/* nag_ode_bvp_ps_lin_grid_vals (d02uwc) Example Program.
 *
 * Copyright 2011, Numerical Algorithms Group.
 *
 * Mark 23, 2011.
 */
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagd02.h>
#include <nagx02.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, n, nip;
  double      a = -1.0, b = 1.0;
  double      uerr = 0.0;
  double      teneps = 10.0 * nag_machine_precision;
  /*  Arrays */
  double      *f = 0, *fip = 0, *x = 0, *xip = 0;
  /* NAG types */
  Nag_Boolean reqerr = Nag_FALSE;
  NagError    fail;

  INIT_FAIL(fail);

  printf("nag_ode_bvp_ps_lin_grid_vals (d02uwc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");

  scanf("%"NAG_IFMT "%*[^\n] ", &n);
  scanf("%"NAG_IFMT "%*[^\n] ", &nip);
  if (
    !(f = NAG_ALLOC((n + 1), double)) ||
    !(fip = NAG_ALLOC((nip), double)) ||
    !(xip = NAG_ALLOC((nip), double)) ||
    !(x = NAG_ALLOC((n + 1), double))
    )
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }

  /* Set up solution grid:
   * nag_ode_bvp_ps_lin_cgl_grid (d02ucc).
   * Generate Chebyshev Gauss-Lobatto grid.
   */
  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;
  }

  /* Set up problem right hand sides for grid. */
  for (i = 0; i < n + 1; i++) f[i] = exact(x[i]);

  /* Map to an equally spaced grid:
   * nag_ode_bvp_ps_lin_grid_vals (d02uwc).
   * Interpolate a function from Chebyshev grid to uniform grid
   * using barycentric Lagrange interpolation.
   */
  nag_ode_bvp_ps_lin_grid_vals(n, nip, x, f, xip, fip, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_ode_bvp_ps_lin_grid_vals (d02uwc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Print solution. */
  printf("Numerical solution f\n\n");
  printf("       x          f\n");
  for (i = 0; i < nip; i++) printf("%10.4f %10.4f\n", xip[i], fip[i]);

  if (reqerr) {
    for (i = 0; i < nip; i++) uerr = MAX(uerr, fabs(fip[i] - exact(xip[i])));
    printf("f is within a multiple %"NAG_IFMT " of machine precision.\n",
           10 * ((Integer) (uerr/teneps) + 1));
  }
 END:
  if (f) NAG_FREE(f);
  if (fip) NAG_FREE(fip);
  if (x) NAG_FREE(x);
  if (xip) NAG_FREE(xip);
  return exit_status;
}

static double exact(double x)
{
  return x + cos(5.0 * x);
}