#! /usr/bin/env python
#
def heart_b ( m ):

#*****************************************************************************80
#
## HEART_B returns the bounds in the heart problem.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 December 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Cesar Munoz, Anthony Narkawicz,
#    Formalization of Bernstein polynomials and applications to global 
#    optimization,
#    Journal of Automated Reasoning,
#    Volume 51, Number 2, 2013, pages 151-196.
#
#  Parameters:
#
#    Input, integer M, the number of variables.
#
#    Output, integer L(M), U(M), the lower and upper bounds.
#
  import numpy as np

  l = np.array ( [ -0.1,  0.4, -0.7, -0.7, +0.1, -0.1, -0.3, -1.1 ] )
  u = np.array ( [  0.4, +1.0, -0.4, +0.4, +0.2, +0.2, +1.1, -0.3 ] )

  return l, u

def heart_f ( m, n, x ):

#*****************************************************************************80
#
## HEART_F returns the function in the heart problem.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 December 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Cesar Munoz, Anthony Narkawicz,
#    Formalization of Bernstein polynomials and applications to global 
#    optimization,
#    Journal of Automated Reasoning,
#    Volume 51, Number 2, 2013, pages 151-196.
#
#  Parameters:
#
#    Input, integer M, the number of variables.
#
#    Input, integer N, the number of points.
#
#    Input, real x[M,N), the points.
#
#    Output, integer VALUE(N), the value of the function at X.
#
  value = ( \
    +       x[0,0:n] * x[5,0:n] ** 3                 \
    - 3.0 * x[0,0:n] * x[5,0:n]      * x[6,0:n] ** 2 \
    +       x[2,0:n] * x[6,0:n] ** 3                 \
    - 3.0 * x[2,0:n] * x[6,0:n]      * x[5,0:n] ** 2 \
    +       x[1,0:n] * x[4,0:n] ** 3                 \
    - 3.0 * x[1,0:n] * x[4,0:n]      * x[7,0:n] ** 2 \
    +       x[3,0:n] * x[7,0:n] ** 3                 \
    - 3.0 * x[3,0:n] * x[7,0:n]      * x[4,0:n] ** 2 \
    + 0.9563453 )
 
  return value

def heart_m ( ):

#*****************************************************************************80
#
## HEART_M returns the number of variables in the heart problem.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 December 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Cesar Munoz, Anthony Narkawicz,
#    Formalization of Bernstein polynomials and applications to global 
#    optimization,
#    Journal of Automated Reasoning,
#    Volume 51, Number 2, 2013, pages 151-196.
#
#  Parameters:
#
#    Output, integer M, the number of variables.
#
  m = 8

  return m

def heart_test ( ):

#*****************************************************************************80
#
## HEART_TEST uses sampling to estimate the range of the HEART polynomial.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    06 December 2016
#
#  Author:
#
#    John Burkardt
#
  import platform
  from r8mat_uniform_abvec import r8mat_uniform_abvec

  print ( '' )
  print ( 'HEART_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Use N sample values of a polynomial over its domain to estimate' )
  print ( '  its minimum Pmin and maximum Pmax' )
  print ( '' )
  print ( '         N           Pmin             Pmax' )
  print ( '' )

  m = heart_m ( )
  l, u = heart_b ( m )
  print ( '  heart: [-1.36775, +1.74345327935]' )

  seed = 123456789
  n = 8

  for n_log_2 in range ( 4, 21 ):

    n = n * 2
    x, seed = r8mat_uniform_abvec ( m, n, u, l, seed )
    f = heart_f ( m, n, x )
    print ( '  %8d  %16.8g  %16.8g' % ( n, min ( f ), max ( f ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'HEART_TEST:' )
  print ( '  Normal end of execution.' )
  return

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