Source code for niapy.problems.infinity
# encoding=utf8
"""Implementations of Infinity function."""
import numpy as np
from niapy.problems.problem import Problem
__all__ = ['Infinity']
[docs]class Infinity(Problem):
r"""Implementations of Infinity function.
Date: 2018
Author: Klemen Berkovič
License: MIT
Function:
**Infinity Function**
:math:`f(\textbf{x}) = \sum_{i = 1}^D x_i^6 \left( \sin \left( \frac{1}{x_i} \right) + 2 \right)`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-1, 1]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:**
:math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`
LaTeX formats:
Inline:
$f(\textbf{x}) = \sum_{i = 1}^D x_i^6 \left( \sin \left( \frac{1}{x_i} \right) + 2 \right)$
Equation:
\begin{equation} f(\textbf{x}) = \sum_{i = 1}^D x_i^6 \left( \sin \left( \frac{1}{x_i} \right) + 2 \right) \end{equation}
Domain:
$-1 \leq x_i \leq 1$
Reference:
http://infinity77.net/global_optimization/test_functions_nd_I.html#go_benchmark.Infinity
"""
[docs] def __init__(self, dimension=2, lower=-1.0, upper=1.0, *args, **kwargs):
r"""Initialize Infinity 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.
See Also:
: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'''$f(\textbf{x}) = \sum_{i = 1}^D x_i^6 \left( \sin \left( \frac{1}{x_i} \right) + 2 \right)$'''
def _evaluate(self, x):
return np.sum(x ** 6.0 * (np.sin(1.0 / x) + 2.0))
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