/* nag_inteq_abel1_weak (d05bec) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 *
 * Mark 28.3, 2022.
 */
#include <math.h>
#include <nag.h>

#ifdef __cplusplus
extern "C" {
#endif
static double NAG_CALL ck1(double t, Nag_Comm *comm);
static double NAG_CALL cf1(double t, Nag_Comm *comm);
static double NAG_CALL cg1(double s, double y, Nag_Comm *comm);
static double NAG_CALL ck2(double t, Nag_Comm *comm);
static double NAG_CALL cf2(double t, Nag_Comm *comm);
static double NAG_CALL cg2(double s, double y, Nag_Comm *comm);
#ifdef __cplusplus
}
#endif

static double sol1(double t);
static double sol2(double t);

int main(void) {
  /* Scalars */
  double err, errmax, h, hi1, soln, t, tlim, tolnl;
  Integer exit_status = 0;
  Integer iorder = 4;
  Integer i, iskip, exno, nmesh, lrwsav;
  /* Arrays */
  static double ruser[6] = {-1.0, -1.0, -1.0, -1.0, -1.0, -1.0};
  double *rwsav = 0, *yn = 0;
  /* NAG types */
  Nag_Comm comm;
  NagError fail;
  Nag_WeightMode wtmode;

  INIT_FAIL(fail);

  printf("nag_inteq_abel1_weak (d05bec) Example Program Results\n");

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

  nmesh = pow(2, 6) + 7;
  lrwsav = (2 * iorder + 6) * nmesh + 8 * pow(iorder, 2) - 16 * iorder + 1;

  if (!(yn = NAG_ALLOC(nmesh, double)) ||
      !(rwsav = NAG_ALLOC(lrwsav, double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  tolnl = sqrt(nag_machine_precision);

  for (exno = 1; exno <= 2; exno++) {
    printf("\nExample %" NAG_IFMT "\n\n", exno);

    if (exno == 1) {
      tlim = 7.0;
      iskip = 5;
      h = tlim / (double)(nmesh - 1);
      wtmode = Nag_InitWeights;
      yn[0] = 0.0;

      /*
         nag_inteq_abel1_weak (d05bec).
         Nonlinear convolution Volterra-Abel equation, first kind,
         weakly singular.
       */
      nag_inteq_abel1_weak(ck1, cf1, cg1, wtmode, iorder, tlim, tolnl, nmesh,
                           yn, rwsav, lrwsav, &comm, &fail);
    } else {
      tlim = 5.0;
      iskip = 7;
      h = tlim / (double)(nmesh - 1);
      wtmode = Nag_ReuseWeights;
      yn[0] = 1.0;

      /* nag_inteq_abel1_weak (d05bec) as above. */
      nag_inteq_abel1_weak(ck2, cf2, cg2, wtmode, iorder, tlim, tolnl, nmesh,
                           yn, rwsav, lrwsav, &comm, &fail);
    }
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_inteq_abel1_weak (d05bec).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

    printf("The stepsize h = %8.4f\n\n", h);
    printf("     t        Approximate\n");
    printf("                Solution\n\n");
    errmax = 0.0;
    t = 0.0;
    soln = 0.0;

    for (i = 0; i < nmesh; i++) {
      hi1 = (double)(i)*h;
      err = fabs(yn[i] - ((exno == 1) ? sol1(hi1) : sol2(hi1)));

      if (err > errmax) {
        errmax = err;
        t = hi1;
        soln = yn[i];
      }

      if (i > 0 && i % iskip == 0)
        printf("%8.4f%15.4f\n", hi1, yn[i]);
    }

    printf("\nThe maximum absolute error, %10.2e, occurred at t = %8.4f\n",
           errmax, t);
    printf("with solution %8.4f\n", soln);
  }

END:
  NAG_FREE(rwsav);
  NAG_FREE(yn);

  return exit_status;
}

static double sol1(double t) {
  if (t == 0.0)
    return 0.0;
  else
    return (1.0 / (sqrt(2.0 * nag_math_pi) * pow(t, 1.5))) *
           exp(-pow(1.0 + t, 2) / (2.0 * t));
}

static double sol2(double t) { return 1.0 / (1.0 + t); }

static double NAG_CALL ck1(double t, Nag_Comm *comm) {
  if (comm->user[0] == -1.0) {
    printf("(User-supplied callback ck1, first invocation.)\n");
    comm->user[0] = 0.0;
  }
  return exp(-0.5 * t);
}

static double NAG_CALL cf1(double t, Nag_Comm *comm) {
  if (comm->user[1] == -1.0) {
    printf("(User-supplied callback cf1, first invocation.)\n");
    comm->user[1] = 0.0;
  }
  return (-1.0 / sqrt(nag_math_pi * t)) * exp(-0.5 * pow(1.0 + t, 2) / t);
}

static double NAG_CALL cg1(double s, double y, Nag_Comm *comm) {
  if (comm->user[2] == -1.0) {
    printf("(User-supplied callback cg1, first invocation.)\n");
    comm->user[2] = 0.0;
  }
  return y;
}

static double NAG_CALL ck2(double t, Nag_Comm *comm) {
  if (comm->user[3] == -1.0) {
    printf("(User-supplied callback ck2, first invocation.)\n");
    comm->user[3] = 0.0;
  }
  return sqrt(nag_math_pi);
}

static double NAG_CALL cf2(double t, Nag_Comm *comm) {
  /* Scalars */
  double st1;

  if (comm->user[4] == -1.0) {
    printf("(User-supplied callback cf2, first invocation.)\n");
    comm->user[4] = 0.0;
  }
  st1 = sqrt(1.0 + t);
  return -2.0 * log(st1 + sqrt(t)) / st1;
}

static double NAG_CALL cg2(double s, double y, Nag_Comm *comm) {
  if (comm->user[5] == -1.0) {
    printf("(User-supplied callback cg2, first invocation.)\n");
    comm->user[5] = 0.0;
  }
  return y;
}