# Copyright 2020 Huawei Technologies Co., Ltd
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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# http://www.apache.org/licenses/LICENSE-2.0
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# ============================================================================
"""Geometric Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.ops.operations import _inner_ops as inner
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_prob, check_distribution_name
from ._utils.custom_ops import exp_generic, log_generic
[docs]class Geometric(Distribution):
"""
Geometric Distribution.
A Geometric Distribution is a discrete distribution with the range as the non-negative integers,
and the probability mass function as :math:`P(X = i) = p(1-p)^{i-1}, i = 1, 2, ...`.
It represents that there are k failures before the first success, namely that there are in total k+1 Bernoulli
trials when the first success is achieved.
Args:
probs (float, list, numpy.ndarray, Tensor): The probability of success. Default: None.
seed (int): The seed used in sampling. Global seed is used if it is None. Default: None.
dtype (mindspore.dtype): The type of the event samples. Default: mstype.int32.
name (str): The name of the distribution. Default: 'Geometric'.
Note:
`probs` must be a proper probability (0 < p < 1).
`dist_spec_args` is `probs`.
Raises:
ValueError: When p <= 0 or p >= 1.
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 Geometric distribution of the probability 0.5.
>>> g1 = msd.Geometric(0.5, dtype=mindspore.int32)
>>> # A Geometric distribution can be initialized without arguments.
>>> # In this case, `probs` must be passed in through arguments during function calls.
>>> g2 = msd.Geometric(dtype=mindspore.int32)
>>>
>>> # Here are some tensors used below for testing
>>> value = Tensor([1, 0, 1], dtype=mindspore.int32)
>>> probs_a = Tensor([0.6], dtype=mindspore.float32)
>>> probs_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`,
>>> # have the same arguments as follows.
>>> # Args:
>>> # value (Tensor): the value to be evaluated.
>>> # probs1 (Tensor): the probability of success of a Bernoulli trial. Default: self.probs.
>>> # Examples of `prob`.
>>> # Similar calls can be made to other probability functions
>>> # by replacing `prob` by the name of the function.
>>> ans = g1.prob(value)
>>> print(ans.shape)
(3,)
>>> # Evaluate with respect to distribution b.
>>> ans = g1.prob(value, probs_b)
>>> print(ans.shape)
(3,)
>>> # `probs` must be passed in during function calls.
>>> ans = g2.prob(value, probs_a)
>>> print(ans.shape)
(3,)
>>> # Functions `mean`, `sd`, `var`, and `entropy` have the same arguments.
>>> # Args:
>>> # probs1 (Tensor): the probability of success of a Bernoulli trial. Default: self.probs.
>>> # Examples of `mean`. `sd`, `var`, and `entropy` are similar.
>>> ans = g1.mean() # return 1.0
>>> print(ans.shape)
()
>>> ans = g1.mean(probs_b)
>>> print(ans.shape)
(3,)
>>> # Probs must be passed in during function calls
>>> ans = g2.mean(probs_a)
>>> print(ans.shape)
(1,)
>>> # Interfaces of 'kl_loss' and 'cross_entropy' are the same.
>>> # Args:
>>> # dist (str): the name of the distribution. Only 'Geometric' is supported.
>>> # probs1_b (Tensor): the probability of success of a Bernoulli trial of distribution b.
>>> # probs1_a (Tensor): the probability of success of a Bernoulli trial of distribution a.
>>> # Examples of `kl_loss`. `cross_entropy` is similar.
>>> ans = g1.kl_loss('Geometric', probs_b)
>>> print(ans.shape)
(3,)
>>> ans = g1.kl_loss('Geometric', probs_b, probs_a)
>>> print(ans.shape)
(3,)
>>> # An additional `probs` must be passed in.
>>> ans = g2.kl_loss('Geometric', probs_b, probs_a)
>>> print(ans.shape)
(3,)
>>> # Examples of `sample`.
>>> # Args:
>>> # shape (tuple): the shape of the sample. Default: ()
>>> # probs1 (Tensor): the probability of success of a Bernoulli trial. Default: self.probs.
>>> ans = g1.sample()
>>> print(ans.shape)
()
>>> ans = g1.sample((2,3))
>>> print(ans.shape)
(2, 3)
>>> ans = g1.sample((2,3), probs_b)
>>> print(ans.shape)
(2, 3, 3)
>>> ans = g2.sample((2,3), probs_a)
>>> print(ans.shape)
(2, 3, 1)
"""
def __init__(self,
probs=None,
seed=None,
dtype=mstype.int32,
name="Geometric"):
"""
Constructor of Geometric distribution.
"""
param = dict(locals())
param['param_dict'] = {'probs': probs}
valid_dtype = mstype.int_type + mstype.uint_type + mstype.float_type
Validator.check_type_name(
"dtype", dtype, valid_dtype, type(self).__name__)
super(Geometric, self).__init__(seed, dtype, name, param)
self._probs = self._add_parameter(probs, 'probs')
if self._probs is not None:
check_prob(self.probs)
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.floor = P.Floor()
self.issubclass = inner.IsSubClass()
self.less = P.Less()
self.pow = P.Pow()
self.select = P.Select()
self.shape = P.Shape()
self.sq = P.Square()
self.uniform = C.uniform
def extend_repr(self):
"""Display instance object as string."""
if not self.is_scalar_batch:
s = 'batch_shape = {}'.format(self._broadcast_shape)
else:
s = 'probs = {}'.format(self.probs)
return s
@property
def probs(self):
"""
Return the probability of success of the Bernoulli trial, after casting to dtype.
