# Source code for niapy.problems.zakharov

# encoding=utf8
"""Implementations of Zakharov function."""

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

__all__ = ['Zakharov']

[docs]class Zakharov(Problem):
r"""Implementations of Zakharov functions.

Date: 2018

Author: Klemen Berkovič

Function:
**Zakharov Function**

:math:f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-5, 10], for all :math:i = 1, 2,..., D.

**Global minimum:**
:math:f(\textbf{x}^*) = 0 at :math:\textbf{x}^* = (0, \cdots, 0)

LaTeX formats:
Inline:
$f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4$

Equation:
$$f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4$$

Domain:
$-5 \leq x_i \leq 10$

Reference:
https://www.sfu.ca/~ssurjano/zakharov.html

"""

[docs]    def __init__(self, dimension=4, lower=-5.0, upper=10.0, *args, **kwargs):
r"""Initialize Zakharov 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.

: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'''$f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4$'''

def _evaluate(self, x):
sum1 = np.sum(x * x)
sum2 = np.sum(0.5 * np.arange(1, self.dimension + 1) * x)
return sum1 + sum2 ** 2 + sum2 ** 4