# Source code for niapy.problems.dixon_price

# encoding=utf8

"""Implementations of Dixon Price function."""
import numpy as np

from niapy.problems.problem import Problem

__all__ = ['DixonPrice']

[docs]class DixonPrice(Problem):
r"""Implementations of Dixon Price function.

Date: 2018

Author: Klemen Berkovič

Function:
**Dixon Price Function**

:math:f(\textbf{x}) = (x_1 - 1)^2 + \sum_{i = 2}^D i (2x_i^2 - x_{i - 1})^2

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

**Global minimum:**
:math:f(\textbf{x}^*) = 0 at :math:\textbf{x}^* = (2^{-\frac{2^1 - 2}{2^1}}, \cdots , 2^{-\frac{2^i - 2}{2^i}} , \cdots , 2^{-\frac{2^D - 2}{2^D}})

LaTeX formats:
Inline:
$f(\textbf{x}) = (x_1 - 1)^2 + \sum_{i = 2}^D i (2x_i^2 - x_{i - 1})^2$

Equation:
$$f(\textbf{x}) = (x_1 - 1)^2 + \sum_{i = 2}^D i (2x_i^2 - x_{i - 1})^2$$

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

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

"""

[docs]    def __init__(self, dimension=4, lower=-10.0, upper=10.0, *args, **kwargs):
r"""Initialize Dixon Price 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'''$f(\textbf{x}) = (x_1 - 1)^2 + \sum_{i = 2}^D i (2x_i^2 - x_{i - 1})^2$'''

def _evaluate(self, x):
indices = np.arange(2, self.dimension)
val = np.sum(indices * (2 * x[2:] ** 2 - x[1:self.dimension - 1]) ** 2)
return (x[0] - 1) ** 2 + val