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304 lines
13 KiB
304 lines
13 KiB
# Copyright 2020 Huawei Technologies Co., Ltd
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# ============================================================================
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"""Normal Distribution"""
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import numpy as np
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from mindspore.ops import operations as P
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from mindspore.ops import composite as C
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from mindspore.common import dtype as mstype
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from .distribution import Distribution
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from ._utils.utils import cast_to_tensor, check_greater_zero, check_type, check_distribution_name,\
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set_param_type
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from ._utils.custom_ops import exp_generic, expm1_generic, log_generic, erf_generic
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class Normal(Distribution):
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"""
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Normal distribution.
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Args:
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mean (int, float, list, numpy.ndarray, Tensor, Parameter): The mean of the Normal distribution.
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sd (int, float, list, numpy.ndarray, Tensor, Parameter): The standard deviation of the Normal distribution.
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seed (int): The seed used in sampling. The global seed is used if it is None. Default: None.
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dtype (mindspore.dtype): The type of the event samples. Default: mstype.float32.
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name (str): The name of the distribution. Default: 'Normal'.
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Note:
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`sd` should be greater than zero.
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`dist_spec_args` are `mean` and `sd`.
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`dtype` should be a float type because Normal distributions are continuous.
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Examples:
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>>> # To initialize a Normal distribution of the mean 3.0 and the standard deviation 4.0.
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>>> import mindspore.nn.probability.distribution as msd
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>>> n = msd.Normal(3.0, 4.0, dtype=mstype.float32)
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>>>
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>>> # The following creates two independent Normal distributions.
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>>> n = msd.Normal([3.0, 3.0], [4.0, 4.0], dtype=mstype.float32)
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>>>
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>>> # A Normal distribution can be initilize without arguments.
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>>> # In this case, `mean` and `sd` must be passed in through arguments.
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>>> n = msd.Normal(dtype=mstype.float32)
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>>>
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>>> # To use a Normal distribution in a network.
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>>> class net(Cell):
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>>> def __init__(self):
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>>> super(net, self).__init__():
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>>> self.n1 = msd.Nomral(0.0, 1.0, dtype=mstype.float32)
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>>> self.n2 = msd.Normal(dtype=mstype.float32)
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>>>
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>>> # The following calls are valid in construct.
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>>> def construct(self, value, mean_b, sd_b, mean_a, sd_a):
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>>>
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>>> # Private interfaces of probability functions corresponding to public interfaces, including
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>>> # `prob`, `log_prob`, `cdf`, `log_cdf`, `survival_function`, and `log_survival`, have the same arguments as follows.
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>>> # Args:
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>>> # value (Tensor): the value to be evaluated.
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>>> # mean (Tensor): the mean of distribution. Default: self._mean_value.
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>>> # sd (Tensor): the standard deviation of distribution. Default: self._sd_value.
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>>>
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>>> # Examples of `prob`.
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>>> # Similar calls can be made to other probability functions
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>>> # by replacing 'prob' by the name of the function
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>>> ans = self.n1.prob(value)
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>>> # Evaluate with respect to distribution b.
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>>> ans = self.n1.prob(value, mean_b, sd_b)
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>>> # `mean` and `sd` must be passed in during function calls
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>>> ans = self.n2.prob(value, mean_a, sd_a)
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>>>
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>>>
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>>> # Functions `mean`, `sd`, `var`, and `entropy` have the same arguments.
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>>> # Args:
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>>> # mean (Tensor): the mean of distribution. Default: self._mean_value.
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>>> # sd (Tensor): the standard deviation of distribution. Default: self._sd_value.
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>>>
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>>> # Example of `mean`. `sd`, `var`, and `entropy` are similar.
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>>> ans = self.n1.mean() # return 0.0
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>>> ans = self.n1.mean(mean_b, sd_b) # return mean_b
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>>> # `mean` and `sd` must be passed in during function calls.
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>>> ans = self.n2.mean(mean_a, sd_a)
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>>>
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>>>
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>>> # Interfaces of 'kl_loss' and 'cross_entropy' are the same:
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>>> # Args:
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>>> # dist (str): the type of the distributions. Only "Normal" is supported.
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>>> # mean_b (Tensor): the mean of distribution b.
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>>> # sd_b (Tensor): the standard deviation distribution b.
