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

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"""LogNormal Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.ops import functional as F
from mindspore.common import dtype as mstype
import mindspore.nn.probability.bijector as msb
import mindspore.nn.probability.distribution as msd
from ._utils.utils import check_distribution_name
from ._utils.custom_ops import exp_generic, log_generic


[docs]class LogNormal(msd.TransformedDistribution): r""" LogNormal distribution. A log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. The log-normal distribution has the range :math:`(0, \inf)` with the pdf as .. math:: f(x, \mu, \sigma) = 1 / x\sigma\sqrt{2\pi} \exp(-(\ln(x) - \mu)^2 / 2\sigma^2). where :math:`\mu, \sigma` are the mean and the standard deviation of the underlying normal distribution respectively. It is constructed as the exponential transformation of a Normal distribution. Args: loc (int, float, list, numpy.ndarray, Tensor): The mean of the underlying Normal distribution. Default: ``None`` . scale (int, float, list, numpy.ndarray, Tensor): The standard deviation of the underlying Normal distribution. Default: ``None`` . seed (int): the seed used in sampling. The global seed is used if it is None. Default: ``0`` . dtype (mindspore.dtype): type of the distribution. Default: ``mstype.float32`` . name (str): the name of the distribution. Default: ``'LogNormal'`` . Note: `scale` must be greater than zero. `dist_spec_args` are `loc` and `scale`. `dtype` must be a float type because LogNormal distributions are continuous. Raises: ValueError: When scale <= 0. TypeError: When the input `dtype` is not a subclass of float. Supported Platforms: ``Ascend`` ``GPU`` Examples: >>> import numpy as np >>> import mindspore >>> import mindspore.nn as nn >>> import mindspore.nn.probability.distribution as msd >>> from mindspore import Tensor >>> class Prob(nn.Cell): ... def __init__(self): ... super(Prob, self).__init__() ... self.ln = msd.LogNormal(np.array([0.3]), np.array([[0.2], [0.4]]), dtype=mindspore.float32) ... def construct(self, x_): ... return self.ln.prob(x_) >>> pdf = Prob() >>> output = pdf(Tensor([1.0, 2.0], dtype=mindspore.float32)) >>> print(output.shape) (2, 2) """ def __init__(self, loc=None, scale=None, seed=0, dtype=mstype.float32, name="LogNormal"): """ Constructor of LogNormal distribution. """ super(LogNormal, self).__init__(distribution=msd.Normal(loc, scale, dtype=dtype), bijector=msb.Exp(), seed=seed, name=name) # overwrite default_parameters and parameter_names self._reset_parameters() self._loc = self._add_parameter(loc, 'loc') self._scale = self._add_parameter(scale, 'scale') self.log_2pi = np.log(2 * np.pi) # ops needed for the class self.dtypeop = P.DType() self.exp = exp_generic self.expm1 = P.Expm1() self.log = log_generic self.erf = P.Erf() self.greater = P.Greater() self.select = P.Select() self.shape = P.Shape() self.sq = P.Square() self.sqrt = P.Sqrt() self.cast = P.Cast() self.squeeze = P.Squeeze(0) @property def loc(self): """ Distribution parameter for the pre-transformed mean after casting to dtype. Output: Tensor, the loc parameter of the distribution. """ return self._loc @property def scale(self): """ Distribution parameter for the pre-transformed standard deviation after casting to dtype. Output: Tensor, the scale parameter of the distribution. """ return self._scale def _get_dist_type(self): return "LogNormal" def _get_dist_args(self, loc=None, scale=None): if loc is not None: self.checktensor(loc, 'loc') else: loc = self.loc if scale is not None: self.checktensor(scale, 'scale') else: scale = self.scale return loc, scale def extend_repr(self): """Display instance object as string.""" if self.is_scalar_batch: s = 