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mindspore.nn.probability.distribution.Normal

class mindspore.nn.probability.distribution.Normal(mean=None, sd=None, seed=None, dtype=mstype.float32, name='Normal')

Normal distribution. A Normal distributio is a continuous distribution with the range $(-inf,inf)$ and the probability density function:

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

where $\mu ,\sigma$ are the mean and the standard deviation of the normal distribution respectively.

Parameters

• 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’.

Inputs and Outputs of APIs:

The accessible APIs of the 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 all APIs of the Normal distribution, please refer to mindspore.nn.probability.distribution.Distribution, and examples below.

Supported Platforms:

Ascend GPU

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.

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)

extend_repr()

Display instance object as string.