# 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
# limitations under the License.
# ============================================================================
"""Softplus Bijector"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.nn.layer.activation import LogSigmoid
from ..distribution._utils.custom_ops import exp_generic, log_generic
from .bijector import Bijector
[docs]class Softplus(Bijector):
r"""
Softplus Bijector.
This Bijector performs the operation:
.. math::
Y = \frac{\log(1 + e ^ {kX})}{k}
where k is the sharpness factor.
Args:
sharpness (float, list, numpy.ndarray, Tensor): The scale factor. Default: ``1.0`` .
name (str): The name of the Bijector. Default: ``'Softplus'`` .
Note:
The dtype of `sharpness` must be float.
Raises:
TypeError: When the dtype of the sharpness is not float.
Supported Platforms:
``Ascend`` ``GPU`` ``CPU``
Examples:
>>> import mindspore
>>> import mindspore.nn as nn
>>> import mindspore.nn.probability.bijector as msb
>>> from mindspore import Tensor
>>>
>>> # To initialize a Softplus bijector of sharpness 2.0.
>>> softplus = msb.Softplus(2.0)
>>> # To use a Softplus bijector in a network.
>>> value = Tensor([1, 2, 3], dtype=mindspore.float32)
>>> ans1 = softplus.forward(value)
>>> print(ans1.shape)
(3,)
>>> ans2 = softplus.inverse(value)
>>> print(ans2.shape)
(3,)
>>> ans3 = softplus.forward_log_jacobian(value)
>>> print(ans3.shape)
(3,)
>>> ans4 = softplus.inverse_log_jacobian(value)
>>> print(ans4.shape)
(3,)
"""
def __init__(self,
sharpness=1.0,
name='Softplus'):
"""
Constructor of Softplus Bijector.
"""
param = dict(locals())
param['param_dict'] = {'sharpness': sharpness}
super(Softplus, self).__init__(name=name, dtype=None, param=param)
self._sharpness = self._add_parameter(sharpness, 'sharpness')
self.exp = exp_generic
self.log = log_generic
self.expm1 = P.Expm1()
self.abs = P.Abs()
self.dtypeop = P.DType()
self.cast = P.Cast()
self.fill = P.Fill()
self.greater = P.Greater()
self.less = P.Less()
self.log_sigmoid = LogSigmoid()
self.logicalor = P.LogicalOr()
self.select = P.Select()
self.shape = P.Shape()
self.sigmoid = P.Sigmoid()
self.softplus = self._softplus
self.inverse_softplus = self._inverse_softplus
self.threshold = np.log(np.finfo(np.float32).eps) + 1
self.tiny = np.exp(self.threshold)
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
ones = self.fill(self.dtypeop(x), self.shape(x), 1.0)
too_small_or_too_large = self.logicalor(too_small, too_large)
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 _inverse_softplus(self, x):
r"""
.. math::
f(x) = \frac{\log(1 + e^{x}))}
f^{-1}(y) = \frac{\log(e^{y} - 1)}
"""
too_small = self.less(x, self.tiny)
too_large = self.greater(x, (-1) * self.threshold)
too_small_value = self.log(x)
too_large_value = x
ones = self.fill(self.dtypeop(x), self.shape(x), 1.0)
too_small_or_too_large = self.logicalor(too_small, too_large)
x = self.select(too_small_or_too_large, ones, x)
y = x + self.log(self.abs(self.expm1((-1)*x)))
return self.select(too_small, too_small_value, self.select(too_large, too_large_value, y))
@property
def sharpness(self):
"""
Return the sharpness parameter of the bijector.
Output:
Tensor, the sharpness parameter of the bijector.
"""
return self._sharpness
def extend_repr(self):
"""Display instance object as string."""
if self.is_scalar_batch:
str_info = 'sharpness = {}'.format(self.sharpness)
else:
str_info = 'batch_shape = {}'.format(self.batch_shape)
return str_info
def _forward(self, x):
x = self._check_value_dtype(x)
sharpness_local = self.cast_param_by_value(x, self.sharpness)
scaled_value = sharpness_local * x
forward_v = self.softplus(scaled_value) / sharpness_local
return forward_v
def _inverse(self, y):
r"""
.. math::
f(x) = \frac{\log(1 + e^{kx}))}{k}
f^{-1}(y) = \frac{\log(e^{ky} - 1)}{k}
"""
y = self._check_value_dtype(y)
sharpness_local = self.cast_param_by_value(y, self.sharpness)
scaled_value = sharpness_local * y
inverse_v = self.inverse_softplus(scaled_value) / sharpness_local
return inverse_v
def _forward_log_jacobian(self, x):
r"""
.. math:
f(x) = \log(1 + e^{kx}) / k
f'(x) = \frac{e^{kx}}{ 1 + e^{kx}}
\log(f'(x)) = kx - \log(1 + e^{kx}) = kx - f(kx)
"""
x = self._check_value_dtype(x)
sharpness_local = self.cast_param_by_value(x, self.sharpness)
scaled_value = sharpness_local * x
forward_log_j = self.log_sigmoid(scaled_value)
return forward_log_j
def _inverse_log_jacobian(self, y):
r"""
.. math:
f(y) = \frac{\log(e^{ky} - 1)}{k}
f'(y) = \frac{e^{ky}}{e^{ky} - 1}
\log(f'(y)) = ky - \log(e^{ky} - 1) = ky - f(ky)
"""
y = self._check_value_dtype(y)
sharpness_local = self.cast_param_by_value(y, self.sharpness)
scaled_value = sharpness_local * y
inverse_log_j = scaled_value - self.inverse_softplus(scaled_value)
return inverse_log_j