mindspore2022/mindspore/nn/probability/distribution/log_normal.py

# 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
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# 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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# ============================================================================
"""LogNormal Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.common import dtype as mstype
import mindspore.nn.probability.bijector as msb
import mindspore.nn.probability.distribution as msd
from ._utils.utils import check_distribution_name
from ._utils.custom_ops import exp_generic, expm1_generic, log_generic

class LogNormal(msd.TransformedDistribution):
    """
    LogNormal distribution.
    A log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose
    logarithm is normally distributed. It is constructed as the exponential transformation of a Normal distribution.

    Args:
        loc (int, float, list, numpy.ndarray, Tensor, Parameter): The mean of the underlying Normal distribution.
        scale (int, float, list, numpy.ndarray, Tensor, Parameter): The standard deviation of the underlying
          Normal distribution.
        seed (int): the seed used in sampling. The global seed is used if it is None. Default: None.
        dtype (mindspore.dtype): type of the distribution. Default: mstype.float32.
        name (str): the name of the distribution. Default: 'LogNormal'.

    Note:
        `scale` must be greater than zero.
        `dist_spec_args` are `loc` and `scale`.
        `dtype` must be a float type because LogNormal distributions are continuous.

    Examples:
        >>> # To initialize a LogNormal distribution of `loc` 3.0 and `scale` 4.0.
        >>> n = msd.LogNormal(3.0, 4.0, dtype=mstype.float32)
        >>>
        >>> # The following creates two independent LogNormal distributions.
        >>> n = msd.LogNormal([3.0, 3.0], [4.0, 4.0], dtype=mstype.float32)
        >>>
        >>> # A LogNormal distribution can be initilize without arguments.
        >>> # In this case, `loc` and `scale` must be passed in during function calls.
        >>> n = msd.LogNormal(dtype=mstype.float32)
        >>>
        >>> # To use a LogNormal distribution in a network.
        >>> class net(Cell):
        >>>     def __init__(self):
        >>>         super(net, self).__init__():
        >>>         self.n1 = msd.LogNormal(0.0, 1.0, dtype=mstype.float32)
        >>>         self.n2 = msd.LogNormal(dtype=mstype.float32)
        >>>
        >>>     # The following calls are valid in construct.
        >>>     def construct(self, value, loc_b, scale_b, loc_a, scale_a):
        >>>
        >>>         # 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 loc of distribution. Default: None. If `loc` is passed in as None,
        >>>         #         the mean of the underlying Normal distribution will be used.
        >>>         #     scale (Tensor): the scale of distribution. Default: None. If `scale` is passed in as None,
        >>>         #         the standard deviation of the underlying Normal distribution will be used.
        >>>
        >>>         # Examples of `prob`.
        >>>         # Similar calls can be made to other probability functions
        >>>         # by replacing 'prob' by the name of the function.
        >>>         ans = self.n1.prob(value)
        >>>         # Evaluate with respect to distribution b.
        >>>         ans = self.n1.prob(value, loc_b, scale_b)
        >>>         # `loc` and `scale` must be passed in during function calls since they were not passed in construct.
        >>>         ans = self.n2.prob(value, loc_a, scale_a)
        >>>
        >>>
        >>>         # Functions `mean`, `sd`, `var`, and `entropy` have the same arguments.
        >>>         # Args:
        >>>         #     loc (Tensor): the loc of distribution. Default: None. If `loc` is passed in as None,
        >>>         #         the mean of the underlying Normal distribution will be used.
        >>>         #     scale (Tensor): the scale of distribution. Default: None. If `scale` is passed in as None,
        >>>         #         the standard deviation of the underlying Normal distribution will be used.
        >>>
        >>>         # Example of `mean`. `sd`, `var`, and `entropy` are similar.
        >>>         ans = self.n1.mean() # return 0.0
        >>>         ans = self.n1.mean(loc_b, scale_b) # return mean_b
        >>>         # `loc` and `scale` must be passed in during function calls since they were not passed in construct.
        >>>         ans = self.n2.mean(loc_a, scale_a)
        >>>
        >>>
        >>>         # Interfaces of 'kl_loss' and 'cross_entropy' are the same:
        >>>         # Args:
        >>>         #     dist (str): the type of the distributions. Only "Normal" is supported.
        >>>         #     loc_b (Tensor): the loc of distribution b.
        >>>         #     scale_b (Tensor): the scale distribution b.
        >>>         #     loc_a (Tensor): the loc of distribution a. Default: None. If `loc` is passed in as None,
        >>>         #         the mean of the underlying Normal distribution will be used.
        >>>         #     scale_a (Tensor): the scale distribution a. Default: None. If `scale` is passed in as None,
        >>>         #         the standard deviation of the underlying Normal distribution will be used.
        >>>
        >>>         # Examples of `kl_loss`. `cross_entropy` is similar.
        >>>         ans = self.n1.kl_loss('Normal', loc_b, scale_b)
        >>>         ans = self.n1.kl_loss('Normal', loc_b, scale_b, loc_a, scale_a)
        >>>         # Additional `loc` and `scale` must be passed in since they were not passed in construct.
        >>>         ans = self.n2.kl_loss('Normal', loc_b, scale_b, loc_a, scale_a)
        >>>
        >>>         # Examples of `sample`.
        >>>         # Args:
        >>>         #     shape (tuple): the shape of the sample. Default: ()
        >>>         #     loc (Tensor): the loc of the distribution. Default: None. If `loc` is passed in as None,
        >>>         #         the mean of the underlying Normal distribution will be used.
        >>>         #     scale (Tensor): the scale of the distribution. Default: None. If `scale` is passed in as None,
        >>>         #         the standard deviation of the underlying Normal distribution will be used.
        >>>         ans = self.n1.sample()
        >>>         ans = self.n1.sample((2,3))
        >>>         ans = self.n1.sample((2,3), loc_b, scale_b)
        >>>         ans = self.n2.sample((2,3), loc_a, scale_a)
    """

