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

#*****************************************************************************80
#
## humps_derivative() estimates the derivative of humps_antideriv()
#
#  Discussion:
#
#    The scipy() library used to have a derivative estimator.  Since it is
#    gone now, we just use a simple centered difference estimate stored
#    as the function "derivative(f,x,dx)".
#
  from humps import humps_fun, humps_deriv, humps_antideriv
  import matplotlib.pyplot as plt
  import numpy as np

  print ( '' )
  print ( 'humps_derivative():' )
  print ( '  Estimate the derivative of the humps_antideriv function' )
  print ( '  Use user-written "derivative()" estimator.' )

  x = np.linspace ( 0.0, 2.0, 11 )
#
#  Reduce dx for better results!
#
  dx = 1.0E-00
  y = derivative ( humps_antideriv, x, dx )
#
#  Evaluate humps_fun() for comparison.
#
  x2 = np.linspace ( 0.0, 2.0, 201 )
  y2 = humps_fun ( x2 )
#
#  Plot estimated derivative and exact derivative.
#
  plt.plot ( x, y, 'ro' )
  plt.plot ( x2, y2, 'b-' )
  plt.grid ( True )
  plt.title ( 'Finite difference derivative with dx =' + str ( dx ) )
  plt.legend ( [ 'Estimate', 'Exact' ] )
  filename = 'humps_derivative.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "' + filename + '"' )
  plt.show ( )

  return

def derivative ( f, x, dx ):

#*****************************************************************************80
#
## derivative() estimates the derivative of f() at x, with step dx.
#
  dfdx = ( f(x+dx) - f(x-dx) ) / 2.0 / dx
  return dfdx

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