mindspore.nn.probability.distribution.Cauchy

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

Cauchy distribution. A Cauchy distributio is a continuous distribution with the range \([0, 1]\) and the probability density function:

\[f(x, a, b) = 1 / \pi b(1 - ((x - a)/b)^2),\]

where a and b are loc and scale parameter respectively.

Parameters

loc (int, float, list, numpy.ndarray, Tensor) – The location of the Cauchy distribution. Default: None.
scale (int, float, list, numpy.ndarray, Tensor) – The scale of the Cauchy 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: ‘Cauchy’.

Inputs and Outputs of APIs:

The accessible APIs of the Cauchy distribution are defined in the base class, including:

prob, log_prob, cdf, log_cdf, survival_function, and log_survival
mode and entropy
kl_loss and cross_entropy
sample

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

Supported Platforms:

Ascend

Note

scale must be greater than zero. dist_spec_args are loc and scale. dtype must be a float type because Cauchy distributions are continuous. Cauchy distribution is not supported on GPU backend.

Raises

ValueError – When scale <= 0.
TypeError – When the input dtype is not a subclass of float.

Examples

>>> import mindspore
>>> import mindspore.nn as nn
>>> import mindspore.nn.probability.distribution as msd
>>> from mindspore import Tensor
>>> # To initialize a Cauchy distribution of loc 3.0 and scale 4.0.
>>> cauchy1 = msd.Cauchy(3.0, 4.0, dtype=mindspore.float32)
>>> # A Cauchy distribution can be initialized without arguments.
>>> # In this case, 'loc' and `scale` must be passed in through arguments.
>>> cauchy2 = msd.Cauchy(dtype=mindspore.float32)
>>> # Here are some tensors used below for testing
>>> value = Tensor([1.0, 2.0, 3.0], dtype=mindspore.float32)
>>> loc_a = Tensor([2.0], dtype=mindspore.float32)
>>> scale_a = Tensor([2.0, 2.0, 2.0], dtype=mindspore.float32)
>>> loc_b = Tensor([1.0], dtype=mindspore.float32)
>>> scale_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.
>>> #     loc (Tensor): the location of the distribution. Default: self.loc.
>>> #     scale (Tensor): the scale of the distribution. Default: self.scale.
>>> # Examples of `prob`.
>>> # Similar calls can be made to other probability functions
>>> # by replacing 'prob' by the name of the function
>>> ans = cauchy1.prob(value)
>>> print(ans.shape)
(3,)
>>> # Evaluate with respect to distribution b.
>>> ans = cauchy1.prob(value, loc_b, scale_b)
>>> print(ans.shape)
(3,)
>>> # `loc` and `scale` must be passed in during function calls
>>> ans = cauchy2.prob(value, loc_a, scale_a)
>>> print(ans.shape)
(3,)
>>> # Functions `mode` and `entropy` have the same arguments.
>>> # Args:
>>> #     loc (Tensor): the location of the distribution. Default: self.loc.
>>> #     scale (Tensor): the scale of the distribution. Default: self.scale.
>>> # Example of `mode`.
>>> ans = cauchy1.mode() # return 3.0
>>> print(ans.shape)
()
>>> ans = cauchy1.mode(loc_b, scale_b) # return loc_b
>>> print(ans.shape)
(3,)
>>> # `loc` and `scale` must be passed in during function calls.
>>> ans = cauchy2.mode(loc_a, scale_a)
>>> print(ans.shape)
(3,)
>>> # Interfaces of 'kl_loss' and 'cross_entropy' are the same:
>>> # Args:
>>> #     dist (str): the type of the distributions. Only "Cauchy" is supported.
>>> #     loc_b (Tensor): the loc of distribution b.
>>> #     scale_b (Tensor): the scale distribution b.
>>> #     loc (Tensor): the loc of distribution a. Default: self.loc.
>>> #     scale (Tensor): the scale distribution a. Default: self.scale.
>>> # Examples of `kl_loss`. `cross_entropy` is similar.
>>> ans = cauchy1.kl_loss('Cauchy', loc_b, scale_b)
>>> print(ans.shape)
(3,)
>>> ans = cauchy1.kl_loss('Cauchy', loc_b, scale_b, loc_a, scale_a)
>>> print(ans.shape)
(3,)
>>> # Additional `loc` and `scale` must be passed in.
>>> ans = cauchy2.kl_loss('Cauchy', loc_b, scale_b, loc_a, scale_a)
>>> print(ans.shape)
(3,)
>>> # Examples of `sample`.
>>> # Args:
>>> #     shape (tuple): the shape of the sample. Default: ()
>>> #     loc (Tensor): the location of the distribution. Default: self.loc.
>>> #     scale (Tensor): the scale of the distribution. Default: self.scale.
>>> ans = cauchy1.sample()
>>> print(ans.shape)
()
>>> ans = cauchy1.sample((2,3))
>>> print(ans.shape)
(2, 3)
>>> ans = cauchy1.sample((2,3), loc_b, scale_b)
>>> print(ans.shape)
(2, 3, 3)
>>> ans = cauchy2.sample((2,3), loc_a, scale_a)
>>> print(ans.shape)
(2, 3, 3)

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.