# Source code for niapy.problems.quintic

# encoding=utf8

"""Implementation of Quintic funcion."""

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

__all__ = ['Quintic']

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

Date: 2018

Author: Lucija Brezočnik

Function: **Quintic function**

:math:f(\mathbf{x}) = \sum_{i=1}^D \left| x_i^5 - 3x_i^4 +
4x_i^3 + 2x_i^2 - 10x_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 ∈ [-10, 10], for all :math:i = 1, 2,..., D.

**Global minimum:** :math:f(x^*) = 0, at :math:x^* = f(-1\; \text{or}\; 2)

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

Equation:
f(\mathbf{x}) =
\sum_{i=1}^D \left| x_i^5 - 3x_i^4 + 4x_i^3 + 2x_i^2 -
10x_i - 4\right|

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

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=-10.0, upper=10.0, *args, **kwargs):
r"""Initialize Quintic 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'''$f(\mathbf{x}) = \sum_{i=1}^D \left| x_i^5 - 3x_i^4 + 4x_i^3 + 2x_i^2 - 10x_i - 4\right|$'''

def _evaluate(self, x):
return np.sum(np.abs(x ** 5 - 3.0 * x ** 4 + 4.0 * x ** 3 + 2.0 * x ** 2 - 10.0 * x - 4.0))