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>>> # mean_a (Tensor): the mean of distribution a. Default: self._mean_value.
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>>> # sd_a (Tensor): the standard deviation distribution a. Default: self._sd_value.
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>>>
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>>> # Examples of `kl_loss`. `cross_entropy` is similar.
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>>> ans = self.n1.kl_loss('Normal', mean_b, sd_b)
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>>> ans = self.n1.kl_loss('Normal', mean_b, sd_b, mean_a, sd_a)
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>>> # Additional `mean` and `sd` must be passed in.
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>>> ans = self.n2.kl_loss('Normal', mean_b, sd_b, mean_a, sd_a)
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>>>
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>>> # Examples of `sample`.
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>>> # Args:
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>>> # shape (tuple): the shape of the sample. Default: ()
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>>> # mean (Tensor): the mean of the distribution. Default: self._mean_value.
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>>> # sd (Tensor): the standard deviation of the distribution. Default: self._sd_value.
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>>> ans = self.n1.sample()
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>>> ans = self.n1.sample((2,3))
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>>> ans = self.n1.sample((2,3), mean_b, sd_b)
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>>> ans = self.n2.sample((2,3), mean_a, sd_a)
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"""
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def __init__(self,
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mean=None,
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sd=None,
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seed=None,
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dtype=mstype.float32,
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name="Normal"):
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"""
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Constructor of Normal.
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"""
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param = dict(locals())
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valid_dtype = mstype.float_type
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check_type(dtype, valid_dtype, type(self).__name__)
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super(Normal, self).__init__(seed, dtype, name, param)
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self.parameter_type = set_param_type(
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{'mean': mean, 'sd': sd}, self.dtype)
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if mean is not None and sd is not None:
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self._mean_value = cast_to_tensor(mean, self.parameter_type)
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self._sd_value = cast_to_tensor(sd, self.parameter_type)
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check_greater_zero(self._sd_value, "Standard deviation")
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else:
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self._mean_value = mean if mean is None else cast_to_tensor(
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mean, self.parameter_type)
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self._sd_value = sd if sd is None else cast_to_tensor(
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sd, self.parameter_type)
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self.default_parameters = [self._mean_value, self._sd_value]
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self.parameter_names = ['mean', 'sd']
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# ops needed for the class
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self.exp = exp_generic
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self.expm1 = expm1_generic
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self.log = log_generic
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self.erf = erf_generic
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self.squeeze = P.Squeeze(0)
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self.cast = P.Cast()
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self.const = P.ScalarToArray()
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self.fill = P.Fill()
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self.shape = P.Shape()
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self.sq = P.Square()
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self.sqrt = P.Sqrt()
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self.zeroslike = P.ZerosLike()
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self.dtypeop = P.DType()
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self.sametypeshape = P.SameTypeShape()
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def extend_repr(self):
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if self.is_scalar_batch:
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str_info = f'mean = {self._mean_value}, standard deviation = {self._sd_value}'
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else:
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str_info = f'batch_shape = {self._broadcast_shape}'
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return str_info
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def _mean(self, mean=None, sd=None):
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"""
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The mean of the distribution.
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"""
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mean, sd = self._check_param_type(mean, sd)
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return mean
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def _mode(self, mean=None, sd=None):
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"""
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The mode of the distribution.
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"""
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mean, sd = self._check_param_type(mean, sd)
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return mean
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def _sd(self, mean=None, sd=None):
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"""
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The standard deviation of the distribution.
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"""
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mean, sd = self._check_param_type(mean, sd)
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return sd
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def _entropy(self, mean=None, sd=None):
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r"""
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Evaluate entropy.
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.. math::
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H(X) = \log(\sqrt(numpy.e * 2. * numpy.pi * \sq(\sigma)))
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"""
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mean, sd = self._check_param_type(mean, sd)
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return self.log(self.sqrt(self.const(np.e * 2. * np.pi))) + self.log(sd)
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def _cross_entropy(self, dist, mean_b, sd_b, mean=None, sd=None):
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r"""
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Evaluate cross entropy between normal distributions.
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Args:
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dist (str): Type of the distributions. Should be "Normal" in this case.
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mean_b (Tensor): Mean of distribution b.
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sd_b (Tensor): Standard deviation distribution b.
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mean_a (Tensor): Mean of distribution a. Default: self._mean_value.
