# Source code for niapy.problems.perm

# encoding=utf8

"""Implementations of Perm function."""
import numpy as np

from niapy.problems.problem import Problem

__all__ = ['Perm']

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

Date: 2018

Author: Klemen Berkovič

Function:
**Perm Function**

:math:f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2

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

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

LaTeX formats:
Inline:
$f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2$

Equation:
$$f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2$$

Domain:
$-D \leq x_i \leq D$

Reference:
https://www.sfu.ca/~ssurjano/perm0db.html

"""

[docs]    def __init__(self, dimension=4, beta=0.5, *args, **kwargs):
r"""Initialize Perm problem.

Args:
dimension (Optional[int]): Dimension of the problem.
beta (Optional[float]): Beta parameter.

:func:niapy.problems.Problem.__init__

"""
super().__init__(dimension, -dimension, dimension, *args, **kwargs)
self.beta = beta

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

Returns:
str: Latex code.

"""
return r'''$f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2$'''

def _evaluate(self, x):
ii = np.arange(1, self.dimension + 1)
jj = np.tile(ii, (self.dimension, 1))
x_matrix = np.tile(x, (self.dimension, 1))
inner = np.sum((jj + self.beta) * (np.power(x_matrix, ii) - np.power(1.0 / jj, ii)), axis=0)
return np.sum(inner ** 2)