/* nag_pde_dim1_parab_keller (d03pec) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.3, 2023.
 */

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

#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL pdedef(Integer, double, double, const double[],
                            const double[], const double[], double[], Integer *,
                            Nag_Comm *);
static void NAG_CALL bndary(Integer, double, Integer, Integer, const double[],
                            const double[], double[], Integer *, Nag_Comm *);
static void NAG_CALL exact(double, Integer, Integer, double *, double *);
static void NAG_CALL uinit(Integer, Integer, double *, double *);
#ifdef __cplusplus
}
#endif

#define U(I, J) u[npde * ((J)-1) + (I)-1]
#define EU(I, J) eu[npde * ((J)-1) + (I)-1]

int main(void) {
  const Integer npde = 2, npts = 41, nleft = 1, neqn = npde * npts;
  const Integer lisave = neqn + 24,
                nwkres = npde * (npts + 21 + 3 * npde) + 7 * npts + 4;
  const Integer lrsave =
      11 * neqn + (4 * npde + nleft + 2) * neqn + 50 + nwkres;
  static double ruser[2] = {-1.0, -1.0};
  Integer exit_status = 0, i, ind, it, itask, itrace;
  double acc, tout, ts;
  double *eu = 0, *rsave = 0, *u = 0, *x = 0;
  Integer *isave = 0;
  NagError fail;
  Nag_Comm comm;
  Nag_D03_Save saved;

  INIT_FAIL(fail);

  printf("nag_pde_dim1_parab_keller (d03pec) Example Program Results\n\n");

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

  /* Allocate memory */

  if (!(eu = NAG_ALLOC(npde * npts, double)) ||
      !(rsave = NAG_ALLOC(lrsave, double)) ||
      !(u = NAG_ALLOC(npde * npts, double)) || !(x = NAG_ALLOC(npts, double)) ||
      !(isave = NAG_ALLOC(lisave, Integer))) {
    printf("Allocation failure\n");
    exit_status = 1;
    goto END;
  }

  itrace = 0;
  acc = 1e-6;

  printf("  Accuracy requirement =%12.3e", acc);
  printf(" Number of points = %3" NAG_IFMT "\n\n", npts);

  /* Set spatial-mesh points */

  for (i = 0; i < npts; ++i)
    x[i] = i / (npts - 1.0);

  printf(" x        ");
  printf("%10.4f%10.4f%10.4f%10.4f%10.4f\n\n", x[4], x[12], x[20], x[28],
         x[36]);

  ind = 0;
  itask = 1;

  uinit(npde, npts, x, u);

  /* Loop over output value of t */

  ts = 0.0;
  for (it = 0; it < 5; ++it) {
    tout = 0.2 * (it + 1);
    /* nag_pde_dim1_parab_keller (d03pec).
     * General system of first-order PDEs, method of lines,
     * Keller box discretization, one space variable
     */
    nag_pde_dim1_parab_keller(npde, &ts, tout, pdedef, bndary, u, npts, x,
                              nleft, acc, rsave, lrsave, isave, lisave, itask,
                              itrace, 0, &ind, &comm, &saved, &fail);

    if (fail.code != NE_NOERROR) {
      printf("Error from nag_pde_dim1_parab_keller (d03pec).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }

    /* Check against the exact solution */

    exact(tout, npde, npts, x, eu);

    printf(" t = %5.2f\n", ts);
    printf(" Approx u1");
    printf("%10.4f%10.4f%10.4f%10.4f%10.4f\n", U(1, 5), U(1, 13), U(1, 21),
           U(1, 29), U(1, 37));

    printf(" Exact  u1");
    printf("%10.4f%10.4f%10.4f%10.4f%10.4f\n", EU(1, 5), EU(1, 13), EU(1, 21),
           EU(1, 29), EU(1, 37));

    printf(" Approx u2");
    printf("%10.4f%10.4f%10.4f%10.4f%10.4f\n", U(2, 5), U(2, 13), U(2, 21),
           U(2, 29), U(2, 37));

    printf(" Exact  u2");
    printf("%10.4f%10.4f%10.4f%10.4f%10.4f\n\n", EU(2, 5), EU(2, 13), EU(2, 21),
           EU(2, 29), EU(2, 37));
  }
  printf(" Number of integration steps in time = %6" NAG_IFMT "\n", isave[0]);
  printf(" Number of function evaluations = %6" NAG_IFMT "\n", isave[1]);
  printf(" Number of Jacobian evaluations =%6" NAG_IFMT "\n", isave[2]);
  printf(" Number of iterations = %6" NAG_IFMT "\n\n", isave[4]);

END:
  NAG_FREE(eu);
  NAG_FREE(rsave);
  NAG_FREE(u);
  NAG_FREE(x);
  NAG_FREE(isave);

  return exit_status;
}

static void NAG_CALL pdedef(Integer npde, double t, double x, const double u[],
                            const double udot[], const double dudx[],
                            double res[], Integer *ires, Nag_Comm *comm) {
  if (comm->user[0] == -1.0) {
    printf("(User-supplied callback pdedef, first invocation.)\n");
    comm->user[0] = 0.0;
  }
  if (*ires == -1) {
    res[0] = udot[0];
    res[1] = udot[1];
  } else {
    res[0] = udot[0] + dudx[0] + dudx[1];
    res[1] = udot[1] + 4.0 * dudx[0] + dudx[1];
  }
  return;
}

static void NAG_CALL bndary(Integer npde, double t, Integer ibnd, Integer nobc,
                            const double u[], const double udot[], double res[],
                            Integer *ires, Nag_Comm *comm) {
  if (comm->user[1] == -1.0) {
    printf("(User-supplied callback bndary, first invocation.)\n");
    comm->user[1] = 0.0;
  }
  if (ibnd == 0) {
    if (*ires == -1) {
      res[0] = 0.0;
    } else {
      res[0] = u[0] - 0.5 * (exp(t) + exp(-3.0 * t)) -
               0.25 * (sin(-3.0 * t) - sin(t));
    }
  } else {
    if (*ires == -1) {
      res[0] = 0.0;
    } else {
      res[0] = u[1] - exp(1.0 - 3.0 * t) + exp(t + 1.0) -
               0.5 * (sin(1.0 - 3.0 * t) + sin(t + 1.0));
    }
  }
  return;
}

static void NAG_CALL uinit(Integer npde, Integer npts, double *x, double *u) {
  /* Routine for PDE initial values */

  Integer i;

  for (i = 1; i <= npts; ++i) {
    U(1, i) = exp(x[i - 1]);
    U(2, i) = sin(x[i - 1]);
  }
  return;
}

static void NAG_CALL exact(double t, Integer npde, Integer npts, double *x,
                           double *u) {
  /* Exact solution (for comparison purposes) */

  Integer i;

  for (i = 1; i <= npts; ++i) {
    U(1, i) = 0.5 * (exp(x[i - 1] + t) + exp(x[i - 1] - 3.0 * t)) +
              0.25 * (sin(x[i - 1] - 3.0 * t) - sin(x[i - 1] + t));
    U(2, i) = exp(x[i - 1] - 3.0 * t) - exp(x[i - 1] + t) +
              0.5 * (sin(x[i - 1] - 3.0 * t) + sin(x[i - 1] + t));
  }
  return;
}