Source code for niapy.problems.ridge

# encoding=utf8

"""Implementation of Ridge function."""

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

__all__ = ['Ridge']

[docs]class Ridge(Problem): r"""Implementation of Ridge function. Date: 2018 Author: Lucija Brezočnik License: MIT Function: **Ridge function** :math:`f(\mathbf{x}) = \sum_{i=1}^D (\sum_{j=1}^i x_j)^2` **Input domain:** The function can be defined on any input domain but it is usually evaluated on the hypercube :math:`x_i ∈ [-64, 64]`, for all :math:`i = 1, 2,..., D`. **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)` LaTeX formats: Inline: $f(\mathbf{x}) = \sum_{i=1}^D (\sum_{j=1}^i x_j)^2 $ Equation: \begin{equation} f(\mathbf{x}) = \sum_{i=1}^D (\sum_{j=1}^i x_j)^2 \end{equation} Domain: $-64 \leq x_i \leq 64$ Reference: """
[docs] def __init__(self, dimension=4, lower=-64.0, upper=64.0, *args, **kwargs): r"""Initialize Ridge 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(\mathbf{x}) = \sum_{i=1}^D (\sum_{j=1}^i x_j)^2 $'''
def _evaluate(self, x): inner = np.array([np.sum(x[:i]) for i in range(1, self.dimension + 1)]) return np.sum(inner ** 2)