'loc = {}, scale = {}'.format(self.loc, self.scale) else: s = 'batch_shape = {}'.format(self.broadcast_shape) return s def _mean(self, loc=None, scale=None): """ The mean of the distribution. """ mean, sd = self._check_param_type(loc, scale) var = self.distribution("var", mean=mean, sd=sd) return self.exp(mean + 0.5 * var) def _mode(self, loc=None, scale=None): """ The mode of the distribution. """ mean, sd = self._check_param_type(loc, scale) var = self.distribution("var", mean=mean, sd=sd) return self.exp(mean - var) def _var(self, loc=None, scale=None): """ The variance of the distribution. """ mean, sd = self._check_param_type(loc, scale) var = self.distribution("var", mean=mean, sd=sd) return self.expm1(var) * self.exp(2. * mean + var) def _entropy(self, loc=None, scale=None): r""" Evaluate entropy. .. math:: H(X) = μ + 0.5 + \log(σ) + 0.5 * \log(2pi) """ mean, sd = self._check_param_type(loc, scale) return mean + 0.5 + self.log(sd) + 0.5 * self.log_2pi def _cdf(self, value, loc=None, scale=None): r""" Compute the cdf via the below formula, where g is the exp bijector, and P is the cdf of the underlying normal dist .. math:: Y = g(X) P(Y <= a) = P(X <= g^{-1}(a)) """ mean, sd = self._check_param_type(loc, scale) inverse_value = self.bijector("inverse", value) cdf = self.distribution("cdf", inverse_value, mean, sd) # to increase numerical stability, set cdf = 0 when value <= 0 zeros = F.fill(self.dtypeop(cdf), self.shape(cdf), 0.0) return self.select(self.greater(value, 0.), cdf, zeros) def _log_prob(self, value, loc=None, scale=None): r""" Compute the log prob via the below formula, where g is the exp bijector, and P is the pdf of the underlying normal dist .. math:: Y = g(X) Py(a) = Px(g^{-1}(a)) * (g^{-1})'(a) \log(Py(a)) = \log(Px(g^{-1}(a))) + \log((g^{-1})'(a)) """ mean, sd = self._check_param_type(loc, scale) inverse_value = self.bijector("inverse", value) unadjust_prob = self.distribution("log_prob", inverse_value, mean, sd) log_jacobian = self.bijector("inverse_log_jacobian", value) return unadjust_prob + log_jacobian def _cross_entropy(self, dist, loc_b, scale_b, loc_a=None, scale_a=None): r""" Evaluate cross entropy between lognormal distributions. Args: dist (str): The type of the distributions. Should be "LogNormal" in this case. loc_b (Tensor): The loc of distribution b. scale_b (Tensor): The scale of distribution b. loc_a (Tensor): The loc of distribution a. Default: ``None``. scale_a (Tensor): The scale of distribution a. Default: ``None``. """ check_distribution_name(dist, 'LogNormal') return self._entropy(loc_a, scale_a) + self._kl_loss(dist, loc_b, scale_b, loc_a, scale_a) def _kl_loss(self, dist, loc_b, scale_b, loc_a=None, scale_a=None): r""" Evaluate LogNormal-LogNormal kl divergence, i.e. KL(a||b). Args: dist (str): The type of the distributions. Should be "LogNormal" in this case. loc_b (Tensor): The loc of distribution b. scale_b (Tensor): The scale of distribution b. loc_a (Tensor): The loc of distribution a. Default: ``None``. scale_a (Tensor): The scale of distribution a. Default: ``None``. .. math:: KL(a||b) = 0.5 * (\fract{MEAN(a)}{STD(b)} - \fract{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, 'LogNormal') return self.distribution("kl_loss", 'Normal', loc_b, scale_b, loc_a, scale_a) def _sample(self, shape=(), loc=None, scale=None): r""" Generate samples via mapping the samples from the underlying normal dist. """ shape = self.checktuple(shape, 'shape') mean, sd = self._check_param_type(loc, scale) if shape == (): sample_shape = (1,) else: sample_shape = shape org_sample = self.distribution("sample", sample_shape, mean, sd) org_sample = self.cast(org_sample, self.dtype) value = self.bijector("forward", org_sample) if shape == (): value = self.squeeze(value) return value