# Source code for niapy.problems.rastrigin

# encoding=utf8

"""Implementation of Rastrigin function."""

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

__all__ = ['Rastrigin']

[docs]class Rastrigin(Problem):
r"""Implementation of Rastrigin problem.

Date: 2018

Authors: Lucija Brezočnik and Iztok Fister Jr.

Function: **Rastrigin function**

:math:f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-5.12, 5.12], for all :math:i = 1, 2,..., D.

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

LaTeX formats:
Inline:
$f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)$

Equation:
f(\mathbf{x}) =
10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)

Domain:
$-5.12 \leq x_i \leq 5.12$

Reference:
https://www.sfu.ca/~ssurjano/rastr.html

"""

[docs]    def __init__(self, dimension=4, lower=-5.12, upper=5.12, *args, **kwargs):
r"""Initialize Rastrigin 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'''$f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)$'''

def _evaluate(self, x):
return 10.0 * self.dimension + np.sum(x * x - 10.0 * np.cos(2 * np.pi * x))