<|file_name|>cauchy.py<|end_file_name|><｜fim▁begin｜># Licensed to the Apache Software Foundation (ASF) under one
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# to you under the Apache License, Version 2.0 (the
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#
#   http://www.apache.org/licenses/LICENSE-2.0
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# under the License.

# coding: utf-8
# pylint: disable=wildcard-import
"""Cauchy distribution"""

__all__ = ['Cauchy']

from numbers import Number
from numpy import nan, pi
from .constraint import Real
from .distribution import Distribution
from .utils import sample_n_shape_converter
from .... import np


class Cauchy(Distribution):
    r"""Create a relaxed Cauchy distribution object.

    Parameters
    ----------
    loc : Tensor or scalar, default 0
        mode or median of the distribution
    scale : Tensor or scalar, default 1
        half width at half maximum
    """
    # pylint: disable=abstract-method

    has_grad = True
    support = Real()
    arg_constraints = {'loc': Real(), 'scale': Real()}

    def __init__(self, loc=0.0, scale=1.0, validate_args=None):
        self.loc = loc
        self.scale = scale
        super(Cauchy, self).__init__(
            event_dim=0, validate_args=validate_args)

    @property
    def mean(self):
        return nan

    @property
    def variance(self):
        return nan

    def sample(self, size=None):
        # TODO: Implement sampling op in the backend.
        # `np.zeros_like` does not support scalar at this moment.
        if (isinstance(self.loc, Number), isinstance(self.scale, Number)) == (True, True):
                        <|fim_middle|>

        else:
            u = np.random.uniform(np.zeros_like(  # pylint: disable=too-many-function-args
                self.loc + self.scale), size=size)
        return self.icdf(u)

    def sample_n(self, size=None):
        return self.sample(sample_n_shape_converter(size))

    def log_prob(self, value):
        if self._validate_args:
            self._validate_samples(value)
        return (-np.log(pi) - np.log(self.scale) -
                np.log(1 + ((value - self.loc) / self.scale) ** 2))

    def cdf(self, value):
        if self._validate_args:
            self._validate_samples(value)
        return np.arctan((value - self.loc) / self.scale) / pi + 0.5

    def icdf(self, value):
        return np.tan(pi * (value - 0.5)) * self.scale + self.loc

    def entropy(self):
        return np.log(4 * pi) + np.log(self.scale)
<｜fim▁end｜>
            u = np.random.uniform(size=size)