# Source code for niapy.problems.happy_cat

# encoding=utf8

"""Implementation of Happy Cat function."""

import numpy as np
from niapy.problems.problem import Problem

__all__ = ['HappyCat']

[docs]class HappyCat(Problem):
r"""Implementation of Happy cat function.

Date: 2018

Author: Lucija Brezočnik

Function: **Happy cat function**

:math:f(\mathbf{x}) = {\left |\sum_{i = 1}^D {x_i}^2 - D \right|}^{1/4} + (0.5 \sum_{i = 1}^D {x_i}^2 + \sum_{i = 1}^D x_i) / D + 0.5

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-100, 100], for all :math:i = 1, 2,..., D.

**Global minimum:** :math:f(x^*) = 0, at :math:x^* = (-1,...,-1)

LaTeX formats:
Inline:
$f(\mathbf{x}) = {\left|\sum_{i = 1}^D {x_i}^2 - D \right|}^{1/4} + (0.5 \sum_{i = 1}^D {x_i}^2 + \sum_{i = 1}^D x_i) / D + 0.5$

Equation:
f(\mathbf{x}) = {\left| \sum_{i = 1}^D {x_i}^2 -
D \right|}^{1/4} + (0.5 \sum_{i = 1}^D {x_i}^2 +
\sum_{i = 1}^D x_i) / D + 0.5

Domain:
$-100 \leq x_i \leq 100$

Reference: http://bee22.com/manual/tf_images/Liang%20CEC2014.pdf &
Beyer, H. G., & Finck, S. (2012). HappyCat - A Simple Function Class Where Well-Known Direct Search Algorithms Do Fail.
In International Conference on Parallel Problem Solving from Nature (pp. 367-376). Springer, Berlin, Heidelberg.

"""

[docs]    def __init__(self, dimension=4, lower=-100.0, upper=100.0, alpha=0.25, *args, **kwargs):
r"""Initialize Happy cat problem..

Args:
dimension (Optional[int]): Dimension of the problem.
lower (Optional[Union[float, Iterable[float]]]): Lower bounds of the problem.
upper (Optional[Union[float, Iterable[float]]]): Upper bounds of the problem.

:func:niapy.problems.Problem.__init__

"""
super().__init__(dimension, lower, upper, *args, **kwargs)
self.alpha = alpha

[docs]    @staticmethod
def latex_code():
r"""Return the latex code of the problem.

Returns:
str: Latex code.

"""
return r'''$f(\mathbf{x}) = {\left|\sum_{i = 1}^D {x_i}^2 - D \right|}^{1/4} + (0.5 \sum_{i = 1}^D {x_i}^2 + \sum_{i = 1}^D x_i) / D + 0.5$'''

def _evaluate(self, x):
val1 = np.sum(np.abs(x * x - self.dimension) ** self.alpha)
val2 = np.sum((0.5 * x * x + x) / self.dimension)
return val1 + val2 + 0.5