Source code for niapy.problems.rosenbrock

# encoding=utf8

"""Rosenbrock problem."""

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

__all__ = ['Rosenbrock']


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

    Date: 2018

    Authors: Iztok Fister Jr. and Lucija Brezočnik

    License: MIT

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

        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.

    """

    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.

        See Also:
            :func:`niapy.problems.Problem.__init__`

        """
        super().__init__(dimension, lower, upper, *args, **kwargs)

    @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)