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 of all real numbers and the probability density function:
\[f(x, a, b) = 1 / \pi b(1 - ((x - a)/b)^2),\]where \(a, b\) 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'
.
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.
- Supported Platforms:
Ascend
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:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
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:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
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:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
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:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
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:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
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:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
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:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
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:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
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:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
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:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
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:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
None
.
- Returns
Tensor, the sample following the distribution.
- sd(loc, scale)
The standard deviation.
- Parameters
loc (Tensor) - the loc parameter of the distribution. Default:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
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:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
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:
None
.scale (Tensor) - the scale parameter of the distribution. Default:
None
.
- Returns
Tensor, the variance of the distribution.