/* nag_ode_ivp_adams_zero_simple (d02cjc) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 *
 * Mark 28.3, 2022.
 *
 */

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

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

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

int main(void) {
  static Integer use_comm[2] = {1, 1};
  Integer exit_status = 0, i, j, neq;
  Nag_User comm;
  double pi, tol, x, y[3];
  struct user s;
  NagError fail;

  INIT_FAIL(fail);

  printf("nag_ode_ivp_adams_zero_simple (d02cjc) Example Program Results\n");

  /* For communication with user-supplied functions
   * assign address of user defined structure
   * to Nag pointer.
   */
  s.use_comm = use_comm;
  comm.p = (Pointer)&s;

  neq = 3;
  s.xend = 10.0;
  /* nag_math_pi (x01aac).
   * pi
   */
  pi = nag_math_pi;
  printf("\nCase 1: intermediate output, root-finding\n");
  for (j = 4; j <= 5; ++j) {
    tol = pow(10.0, (double)(-j));
    printf("\n  Calculation with tol = %10.1e\n", tol);
    x = 0.0;
    y[0] = 0.5;
    y[1] = 0.5;
    y[2] = pi / 5.0;
    s.k = 4;
    s.h = (s.xend - x) / (double)(s.k + 1);
    printf("\n     X         Y(1)         Y(2)         Y(3)\n");

    /* nag_ode_ivp_adams_zero_simple (d02cjc).
     * Ordinary differential equation solver using a
     * variable-order variable-step Adams method (Black Box)
     */
    nag_ode_ivp_adams_zero_simple(neq, fcn, &x, y, s.xend, tol, Nag_Mixed, out,
                                  g, &comm, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_ode_ivp_adams_zero_simple (d02cjc).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }

    printf("\n  Root of Y(1) = 0.0 at %7.3f\n", x);
    printf("\n  Solution is");
    for (i = 0; i < 3; ++i)
      printf("%10.5f", y[i]);
    printf("\n");
  }
  printf("\n\nCase 2: no intermediate output, root-finding\n");
  for (j = 4; j <= 5; ++j) {
    tol = pow(10.0, (double)(-j));
    printf("\n  Calculation with tol = %10.1e\n", tol);
    x = 0.0;
    y[0] = 0.5;
    y[1] = 0.5;
    y[2] = pi / 5.0;

    /* nag_ode_ivp_adams_zero_simple (d02cjc), see above. */
    nag_ode_ivp_adams_zero_simple(neq, fcn, &x, y, s.xend, tol, Nag_Mixed,
                                  NULLFN, g, &comm, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_ode_ivp_adams_zero_simple (d02cjc).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }
    printf("\n  Root of Y(1) = 0.0 at %7.3f\n", x);
    printf("\n  Solution is");
    for (i = 0; i < 3; ++i)
      printf("%10.5f", y[i]);
    printf("\n");
  }
  printf("\n\nCase 3: intermediate output, no root-finding\n");
  for (j = 4; j <= 5; ++j) {
    tol = pow(10.0, (double)(-j));
    printf("\n  Calculation with tol = %10.1e\n", tol);
    x = 0.0;
    y[0] = 0.5;
    y[1] = 0.5;
    y[2] = pi / 5.0;
    s.k = 4;
    s.h = (s.xend - x) / (double)(s.k + 1);
    printf("\n     X         Y(1)         Y(2)         Y(3)\n");

    /* nag_ode_ivp_adams_zero_simple (d02cjc), see above. */
    nag_ode_ivp_adams_zero_simple(neq, fcn, &x, y, s.xend, tol, Nag_Mixed, out,
                                  NULLDFN, &comm, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_ode_ivp_adams_zero_simple (d02cjc).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }
  }

  printf("\n\nCase 4: no intermediate output, no root-finding");
  printf(" ( integrate to xend)\n");
  for (j = 4; j <= 5; ++j) {
    tol = pow(10.0, (double)(-j));
    printf("\n  Calculation with tol = %10.1e\n", tol);
    x = 0.0;
    y[0] = 0.5;
    y[1] = 0.5;
    y[2] = pi / 5.0;
    printf("\n     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_adams_zero_simple (d02cjc), see above. */
    nag_ode_ivp_adams_zero_simple(neq, fcn, &x, y, s.xend, tol, Nag_Mixed,
                                  NULLFN, NULLDFN, &comm, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_ode_ivp_adams_zero_simple (d02cjc).\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:
  return exit_status;
}

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

  printf("%8.2f", *xsol);
  for (i = 0; i < 3; ++i) {
    printf("%13.5f", y[i]);
  }
  printf("\n");
  *xsol = s->xend - (double)s->k * s->h;
  s->k--;
}

static void NAG_CALL fcn(Integer neq, double x, const double y[], double f[],
                         Nag_User *comm) {
  double pwr;
  struct user *s = (struct user *)comm->p;

  if (s->use_comm[0]) {
    printf("(User-supplied callback fcn, first invocation.)\n");
    s->use_comm[0] = 0;
  }

  f[0] = tan(y[2]);
  f[1] = -0.032 * tan(y[2]) / y[1] - 0.02 * y[1] / cos(y[2]);

  pwr = y[1];
  f[2] = -0.032 / (pwr * pwr);
}

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

  if (s->use_comm[1]) {
    printf("(User-supplied callback g, first invocation.)\n");
    s->use_comm[1] = 0;
  }

  return y[0];
}