# Source code for mindspore.nn.probability.distribution.geometric

# Copyright 2020 Huawei Technologies Co., Ltd
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
[文档]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'. Supported Platforms: Ascend GPU Note: probs must be a proper probability (0 < p < 1). dist_spec_args is probs. Raises: ValueError: When p <= 0 or p >= 1. 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.ScalarToArray() self.dtypeop = P.DType() self.fill = P.Fill() self.floor = P.Floor() self.issubclass = P.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) maxval = self.const(1.0) 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