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

# include "lagrange_approx_1d.h"
# include "qr_solve.h"
# include "r8lib.h"
# include "test_interp_1d.h"

int main ( );
void test02 ( int prob, int m, int nd );
void test03 ( int prob, int m, int nd );

/******************************************************************************/

int main ( )

/******************************************************************************/
/*
  Purpose:

    MAIN is the main program for LAGRANGE_APPROX_1D_TEST.

  Discussion:

    LAGRANGE_APPROX_1D_TEST tests LAGRANGE_APPROX_1D.

  Licensing:

    This code is distributed under the GNU LGPL license.

  Modified:

    08 October 2012

  Author:

    John Burkardt
*/
{
  int j;
  int k;
  int m;
  int m_test[7] = { 0, 1, 2, 3, 4, 8, 16 };
  int m_test_num = 7;
  int nd;
  int nd_test[3] = { 16, 64, 1000 };
  int nd_test_num = 3;
  int prob;
  int prob_num;

  timestamp ( );
  printf ( "\n" );
  printf ( "LAGRANGE_APPROX_1D_TEST:\n" );
  printf ( "  C version\n" );
  printf ( "  Test the LAGRANGE_APPROX_1D library.\n" );
  printf ( "  The R8LIB library is needed.\n" );
  printf ( "  The QR_SOLVE library is needed.\n" );
  printf ( "  These tests need the TEST_INTERP_1D library.\n" );

  prob_num = p00_prob_num ( );

  for ( prob = 1; prob <= prob_num; prob++ )
  {
    for ( j = 0; j < m_test_num; j++ )
    {
      m = m_test[j];
      for ( k = 0; k < nd_test_num; k++ )
      {
        nd = nd_test[k];
        test02 ( prob, m, nd );
      }
    }
  }

  for ( prob = 1; prob <= prob_num; prob++ )
  {
    for ( j = 0; j < m_test_num; j++ )
    {
      m = m_test[j];
      for ( k = 0; k < nd_test_num; k++ )
      {
        nd = nd_test[k];
        test03 ( prob, m, nd );
      }
    }
  }
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "LAGRANGE_APPROX_1D_TEST:\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

  return 0;
}
/******************************************************************************/

void test02 ( int prob, int m, int nd )

/******************************************************************************/
/*
  Purpose:

    TEST02 tests LAGRANGE_APPROX_1D with evenly spaced data

  Licensing:

    This code is distributed under the GNU LGPL license.

  Modified:

    08 October 2012

  Author:

    John Burkardt

  Parameters:

    Input, int PROB, the problem index.

    Input, int M, the polynomial approximant degree.

    Input, int ND, the number of data points.
*/
{
  double a;
  double b;
  double int_error;
  int ni;
  double *xd;
  double *xi;
  double *yd;
  double *yi;

  printf ( "\n" );
  printf ( "TEST02:\n" );
  printf ( "  Approximate evenly spaced data from TEST_INTERP_1D problem #%d\n", prob );
  printf ( "  Use polynomial approximant of degree %d\n", m );
  printf ( "  Number of data points = %d\n", nd );

  a = 0.0;
  b = 1.0;
  xd = r8vec_linspace_new ( nd, a, b );

  yd = p00_f ( prob, nd, xd );

  if ( nd < 10 )
  {
    r8vec2_print ( nd, xd, yd, "  Data array:" );
  }
/*
  #1:  Does approximant come close to function at data points?
*/
  ni = nd;
  xi = r8vec_copy_new ( ni, xd );
  yi = lagrange_approx_1d ( m, nd, xd, yd, ni, xi );

  int_error = r8vec_norm_affine ( nd, yi, yd ) / ( double ) ( ni );

  printf ( "\n" );
  printf ( "  L2 approximation error averaged per data node = %g\n", int_error );

  free ( xd );
  free ( xi );
  free ( yd );
  free ( yi );

  return;
}
/******************************************************************************/

void test03 ( int prob, int m, int nd )

/******************************************************************************/
/*
  Purpose:

    TEST03 tests LAGRANGE_APPROX_1D with Chebyshev spaced data.

  Licensing:

    This code is distributed under the GNU LGPL license.

  Modified:

    08 October 2012

  Author:

    John Burkardt

  Parameters:

    Input, int PROB, the problem index.

    Input, int M, the polynomial approximant degree.

    Input, int ND, the number of data points.
*/
{
  double a;
  double b;
  double int_error;
  int ni;
  double *xd;
  double *xi;
  double *yd;
  double *yi;

  printf ( "\n" );
  printf ( "TEST03:\n" );
  printf ( "  Approximate Chebyshev-spaced data from TEST_INTERP_1D problem #%d\n", prob );
  printf ( "  Use polynomial approximant of degree %d\n", m );
  printf ( "  Number of data points = %d\n", nd );

  a = 0.0;
  b = 1.0;
  xd = r8vec_cheby_extreme_new ( nd, a, b );

  yd = p00_f ( prob, nd, xd );

  if ( nd < 10 )
  {
    r8vec2_print ( nd, xd, yd, "  Data array:" );
  }
/*
  #1:  Does interpolant match function at interpolation points?
*/
  ni = nd;
  xi = r8vec_copy_new ( ni, xd );
  yi = lagrange_approx_1d ( m, nd, xd, yd, ni, xi );

  int_error = r8vec_norm_affine ( nd, yi, yd ) / ( double ) ( ni );

  printf ( "\n" );
  printf ( "  L2 approximation error averaged per data node = %g\n", int_error );

  free ( xd );
  free ( xi );
  free ( yd );
  free ( yi );

  return;
}