#! /usr/bin/env python3
#
def cvxopt_example ( ):
#
  from cvxopt import matrix
  from cvxopt import solvers

  print ( '' )
  print ( 'cvxopt_example:' )
  print ( '  cvxopt is a quadratic programming package.' )
  print ( '' )
  print ( '  Use it to solve the following system:' )
  print ( '' )
  print ( '  minimize:' )
  print ( '    2 x0^2 + x1^2 + x0 x1 + x0 + x1' )
  print ( '  subject to:' )
  print ( '    x0 >= 0' )
  print ( '    x1 >= 0' )
  print ( '    x0 + x1 = 1' )
  print ( '' )
  print ( '  Reformulated for cvxopt as follows:' )
  print ( '' )
  print ( '  minimize:' )
  print ( '    1/2 x\' Q x + p' )
  print ( '  subject to: ')
  print ( '    G x <= h' )
  print ( '    A x = b' ) 

  Q = 2*matrix([ [2, .5], [.5, 1] ])
  p = matrix([1.0, 1.0])

  G = matrix([[-1.0,0.0],[0.0,-1.0]])
  h = matrix([0.0,0.0])
#
# A must be a matrix.  
# We have to add the (1,2) argument at the end here to indicate
# that A should be set up as a two-dimensional object, not a vector.
#
  A = matrix([1.0, 1.0], (1,2))
  b = matrix(1.0)
#
#  The output "sol" is a dictionary.  
#  The information we want is stored under 'x'.
#
  sol = solvers.qp ( Q, p, G, h, A, b )

  import numpy as np

  x = np.array ( sol['x'] )
  x = np.squeeze ( x )

  print ( '' )
  print ( '  Cost is minimized at x = [', x[0],',', x[1], ']' )
  cost = 2.0 * x[0]**2 + x[1]**2 + x[0]*x[1] + x[0] + x[1]
  print ( '  Minimized cost is ', cost )

  return

if ( __name__ == '__main__' ):
  cvxopt_example ( )