# Copyright 2020 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
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# ============================================================================
"""Normal Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.ops import composite as C
from .distribution import Distribution
from ._utils.utils import convert_to_batch, check_greater_equal_zero
from ...common import dtype as mstype
from ...context import get_context
[docs]class Normal(Distribution):
"""
Example class: Normal distribution.
Args:
mean (int, float, list, numpy.ndarray, Tensor, Parameter): mean of the Gaussian distribution.
sd (int, float, list, numpy.ndarray, Tensor, Parameter): stddev of the Gaussian distribution.
seed (int): seed to use in sampling. Default: 0.
dtype (mindspore.dtype): type of the distribution. Default: mstype.float32.
name (str): name of the distribution. Default: Normal.
Note:
Standard deviation should be greater than zero.
Examples:
>>> # To initialize a normal distribution of mean 3.0 and standard deviation 4.0
>>> n = nn.Normal(3.0, 4.0, dtype=mstype.float32)
>>> # The following create two independent normal distributions
>>> n = nn.Normal([3.0, 3.0], [4.0, 4.0], dtype=mstype.float32)
"""
def __init__(self,
mean=None,
sd=None,
seed=0,
dtype=mstype.float32,
name="Normal"):
"""
Constructor of normal distribution.
"""
param = dict(locals())
super(Normal, self).__init__(dtype, name, param)
if mean is not None and sd is not None:
self._mean_value = convert_to_batch(mean, self._broadcast_shape, dtype)
self._sd_value = convert_to_batch(sd, self._broadcast_shape, dtype)
check_greater_equal_zero(self._sd_value, "Standard deviation")
else:
self._mean_value = mean
self._sd_value = sd
self.seed = seed
#ops needed for the class
self.exp = P.Exp()
self.add = P.TensorAdd()
self.mul = P.Mul()
self.sq = P.Square()
self.log = P.Log()
self.sqrt = P.Sqrt()
self.realdiv = P.RealDiv()
self.expm1 = P.Expm1() if get_context('device_target') == 'Ascend' else self._expm1_by_step
self.shape = P.Shape()
self.zeroslike = P.ZerosLike()
self.const = P.ScalarToArray()
def extend_repr(self):
str_info = f'mean = {self._mean_value}, standard deviation = {self._sd_value}'
return str_info
def _expm1_by_step(self, x):
"""
Expm1 ops under GPU context.
"""
return self.add(self.exp(x), -1)
def _mean(self, name='mean', mean=None, sd=None):
"""
Mean of the distribution.
"""
if name == 'mean':
mean = self._mean_value if mean is None or sd is None else mean
return mean
return None
def _sd(self, name='sd', mean=None, sd=None):
"""
Standard deviation of the distribution.
"""
if name in ('sd', 'var'):
sd = self._sd_value if mean is None or sd is None else sd
return sd
return None
def _log_likelihood(self, name, value, mean=None, sd=None):
r"""
Evaluate log probability.
.. math::
L(x) = -1* \fract{(x - \mu)^2}{2. * \sigma^2} - \log(\sqrt(2* \pi * \sigma^2))
"""
if name in ('prob', 'log_prob'):
mean = self._mean_value if mean is None else mean
sd = self._sd_value if sd is None else sd
unnormalized_log_prob = -1. * self.realdiv(self.sq(self.add(value, -1. * mean)),
2. * self.sq(sd))
neg_normalization = -1. * self.log(self.sqrt(2. * np.pi * self.sq(sd)))
return self.add(unnormalized_log_prob, neg_normalization)
return None
def _kl_loss(self, name, dist, mean_b, sd_b, mean_a=None, sd_a=None):
r"""
Evaluate Normal-Normal kl divergence, i.e. KL(a||b).
Args:
name (str): name of the funtion passed in from construct. Should always be "kl_loss".
dist (str): type of the distributions. Should be "Normal" in this case.
mean_b (Tensor): mean of distribution b.
sd_b (Tensor): standard deviation distribution b.
mean_a (Tensor): mean of distribution a. Default: self._mean_value.
sd_a (Tensor): standard deviation distribution a. Default: self._sd_value.
.. math::
KL(a||b) = 0.5 * (\fract{MEAN(a)}{STD(b)} - \fract{MEAN(b)}{STD(b)}) ^ 2 +
0.5 * EXPM1(2 * (\log(STD(a)) - \log(STD(b))) - (\log(STD(a)) - \log(STD(b)))
"""
if name == 'kl_loss' and dist == 'Normal':
mean_a = self._mean_value if mean_a is None else mean_a
sd_a = self._sd_value if sd_a is None else sd_a
diff_log_scale = self.add(self.log(sd_a), - self.log(sd_b))
squared_diff = self.sq(self.add(self.realdiv(mean_a, sd_b), - self.realdiv(mean_b, sd_b)))
return self.add(self.add(0.5 * squared_diff, 0.5 * self.expm1(2 * diff_log_scale)), - diff_log_scale)
return None
def _sample(self, name, shape=(), mean=None, sd=None):
"""
Sampling.
Args:
name (str): name of the function. Should always be 'sample' when passed in from construct.
shape (tuple): shape of the sample. Default: ().
mean (Tensor): mean of the samples. Default: self._mean_value.
sd (Tensor): standard deviation of the samples. Default: self._sd_value.
Returns:
Tensor, shape is shape + batch_shape.
"""
if name == 'sample':
mean = self._mean_value if mean is None else mean
sd = self._sd_value if sd is None else sd
batch_shape = self.shape(self.add(self.zeroslike(mean), self.zeroslike(sd)))
sample_shape = shape + batch_shape
mean_zero = self.const(0.0)
sd_one = self.const(1.0)
sample_norm = C.normal(sample_shape, mean_zero, sd_one, self.seed)
sample = self.add(mean, self.mul(sample_norm, sd))
return sample
return None