# 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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# ============================================================================
"""Poisson Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.ops import composite as C
import mindspore.nn as nn
from mindspore._checkparam import Validator
from mindspore.common import dtype as mstype
from .distribution import Distribution
from ._utils.utils import check_greater_zero
from ._utils.custom_ops import exp_generic, log_generic
[文档]class Poisson(Distribution):
r"""
Poisson Distribution.
A Poisson Distribution is a discrete distribution with the range as the non-negative integers,
and the probability mass function as :math:`P(X = k) = \lambda^k \exp(-\lambda) / k!, k = 1, 2, ...`,
where :math:`\lambda` is the rate of the distribution.
Args:
rate (list, numpy.ndarray, Tensor): The rate of the Poisson distribution. 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: 'Poisson'.
Note:
`rate` must be strictly greater than 0.
`dist_spec_args` is `rate`.
Raises:
ValueError: When rate <= 0.
Supported Platforms:
``Ascend``
Examples:
>>> import mindspore
>>> import mindspore.nn as nn
>>> import mindspore.nn.probability.distribution as msd
>>> from mindspore import Tensor
>>> # To initialize an Poisson distribution of the rate 0.5.
>>> p1 = msd.Poisson([0.5], dtype=mindspore.float32)
>>> # An Poisson distribution can be initialized without arguments.
>>> # In this case, `rate` must be passed in through `args` during function calls.
>>> p2 = msd.Poisson(dtype=mindspore.float32)
>>>
>>> # Here are some tensors used below for testing
>>> value = Tensor([1, 2, 3], dtype=mindspore.int32)
>>> 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 = p1.prob(value)
>>> print(ans.shape)
(3,)
>>> # Evaluate with respect to distribution b.
>>> ans = p1.prob(value, rate_b)
>>> print(ans.shape)
(3,)
>>> # `rate` must be passed in during function calls.
>>> ans = p2.prob(value, rate_a)
>>> print(ans.shape)
(3,)
>>> # Functions `mean`, `mode`, `sd`, and 'var' have the same arguments as follows.
>>> # Args:
>>> # rate (Tensor): the rate of the distribution. Default: self.rate.
>>> # Examples of `mean`, `sd`, `mode`, and `var` are similar.
>>> ans = p1.mean() # return 2
>>> print(ans.shape)
(1,)
>>> ans = p1.mean(rate_b) # return 1 / rate_b
>>> print(ans.shape)
(3,)
>>> # `rate` must be passed in during function calls.
>>> ans = p2.mean(rate_a)
>>> print(ans.shape)
(1,)
>>> # Examples of `sample`.
>>> # Args:
>>> # shape (tuple): the shape of the sample. Default: ()
>>> # probs1 (Tensor): the rate of the distribution. Default: self.rate.
>>> ans = p1.sample()
>>> print(ans.shape)
(1, )
>>> ans = p1.sample((2,3))
>>> print(ans.shape)
(2, 3, 1)
>>> ans = p1.sample((2,3), rate_b)
>>> print(ans.shape)
(2, 3, 3)
>>> ans = p2.sample((2,3), rate_a)
>>> print(ans.shape)
(2, 3, 1)
"""
def __init__(self,
rate=None,
seed=None,
dtype=mstype.float32,
name="Poisson"):
"""
Constructor of Poisson.
"""
param = dict(locals())
param['param_dict'] = {'rate': rate}
valid_dtype = mstype.int_type + mstype.uint_type + mstype.float_type
Validator.check_type_name(
"dtype", dtype, valid_dtype, type(self).__name__)
# As some operators can't accept scalar input, check the type here
if isinstance(rate, (int, float)):
raise TypeError("Input rate can't be scalar")
super(Poisson, 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')
# ops needed for the class
self.exp = exp_generic
self.log = log_generic
self.squeeze = P.Squeeze(0)
self.cast = P.Cast()
self.floor = P.Floor()
self.dtypeop = P.DType()
self.shape = P.Shape()
self.fill = P.Fill()
self.less = P.Less()
self.equal = P.Equal()
self.select = P.Select()
self.lgamma = nn.LGamma()
self.igamma = nn.IGamma()
self.poisson = C.poisson
@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 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
def _get_dist_type(self):
return "Poisson"
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(POISSON) = \lambda.
"""
rate = self._check_param_type(rate)
return rate
def _mode(self, rate=None):
r"""
.. math::
MODE(POISSON) = \lfloor{\lambda}.
"""
rate = self._check_param_type(rate)
return self.floor(rate)
def _var(self, rate=None):
r"""
.. math::
VAR(POISSON) = \lambda.
"""
rate = self._check_param_type(rate)
return rate
def _log_prob(self, value, rate=None):
r"""
Log probability density function of Poisson 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) = x * \log(\lambda) - \lambda - \log(\Gamma(x)) if x >= 0 else -inf
"""
value = self._check_value(value, "value")
value = self.cast(value, self.dtype)
rate = self._check_param_type(rate)
log_rate = self.log(rate)
zeros = self.fill(self.dtypeop(value), self.shape(value), 0.0)
inf = self.fill(self.dtypeop(value), self.shape(value), np.inf)
safe_x = self.select(self.less(value, zeros), zeros, value)
y = log_rate * safe_x - self.lgamma(safe_x + 1.)
comp = self.equal(value, safe_x)
log_unnormalized_prob = self.select(comp, y, (-1) * inf)
log_normalization = self.exp(log_rate)
return log_unnormalized_prob - log_normalization
def _cdf(self, value, rate=None):
r"""
Cumulative distribution function (cdf) of Poisson 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) = \Gamma(x + 1) if x >= 0 else 0
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
rate = self._check_param_type(rate)
zeros = self.fill(self.dtypeop(value), self.shape(value), 0.0)
comp = self.less(value, zeros)
safe_x = self.select(comp, zeros, value)
cdf = 1. - self.igamma(1. + safe_x, rate)
return self.select(comp, zeros, cdf)
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)
# now Poisson sampler supports only fp32
rate = self.cast(rate, mstype.float32)
origin_shape = shape + self.shape(rate)
if origin_shape == ():
sample_shape = (1,)
else:
sample_shape = origin_shape
sample_poisson = self.poisson(sample_shape, rate, self.seed)
value = self.cast(sample_poisson, self.dtype)
if origin_shape == ():
value = self.squeeze(value)
return value