mindspore.nn.probability.distribution.LogNormal

class mindspore.nn.probability.distribution.LogNormal(loc=None, scale=None, seed=0, dtype=mstype.float32, name='LogNormal')[source]

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 \((0, \inf)\) with the pdf as

\[f(x, \mu, \sigma) = 1 / x\sigma\sqrt{2\pi} \exp(-(\ln(x) - \mu)^2 / 2\sigma^2).\]

where \(\mu, \sigma\) are the mean and the standard deviation of the underlying normal distribution respectively. It is constructed as the exponential transformation of a Normal distribution.

Parameters

  • 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’.

Inputs and Outputs of APIs:

The accessible APIs of the Log-Normal distribution are defined in the base class, including:

  • prob, log_prob, cdf, log_cdf, survival_function, and log_survival

  • mean, sd, mode, var, and entropy

  • kl_loss and cross_entropy

  • sample

For more details of all APIs, including the inputs and outputs of APIs of the Log-Normal distribution, please refer to mindspore.nn.probability.distribution.Distribution, and examples below.

Supported Platforms:

Ascend GPU

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.

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)
property loc

Return the loc parameter of the distribution.

Returns

Tensor, the loc parameter of the distribution.

property scale

Return the scale parameter of the distribution.

Returns

Tensor, the scale parameter of the distribution.

cdf(value, loc, scale)

Compute the cumulatuve distribution function(CDF) of the given value.

Parameters

  • value (Tensor) - the value to compute.

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the value of the cumulatuve distribution function for the given input.

cross_entropy(dist, loc_b, scale_b, loc, scale)

Compute the cross entropy of two distribution

Parameters

  • dist (str) - the type of the other distribution.

  • loc_b (Tensor) - the loc parameter of the other distribution.

  • scale_b (Tensor) - the scale parameter of the other distribution.

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the value of the cross entropy.

entropy(loc, scale)

Compute the value of the entropy.

Parameters

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the value of the entropy.

kl_loss(dist, loc_b, scale_b, loc, scale)

Compute the value of the K-L loss between two distribution, namely KL(a||b).

Parameters

  • dist (str) - the type of the other distribution.

  • loc_b (Tensor) - the loc parameter of the other distribution.

  • scale_b (Tensor) - the scale parameter of the other distribution.

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the value of the K-L loss.

log_cdf(value, loc, scale)

Compute the log value of the cumulatuve distribution function.

Parameters

  • value (Tensor) - the value to compute.

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the log value of the cumulatuve distribution function.

log_prob(value, loc, scale)

the log value of the probability.

Parameters

  • value (Tensor) - the value to compute.

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the log value of the probability.

log_survival(value, loc, scale)

Compute the log value of the survival function.

Parameters

  • value (Tensor) - the value to compute.

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the value of the K-L loss.

mean(loc, scale)

Compute the mean value of the distribution.

Parameters

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the mean of the distribution.

mode(loc, scale)

Compute the mode value of the distribution.

Parameters

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the mode of the distribution.

prob(value, loc, scale)

The probability of the given value. For the continuous distribution, it is the probability density function.

Parameters

  • value (Tensor) - the value to compute.

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the value of the probability.

sample(shape, loc, scale)

Generate samples.

Parameters

  • shape (tuple) - the shape of the sample.

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the sample following the distribution.

sd(loc, scale)

The standard deviation.

Parameters

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the standard deviation of the distribution.

survival_function(value, loc, scale)

Compute the value of the survival function.

Parameters

  • value (Tensor) - the value to compute.

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the value of the survival function.

var(loc, scale)

Compute the variance of the distribution.

Parameters

  • loc (Tensor) - the loc parameter of the distribution. Default value: None.

  • scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the variance of the distribution.