# Copyright 2020 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
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# ============================================================================
"""Gumbel Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.ops import functional as F
from mindspore import _checkparam as Validator
from mindspore.common import dtype as mstype
import mindspore.nn.probability.bijector as msb
import mindspore.nn.probability.distribution as msd
from .transformed_distribution import TransformedDistribution
from ._utils.utils import check_distribution_name
from ._utils.custom_ops import exp_generic, log_generic
[docs]class Gumbel(TransformedDistribution):
r"""
Gumbel distribution.
A Gumbel distributio is a continuous distribution with the range of all real numbers
and the probability density function:
.. math::
f(x, a, b) = 1 / b \exp(\exp(-(x - a) / b) - x),
where :math:`a, b` are loc and scale parameter respectively.
Args:
loc (int, float, list, numpy.ndarray, Tensor): The location of Gumbel distribution.
scale (int, float, list, numpy.ndarray, Tensor): The scale of Gumbel distribution.
seed (int): the seed used in sampling. The global seed is used if it is None. Default: ``0`` .
dtype (mindspore.dtype): type of the distribution. Default: ``mstype.float32`` .
name (str): the name of the distribution. Default: ``'Gumbel'`` .
Note:
`scale` must be greater than zero.
`dist_spec_args` are `loc` and `scale`.
`dtype` must be a float type because Gumbel distributions are continuous.
Raises:
ValueError: When scale <= 0.
TypeError: When the input `dtype` is not a subclass of float.
Supported Platforms:
``Ascend`` ``GPU``
Examples:
>>> import mindspore
>>> import numpy as np
>>> import mindspore.nn.probability.distribution as msd
>>> import mindspore.nn as nn
>>> from mindspore import Tensor
>>> class Prob(nn.Cell):
... def __init__(self):
... super(Prob, self).__init__()
... self.gum = msd.Gumbel(np.array([0.0]), np.array([[1.0], [2.0]]), dtype=mindspore.float32)
...
... def construct(self, x_):
... return self.gum.prob(x_)
>>> value = np.array([1.0, 2.0]).astype(np.float32)
>>> pdf = Prob()
>>> output = pdf(Tensor(value, dtype=mindspore.float32))
"""
def __init__(self,
loc,
scale,
seed=0,
dtype=mstype.float32,
name="Gumbel"):
"""
Constructor of Gumbel distribution.
"""
valid_dtype = mstype.float_type
Validator.check_type_name(
"dtype", dtype, valid_dtype, type(self).__name__)
gumbel_cdf = msb.GumbelCDF(loc, scale)
super(Gumbel, self).__init__(
distribution=msd.Uniform(0.0, 1.0, dtype=dtype),
bijector=msb.Invert(gumbel_cdf),
seed=seed, name=name)
# overwrite default_parameters and parameter_names
self._reset_parameters()
self._loc = self._add_parameter(loc, 'loc')
self._scale = self._add_parameter(scale, 'scale')
self._gumbel_bijector = gumbel_cdf
# ops needed for the class
self.cast = P.Cast()
self.const = P.ScalarToTensor()
self.exp = exp_generic
self.expm1 = P.Expm1()
self.lgamma = P.Lgamma()
self.log = log_generic
self.shape = P.Shape()
self.squeeze = P.Squeeze(0)
self.sqrt = P.Sqrt()
@property
def loc(self):
"""
Return the location of the distribution after casting to dtype.
Output:
Tensor, the loc parameter of the distribution.
"""
return self._loc
@property
def scale(self):
"""
Return the scale of the distribution after casting to dtype.
Output:
Tensor, the scale parameter of the distribution.
"""
return self._scale
def extend_repr(self):
"""Display instance object as string."""
if self.is_scalar_batch:
str_info = 'loc = {}, scale = {}'.format(self._loc, self._scale)
else:
str_info = 'batch_shape = {}'.format(self._broadcast_shape)
return str_info
def _get_dist_type(self):
return "Gumbel"
def _get_dist_args(self, loc=None, scale=None):
if scale is None:
scale = self.scale
else:
self.checktensor(scale, 'scale')
if loc is None:
loc = self.loc
else:
self.checktensor(loc, 'loc')
return loc, scale
def _mean(self):
r"""
The mean of the distribution.
.. math::
MEAN(X) = loc + scale * Euler-Mascheroni_constant
"""
return self.loc + self.scale * np.euler_gamma
def _mode(self):
"""
The mode of the distribution.
"""
return self.loc * F.fill(self.parameter_type, self.shape(self.scale), 1.0)
def _sd(self):
r"""
The standard deviation of the distribution.
.. math::
STD(X) = \frac{\pi}{\sqrt(6)} * scale
"""
scale = self.scale * \
F.fill(self.parameter_type, self.broadcast_shape, 1.0)
return scale * np.pi / self.sqrt(self.const(6., mstype.float32))
def _entropy(self):
r"""
Evaluate entropy.
.. math::
H(X) = 1. + \log(scale) + Euler-Mascheroni_constant
"""
scale = self.scale * \
F.fill(self.parameter_type, self.broadcast_shape, 1.0)
return 1. + self.log(scale) + np.euler_gamma
def _log_prob(self, value):
r"""
.. math::
log_pdf(X) = -(z + \exp(-z)) - \log(scale)
where z = \frac{x - loc}{scale}
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
z = (value - self.loc) / self.scale
return -(z + self.exp(-z)) - self.log(self.scale)
def _cdf(self, value):
r"""
.. math::
cdf_pdf(X) = \exp(-\exp(-\frac{x - loc}{scale})
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
return self._gumbel_bijector("forward", value)
def _cross_entropy(self, dist, loc_b, scale_b):
r"""
Evaluate cross entropy between Gumbel distributions.
Args:
dist (str): The type of the distributions. Should be "Gumbel" in this case.
loc_b (Tensor): The loc of distribution b.
scale_b (Tensor): The scale of distribution b.
"""
check_distribution_name(dist, 'Gumbel')
return self._entropy() + self._kl_loss(dist, loc_b, scale_b)
def _kl_loss(self, dist, loc_b, scale_b):
r"""
Evaluate Gumbel-Gumbel kl divergence, i.e. KL(a||b).
Args:
dist (str): The type of the distributions. Should be "Gumbel" in this case.
loc_b (Tensor): The loc of distribution b.
scale_b (Tensor): The scale of distribution b.
.. math::
KL(a||b) = \log(scale_b / scale_a) + Euler-Mascheroni_constant * (scale_a / scale_b - 1.) +
\exp(\frac{(loc_b - loc_a)}{scale_b}) * \Gamma(scale_a / scale_b + 1.) - 1.
"""
check_distribution_name(dist, 'Gumbel')
loc_b = self._check_value(loc_b, 'loc_b')
scale_b = self._check_value(scale_b, 'scale_b')
loc_b = self.cast(loc_b, self.parameter_type)
scale_b = self.cast(scale_b, self.parameter_type)
return self.log(scale_b / self.scale) +\
np.euler_gamma * (self.scale / scale_b - 1.) + (self.loc - loc_b) / scale_b +\
self.expm1((loc_b - self.loc) / scale_b +
self.lgamma(self.scale / scale_b + 1.))
def _sample(self, shape=()):
shape = self.checktuple(shape, 'shape')
origin_shape = shape + self._broadcast_shape
if origin_shape == ():
sample_shape = (1,)
else:
sample_shape = origin_shape
org_sample = self.distribution("sample", sample_shape)
org_sample = self.cast(org_sample, self.dtype)
value = self.bijector("forward", org_sample)
if origin_shape == ():
value = self.squeeze(value)
return value