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sd_a (Tensor): Standard deviation distribution a. Default: self._sd_value.
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"""
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check_distribution_name(dist, 'Normal')
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return self._entropy(mean, sd) + self._kl_loss(dist, mean_b, sd_b, mean, sd)
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def _log_prob(self, value, mean=None, sd=None):
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r"""
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Evaluate log probability.
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Args:
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value (Tensor): The value to be evaluated.
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mean (Tensor): The mean of the distribution. Default: self._mean_value.
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sd (Tensor): The standard deviation the distribution. Default: self._sd_value.
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.. math::
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L(x) = -1* \frac{(x - \mu)^2}{2. * \sigma^2} - \log(\sqrt(2* \pi * \sigma^2))
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"""
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value = self._check_value(value, 'value')
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value = self.cast(value, self.dtype)
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mean, sd = self._check_param_type(mean, sd)
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unnormalized_log_prob = -1. * \
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(self.sq(value - mean)) / (2. * self.sq(sd))
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neg_normalization = -1. * \
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self.log(self.const(2. * np.pi)) / 2. - self.log(sd)
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return unnormalized_log_prob + neg_normalization
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def _cdf(self, value, mean=None, sd=None):
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r"""
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Evaluate the cumulative distribution function on the given value.
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Args:
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value (Tensor): The value to be evaluated.
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mean (Tensor): The mean of the distribution. Default: self._mean_value.
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sd (Tensor): The standard deviation the distribution. Default: self._sd_value.
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.. math::
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cdf(x) = 0.5 * (1+ Erf((x - \mu) / ( \sigma * \sqrt(2))))
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"""
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value = self._check_value(value, 'value')
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value = self.cast(value, self.dtype)
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mean, sd = self._check_param_type(mean, sd)
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sqrt2 = self.sqrt(self.const(2.0))
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adjusted = (value - mean) / (sd * sqrt2)
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return 0.5 * (1.0 + self.erf(adjusted))
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def _kl_loss(self, dist, mean_b, sd_b, mean=None, sd=None):
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r"""
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Evaluate Normal-Normal KL divergence, i.e. KL(a||b).
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Args:
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dist (str): The type of the distributions. Should be "Normal" in this case.
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mean_b (Tensor): The mean of distribution b.
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sd_b (Tensor): The standard deviation distribution b.
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mean_a (Tensor): The mean of distribution a. Default: self._mean_value.
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sd_a (Tensor): The standard deviation distribution a. Default: self._sd_value.
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.. math::
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KL(a||b) = 0.5 * (\frac{MEAN(a)}{STD(b)} - \frac{MEAN(b)}{STD(b)}) ^ 2 +
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0.5 * EXPM1(2 * (\log(STD(a)) - \log(STD(b))) - (\log(STD(a)) - \log(STD(b)))
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"""
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check_distribution_name(dist, 'Normal')
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mean_b = self._check_value(mean_b, 'mean_b')
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sd_b = self._check_value(sd_b, 'sd_b')
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mean_b = self.cast(mean_b, self.parameter_type)
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sd_b = self.cast(sd_b, self.parameter_type)
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mean_a, sd_a = self._check_param_type(mean, sd)
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diff_log_scale = self.log(sd_a) - self.log(sd_b)
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squared_diff = self.sq(mean_a / sd_b - mean_b / sd_b)
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return 0.5 * squared_diff + 0.5 * self.expm1(2 * diff_log_scale) - diff_log_scale
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def _sample(self, shape=(), mean=None, sd=None):
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"""
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Sampling.
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Args:
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shape (tuple): The shape of the sample. Default: ().
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mean (Tensor): The mean of the samples. Default: self._mean_value.
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sd (Tensor): The standard deviation of the samples. Default: self._sd_value.
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Returns:
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Tensor, with the shape being shape + batch_shape.
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"""
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shape = self.checktuple(shape, 'shape')
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mean, sd = self._check_param_type(mean, sd)
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batch_shape = self.shape(mean + sd)
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origin_shape = shape + batch_shape
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if origin_shape == ():
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sample_shape = (1,)
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else:
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sample_shape = origin_shape
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sample_norm = C.normal(sample_shape, mean, sd, self.seed)
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value = self.cast(sample_norm, self.dtype)
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if origin_shape == ():
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value = self.squeeze(value)
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return value
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