1] = y[3] - ydot[1];
  r[2] = -y[4] * y[0] - ydot[2];
  r[3] = -y[4] * y[1] - ydot[3] - 1.0;
  r[4] = y[2] * y[2] + y[3] * y[3] - y[4] - y[1];
  return;
}

static void NAG_CALL jac(Integer neq, double t, const double y[],
                         const double ydot[], double *pd, double cj,
                         Nag_Comm *comm)
{
  Integer pdpd;
  if (comm->user[1] == -1.0) {
    printf("(User-supplied callback jac, first invocation.)\n");
    comm->user[1] = 0.0;
  }
  pdpd = neq;
#define PD(I, J) pd[(J-1)*pdpd + I-1]
  PD(1, 1) = -cj;
  PD(1, 3) = 1.0;
  PD(2, 2) = -cj;
  PD(2, 4) = 1.0;
  PD(3, 1) = -y[4];
  PD(3, 3) = -cj;
  PD(3, 5) = -y[0];
  PD(4, 2) = -y[4];
  PD(4, 4) = -cj;
  PD(4, 5) = -y[1];
  PD(5, 2) = -1.0;
  PD(5, 3) = 2.0 * y[2];
  PD(5, 4) = 2.0 * y[3];
  PD(5, 5) = -1.0;
  return;
}