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# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
#
# 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.
# ==============================================================================
"""The Logistic distribution class."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import math
import numpy as np
from tensorflow.contrib.distributions.python.ops import distribution
from tensorflow.contrib.framework.python.framework import tensor_util as contrib_tensor_util
from tensorflow.python.framework import common_shapes
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.framework import tensor_shape
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import check_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import nn_ops
from tensorflow.python.ops import random_ops
class _Logistic(distribution.Distribution):
"""The scalar Logistic distribution with location and scale parameters.
#### Mathematical details
The CDF of this distribution is:
```cdf(x) = 1/(1+exp(-(x - loc) / scale))```
with support on (-inf, inf).
#### Examples
Examples of initialization of one or a batch of distributions.
```python
# Define a single scalar Logistic distribution.
dist = tf.contrib.distributions.Logistic(loc=0., scale=3.)
# Evaluate the cdf at 1, returning a scalar.
dist.cdf(1.)
# Define a batch of two scalar valued Logistics.
# The first has mean 1 and scale 11, the second 2 and 22.
dist = tf.contrib.distributions.Logistic(loc=[1, 2.], scale=[11, 22.])
# Evaluate the pdf of the first distribution on 0, and the second on 1.5,
# returning a length two tensor.
dist.pdf([0, 1.5])
# Get 3 samples, returning a 3 x 2 tensor.
dist.sample([3])
```
Arguments are broadcast when possible.
```python
# Define a batch of two scalar valued Logistics.
# Both have mean 1, but different scales.
dist = tf.contrib.distributions.Logistic(loc=1., scale=[11, 22.])
# Evaluate the pdf of both distributions on the same point, 3.0,
# returning a length 2 tensor.
dist.pdf(3.0)
```
"""
def __init__(self,
loc,
scale,
validate_args=False,
allow_nan_stats=True,
name="Logistic"):
"""Construct Logistic distributions with mean and scale `loc` and `scale`.
The parameters `loc` and `scale` must be shaped in a way that supports
broadcasting (e.g. `loc + scale` is a valid operation).
Args:
loc: Floating point tensor, the means of the distribution(s).
scale: Floating point tensor, the scales of the distribution(s).
scale must contain only positive values.
validate_args: `Boolean`, default `False`. Whether to assert that
`scale > 0`. If `validate_args` is `False`, correct output is not
guaranteed when input is invalid.
allow_nan_stats: `Boolean`, default `True`. If `False`, raise an
exception if a statistic (e.g. mean/mode/etc...) is undefined for any
batch member. If `True`, batch members with valid parameters leading to
undefined statistics will return NaN for this statistic.
name: The name to give Ops created by the initializer.
Raises:
TypeError: if loc and scale are different dtypes.
"""
parameters = locals()
parameters.pop("self")
with ops.name_scope(name, values=[loc, scale]) as ns:
with ops.control_dependencies([check_ops.assert_positive(scale)] if
validate_args else []):
self._loc = array_ops.identity(loc, name="loc")
self._scale = array_ops.identity(scale, name="scale")
contrib_tensor_util.assert_same_float_dtype((self._loc, self._scale))
super(_Logistic, self).__init__(
dtype=self._scale.dtype,
is_continuous=True,
is_reparameterized=True,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
parameters=parameters,
graph_parents=[self._loc, self._scale],
name=ns)
@staticmethod
def _param_shapes(sample_shape):
return dict(
zip(("loc", "scale"), ([ops.convert_to_tensor(
sample_shape, dtype=dtypes.int32)] * 2)))
@property
def loc(self):
"""Distribution parameter for the location."""
return self._loc
@property
def scale(self):
"""Distribution parameter for scale."""
return self._scale
def _batch_shape(self):
return array_ops.shape(self.loc + self.scale)
def _get_batch_shape(self):
return common_shapes.broadcast_shape(self.loc.get_shape(),
self.scale.get_shape())
def _event_shape(self):
return constant_op.constant([], dtype=dtypes.int32)
def _get_event_shape(self):
return tensor_shape.scalar()
def _sample_n(self, n, seed=None):
shape = array_ops.concat(0, ([n], array_ops.shape(self.mean())))
np_dtype = self.dtype.as_numpy_dtype()
minval = np.nextafter(np_dtype(0), np_dtype(1))
uniform = random_ops.random_uniform(shape=shape,
minval=minval,
maxval=1,
dtype=self.dtype,
seed=seed)
sampled = math_ops.log(uniform) - math_ops.log(1-uniform)
return sampled * self.scale + self.loc
def _log_prob(self, x):
z = self._z(x)
return - z - math_ops.log(self.scale) - 2*nn_ops.softplus(-z)
def _prob(self, x):
return math_ops.exp(self._log_prob(x))
def _log_cdf(self, x):
return nn_ops.softplus(-self._z(x))
def _cdf(self, x):
return math_ops.sigmoid(self._z(x))
def _log_survival_function(self, x):
return nn_ops.softplus(self._z(x))
def _survival_function(self, x):
return math_ops.sigmoid(-self._z(x))
def _entropy(self):
# Use broadcasting rules to calculate the full broadcast sigma.
scale = self.scale * array_ops.ones_like(self.loc)
return 2 + math_ops.log(scale)
def _mean(self):
return self.loc * array_ops.ones_like(self.scale)
def _variance(self):
return math_ops.square(self.std())
def _std(self):
return self.scale * array_ops.ones_like(self.loc) * math.pi / math.sqrt(3)
def _mode(self):
return self._mean()
def _z(self, x):
"""Standardize input `x` to a unit logistic."""
with ops.name_scope("standardize", values=[x]):
return (x - self.loc) / self.scale
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