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

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"""Normal Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.ops import composite as C
from mindspore._checkparam import Validator
from mindspore.common import dtype as mstype
from mindspore.common import Tensor
from .distribution import Distribution
from ._utils.utils import check_greater_zero, check_distribution_name


[docs]class Normal(Distribution): r""" Normal distribution. A Normal distribution is a continuous distribution with the range :math:`(-\inf, \inf)` and the probability density function: .. math:: f(x, \mu, \sigma) = 1 / \sigma\sqrt{2\pi} \exp(-(x - \mu)^2 / 2\sigma^2). where :math:`\mu, \sigma` are the mean and the standard deviation of the normal distribution respectively. Args: mean (int, float, list, numpy.ndarray, Tensor): The mean of the Normal distribution. Default: None. sd (int, float, list, numpy.ndarray, Tensor): The standard deviation of the Normal 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: 'Normal'. Note: `sd` must be greater than zero. `dist_spec_args` are `mean` and `sd`. `dtype` must be a float type because Normal distributions are continuous. Raises: ValueError: When sd <= 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 Normal distribution of the mean 3.0 and the standard deviation 4.0. >>> n1 = msd.Normal(3.0, 4.0, dtype=mindspore.float32) >>> # A Normal distribution can be initialized without arguments. >>> # In this case, `mean` and `sd` must be passed in through arguments. >>> n2 = msd.Normal(dtype=mindspore.float32) >>> # Here are some tensors used below for testing >>> value = Tensor([1.0, 2.0, 3.0], dtype=mindspore.float32) >>> mean_a = Tensor([2.0], dtype=mindspore.float32) >>> sd_a = Tensor([2.0, 2.0, 2.0], dtype=mindspore.float32) >>> mean_b = Tensor([1.0], dtype=mindspore.float32) >>> sd_b = Tensor([1.0, 1.5, 2.0], 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. >>> # mean (Tensor): the mean of the distribution. Default: self._mean_value. >>> # sd (Tensor): the standard deviation of the distribution. Default: self._sd_value. >>> # Examples of `prob`. >>> # Similar calls can be made to other probability functions >>> # by replacing 'prob' by the name of the function >>> ans = n1.prob(value) >>> print(ans.shape) (3,) >>> # Evaluate with respect to the distribution b. >>> ans = n1.prob(value, mean_b, sd_b) >>> print(ans.shape) (3,) >>> # `mean` and `sd` must be passed in during function calls >>> ans = n2.prob(value, mean_a, sd_a) >>> print(ans.shape) (3,) >>> # Functions `mean`, `sd`, `var`, and `entropy` have the same arguments. >>> # Args: >>> # mean (Tensor): the mean of the distribution. Default: self._mean_value. >>> # sd (Tensor): the standard deviation of the distribution. Default: self._sd_value. >>> # Example of `mean`. `sd`, `var`, and `entropy` are similar. >>> ans = n1.mean() # return 0.0 >>> print(ans.shape) () >>> ans = n1.mean(mean_b, sd_b) # return mean_b >>> print(ans.shape) (3,) >>> # `mean` and `sd` must be passed in during function calls. >>> ans = n2.mean(mean_a, sd_a) >>> print(ans.shape) (3,) >>> # Interfaces of 'kl_loss' and 'cross_entropy' are the same: >>> # Args: >>> # dist (str): the type of the distributions. Only "Normal" is supported. >>> # mean_b (Tensor): the mean of distribution b. >>> # sd_b (Tensor): the standard deviation of distribution b. >>> # mean_a (Tensor): the mean of distribution a. Default: self._mean_value. >>> # sd_a (Tensor): the standard deviation of distribution a. Default: self._sd_value. >>> # Examples of `kl_loss`. `cross_entropy` is similar. >>> ans = n1.kl_loss('Normal', mean_b, sd_b) >>> print(ans.shape) (3,) >>> ans = n1.kl_loss('Normal', mean_b, sd_b, mean_a, sd_a) >>> print(ans.shape) (3,) >>> # Additional `mean` and `sd` must be passed in. >>> ans = n2.kl_loss('Normal', mean_b, sd_b, mean_a, sd_a) >>> print(ans.shape) (3,) >>> # Examples of `sample`. >>> # Args: >>> # shape (tuple): the shape of the sample. Default: () >>> # mean (Tensor): the mean of the distribution. Default: self._mean_value. >>> # sd (Tensor): the standard deviation of the distribution. Default: self._sd_value. >>> ans = n1.sample() >>> print(ans.shape) () >>> ans = n1.sample((2,3)) >>> print(ans.shape) (2, 3) >>> ans = n1.sample((2,3), mean_b, sd_b) >>> print(ans.shape) (2, 3, 3) >>> ans = n2.sample((2,3), mean_a, sd_a) >>> print(ans.shape) (2, 3, 3) """ def __init__(self, mean=None, sd=None, seed=None, dtype=mstype.float32, name="Normal"): """ Constructor of Normal. """ param = dict(locals()) param['param_dict'] = {'mean': mean, 'sd': sd} valid_dtype = mstype.float_type Validator.check_type_name( "dtype", dtype, valid_dtype, type(self).__name__) super(Normal, self).