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# Licensed under the Apache License, Version 2.0 (the "License");
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"""HalfNormal Distribution"""
from __future__ import absolute_import
from __future__ import division
import numpy as np
from mindspore import ops
from mindspore.ops import operations as P
from mindspore import _checkparam as Validator
from mindspore.common import dtype as mstype
from mindspore.nn.probability.distribution import Distribution
from mindspore.nn.probability.distribution._utils.utils import check_greater_zero
[docs]class HalfNormal(Distribution):
r"""
HalfNormal distribution.
A HalfNormal distribution is a continuous distribution with the range :math:`[\mu, \inf)`
and the probability density function:
.. math::
f(x, \mu, \sigma) = 1 / \sigma\sqrt{2\pi} \exp(-(x - \mu)^2 / 2\sigma^2).
where :math:`\mu, \sigma` are the mean and the standard deviation of the half normal distribution respectively.
Args:
mean (Union[int, float, list, numpy.ndarray, Tensor], optional): The mean of the distribution.
If this arg is ``None`` , then the mean of the distribution will be passed in runtime. Default: ``None`` .
sd (Union[int, float, list, numpy.ndarray, Tensor], optional): The standard deviation of the distribution.
If this arg is ``None`` , then the sd of the distribution will be passed in runtime. Default: ``None`` .
seed (int, optional): The seed used in sampling. The global seed is used if it is None. Default: ``None`` .
dtype (mindspore.dtype, optional): The type of the event samples. Default: ``mstype.float32`` .
name (str, optional): The name of the distribution. Default: ``'HalfNormal'`` .
Note:
- `sd` must be greater than zero.
- `dtype` must be a float type because HalfNormal distributions are continuous.
- If the arg `mean` or `sd` is passed in runtime, then it will be used as the parameter value.
Otherwise, the value passed in the constructor will be used.
Raises:
ValueError: When sd <= 0.
TypeError: When the input `dtype` is not a subclass of float.
Supported Platforms:
``CPU``
Examples:
>>> import mindspore
>>> import mindspore.nn as nn
>>> from mindspore.nn.probability.distribution import HalfNormal
>>> from mindspore import Tensor
>>> # To initialize a HalfNormal distribution of the mean 3.0 and the standard deviation 4.0.
>>> n1 = HalfNormal(3.0, 4.0, dtype=mindspore.float32)
>>> # A HalfNormal distribution can be initialized without arguments.
>>> # In this case, `mean` and `sd` must be passed in through arguments.
>>> hn = HalfNormal(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, 2.5], dtype=mindspore.float32)
>>> ans = n1.log_prob(value)
>>> print(ans.shape)
(3,)
>>> # Evaluate with respect to the distribution b.
>>> ans = n1.log_prob(value, mean_b, sd_b)
>>> print(ans.shape)
(3,)
>>> # `mean` and `sd` must be passed in during function calls
>>> ans = hn.log_prob(value, mean_a, sd_a)
>>> print(ans.shape)
(3,)
"""
def __init__(self,
mean=None,
sd=None,
seed=None,
dtype=mstype.float32,
name="HalfNormal"):
"""
Constructor of HalfNormal.
"""
param = dict(locals())
param['param_dict'] = {'mean': mean, 'sd': sd}
valid_dtype = mstype.float_type
Validator.check_type_name("dtype", dtype, valid_dtype, type(self).__name__)
super(HalfNormal, self).__init__(seed, dtype, name, param)
self._mean_value = self._add_parameter(mean, 'mean')
self._sd_value = self._add_parameter(sd, 'sd')
if self._sd_value is not None:
check_greater_zero(self._sd_value, "Standard deviation")
self.exp = P.Exp()
self.cast = P.Cast()
self.const = ops.scalar_to_tensor(np.sqrt(2. / np.pi))
self.sq = P.Square()
self.type = dtype
def _prob(self, value, mean=None, sd=None):
r"""
Evaluate probability of the value of the HalfNormal distribution.
Args:
value (Tensor): The value to be evaluated.
mean (Tensor, optional): The mean of the distribution. Default: self._mean_value.
sd (Tensor, optional): The standard deviation the distribution. Default: self._sd_value.
.. math::
P(x) = 1 / \sigma \sqrt{2\pi} \exp(-(x - \mu)^2 / 2\sigma^2)
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
mean, sd = self._check_param_type(mean, sd)
coeff = self.const / sd
pdf = coeff * self.exp(-0.5 * self.sq((value - mean) / sd))
return pdf * self.cast(value >= 0, self.type)