# Source code for niapy.problems.katsuura

# encoding=utf8

"""Implementations of Katsuura functions."""

from math import fabs
from niapy.problems.problem import Problem

__all__ = ['Katsuura']

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

Date: 2018

Author: Klemen Berkovič

Function:
**Katsuura Function**

:math:f(\textbf{x}) = \frac{10}{D^2} \prod_{i=1}^D \left( 1 + i \sum_{j=1}^{32} \frac{\lvert 2^j x_i - round\left(2^j x_i \right) \rvert}{2^j} \right)^\frac{10}{D^{1.2}} - \frac{10}{D^2}

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-100, 100], for all :math:i = 1, 2,..., D.

**Global minimum:** :math:f(x^*) = 0, at :math:x^* = (420.968746,...,420.968746)

LaTeX formats:
Inline:
$f(\textbf{x}) = \frac{10}{D^2} \prod_{i=1}^D \left( 1 + i \sum_{j=1}^{32} \frac{\lvert 2^j x_i - round\left(2^j x_i \right) \rvert}{2^j} \right)^\frac{10}{D^{1.2}} - \frac{10}{D^2}$
Equation:
$$f(\textbf{x}) = \frac{10}{D^2} \prod_{i=1}^D \left( 1 + i \sum_{j=1}^{32} \frac{\lvert 2^j x_i - round\left(2^j x_i \right) \rvert}{2^j} \right)^\frac{10}{D^{1.2}} - \frac{10}{D^2}$$

Domain:
$-100 \leq x_i \leq 100$

Reference:

"""

[docs]    def __init__(self, dimension=5, lower=-100.0, upper=100.0, *args, **kwargs):
r"""Initialize Katsuura 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'''$f(\textbf{x}) = \frac{10}{D^2} \prod_{i=1}^D \left( 1 + i \sum_{j=1}^{32} \frac{| 2^j x_i - round\left(2^j x_i \right) |}{2^j} \right)^\frac{10}{D^{1.2}} - \frac{10}{D^2}$'''

def _evaluate(self, x):
val = 1.0
for i in range(self.dimension):
val_t = 1.0
for j in range(1, 33):
val_t += fabs(2 ** j * x[i] - round(2 ** j * x[i])) / 2 ** j
val *= (1 + (i + 1) * val_t) ** (10 / self.dimension ** 1.2) - (10 / self.dimension ** 2)
return 10 / self.dimension ** 2 * val