# encoding=utf8
"""Implementations of Infinity function."""
import numpy as np
from NiaPy.benchmarks.benchmark import Benchmark
__all__ = ['Infinity']
[docs]class Infinity(Benchmark):
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:
$-1 \leq x_i \leq 1$
Attributes:
Name (List[str]): Names of the benchmark.
See Also:
* :class:`NiaPy.benchmarks.Benchmark`
Reference:
http://infinity77.net/global_optimization/test_functions_nd_I.html#go_benchmark.Infinity
"""
Name = ['Infinity', 'infinity']
[docs] def __init__(self, Lower=-1.0, Upper=1.0):
r"""Initialize of Infinity benchmark.
Args:
Lower (Optional[float]): Lower bound of problem.
Upper (Optional[float]): Upper bound of problem.
See Also:
:func:`NiaPy.benchmarks.Benchmark.__init__`
"""
Benchmark.__init__(self, Lower, Upper)
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code
"""
return r'''$f(\textbf{x}) = \sum_{i = 1}^D x_i^6 \left( \sin \left( \frac{1}{x_i} \right) + 2 \right)$'''
[docs] def function(self):
r"""Return benchmark evaluation function.
Returns:
Callable[[int, Union[int, float, list, numpy.ndarray], Dict[str, Any]], float]: Fitness function
"""
def f(D, X, **kwargs):
r"""Fitness function.
Args:
D (int): Dimensionality of the problem
X (Union[int, float, list, numpy.ndarray]): Solution to check.
kwargs (Dict[str, Any]): Additional arguments.
Returns:
float: Fitness value for the solution.
"""
val = 0.0
for i in range(D): val += X[i] ** 6 * (np.sin(1 / X[i]) + 2)
return val
return f