# Source code for niapy.problems.rosenbrock

# encoding=utf8

"""Rosenbrock problem."""

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

__all__ = ['Rosenbrock']

[docs]class Rosenbrock(Problem):
r"""Implementation of Rosenbrock problem.

Date: 2018

Authors: Iztok Fister Jr. and Lucija Brezočnik

Function: **Rosenbrock function**

:math:f(\mathbf{x}) = \sum_{i=1}^{D-1} \left (100 (x_{i+1} - x_i^2)^2 + (x_i - 1)^2 \right)

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-30, 30], for all :math:i = 1, 2,..., D.

**Global minimum:** :math:f(x^*) = 0, at :math:x^* = (1,...,1)

LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^{D-1} (100 (x_{i+1} - x_i^2)^2 + (x_i - 1)^2)$

Equation:

f(\mathbf{x}) = \sum_{i=1}^{D-1} (100 (x_{i+1} - x_i^2)^2 + (x_i - 1)^2)

Domain:
$-30 \leq x_i \leq 30$

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=-30.0, upper=30.0, *args, **kwargs):
r"""Initialize Rosenbrock 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'''$f(\mathbf{x}) = \sum_{i=1}^{D-1} (100 (x_{i+1} - x_i^2)^2 + (x_i - 1)^2)$'''

def _evaluate(self, x):
return np.sum(100.0 * (x[1:] - x[:-1] ** 2.0) ** 2.0 + (1 - x[:-1]) ** 2.0, axis=0)