#! /usr/bin/env python
#
def shepard_basis_1d ( nd, xd, p, ni, xi ):

#*****************************************************************************80
#
## SHEPARD_BASIS_1D evaluates a 1D Shepard basis function.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    03 July 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Donald Shepard,
#    A two-dimensional interpolation function for irregularly spaced data,
#    ACM '68: Proceedings of the 1968 23rd ACM National Conference,
#    ACM, pages 517-524, 1969.
#
#  Parameters:
#
#    Input, integer ND, the number of data points.
#
#    Input, real XD(ND,1), the data points.
#
#    Input, integer K, the index of the desired basis function,
#    1 <= K <= ND.
#
#    Input, real P, the power.
#
#    Input, integer NI, the number of interpolation points.
#
#    Input, real XI(NI,1), the interpolation points.
#
#    Output, real BK(NI,ND), the basis function at the interpolation points.
#
  import numpy as np

  bk = np.zeros ( [ ni, nd ] )

  w = np.zeros ( nd )

  for i in range ( 0, ni ):

    if ( p == 0.0 ):

      for j in range ( 0, nd ):
        w[j] = 1.0 / float ( nd )

    else:

      z = -1
      for j in range ( 0, nd ):
        w[j] = abs ( xi[i] - xd[j] )
        if ( w[j] == 0.0 ):
          z = j

      if ( z != -1 ):
        for j in range ( 0, nd ):
          w[j] = 0.0
        w[z] = 1.0
      else:
        for j in range ( 0, nd ):
          w[j] = 1.0 / w[j] ** p
        s = np.sum ( w )
        for j in range ( 0, nd ):
          w[j] = w[j] / s
 
    for j in range ( 0, nd ):
      bk[i,j] = w[j]

  return bk

def shepard_basis_1d_test ( ):

#*****************************************************************************80
#
## SHEPARD_BASIS_1D_TEST tests SHEPARD_BASIS_1D.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    02 July 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8mat_print import r8mat_print

  nd = 4
  ni = 21

  p = 2.0

  xd = np.array ( [ 0.0, 2.0, 5.0, 10.0 ] )

  print ( '' )
  print ( 'SHEPARD_BASIS_1D_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  SHEPARD_BASIS_1D evaluates the Shepard 1D basis' )
  print ( '  functions.' )
  print ( '' )
  print ( '  Using power P = %g' % ( p ) )

  x_min = 0.0
  x_max = 10.0
  xi = np.linspace ( x_min, x_max, ni )

  lb = shepard_basis_1d ( nd, xd, p, ni, xi )

  r8mat_print ( ni, nd, lb, '  The Shepard basis functions:' )
#
#  Terminate.
#
  print ( '' )
  print ( 'SHEPARD_BASIS_1D_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  shepard_basis_1d_test ( )
  timestamp ( )