#! /usr/bin/env python
#
def newton_coef_1d ( nd, xd, yd ):

#*****************************************************************************80
#
## NEWTON_COEF_1D computes coefficients of a Newton 1D interpolant.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    10 July 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Carl deBoor,
#    A Practical Guide to Splines,
#    Springer, 2001,
#    ISBN: 0387953663,
#    LC: QA1.A647.v27.
#
#  Parameters:
#
#    Input, integer ND, the number of data values.
#
#    Input, real XD(ND), the X values at which data was taken.
#
#    Input, real YD(ND), the corresponding Y values.
#
#    Output, real CD(ND), the divided difference
#    coefficients corresponding to the input (XTAB,YTAB).
#
  import numpy as np

  cd = np.zeros ( nd, dtype = np.float64 )

  for i in range ( 0, nd ):
    cd[i] = yd[i]

  for i in range ( 1, nd ):
    for j in range ( nd - 1, i - 1, -1 ):
      cd[j] = ( cd[j] - cd[j-1] ) / ( xd[j] - xd[j-i] )

  return cd

def newton_coef_1d_test ( ):

#*****************************************************************************80
#
## NEWTON_COEF_1D_TEST tests NEWTON_COEF_1D.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    10 July 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from r8vec_print import r8vec_print
  from r8vec2_print import r8vec2_print

  nd = 5
  xd = np.array ( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] )
  yd = np.array ( [ 24.0, 0.0, 0.0, 0.0, 0.0 ] )

  print ( '' )
  print ( 'NEWTON_COEF_1D_TEST' )
  print ( '  NEWTON_COEF_1D sets the coefficients for a 1D Newton interpolation.' )

  r8vec2_print ( nd, xd, yd, '  Interpolation data:' )

  cd = newton_coef_1d ( nd, xd, yd )

  r8vec_print ( nd, cd, '  Newton interpolant coefficients:' )
#
#  Terminate.
#
  print ( '' )
  print ( 'NEWTON_COEF_1D_TEST:' )
  print ( '  Normal end of execution.' )

  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  newton_coef_1d_test ( )
  timestamp ( )