# 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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# ============================================================================
"""Logistic Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.ops import composite as C
from mindspore import _checkparam as Validator
from mindspore.common import dtype as mstype
from .distribution import Distribution
from ._utils.utils import check_greater_zero
from ._utils.custom_ops import exp_generic, log_generic
[docs]class Logistic(Distribution):
r"""
Logistic distribution.
A Logistic distributio is a continuous distribution with the range :math:`(-\inf, \inf)`
and the probability density function:
.. math::
f(x, a, b) = 1 / b \exp(\exp(-(x - a) / b) - x).
where :math:`a, b` are loc and scale parameter respectively.
Args:
loc (float, list, numpy.ndarray, Tensor): The location of the Logistic distribution. Default: None.
scale (float, list, numpy.ndarray, Tensor): The scale of the Logistic 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: 'Logistic'.
Note:
`scale` must be greater than zero.
`dist_spec_args` are `loc` and `scale`.
`dtype` must be a float type because Logistic distributions are continuous.
Raises:
ValueError: When scale <= 0.
TypeError: When the input `dtype` is not a subclass of float.
Supported Platforms:
``Ascend`` ``GPU``
Examples:
>>> import mindspore
>>> import mindspore.nn as nn
>>> import mindspore.nn.probability.distribution as msd
>>> from mindspore import Tensor
>>> # To initialize a Logistic distribution of loc 3.0 and scale 4.0.
>>> l1 = msd.Logistic(3.0, 4.0, dtype=mindspore.float32)
>>> # A Logistic distribution can be initialized without arguments.
>>> # In this case, `loc` and `scale` must be passed in through arguments.
>>> l2 = msd.Logistic(dtype=mindspore.float32)
>>>
>>> # Here are some tensors used below for testing
>>> value = Tensor([1.0, 2.0, 3.0], dtype=mindspore.float32)
>>> loc_a = Tensor([2.0], dtype=mindspore.float32)
>>> scale_a = Tensor([2.0, 2.0, 2.0], dtype=mindspore.float32)
>>> loc_b = Tensor([1.0], dtype=mindspore.float32)
>>> scale_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.
>>> # loc (Tensor): the location of the distribution. Default: self.loc.
>>> # scale (Tensor): the scale of the distribution. Default: self.scale.
>>> # Examples of `prob`.
>>> # Similar calls can be made to other probability functions
>>> # by replacing 'prob' by the name of the function
>>> ans = l1.prob(value)
>>> print(ans.shape)
(3,)
>>> # Evaluate with respect to distribution b.
>>> ans = l1.prob(value, loc_b, scale_b)
>>> print(ans.shape)
(3,)
>>> # `loc` and `scale` must be passed in during function calls
>>> ans = l1.prob(value, loc_a, scale_a)
>>> print(ans.shape)
(3,)
>>> # Functions `mean`, `mode`, `sd`, `var`, and `entropy` have the same arguments.
>>> # Args:
>>> # loc (Tensor): the location of the distribution. Default: self.loc.
>>> # scale (Tensor): the scale of the distribution. Default: self.scale.
>>> # Example of `mean`. `mode`, `sd`, `var`, and `entropy` are similar.
>>> ans = l1.mean()
>>> print(ans.shape)
()
>>> ans = l1.mean(loc_b, scale_b)
>>> print(ans.shape)
(3,)
>>> # `loc` and `scale` must be passed in during function calls.
>>> ans = l1.mean(loc_a, scale_a)
>>> print(ans.shape)
(3,)
>>> # Examples of `sample`.
>>> # Args:
>>> # shape (tuple): the shape of the sample. Default: ()
>>> # loc (Tensor): the location of the distribution. Default: self.loc.
>>> # scale (Tensor): the scale of the distribution. Default: self.scale.
>>> ans = l1.sample()
>>> print(ans.shape)
()
>>> ans = l1.sample((2,3))
>>> print(ans.shape)
(2, 3)
>>> ans = l1.sample((2,3), loc_b, scale_b)
>>> print(ans.shape)
(2, 3, 3)
>>> ans = l1.sample((2,3), loc_a, scale_a)
>>> print(ans.shape)
(2, 3, 3)
"""
def __init__(self,
loc=None,
scale=None,
seed=None,
dtype=mstype.float32,
name="Logistic"):
"""
Constructor of Logistic.
"""
param = dict(locals())
param['param_dict'] = {'loc': loc, 'scale': scale}
valid_dtype = mstype.float_type
Validator.check_type_name(
"dtype", dtype, valid_dtype, type(self).__name__)
super(Logistic, self).__init__(seed, dtype, name, param)
self._loc = self._add_parameter(loc, 'loc')
self._scale = self._add_parameter(scale, 'scale')
if self._scale is not None:
check_greater_zero(self._scale, "scale")
# ops needed for the class
self.cast = P.Cast()
self.consttensor = P.ScalarToTensor()
self.dtypeop = P.DType()
self.exp = exp_generic
self.expm1 = P.Expm1()
self.fill = P.Fill()
self.less = P.Less()
self.log = log_generic
self.log1p = P.Log1p()
self.logicalor = P.LogicalOr()
self.erf = P.Erf()
self.greater = P.Greater()
self.sigmoid = P.Sigmoid()
self.squeeze = P.Squeeze(0)
self.select = P.Select()
self.shape = P.Shape()
self.softplus = self._softplus
self.sqrt = P.Sqrt()
self.uniform = C.uniform
self.neg = P.Neg()
self.threshold = np.log(np.finfo(np.float32).eps) + 1.
self.tiny = np.finfo(np.float).tiny
self.sd_const = np.pi / np.sqrt(3)
def _softplus(self, x):
too_small = self.less(x, self.threshold)
too_large = self.greater(x, -self.threshold)
too_small_value = self.exp(x)
too_large_value = x
too_small_or_too_large = self.logicalor(too_small, too_large)
ones = self.fill(self.dtypeop(x), self.shape(x), 1.0)
x = self.select(too_small_or_too_large, ones, x)
y = self.log(self.exp(x) + 1.0)
return self.select(too_small, too_small_value, self.select(too_large, too_large_value, y))
def extend_repr(self):
"""Display instance object as string."""
if self.is_scalar_batch:
s = 'location = {}, scale = {}'.format(self._loc, self._scale)
else:
s = 'batch_shape = {}'.format(self._broadcast_shape)
return s
@property
def loc(self):
"""
Return the location of the distribution after casting to dtype.
