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

# include "newton_interp_1d.h"

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

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

/******************************************************************************/
/*
  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 = ( double * ) malloc ( nd * sizeof ( double ) );

  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 )
      {
        fprintf ( stderr, "\n" );
        fprintf ( stderr, "newton_coef_1d(): Fatal error!\n" );
        fprintf ( stderr, "  Two entries of XD are equal!\n" );
        fprintf ( stderr, "  XD[%d] = %f\n", i, xd[i] );
        fprintf ( stderr, "  XD[%d] = %f\n", j, xd[j] );
        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;
}
/******************************************************************************/

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

/******************************************************************************/
/*
  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 = ( double * ) malloc ( ni * sizeof ( double ) );

  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;
}