# Source code for niapy.problems.ridge

# encoding=utf8

"""Implementation of Ridge function."""

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

__all__ = ['Ridge']

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

Date: 2018

Author: Lucija Brezočnik

Function: **Ridge function**

:math:f(\mathbf{x}) = \sum_{i=1}^D (\sum_{j=1}^i x_j)^2

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-64, 64], for all :math:i = 1, 2,..., D.

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

LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D (\sum_{j=1}^i x_j)^2$

Equation:
f(\mathbf{x}) =
\sum_{i=1}^D (\sum_{j=1}^i x_j)^2

Domain:
$-64 \leq x_i \leq 64$

Reference:
http://www.cs.unm.edu/~neal.holts/dga/benchmarkFunction/ridge.html

"""

[docs]    def __init__(self, dimension=4, lower=-64.0, upper=64.0, *args, **kwargs):
r"""Initialize Ridge 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'''$f(\mathbf{x}) = \sum_{i=1}^D (\sum_{j=1}^i x_j)^2$'''

def _evaluate(self, x):
inner = np.array([np.sum(x[:i]) for i in range(1, self.dimension + 1)])
return np.sum(inner ** 2)