Source code for mindspore.nn.probability.distribution.exponential

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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