#! /usr/bin/env python
#
def sag ( x ):

#*****************************************************************************80
#
## sag is a test function with a minimizer near x=7.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    01 October 2019
#
#  Input:
#
#    real x: the argument.
#
#  Output:
#
#    real value: the function value.
#
  import numpy as np

  value = x**2 * np.cos ( ( x + 3.0 * np.pi ) / 4.0 )

  return value

def sag_df ( x ):

#*****************************************************************************80
#
## sag_df returns the derivative of the sag() function.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    01 October 2019
#
#  Input:
#
#    real x: the argument.
#
#  Output:
#
#    real value: the derivative value.
#
  import numpy as np

  value = 2.0 * x * np.cos ( ( x + 3.0 * np.pi ) / 4.0 ) \
    - x**2 * np.sin ( ( x + 3.0 * np.pi ) / 4.0 ) / 4.0

  return value