#! /usr/bin/env python
#
def pwl_value_1d ( nd, xd, yd, ni, xi ):

#*****************************************************************************80
#
## PWL_VALUE_1D evaluates the piecewise linear interpolant.
#
#  Discussion:
#
#    The piecewise linear interpolant L(ND,XD,YD)(X) is the piecewise
#    linear function which interpolates the data (XD(I),YD(I)) for I = 1
#    to ND.
#
#  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.
#    ND must be at least 1.
#
#    Input, real XD(ND), the data points.
#
#    Input, real YD(ND), the data values.
#
#    Input, integer NI, the number of interpolation points.
#
#    Input, real XI(NI), the interpolation points.
#
#    Output, real YI(NI), the interpolated values.
#
  import numpy as np

  if ( nd == 1 ):
    yi = np.ones ( ni ) * yd[0]
    return yi

  yi = np.zeros ( ni )

  for i in range ( 0, ni ):
 
    if ( xi[i] <= xd[0] ):

      t = ( xi[i] - xd[0] ) / ( xd[1] - xd[0] )
      yi[i] = ( 1.0 - t ) * yd[0] + t * yd[1]

    elif ( xd[nd-2] <= xi[i] ):

      t = ( xi[i] - xd[nd-2] ) / ( xd[nd-1] - xd[nd-2] )
      yi[i] = ( 1.0 - t ) * yd[nd-2] + t * yd[nd-1]

    else:

      for k in range ( 1, nd ):
 
        if ( xd[k-1] <= xi[i] and xi[i] <= xd[k] ):

          t = ( xi[i] - xd[k-1] ) / ( xd[k] - xd[k-1] )
          yi[i] = ( 1.0 - t ) * yd[k-1] + t * yd[k]
  
  return yi

def pwl_value_1d_test ( ):

#*****************************************************************************80
#
## PWL_VALUE_1D_TEST tests PWL_VALUE_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 r8vec2_print import r8vec2_print

  nd = 4
  ni = 21
#
#  Values of f(x) = x^3 - 12 x^2 + 39 x -28 = ( x - 1 ) * ( x - 4 ) * ( x - 7 )
#
  xd = np.array ( [ 0.0, 2.0, 5.0, 10.0 ] )
  yd = np.array ( [ -28.0, +10.0, -8.0, +162.0 ] )
 
  print ( '' )
  print ( 'PWL_VALUE_1D_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  PWL_VALUE_1D evaluates a piecewise linear 1D interpolant.' )

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

  yi = pwl_value_1d ( nd, xd, yd, ni, xi )

  r8vec2_print ( ni, xi, yi, '  Table of interpolant values:' )
#
#  Terminate.
#
  print ( '' )
  print ( 'PWL_VALUE_1D_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  pwl_value_1d_test ( )
  timestamp ( )