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

  from sympy import cos
  from sympy import exp
  from sympy import pprint
  from sympy import symbols
  from sympy.matrices.dense import hessian
  import sympy

  print ( '' )
  print ( 'hessian_example():' )
  print ( '  sympy version: ' + sympy.__version__ )
  print ( '  Given a scalar function of two variables f(x,y).' )
  print ( '  Compute the Hessian matrix of second derivatives.' )

  x = symbols ( 'x' )
  y = symbols ( 'y' )

  f = 3 * exp ( - x**2 ) + 7 * x**2 / y + 5 * cos ( y )
  print ( '' )
  print ( '  f(x,y):' )
  print ( '' )
  pprint ( f )

  H = hessian ( f, ( x, y ) )
  print ( '' )
  print ( '  Hessian(i,j) = d2 f/dxi dxj' )
  print ( '' )
  pprint ( H )

  return

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