#! /usr/bin/env python
#
def newton_value_1d ( nd, xd, cd, ni, xi ):

#*****************************************************************************80
#
## NEWTON_VALUE_1D evaluates a Newton 1D interpolant.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    11 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 order of the difference table.
#
#    Input, real XD(ND), the X values of the difference table.
#
#    Input, real CD(ND), the divided differences.
#
#    Input, integer NI, the number of interpolation points.
#
#    Input, real XI(NI), the interpolation points.
#
#    Output, real YI(NI), the interpolation values.
#
  import numpy as np

  yi = np.zeros ( ni )

  for i in range ( 0, ni ):
    yi[i] = cd[nd-1]

  for j in range ( 1, nd ):
    for i in range ( 0, ni ):
      yi[i] = cd[nd-j-1] + ( xi[i] - xd[nd-j-1] ) * yi[i]

  return yi

def newton_value_1d_test ( ):

#*****************************************************************************80
#
## NEWTON_VALUE_1D_TEST tests NEWTON_VALUE_1D.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    11 July 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from r8vec2_print import r8vec2_print

  print ( '' )
  print ( 'NEWTON_VALUE_1D_TEST' )
  print ( '  NEWTON_VALUE_1D evaluates a Newton 1d interpolant.' )

  nd = 5
  xd = np.array ( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] )
  cd = np.array ( [ 24.0, -24.0, +12.0, -4.0, 1.0 ] )
  r8vec2_print ( nd, xd, cd, '  The Newton interpolant data:' )

  ni = 16
  x_lo = 0.0
  x_hi = 5.0
  xi = np.linspace ( x_lo, x_hi, ni )

  yi = newton_value_1d ( nd, xd, cd, ni, xi )

  r8vec2_print ( ni, xi, yi, '  Newton interpolant values:' )
#
#  Terminate.
#
  print ( '' )
  print ( 'NEWTON_VALUE_1D_TEST:' )
  print ( '  Normal end of execution.' )

  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  newton_value_1d_test ( )
  timestamp ( )