__init__(seed, dtype, name, param) self._mean_value = self._add_parameter(mean, 'mean') self._sd_value = self._add_parameter(sd, 'sd') if self._sd_value is not None: check_greater_zero(self._sd_value, "Standard deviation") # ops needed for the class self.exp = self.exp_base self.log = self.log_base self.expm1 = P.Expm1() self.erf = P.Erf() self.squeeze = P.Squeeze(0) self.cast = P.Cast() self.const = P.ScalarToTensor() self.shape = P.Shape() self.sq = P.Square() self.sqrt = P.Sqrt() self.coff = Tensor(-0.5 * np.log(2. * np.pi), dtype=dtype) def extend_repr(self): """Display instance object as string.""" if self.is_scalar_batch: s = 'mean = {}, standard deviation = {}'.format( self._mean_value, self._sd_value) else: s = 'batch_shape = {}'.format(self._broadcast_shape) return s def _get_dist_type(self): return "Normal" def _get_dist_args(self, mean=None, sd=None): if mean is not None: self.checktensor(mean, 'mean') else: mean = self._mean_value if sd is not None: self.checktensor(sd, 'sd') else: sd = self._sd_value return mean, sd def _mean(self, mean=None, sd=None): """ The mean of the distribution. """ mean, sd = self._check_param_type(mean, sd) return mean def _mode(self, mean=None, sd=None): """ The mode of the distribution. """ mean, sd = self._check_param_type(mean, sd) return mean def _sd(self, mean=None, sd=None): """ The standard deviation of the distribution. """ mean, sd = self._check_param_type(mean, sd) return sd def _entropy(self, mean=None, sd=None): r""" Evaluate entropy. .. math:: H(X) = \log(\sqrt(numpy.e * 2. * numpy.pi * \sq(\sigma))) """ mean, sd = self._check_param_type(mean, sd) return self.log(self.sqrt(self.const(np.e * 2. * np.pi, mstype.float32))) + self.log(sd) def _cross_entropy(self, dist, mean_b, sd_b, mean=None, sd=None): r""" Evaluate cross entropy between normal distributions. Args: dist (str): Type of the distributions. Should be "Normal" in this case. mean_b (Tensor): Mean of distribution b. sd_b (Tensor): Standard deviation distribution b. mean_a (Tensor): Mean of distribution a. Default: self._mean_value. sd_a (Tensor): Standard deviation distribution a. Default: self._sd_value. """ check_distribution_name(dist, 'Normal') return self._entropy(mean, sd) + self._kl_loss(dist, mean_b, sd_b, mean, sd) def _log_prob(self, value, mean=None, sd=None): r""" Evaluate log probability. Args: value (Tensor): The value to be evaluated. mean (Tensor): The mean of the distribution. Default: self._mean_value. sd (Tensor): The standard deviation the distribution. Default: self._sd_value. .. math:: L(x) = -1* \frac{(x - \mu)^2}{2. * \sigma^2} - \log(\sqrt(2* \pi * \sigma^2)) """ value = self._check_value(value, 'value') value = self.cast(value, self.dtype) mean, sd = self._check_param_type(mean, sd) unnormalized_log_prob = -0.5 * (self.sq((value - mean) / sd)) neg_normalization = self.coff - self.log(sd) return unnormalized_log_prob + neg_normalization def _cdf(self, value, mean=None, sd=None): r""" Evaluate the cumulative distribution function on the given value. Args: value (Tensor): The value to be evaluated. mean (Tensor): The mean of the distribution. Default: self._mean_value. sd (Tensor): The standard deviation the distribution. Default: self._sd_value. .. math:: cdf(x) = 0.5 * (1+ Erf((x - \mu) / ( \sigma * \sqrt(2)))) """ value = self._check_value(value, 'value') value = self.cast(value, self.dtype) mean, sd = self._check_param_type(mean, sd) sqrt2 = self.sqrt(self.const(2.0, mstype.float32)) adjusted = (value - mean) / (sd * sqrt2) return 0.5 * (1.0 + self.erf(adjusted)) def _kl_loss(self, dist, mean_b, sd_b, mean=None, sd=None): r""" Evaluate Normal-Normal KL divergence, i.e. KL(a||b). Args: dist (str): The type of the distributions. Should be "Normal" in this case. mean_b (Tensor): The mean of distribution b. sd_b (Tensor): The standard deviation distribution b. mean_a (Tensor): The mean of distribution a. Default: self._mean_value. sd_a (Tensor): The standard deviation distribution a. Default: self._sd_value. .. math:: KL(a||b) = 0.5 * (\frac{MEAN(a)}{STD(b)} - \frac{MEAN(b)}{STD(b)}) ^ 2 + 0.5 * EXPM1(2 * (\log(STD(a)) - \log(STD(b))) - (\log(STD(a)) - \log(STD(b))) """ check_distribution_name(dist, 'Normal') mean_b = self._check_value(mean_b, 'mean_b') sd_b = self._check_value(sd_b, 'sd_b') mean_b = self.cast(mean_b, self.parameter_type) sd_b = self.cast(sd_b, self.parameter_type) mean_a, sd_a = self._check_param_type(mean, sd) diff_log_scale = self.log(sd_a) - self.log(sd_b) squared_diff = self.sq(mean_a / sd_b - mean_b / sd_b) return 0.5 * squared_diff + 0.5 * self.expm1(2 * diff_log_scale) - diff_log_scale def _sample(self, shape=(), mean=None, sd=None): """ Sampling. Args: shape (tuple): The shape of the sample. Default: (). mean (Tensor): The mean of the samples. Default: self._mean_value. sd (Tensor): The standard deviation of the samples. Default: self._sd_value. Returns: Tensor, with the shape being shape + batch_shape. """ shape = self.checktuple(shape, 'shape') mean, sd = self._check_param_type(mean, sd) batch_shape = self.shape(mean + sd) origin_shape = shape + batch_shape if origin_shape == (): sample_shape = (1,) else: sample_shape = origin_shape sample_norm = C.normal(sample_shape, mean, sd, self.seed) value = self.cast(sample_norm, self.dtype) if origin_shape == (): value = self.squeeze(value) return value