#! /usr/bin/env python3
#
def sympy_evaluate ( ):

  from sympy import cos
  from sympy import lambdify
  from sympy import symbols
  import numpy
  import numpy as np
  import sympy

  print ( '' )
  print ( 'sympy_evaluate():' )
  print ( '  sympy version: ' + sympy.__version__ )
  print ( '  Show ways of evaluating the symbolic humps() function.' )
  print ( '' )

  x = symbols ( 'x' )

  humps = 100 / ( ( 10 * x - 3 )**2 + 1 ) \
        + 100 / ( ( 10 * x - 9 )**2 + 4 ) \
        - 6
#
#  subs(x,y) replaces "x" by "y".
#  "y" can be a symbol, an expression, or a number.
#
  y = symbols ( 'y' )
  humps_y = humps.subs ( x, y )
  print ( '  Replace "x" by "y" in the formula.' )
  print ( '  humps.subs(x,y) = ', humps_y )

  humps_cosy = humps.subs ( x, cos(y) )
  print ( '  Replace "x" by "cos(y)" in the formula.' )
  print ( '  humps.subs(x,cos(y)) = ', humps_cosy )

  humps_1 = humps.subs ( x, 1 )
  print ( '  Replace "x" by "1" in the formula.' )
  print ( '  humps.subs(x,1) = ', humps_1 )
#
#  lambdify() creates a numpy function from a symbolic expression.
#
  print ( '' )
  print ( '  Create a numpy function from the symbolic function.' )
  humps_lambda = lambdify ( x, humps, 'numpy' )
  z = np.linspace ( 0.0, 2.0, 5 )
  humps_lambda ( z )
  print ( '' )
  print ( '  Evaluate the numpy function at equally spaced points in [0,2].' )
  print ( '  humps(z) = ', humps_lambda ( z ) )

  return

if ( __name__ == "__main__" ):
  sympy_evaluate ( )