    def __init__(self,
                 loc=None,
                 scale=None,
                 seed=0,
                 dtype=mstype.float32,
                 name="LogNormal"):
        """
        Constructor of LogNormal distribution.
        """
        super(LogNormal, self).__init__(distribution=msd.Normal(loc, scale, dtype=dtype),
                                        bijector=msb.Exp(),
                                        seed=seed, name=name)

        self.log_2pi = np.log(2 * np.pi)

        #ops needed for the class
        self.exp = exp_generic
        self.expm1 = expm1_generic
        self.log = log_generic
        self.const = P.ScalarToArray()
        self.erf = P.Erf()
        self.fill = P.Fill()
        self.shape = P.Shape()
        self.sq = P.Square()
        self.sqrt = P.Sqrt()
        self.zeroslike = P.ZerosLike()

    @property
    def loc(self):
        """Distribution parameter for the pre-transformed mean."""
        return self.distribution("mean")

    @property
    def scale(self):
        """Distribution parameter for the pre-transformed standard deviation."""
        return self.distribution("sd")

    def extend_repr(self):
        if self.is_scalar_batch:
            str_info = f'loc = {self._mean_value}, scale = {self._sd_value}'
        else:
            str_info = f'batch_shape = {self._broadcast_shape}'
        return str_info

    def _mean(self, loc=None, scale=None):
        """
        The mean of the distribution.
        """
        mean, sd = self._check_param_type(loc, scale)
        var = self.distribution("var", mean=mean, sd=sd)
        return self.exp(mean + 0.5 * var)

    def _mode(self, loc=None, scale=None):
        """
        The mode of the distribution.
        """
        mean, sd = self._check_param_type(loc, scale)
        var = self.distribution("var", mean=mean, sd=sd)
        return self.exp(mean - var)

    def _var(self, loc=None, scale=None):
        """
        The varience of the distribution.
        """
        mean, sd = self._check_param_type(loc, scale)
        var = self.distribution("var", mean=mean, sd=sd)
        return self.expm1(var) * self.exp(2. * mean + var)

    def _entropy(self, loc=None, scale=None):
        r"""
        Evaluate entropy.

        .. math::
            H(X) = μ + 0.5 + \log(σ) + 0.5 * \log(2pi)
        """
        mean, sd = self._check_param_type(loc, scale)
        return mean + 0.5 + self.log(sd) + 0.5 * self.log_2pi

    def _cross_entropy(self, dist, loc_b, scale_b, loc_a=None, scale_a=None):
        r"""
        Evaluate cross entropy between lognormal distributions.

        Args:
            dist (str): The type of the distributions. Should be "LogNormal" in this case.
            loc_b (Tensor): The loc of distribution b.
            scale_b (Tensor): The scale of distribution b.
            loc_a (Tensor): The loc of distribution a. Default: None.
            scale_a (Tensor): The scale of distribution a. Default: None.
        """
        check_distribution_name(dist, 'LogNormal')
        return self._entropy(loc_a, scale_a) + self._kl_loss(dist, loc_b, scale_b, loc_a, scale_a)

    def _kl_loss(self, dist, loc_b, scale_b, loc_a=None, scale_a=None):
        r"""
        Evaluate LogNormal-LogNormal kl divergence, i.e. KL(a||b).

        Args:
            dist (str): The type of the distributions. Should be "LogNormal" in this case.
            loc_b (Tensor): The loc of distribution b.
            scale_b (Tensor): The scale of distribution b.
            loc_a (Tensor): The loc of distribution a. Default: None.
            scale_a (Tensor): The scale of distribution a. Default: None.

        .. 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)))
        """
        check_distribution_name(dist, 'LogNormal')
        return self.distribution("kl_loss", 'Normal', loc_b, scale_b, loc_a, scale_a)