#!/usr/bin/env python

"""
Zimmermann's function

References::
    [1] Storn, R. and Price, K. Differential Evolution - A Simple and Efficient
    Heuristic for Global Optimization over Continuous Spaces. Journal of Global
    Optimization 11: 341-359, 1997.

    [2] Storn, R. and Price, K.
    (Same title as above, but as a technical report.)
    http://www.icsi.berkeley.edu/~storn/deshort1.ps
"""


def zimmermann(x):
    """
    Zimmermann function: a non-continuous function, Equation (24-26) of [2]

    minimum is f(x)=0.0 at x=(7.0,2.0)
    """

    x0, x1 = x  # must provide 2 values (x0,y0)
    f8 = 9 - x0 - x1
    c0, c1, c2, c3 = 0, 0, 0, 0
    if x0 < 0:
        c0 = -100 * x0
    if x1 < 0:
        c1 = -100 * x1
    xx = (x0 - 3.0) * (x0 - 3) + (x1 - 2.0) * (x1 - 2)
    if xx > 16:
        c2 = 100 * (xx - 16)
    if x0 * x1 > 14:
        c3 = 100 * (x0 * x1 - 14.0)
    return max(f8, c0, c1, c2, c3)