# Source code for niapy.problems.ackley

# encoding=utf8

"""Implementation of Ackley problem."""

import numpy as np

from niapy.problems.problem import Problem

__all__ = ['Ackley']

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

Date: 2018

Author: Lucija Brezočnik

Function: **Ackley function**

:math:f(\mathbf{x}) = -a\;\exp\left(-b \sqrt{\frac{1}{D}\sum_{i=1}^D x_i^2}\right)
- \exp\left(\frac{1}{D}\sum_{i=1}^D \cos(c\;x_i)\right) + a + \exp(1)

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-32.768, 32.768], for all :math:i = 1, 2,..., D.

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

LaTeX formats:
Inline:
$f(\mathbf{x}) = -a\;\exp\left(-b \sqrt{\frac{1}{D} \sum_{i=1}^D x_i^2}\right) - \exp\left(\frac{1}{D} \sum_{i=1}^D cos(c\;x_i)\right) + a + \exp(1)$

Equation:
f(\mathbf{x}) =
-a\;\exp\left(-b \sqrt{\frac{1}{D} \sum_{i=1}^D x_i^2}\right) -
\exp\left(\frac{1}{D} \sum_{i=1}^D \cos(c\;x_i)\right) +
a + \exp(1)

Domain:
$-32.768 \leq x_i \leq 32.768$

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

"""

[docs]    def __init__(self, dimension=4, lower=-32.768, upper=32.768, a=20.0, b=0.2, c=2 * np.pi, *args, **kwargs):
r"""Initialize Ackley 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.
a (Optional[float]): a parameter.
b (Optional[float]): b parameter.
c (Optional[float]): c parameter.

:func:niapy.problems.Problem.__init__

"""
super().__init__(dimension, lower, upper, *args, **kwargs)
self.a = a
self.b = b
self.c = c

[docs]    @staticmethod
def latex_code():
r"""Return the latex code of the problem.

Returns:
str: Latex code.

"""
return r'''$f(\mathbf{x}) = -a\;\exp\left(-b \sqrt{\frac{1}{D} \sum_{i=1}^D x_i^2}\right) - \exp\left(\frac{1}{D} \sum_{i=1}^D \cos(c\;x_i)\right) + a + \exp(1)$'''

def _evaluate(self, x):
val1 = np.sum(np.square(x))
val2 = np.sum(np.cos(self.c * x))

temp1 = -self.b * np.sqrt(val1 / self.dimension)
temp2 = val2 / self.dimension

return -self.a * np.exp(temp1) - np.exp(temp2) + self.a + np.exp(1)