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:
	**Weierstass 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']
	a, b, k_max = 0.5, 3, 20

	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]): TODO
			b (Optional[float]): TODO
			k (Optional[float]): TODO

		See Also:
			:func:`NiaPy.benchmarks.Benchmark.__init__`
		"""
		Benchmark.__init__(self, Lower, Upper)
		Weierstrass.a, Weierstrass.b, Weierstrass.k_max = a, b, 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
		"""
		a, b, k_max = self.a, self.b, self.k_max
		def f(D, sol, a=a, b=b, k_max=k_max):
			r"""Fitness function.

			Args:
				D (int): Dimensionality of the problem
				sol (Union[int, float, List[int, float], numpy.ndarray]): Solution to check.
				a (Optional[float]): TODO
				b (Optional[float]): TODO
				k (Optional[float]): TODO

			Returns:
				float: Fitness value for the solution.
			"""
			val1 = 0.0
			for i in range(D):
				val = 0.0
				for k in range(k_max): val += a ** k * cos(2 * pi * b ** k * (sol[i] + 0.5))
				val1 += val
			val2 = 0.0
			for k in range(k_max): val2 += a ** k * cos(2 * pi * b ** k * 0.5)
			return val1 - D * val2
		return f

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