# Source code for niapy.problems.qing

# encoding=utf8

"""Implementation of Qing funcion."""

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

__all__ = ['Qing']

[docs]class Qing(Problem):
r"""Implementation of Qing function.

Date: 2018

Author: Lucija Brezočnik

Function: **Qing function**

:math:f(\mathbf{x}) = \sum_{i=1}^D \left(x_i^2 - i\right)^2

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-500, 500], for all :math:i = 1, 2,..., D.

**Global minimum:** :math:f(x^*) = 0, at :math:x^* = (\pm √i))

LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D \left (x_i^2 - i\right)^2$

Equation:
f(\mathbf{x}) =
\sum_{i=1}^D \left{(x_i^2 - i\right)}^2

Domain:
$-500 \leq x_i \leq 500$

Reference paper:
Jamil, M., and Yang, X. S. (2013).
A literature survey of benchmark functions for global optimisation problems.
International Journal of Mathematical Modelling and Numerical Optimisation,
4(2), 150-194.

"""

[docs]    def __init__(self, dimension=4, lower=-500.0, upper=500.0, *args, **kwargs):
r"""Initialize Qing 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'''$f(\mathbf{x}) = \sum_{i=1}^D \left (x_i^2 - i\right)^2$'''

def _evaluate(self, x):
return np.sum(np.power(x ** 2.0 - np.arange(1, self.dimension + 1), 2.0))