/* nag_ode_bvp_ps_lin_cheb_eval (d02uzc) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.3, 2023.
 */

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

#ifdef __cplusplus
extern "C" {
#endif
static double NAG_CALL exact(double x);
#ifdef __cplusplus
}
#endif

int main(void) {
  /*  Scalars */
  Integer exit_status = 0;
  Integer i, k, m, n;
  double a = -0.24 * nag_math_pi, b = 0.5 * nag_math_pi;
  double deven, dmap, fseries, t, uerr, xeven, xmap;
  double teneps = 10.0 * nag_machine_precision;
  /*  Arrays */
  double *c = 0, *f = 0, *x = 0;
  /* NAG types */
  Nag_Boolean reqerr = Nag_FALSE;
  NagError fail;

  INIT_FAIL(fail);

  printf("nag_ode_bvp_ps_lin_cheb_eval (d02uzc) Example Program Results \n\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "", &n);
  scanf("%" NAG_IFMT "", &m);
  if (!(f = NAG_ALLOC((n + 1), double)) || !(c = NAG_ALLOC((n + 1), double)) ||
      !(x = NAG_ALLOC((n + 1), double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Set up Chebyshev grid:
   * nag_ode_bvp_ps_lin_cgl_grid (d02ucc).
   * Chebyshev Gauss-Lobatto grid generation.
   */
  nag_ode_bvp_ps_lin_cgl_grid(n, a, b, x, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_ode_bvp_ps_lin_cgl_grid (d02ucc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Evaluate function on grid and get interpolating Chebyshev coefficients. */
  for (i = 0; i < n + 1; i++)
    f[i] = exact(x[i]);

  /* nag_ode_bvp_ps_lin_coeffs (d02uac).
   * Coefficients of Chebyshev interpolating polynomial
   * from function values on Chebyshev grid.
   */
  nag_ode_bvp_ps_lin_coeffs(n, f, c, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_ode_bvp_ps_lin_coeffs (d02uac).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Evaluate Chebyshev series manually by evaluating each Chebyshev
   * polynomial in turn at new equispaced (m+1) grid points.
   * Chebyshev series on [-1,1] map of [a,b].
   */
  xmap = -1.0;
  dmap = 2.0 / (double)(m - 1);
  xeven = a;
  deven = (b - a) / (double)(m - 1);
  printf("    x_even      x_map      Sum\n");
  uerr = 0.0;
  for (i = 0; i < m; i++) {
    fseries = 0.0;
    for (k = 0; k < n + 1; k++) {
      /* nag_ode_bvp_ps_lin_cheb_eval (d02uzc).
       * Chebyshev polynomial evaluation, T_k(x).
       */
      nag_ode_bvp_ps_lin_cheb_eval(k, xmap, &t, &fail);
      if (fail.code != NE_NOERROR) {
        printf("Error from nag_ode_bvp_ps_lin_cheb_eval (d02uzc).\n%s\n",
               fail.message);
        exit_status = 1;
        goto END;
      }

      fseries = fseries + c[k] * t;
    }
    uerr = MAX(uerr, fabs(fseries - exact(xeven)));
    printf("%10.4f %10.4f %10.4f \n", xeven, xmap, fseries);
    xmap = MIN(1.0, xmap + dmap);
    xeven = xeven + deven;
  }

  if (reqerr) {
    printf("\nError in coefficient sum is < ");
    printf("%8" NAG_IFMT " ", 10 * ((Integer)(uerr / teneps) + 1));
    printf(" * machine precision.\n");
  }
END:
  NAG_FREE(c);
  NAG_FREE(f);
  NAG_FREE(x);
  return exit_status;
}

static double NAG_CALL exact(double x) { return x + exp(-x); }