cauchy.py

import warnings

import numpy

import chainer
from chainer.backends import cuda
from chainer import distribution
from chainer.functions.math import exponential
from chainer.functions.math import trigonometric
from chainer.utils import cache


def _cauchy_icdf(x):
    x = chainer.as_variable(x)
    h = (x - 0.5) * numpy.pi
    y = chainer.functions.tan(h)
    return y


class Cauchy(distribution.Distribution):

    """Cauchy Distribution.

    The probability density function of the distribution is expressed as

    .. math::
        p(x;x_0,\\gamma) = \\frac{1}{\\pi}\\frac{\\gamma}{(x-x_0)^2+\\gamma^2}

    Args:
        loc(:class:`~chainer.Variable` or :ref:`ndarray`): Parameter of
            distribution representing the location :math:`x_0`.
        scale(:class:`~chainer.Variable` or :ref:`ndarray`): Parameter of
            distribution representing the scale :math:`\\gamma`.
    """

    def __init__(self, loc, scale):
        super(Cauchy, self).__init__()
        self.__loc = loc
        self.__scale = scale

    @cache.cached_property
    def loc(self):
        return chainer.as_variable(self.__loc)

    @cache.cached_property
    def scale(self):
        return chainer.as_variable(self.__scale)

    @property
    def batch_shape(self):
        return self.loc.shape

    def cdf(self, x):
        return (
            (1 / numpy.pi
             * trigonometric.arctan((x - self.loc) / self.scale))
            + 0.5)

    @cache.cached_property
    def entropy(self):
        return exponential.log(4 * numpy.pi * self.scale)

    @property
    def event_shape(self):
        return ()

    def icdf(self, x):
        return self.loc + self.scale * _cauchy_icdf(x)

    @property
    def _is_gpu(self):
        return isinstance(self.loc.data, cuda.ndarray)

    def log_prob(self, x):
        return (
            - numpy.log(numpy.pi)
            + exponential.log(self.scale)
            - exponential.log((x - self.loc)**2 + self.scale**2))

    @cache.cached_property
    def mean(self):
        warnings.warn('Mean of the cauchy distribution is undefined.',
                      RuntimeWarning)
        xp = chainer.backend.get_array_module(self.loc)
        return chainer.as_variable(xp.full_like(self.loc.data, xp.nan))

    @property
    def params(self):
        return {'loc': self.loc, 'scale': self.scale}

    def sample_n(self, n):
        xp = chainer.backend.get_array_module(self.loc)
        if xp is cuda.cupy:
            eps = xp.random.standard_cauchy(
                (n,)+self.loc.shape, dtype=self.loc.dtype)
        else:
            eps = xp.random.standard_cauchy(
                (n,)+self.loc.shape).astype(self.loc.dtype)

        noise = self.scale * eps + self.loc

        return noise

    @property
    def support(self):
        return 'real'

    @cache.cached_property
    def variance(self):
        warnings.warn('Variance of the cauchy distribution is undefined.',
                      RuntimeWarning)
        xp = chainer.backend.get_array_module(self.loc)
        return chainer.as_variable(xp.full_like(self.loc.data, xp.nan))