# Source code for niapy.problems.styblinski_tang

# encoding=utf8

"""Styblinski Tang problem."""

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

__all__ = ['StyblinskiTang']

[docs]class StyblinskiTang(Problem):
r"""Implementation of Styblinski-Tang functions.

Date: 2018

Authors: Lucija Brezočnik

Function: **Styblinski-Tang function**

:math:f(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^D \left(
x_i^4 - 16x_i^2 + 5x_i \right)

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-5, 5], for all :math:i = 1, 2,..., D.

**Global minimum:** :math:f(x^*) = -78.332, at :math:x^* = (-2.903534,...,-2.903534)

LaTeX formats:
Inline:
$f(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^D \left( x_i^4 - 16x_i^2 + 5x_i \right)$

Equation:
f(\mathbf{x}) =
\frac{1}{2} \sum_{i=1}^D \left( x_i^4 - 16x_i^2 + 5x_i \right)

Domain:
$-5 \leq x_i \leq 5$

Reference paper:
Jamil, M., and Yang, X. S. (2013).
A literature survey of benchmark functions for global optimisation problems.
International Journal of Mathematical Modelling and Numerical Optimisation,
4(2), 150-194.

"""

[docs]    def __init__(self, dimension=4, lower=-5.0, upper=5.0, *args, **kwargs):
r"""Initialize Styblinski Tang 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)

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

Returns:
str: Latex code.

"""
return r'''$f(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^D \left( x_i^4 - 16x_i^2 + 5x_i \right)$'''

def _evaluate(self, x):
return 0.5 * np.sum(x ** 4 - 16.0 * x ** 2 + 5.0 * x)