# 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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# distributed under the License is distributed on an "AS IS" BASIS,
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# ============================================================================
"""Exponential Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.ops import composite as C
from mindspore import _checkparam as Validator
from mindspore.common import dtype as mstype
from .distribution import Distribution
from ._utils.utils import check_greater_zero, check_distribution_name
from ._utils.custom_ops import exp_generic, log_generic
[docs]class Exponential(Distribution):
r"""
Exponential Distribution.
An Exponential distributio is a continuous distribution with the range :math:`[0, \inf)`
and the probability density function:
.. math::
f(x, \lambda) = \lambda \exp(-\lambda x),
where :math:`\lambda` is the rate of the distribution.
Args:
rate (int, float, list, numpy.ndarray, Tensor): The inverse scale. Default: ``None`` .
seed (int): The seed used in sampling. The global seed is used if it is None. Default: ``None`` .
dtype (mindspore.dtype): The type of the event samples. Default: ``mstype.float32`` .
name (str): The name of the distribution. Default: ``'Exponential'`` .
Note:
`rate` must be strictly greater than 0.
`dist_spec_args` is `rate`.
`dtype` must be a float type because Exponential distributions are continuous.
Raises:
ValueError: When rate <= 0.
TypeError: When the input `dtype` is not a subclass of float.
Supported Platforms:
``Ascend`` ``GPU``
Examples:
>>> import mindspore
>>> import mindspore.nn as nn
>>> import mindspore.nn.probability.distribution as msd
>>> from mindspore import Tensor
>>> # To initialize a Exponential distribution of the probability 0.5.
>>> e1 = msd.Exponential(0.5, dtype=mindspore.float32)
>>> # An Exponential distribution can be initialized without arguments.
>>> # In this case, `rate` must be passed in through `args` during function calls.
>>> e2 = msd.Exponential(dtype=mindspore.float32)
>>> # Here are some tensors used below for testing
>>> value = Tensor([1, 2, 3], dtype=mindspore.float32)
>>> rate_a = Tensor([0.6], dtype=mindspore.float32)
>>> rate_b = Tensor([0.2, 0.5, 0.4], dtype=mindspore.float32)
>>> # Private interfaces of probability functions corresponding to public interfaces, including
>>> # `prob`, `log_prob`, `cdf`, `log_cdf`, `survival_function`, and `log_survival`, are the same as follows.
>>> # Args:
>>> # value (Tensor): the value to be evaluated.
>>> # rate (Tensor): the rate of the distribution. Default: self.rate.
>>> # Examples of `prob`.
>>> # Similar calls can be made to other probability functions
>>> # by replacing `prob` by the name of the function.
>>> ans = e1.prob(value)
>>> print(ans.shape)
(3,)
>>> # Evaluate with respect to distribution b.
>>> ans = e1.prob(value, rate_b)
>>> print(ans.shape)
(3,)
>>> # `rate` must be passed in during function calls.
>>> ans = e2.prob(value, rate_a)
>>> print(ans.shape)
(3,)
>>> # Functions `mean`, `sd`, 'var', and 'entropy' have the same arguments as follows.
>>> # Args:
>>> # rate (Tensor): the rate of the distribution. Default: self.rate.
>>> # Examples of `mean`. `sd`, `var`, and `entropy` are similar.
>>> ans = e1.mean() # return 2
>>> print(ans.shape)
()
>>> ans = e1.mean(rate_b) # return 1 / rate_b
>>> print(ans.shape)
(3,)
>>> # `rate` must be passed in during function calls.
>>> ans = e2.mean(rate_a)
>>> print(ans.shape)
(1,)
>>> # Interfaces of `kl_loss` and `cross_entropy` are the same.
>>> # Args:
>>> # dist (str): The name of the distribution. Only 'Exponential' is supported.
>>> # rate_b (Tensor): the rate of distribution b.
>>> # rate_a (Tensor): the rate of distribution a. Default: self.rate.
>>> # Examples of `kl_loss`. `cross_entropy` is similar.
>>> ans = e1.kl_loss('Exponential', rate_b)
>>> print(ans.shape)
(3,)
>>> ans = e1.kl_loss('Exponential', rate_b, rate_a)
>>> print(ans.shape)
(3,)
>>> # An additional `rate` must be passed in.
>>> ans = e2.kl_loss('Exponential', rate_b, rate_a)
>>> print(ans.shape)
(3,)
>>> # Examples of `sample`.
>>> # Args:
>>> # shape (tuple): the shape of the sample. Default: ()
>>> # probs1 (Tensor): the rate of the distribution. Default: self.rate.
>>> ans = e1.sample()
>>> print(ans.shape)
()
>>> ans = e1.sample((2,3))
>>> print(ans.shape)
(2, 3)
>>> ans = e1.sample((2,3), rate_b)
>>> print(ans.shape)
(2, 3, 3)
>>> ans = e2.sample((2,3), rate_a)
>>> print(ans.shape)
(2, 3, 1)
"""
def __init__(self,
rate=None,
seed=None,
dtype=mstype.float32,
name="Exponential"):
"""
Constructor of Exponential.
