#!/usr/bin/env python
#
# Problem definition:
# Example in reference documentation for cvxopt
# http://cvxopt.org/examples/tutorial/lp.html
# 
# Author: Mike McKerns (mmckerns @caltech and @uqfoundation)
# Copyright (c) 1997-2016 California Institute of Technology.
# Copyright (c) 2016-2024 The Uncertainty Quantification Foundation.
# License: 3-clause BSD.  The full license text is available at:
#  - https://github.com/uqfoundation/mystic/blob/master/LICENSE
"""
    Minimize: f = 2*x[0] + 1*x[1]

    Subject to:  -1*x[0] + 1*x[1] <= 1
                  1*x[0] + 1*x[1] >= 2
                           1*x[1] >= 0
                  1*x[0] - 2*x[1] <= 4

    where:  -inf <= x[0] <= inf
"""

def objective(x):
  x0,x1 = x
  return 2*x0 + x1

equations = """
-x0 + x1 - 1.0 <= 0.0
-x0 - x1 + 2.0 <= 0.0
x0 - 2*x1 - 4.0 <= 0.0
"""
bounds = [(None, None),(0.0, None)]

# with penalty='penalty' applied, solution is:
xs = [0.5, 1.5]
ys = 2.5

from mystic.symbolic import generate_conditions, generate_penalty
pf = generate_penalty(generate_conditions(equations), k=1e3)
from mystic.symbolic import generate_constraint, generate_solvers, simplify
cf = generate_constraint(generate_solvers(simplify(equations)))



if __name__ == '__main__':

  from mystic.solvers import diffev2, fmin_powell
  from mystic.math import almostEqual

  result = diffev2(objective, x0=bounds, bounds=bounds, penalty=pf, constraint=cf, npop=40, disp=False, full_output=True, ftol=1e-10, gtol=100)
  assert almostEqual(result[0], xs, rel=1e-2)
  assert almostEqual(result[1], ys, rel=1e-2)

  result = fmin_powell(objective, x0=[0.0,0.0], bounds=bounds, penalty=pf, constraint=cf, disp=False, full_output=True, gtol=3)
  assert almostEqual(result[0], xs, rel=1e-2)
  assert almostEqual(result[1], ys, rel=1e-2)


# EOF