Output:
Tensor, the probs parameter of the distribution.
"""
return self._probs
def _get_dist_type(self):
return "Geometric"
def _get_dist_args(self, probs1=None):
if probs1 is not None:
self.checktensor(probs1, 'probs')
else:
probs1 = self.probs
return (probs1,)
def _mean(self, probs1=None):
r"""
.. math::
MEAN(Geo) = \fratc{1 - probs1}{probs1}
"""
probs1 = self._check_param_type(probs1)
return (1. - probs1) / probs1
def _mode(self, probs1=None):
r"""
.. math::
MODE(Geo) = 0
"""
probs1 = self._check_param_type(probs1)
return self.fill(self.dtype, self.shape(probs1), 0.)
def _var(self, probs1=None):
r"""
.. math::
VAR(Geo) = \frac{1 - probs1}{probs1 ^ {2}}
"""
probs1 = self._check_param_type(probs1)
return (1.0 - probs1) / self.sq(probs1)
def _entropy(self, probs1=None):
r"""
.. math::
H(Geo) = \frac{-1 * probs0 \log_2 (1-probs0)\ - prob1 * \log_2 (1-probs1)\ }{probs1}
"""
probs1 = self._check_param_type(probs1)
probs0 = 1.0 - probs1
return (-probs0 * self.log(probs0) - probs1 * self.log(probs1)) / probs1
def _cross_entropy(self, dist, probs1_b, probs1=None):
r"""
Evaluate cross entropy between Geometric distributions.
Args:
dist (str): The type of the distributions. Should be "Geometric" in this case.
probs1_b (Tensor): The probability of success of distribution b.
probs1_a (Tensor): The probability of success of distribution a. Default: self.probs.
"""
check_distribution_name(dist, 'Geometric')
return self._entropy(probs1) + self._kl_loss(dist, probs1_b, probs1)
def _prob(self, value, probs1=None):
r"""
Probability mass function of Geometric distributions.
Args:
value (Tensor): A Tensor composed of only natural numbers.
probs (Tensor): The probability of success. Default: self.probs.
.. math::
pmf(k) = probs0 ^k * probs1 if k >= 0;
pmf(k) = 0 if k < 0.
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.parameter_type)
value = self.floor(value)
probs1 = self._check_param_type(probs1)
pmf = self.exp(self.log(1.0 - probs1) * value + self.log(probs1))
zeros = self.fill(self.dtypeop(pmf), self.shape(pmf), 0.0)
comp = self.less(value, zeros)
return self.select(comp, zeros, pmf)
def _cdf(self, value, probs1=None):
r"""
Cumulative distribution function (cdf) of Geometric distributions.
Args:
value (Tensor): A Tensor composed of only natural numbers.
probs (Tensor): The probability of success. Default: self.probs.
.. math::
cdf(k) = 1 - probs0 ^ (k+1) if k >= 0;
cdf(k) = 0 if k < 0.
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.parameter_type)
value = self.floor(value)
probs1 = self._check_param_type(probs1)
probs0 = 1.0 - probs1
cdf = 1.0 - self.pow(probs0, value + 1.0)
zeros = self.fill(self.dtypeop(cdf), self.shape(cdf), 0.0)
comp = self.less(value, zeros)
return self.select(comp, zeros, cdf)
def _kl_loss(self, dist, probs1_b, probs1=None):
r"""
Evaluate Geometric-Geometric kl divergence, i.e. KL(a||b).
Args:
dist (str): The type of the distributions. Should be "Geometric" in this case.
probs1_b (Tensor): The probability of success of distribution b.
probs1_a (Tensor): The probability of success of distribution a. Default: self.probs.
.. math::
KL(a||b) = \log(\frac{probs1_a}{probs1_b}) + \frac{probs0_a}{probs1_a} * \log(\frac{probs0_a}{probs0_b})
"""
check_distribution_name(dist, 'Geometric')
probs1_b = self._check_value(probs1_b, 'probs1_b')
probs1_b = self.cast(probs1_b, self.parameter_type)
probs1_a = self._check_param_type(probs1)
probs0_a = 1.0 - probs1_a
probs0_b = 1.0 - probs1_b
return self.log(probs1_a / probs1_b) + (probs0_a / probs1_a) * self.log(probs0_a / probs0_b)
def _sample(self, shape=(), probs1=None):
"""
Sampling.
Args:
shape (tuple): The shape of the sample. Default: ().
probs (Tensor): The probability of success. Default: self.probs.
Returns:
Tensor, with the shape being shape + batch_shape.
"""
shape = self.checktuple(shape, 'shape')
probs1 = self._check_param_type(probs1)
origin_shape = shape + self.shape(probs1)
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.floor(self.log(sample_uniform) / self.log(1.0 - probs1))
value = self.cast(sample, self.dtype)
if origin_shape == ():
value = self.squeeze(value)
return value