_sphere.py

"""Sphere function, a common benchmark for optimization algorithms."""
# copyright: hyperactive developers, MIT License (see LICENSE file)

import numpy as np

from hyperactive.base import BaseExperiment


class Sphere(BaseExperiment):
    r"""Simple Sphere function, common benchmark for optimization algorithms.

    Sphere function parameterized by the formula:

    .. math::
        f(x_1, x_2, \ldots, x_n) = \sum_{i=1}^n x_i^2 + c

    where :math:`c` is a constant offset added to the sum of squares,
    and :math:`n` is the number of dimensions.
    Both :math:`c` (= `const`) and :math:`n` (= `n_dim`) can be set as parameters.

    The function arguments :math:`x_1`, :math:`x_2`, ..., :math:`x_n`
    are the input variables of the `score` method,
    and are set as `x0`, `x1`, ..., `x[n]` respectively.

    This function is a common test function for optimization algorithms.

    Parameters
    ----------
    const : float, optional, default=0
        A constant offset added to the sum of squares.
    n_dim : int, optional, default=2
        The number of dimensions for the Sphere function. The default is 2.

    Example
    -------
    >>> from hyperactive.experiment.toy import Sphere
    >>> sphere = Sphere(const=0, n_dim=3)
    >>> params = {"x0": 1, "x1": 2, "x2": 3}
    >>> score, add_info = sphere.score(params)

    Quick call without metadata return or dictionary:
    >>> score = sphere(x0=1, x1=2, x2=3)

    Different number of dimensions changes the parameter names:
    >>> sphere4D = Sphere(const=0, n_dim=4)
    >>> score4D = sphere4D(x0=1, x1=2, x2=3, x3=4)
    """

    _tags = {
        "property:randomness": "deterministic",  # random or deterministic
        # if deterministic, two calls of score will result in the same value
        # random = two calls may result in different values; same as "stochastic"
        "property:higher_or_lower_is_better": "lower",
        # values are "higher", "lower", "mixed"
        # whether higher or lower scores are better
    }

    def __init__(self, const=0, n_dim=2):
        self.const = const
        self.n_dim = n_dim

        super().__init__()

    def _paramnames(self):
        return [f"x{i}" for i in range(self.n_dim)]

    def _evaluate(self, params):
        """Evaluate the parameters.

        Parameters
        ----------
        params : dict with string keys
            Parameters to evaluate.

        Returns
        -------
        float
            The value of the parameters as per evaluation.
        dict
            Additional metadata about the search.
        """
        params_vec = np.array([params[f"x{i}"] for i in range(self.n_dim)])
        return np.sum(params_vec ** 2) + self.const, {}

    @classmethod
    def get_test_params(cls, parameter_set="default"):
        """Return testing parameter settings for the skbase object.

        ``get_test_params`` is a unified interface point to store
        parameter settings for testing purposes. This function is also
        used in ``create_test_instance`` and ``create_test_instances_and_names``
        to construct test instances.

        ``get_test_params`` should return a single ``dict``, or a ``list`` of ``dict``.

        Each ``dict`` is a parameter configuration for testing,
        and can be used to construct an "interesting" test instance.
        A call to ``cls(**params)`` should
        be valid for all dictionaries ``params`` in the return of ``get_test_params``.

        The ``get_test_params`` need not return fixed lists of dictionaries,
        it can also return dynamic or stochastic parameter settings.

        Parameters
        ----------
        parameter_set : str, default="default"
            Name of the set of test parameters to return, for use in tests. If no
            special parameters are defined for a value, will return `"default"` set.

        Returns
        -------
        params : dict or list of dict, default = {}
            Parameters to create testing instances of the class
            Each dict are parameters to construct an "interesting" test instance, i.e.,
            `MyClass(**params)` or `MyClass(**params[i])` creates a valid test instance.
            `create_test_instance` uses the first (or only) dictionary in `params`
        """
        params0 = {}
        params1 = {"n_dim": 3, "const": 1.0}
        return [params0, params1]

    @classmethod
    def _get_score_params(self):
        """Return settings for testing score/evaluate functions. Used in tests only.

        Returns a list, the i-th element should be valid arguments for
        self.evaluate and self.score, of an instance constructed with
        self.get_test_params()[i].

        Returns
        -------
        list of dict
            The parameters to be used for scoring.
        """
        score_params0 = {"x0": 0, "x1": 0}
        score_params1 = {"x0": 1, "x1": 2, "x2": 3}
        return [score_params0, score_params1]