# Source code for niapy.problems.powell

# encoding=utf8

"""Implementations of Powell function."""
import numpy as np

from niapy.problems.problem import Problem

__all__ = ['Powell']

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

Date: 2018

Author: Klemen Berkovič

Function:
**Powell Function**

:math:f(\textbf{x}) = \sum_{i = 1}^{D / 4} \left( (x_{4 i - 3} + 10 x_{4 i - 2})^2 + 5 (x_{4 i - 1} - x_{4 i})^2 + (x_{4 i - 2} - 2 x_{4 i - 1})^4 + 10 (x_{4 i - 3} - x_{4 i})^4 \right)

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-4, 5], for all :math:i = 1, 2,..., D.

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

LaTeX formats:
Inline:
$f(\textbf{x}) = \sum_{i = 1}^{D / 4} \left( (x_{4 i - 3} + 10 x_{4 i - 2})^2 + 5 (x_{4 i - 1} - x_{4 i})^2 + (x_{4 i - 2} - 2 x_{4 i - 1})^4 + 10 (x_{4 i - 3} - x_{4 i})^4 \right)$

Equation:
$$f(\textbf{x}) = \sum_{i = 1}^{D / 4} \left( (x_{4 i - 3} + 10 x_{4 i - 2})^2 + 5 (x_{4 i - 1} - x_{4 i})^2 + (x_{4 i - 2} - 2 x_{4 i - 1})^4 + 10 (x_{4 i - 3} - x_{4 i})^4 \right)$$

Domain:
$-4 \leq x_i \leq 5$

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

"""

[docs]    def __init__(self, dimension=4, lower=-4.0, upper=5.0, *args, **kwargs):
r"""Initialize Powell 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'''$f(\textbf{x}) = \sum_{i = 1}^{D / 4} \left( (x_{4 i - 3} + 10 x_{4 i - 2})^2 + 5 (x_{4 i - 1} - x_{4 i})^2 + (x_{4 i - 2} - 2 x_{4 i - 1})^4 + 10 (x_{4 i - 3} - x_{4 i})^4 \right)$'''

def _evaluate(self, x):
x1 = x[range(1, self.dimension - 3, 4)]
x2 = x[range(2, self.dimension - 2, 4)]
x3 = x[range(3, self.dimension - 1, 4)]
x4 = x[range(4, self.dimension, 4)]

term1 = (x1 + 10 * x2) ** 2.0
term2 = 5 * (x3 - x4) ** 2.0
term3 = (x2 - 2 * x3) ** 4.0
term4 = 10 * (x1 - x4) ** 4.0
return np.sum(term1 + term2 + term3 + term4)