Source code for niapy.benchmarks.weierstrass

# encoding=utf8
"""Implementations of Weierstrass functions."""

from math import pi, cos
from niapy.benchmarks.benchmark import Benchmark

__all__ = ['Weierstrass']


class Weierstrass(Benchmark):
    r"""Implementations of Weierstrass functions.

    Date: 2018

    Author: Klemen Berkovič

    License: MIT

    Function:
    **Weierstrass Function**

        :math:`f(\textbf{x}) = \sum_{i=1}^D \left( \sum_{k=0}^{k_{max}} a^k \cos\left( 2 \pi b^k ( x_i + 0.5) \right) \right) - D \sum_{k=0}^{k_{max}} a^k \cos \left( 2 \pi b^k \cdot 0.5 \right)`

        **Input domain:**
        The function can be defined on any input domain but it is usually
        evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
        Default value of a = 0.5, b = 3 and k_max = 20.

        **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`

    LaTeX formats:
        Inline:
            $$f(\textbf{x}) = \sum_{i=1}^D \left( \sum_{k=0}^{k_{max}} a^k \cos\left( 2 \pi b^k ( x_i + 0.5) \right) \right) - D \sum_{k=0}^{k_{max}} a^k \cos \left( 2 \pi b^k \cdot 0.5 \right)

        Equation:
            \begin{equation} f(\textbf{x}) = \sum_{i=1}^D \left( \sum_{k=0}^{k_{max}} a^k \cos\left( 2 \pi b^k ( x_i + 0.5) \right) \right) - D \sum_{k=0}^{k_{max}} a^k \cos \left( 2 \pi b^k \cdot 0.5 \right) \end{equation}

        Domain:
            $-100 \leq x_i \leq 100$

    Reference:
        http://www5.zzu.edu.cn/__local/A/69/BC/D3B5DFE94CD2574B38AD7CD1D12_C802DAFE_BC0C0.pdf

    """

    Name = ['Weierstrass']

    def __init__(self, lower=-100.0, upper=100.0, a=0.5, b=3, k_max=20):
        r"""Initialize of Bent Cigar benchmark.

        Args:
            lower (Optional[float]): Lower bound of problem.
            upper (Optional[float]): Upper bound of problem.
            a (Optional[float]): The a parameter.
            b (Optional[float]): The b parameter.
            k_max (Optional[int]): Number of elements of the series to compute.

        See Also:
            :func:`niapy.benchmarks.Benchmark.__init__`

        """
        super().__init__(lower, upper)
        self.a = a
        self.b = b
        self.k_max = k_max

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

        Returns:
            str: Latex code.

        """
        return r'''$f(\textbf{x}) = \sum_{i=1}^D \left( \sum_{k=0}^{k_{max}} a^k \cos\left( 2 \pi b^k ( x_i + 0.5) \right) \right) - D \sum_{k=0}^{k_{max}} a^k \cos \left( 2 \pi b^k \cdot 0.5 \right)$'''

    def function(self):
        r"""Return benchmark evaluation function.

        Returns:
            Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function.

        """
        def f(dimension, x):
            r"""Fitness function.

            Args:
                dimension (int): Dimensionality of the problem
                x (Union[int, float, List[int, float], numpy.ndarray]): Solution to check.

            Returns:
                float: Fitness value for the solution.

            """
            val1 = 0.0
            for i in range(dimension):
                val = 0.0
                for k in range(self.k_max):
                    val += self.a ** k * cos(2 * pi * self.b ** k * (x[i] + 0.5))
                val1 += val
            val2 = 0.0
            for k in range(self.k_max):
                val2 += self.a ** k * cos(2 * pi * self.b ** k * 0.5)
            return val1 - dimension * val2

        return f

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