"""
param = dict(locals())
param['param_dict'] = {'rate': rate}
valid_dtype = mstype.float_type
Validator.check_type_name(
"dtype", dtype, valid_dtype, type(self).__name__)
super(Exponential, self).__init__(seed, dtype, name, param)
self._rate = self._add_parameter(rate, 'rate')
if self.rate is not None:
check_greater_zero(self.rate, 'rate')
self.minval = np.finfo(np.float).tiny
# ops needed for the class
self.exp = exp_generic
self.log = log_generic
self.squeeze = P.Squeeze(0)
self.cast = P.Cast()
self.const = P.ScalarToTensor()
self.dtypeop = P.DType()
self.fill = P.Fill()
self.less = P.Less()
self.select = P.Select()
self.shape = P.Shape()
self.uniform = C.uniform
def extend_repr(self):
"""Display instance object as string."""
if self.is_scalar_batch:
s = 'rate = {}'.format(self.rate)
else:
s = 'batch_shape = {}'.format(self._broadcast_shape)
return s
@property
def rate(self):
"""
Return `rate` of the distribution after casting to dtype.
Output:
Tensor, the rate parameter of the distribution.
"""
return self._rate
def _get_dist_type(self):
return "Exponential"
def _get_dist_args(self, rate=None):
if rate is not None:
self.checktensor(rate, 'rate')
else:
rate = self.rate
return (rate,)
def _mean(self, rate=None):
r"""
.. math::
MEAN(EXP) = \frac{1.0}{\lambda}.
"""
rate = self._check_param_type(rate)
return 1.0 / rate
def _mode(self, rate=None):
r"""
.. math::
MODE(EXP) = 0.
"""
rate = self._check_param_type(rate)
return self.fill(self.dtype, self.shape(rate), 0.)
def _sd(self, rate=None):
r"""
.. math::
SD(EXP) = \frac{1.0}{\lambda}.
"""
rate = self._check_param_type(rate)
return 1.0 / rate
def _entropy(self, rate=None):
r"""
.. math::
H(Exp) = 1 - \log(\lambda).
"""
rate = self._check_param_type(rate)
return 1.0 - self.log(rate)
def _cross_entropy(self, dist, rate_b, rate=None):
"""
Evaluate cross entropy between Exponential distributions.
Args:
dist (str): The type of the distributions. Should be "Exponential" in this case.
rate_b (Tensor): The rate of distribution b.
rate_a (Tensor): The rate of distribution a. Default: self.rate.
"""
check_distribution_name(dist, 'Exponential')
return self._entropy(rate) + self._kl_loss(dist, rate_b, rate)
def _log_prob(self, value, rate=None):
r"""
Log probability density function of Exponential distributions.
Args:
Args:
value (Tensor): The value to be evaluated.
rate (Tensor): The rate of the distribution. Default: self.rate.
Note:
`value` must be greater or equal to zero.
.. math::
log_pdf(x) = \log(rate) - rate * x if x >= 0 else 0
"""
value = self._check_value(value, "value")
value = self.cast(value, self.dtype)
rate = self._check_param_type(rate)
prob = self.log(rate) - rate * value
zeros = self.fill(self.dtypeop(prob), self.shape(prob), 0.0)
neginf = self.fill(self.dtypeop(prob), self.shape(prob), -np.inf)
comp = self.less(value, zeros)
return self.select(comp, neginf, prob)
def _cdf(self, value, rate=None):
r"""
Cumulative distribution function (cdf) of Exponential distributions.
Args:
value (Tensor): The value to be evaluated.
rate (Tensor): The rate of the distribution. Default: self.rate.
Note:
`value` must be greater or equal to zero.
.. math::
cdf(x) = 1.0 - \exp(-1 * \lambda * x) if x >= 0 else 0
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
rate = self._check_param_type(rate)
cdf = 1.0 - self.exp(-1. * rate * value)
zeros = self.fill(self.dtypeop(cdf), self.shape(cdf), 0.0)
comp = self.less(value, zeros)
return self.select(comp, zeros, cdf)
def _log_survival(self, value, rate=None):
r"""
Log survival_function of Exponential distributions.
Args:
value (Tensor): The value to be evaluated.
rate (Tensor): The rate of the distribution. Default: self.rate.
Note:
`value` must be greater or equal to zero.
.. math::
log_survival_function(x) = -1 * \lambda * x if x >= 0 else 0
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
rate = self._check_param_type(rate)
sf = -1. * rate * value
zeros = self.fill(self.dtypeop(sf), self.shape(sf), 0.0)
comp = self.less(value, zeros)
return self.select(comp, zeros, sf)
def _kl_loss(self, dist, rate_b, rate=None):
"""
Evaluate exp-exp kl divergence, i.e. KL(a||b).
Args:
dist (str): The type of the distributions. Should be "Exponential" in this case.
rate_b (Tensor): The rate of distribution b.
rate_a (Tensor): The rate of distribution a. Default: self.rate.
"""
check_distribution_name(dist, 'Exponential')
rate_b = self._check_value(rate_b, 'rate_b')
rate_b = self.cast(rate_b, self.parameter_type)
rate_a = self._check_param_type(rate)
return self.log(rate_a) - self.log(rate_b) + rate_b / rate_a - 1.0
def _sample(self, shape=(), rate=None):
"""
Sampling.
Args:
shape (tuple): The shape of the sample. Default: ().
rate (Tensor): The rate of the distribution. Default: self.rate.
Returns:
Tensor, shape is shape + batch_shape.
"""
shape = self.checktuple(shape, 'shape')
rate = self._check_param_type(rate)
origin_shape = shape + self.shape(rate)
if origin_shape == ():
sample_shape = (1,)
else:
sample_shape = origin_shape
minval = self.const(self.minval, mstype.float32)
maxval = self.const(1.0, mstype.float32)
sample_uniform = self.uniform(sample_shape, minval, maxval, self.seed)
sample = self.log(sample_uniform) / rate
value = self.cast(-sample, self.dtype)
if origin_shape == ():
value = self.squeeze(value)
return value