#! /usr/bin/env python
#
def pwl_basis_1d ( nd, xd, ni, xi ):

#*****************************************************************************80
#
## PWL_BASIS_1D evaluates a 1D piecewise linear basis function.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    02 July 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer ND, the number of data points.
#
#    Input, real XD(ND), the data points.
#
#    Input, integer NI, the number of interpolation points.
#
#    Input, real XI(NI), the interpolation points.
#
#    Output, real BK(NI,ND), the basis functions at the interpolation points.
#
  import numpy as np

  if ( nd == 1 ):
    bk = np.ones ( [ ni, nd ] )
    return bk

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

  for i in range ( 0, ni ):

    for j in range ( 0, nd ):

      if ( j == 0 and xi[i] <= xd[j] ):

        t = ( xi[i] - xd[j] ) / ( xd[j+1] - xd[j] )
        bk[i,j] = 1.0 - t

      elif ( j == nd - 1 and xd[j] <= xi[i] ):

        t = ( xi[i] - xd[j-1] ) / ( xd[j] - xd[j-1] )
        bk[i,j] = t

      elif ( xd[j-1] < xi[i] and xi[i] <= xd[j] ):

        t = ( xi[i] - xd[j-1] ) / ( xd[j] - xd[j-1] )
        bk[i,j] = t

      elif ( xd[j] <= xi[i] and xi[i] < xd[j+1] ):

        t = ( xi[i] - xd[j] ) / ( xd[j+1] - xd[j] )
        bk[i,j] = 1.0 - t

  return bk

def pwl_basis_1d_test ( ):

#*****************************************************************************80
#
## PWL_BASIS_1D_TEST tests PWL_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

  xd = np.array ( [ 0.0, 2.0, 5.0, 10.0 ] )
 
  print ( '' )
  print ( 'PWL_BASIS_1D_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  PWL_BASIS_1D evaluates the piecewise linear 1D basis' )
  print ( '  functions.' )

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

  lb = pwl_basis_1d ( nd, xd, ni, xi )

  r8mat_print ( ni, nd, lb, '  The PWL basis functions:' )
#
#  Terminate.
#
  print ( '' )
  print ( 'PWL_BASIS_1D_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  pwl_basis_1d_test ( )
  timestamp ( )