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  """Implementation of Rastrigin function."""
  
  import numpy as np
  from niapy.problems.problem import Problem
  
  __all__ = ['Rastrigin']
  
  
  class Rastrigin(Problem):
      r"""Implementation of Rastrigin problem.
  
      Date: 2018
  
      Authors: Lucija Brezočnik and Iztok Fister Jr.
  
      License: MIT
  
      Function: **Rastrigin function**
  
          :math:`f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)`
  
          **Input domain:**
          The function can be defined on any input domain but it is usually
          evaluated on the hypercube :math:`x_i ∈ [-5.12, 5.12]`, for all :math:`i = 1, 2,..., D`.
  
          **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)`
  
      LaTeX formats:
          Inline:
              $f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)$
  
          Equation:
              \begin{equation} f(\mathbf{x}) =
              10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)
              \end{equation}
  
          Domain:
              $-5.12 \leq x_i \leq 5.12$
  
      Reference:
          https://www.sfu.ca/~ssurjano/rastr.html
  
      """
  
      def __init__(self, dimension=4, lower=-5.12, upper=5.12, *args, **kwargs):
          r"""Initialize Rastrigin 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)
  
      @staticmethod
      def latex_code():
          r"""Return the latex code of the problem.
  
          Returns:
              str: Latex code.
  
          """
          return r'''$f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)$'''
  
      def _evaluate(self, x):
          return 10.0 * self.dimension + np.sum(x * x - 10.0 * np.cos(2 * np.pi * x))
  