Output:
Tensor, the loc parameter of the distribution.
"""
return self._loc
@property
def scale(self):
"""
Return the scale of the distribution after casting to dtype.
Output:
Tensor, the scale parameter of the distribution.
"""
return self._scale
def _get_dist_type(self):
return "Logistic"
def _get_dist_args(self, loc=None, scale=None):
if loc is None:
loc = self.loc
else:
self.checktensor(loc, 'loc')
if scale is None:
scale = self.scale
else:
self.checktensor(scale, 'scale')
return loc, scale
def _mean(self, loc=None, scale=None):
"""
The mean of the distribution.
"""
loc, scale = self._check_param_type(loc, scale)
return loc
def _mode(self, loc=None, scale=None):
"""
The mode of the distribution.
"""
loc, scale = self._check_param_type(loc, scale)
return loc
def _sd(self, loc=None, scale=None):
"""
The standard deviation of the distribution.
"""
_, scale = self._check_param_type(loc, scale)
return scale * self.consttensor(self.sd_const, self.dtypeop(scale))
def _entropy(self, loc=None, scale=None):
r"""
Evaluate entropy.
.. math::
H(X) = \log(scale) + 2.
"""
loc, scale = self._check_param_type(loc, scale)
return self.log(scale) + 2.
def _log_prob(self, value, loc=None, scale=None):
r"""
Evaluate log probability.
Args:
value (Tensor): The value to be evaluated.
loc (Tensor): The location of the distribution. Default: self.loc.
scale (Tensor): The scale of the distribution. Default: self.scale.
.. math::
z = (x - \mu) / \sigma
L(x) = -z * -2. * softplus(-z) - \log(\sigma)
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
loc, scale = self._check_param_type(loc, scale)
z = (value - loc) / scale
return -z - 2. * self.softplus(-z) - self.log(scale)
def _cdf(self, value, loc=None, scale=None):
r"""
Evaluate the cumulative distribution function on the given value.
Args:
value (Tensor): The value to be evaluated.
loc (Tensor): The location of the distribution. Default: self.loc.
scale (Tensor): The scale the distribution. Default: self.scale.
.. math::
cdf(x) = sigmoid((x - loc) / scale)
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
loc, scale = self._check_param_type(loc, scale)
z = (value - loc) / scale
return self.sigmoid(z)
def _log_cdf(self, value, loc=None, scale=None):
r"""
Evaluate the log cumulative distribution function on the given value.
Args:
value (Tensor): The value to be evaluated.
loc (Tensor): The location of the distribution. Default: self.loc.
scale (Tensor): The scale the distribution. Default: self.scale.
.. math::
log_cdf(x) = -softplus(-(x - loc) / scale)
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
loc, scale = self._check_param_type(loc, scale)
z = (value - loc) / scale
return (-1) * self.softplus(-z)
def _survival_function(self, value, loc=None, scale=None):
r"""
Evaluate the survival function on the given value.
Args:
value (Tensor): The value to be evaluated.
loc (Tensor): The location of the distribution. Default: self.loc.
scale (Tensor): The scale the distribution. Default: self.scale.
.. math::
survival(x) = sigmoid(-(x - loc) / scale)
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
loc, scale = self._check_param_type(loc, scale)
z = (value - loc) / scale
return self.sigmoid(-z)
def _log_survival(self, value, loc=None, scale=None):
r"""
Evaluate the log survival function on the given value.
Args:
value (Tensor): The value to be evaluated.
loc (Tensor): The location of the distribution. Default: self.loc.
scale (Tensor): The scale the distribution. Default: self.scale.
.. math::
survival(x) = -softplus((x - loc) / scale)
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
loc, scale = self._check_param_type(loc, scale)
z = (value - loc) / scale
return (-1) * self.softplus(z)
def _sample(self, shape=(), loc=None, scale=None):
"""
Sampling.
Args:
shape (tuple): The shape of the sample. Default: ().
loc (Tensor): The location of the samples. Default: self.loc.
scale (Tensor): The scale of the samples. Default: self.scale.
Returns:
Tensor, with the shape being shape + batch_shape.
"""
shape = self.checktuple(shape, 'shape')
loc, scale = self._check_param_type(loc, scale)
batch_shape = self.shape(loc + scale)
origin_shape = shape + batch_shape
if origin_shape == ():
sample_shape = (1,)
else:
sample_shape = origin_shape
l_zero = self.consttensor(self.tiny, mstype.float32)
h_one = self.consttensor(1.0, mstype.float32)
sample_uniform = self.uniform(sample_shape, l_zero, h_one, self.seed)
sample = self.log(sample_uniform) - self.log1p(self.neg(sample_uniform))
sample = sample * scale + loc
value = self.cast(sample, self.dtype)
if origin_shape == ():
value = self.squeeze(value)
return value