# include <cmath>
# include <cstdlib>
# include <cstring>
# include <ctime>
# include <iomanip>
# include <iostream>

using namespace std;

# include "newton_interp_1d.hpp"

//****************************************************************************80

double *newton_coef_1d ( int nd, double xd[], double yd[] )

//****************************************************************************80
//
//  Purpose:
//
//    newton_coef_1d() computes coefficients of a Newton 1D interpolant.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    08 July 2015
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Carl deBoor,
//    A Practical Guide to Splines,
//    Springer, 2001,
//    ISBN: 0387953663,
//    LC: QA1.A647.v27.
//
//  Input:
//
//    int ND, the number of data points.
//
//    double XD[ND], the X values at which data was taken.
//    These values must be distinct.
//
//    double YD[ND], the corresponding Y values.
//
//  Output:
//
//    double NEWTON_COEF_1D[ND], the divided difference coefficients.
//
{
  double *cd;
  int i;
  int j;
//
//  Copy the data values.
//
  cd = new double[nd];

  for ( i = 0; i < nd; i++ )
  {
    cd[i] = yd[i];
  }
//
//  Make sure the abscissas are distinct.
//
  for ( i = 0; i < nd; i++ )
  {
    for ( j = i + 1; j < nd; j++ )
    {
      if ( xd[i] - xd[j] == 0.0 )
      {
        cerr << "\n";
        cerr << "newton_coef_1d(): Fatal error!\n";
        cerr << "  Two entries of XD are equal!\n";
        cerr << "  XD[" << i << "] = " << xd[i] << "\n";
        cerr << "  XD[" << j << "] = " << xd[j] << "\n";
        exit ( 1 );
      }
    }
  }
//
//  Compute the divided differences.
//
  for ( i = 1; i <= nd - 1; i++ )
  {
    for ( j = nd - 1; i <= j; j-- )
    {
      cd[j] = ( cd[j] - cd[j-1] ) / ( xd[j] - xd[j-i] );
    }
  }
  return cd;
}
//****************************************************************************80

double *newton_value_1d ( int nd, double xd[], double cd[], int ni, double xi[] )

//****************************************************************************80
//
//  Purpose:
//
//    newton_value_1d() evaluates a Newton 1D interpolant.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    08 July 2015
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Carl deBoor,
//    A Practical Guide to Splines,
//    Springer, 2001,
//    ISBN: 0387953663,
//    LC: QA1.A647.v27.
//
//  Input:
//
//    int ND, the order of the difference table.
//
//    double XD[ND], the X values of the difference table.
//
//    double CD[ND], the divided differences.
//
//    int NI, the number of interpolation points.
//
//    double XI[NI], the interpolation points.
//
//  Output:
//
//    double NEWTON_VALUE_1D[NI], the interpolated values.
//
{
  int i;
  int j;
  double *yi;

  yi = new double[ni];

  for ( j = 0; j < ni; j++ )
  {
    yi[j] = cd[nd-1];
    for ( i = 2; i <= nd; i++ )
    {
      yi[j] = cd[nd-i] + ( xi[j] - xd[nd-i] ) * yi[j];
    }
  }
  return yi;
}