# 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 Hyperspherical Uniform distribution class."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import math
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 random_ops
from tensorflow.python.ops.distributions import distribution
from tensorflow.python.ops import nn_impl
from tensorflow.python.framework.tensor_shape import TensorShape
from tensorflow.python.ops import gen_math_ops
class HypersphericalUniform(distribution.Distribution):
"""Hyperspherical Uniform distribution with `dim` parameter.
#### Mathematical Details
"""
def __init__(self, dim, dtype=dtypes.float32, validate_args=False, allow_nan_stats=True,
name="HypersphericalUniform"):
"""Initialize a batch of Hyperspherical Uniform distributions.
Args:
dim: Integer tensor, dimensionality of the distribution(s). Must
be `dim > 0`.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`, statistics
(e.g., mean, mode, variance) use the value "`NaN`" to indicate the
result is undefined. When `False`, an exception is raised if one or
more of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
Raises:
InvalidArgumentError: if `dim > 0` and `validate_args=False`.
"""
parameters = locals()
with ops.name_scope(name, values=[dim]):
with ops.control_dependencies([check_ops.assert_positive(dim),
check_ops.assert_integer(dim),
check_ops.assert_scalar(dim)] if validate_args else []):
self._dim = dim
super(HypersphericalUniform, self).__init__(
dtype=dtype,
reparameterization_type=distribution.FULLY_REPARAMETERIZED,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
parameters=parameters,
graph_parents=[],
name=name)
@staticmethod
def _param_shapes(sample_shape):
return {}
@property
def dim(self):
"""Dimensionality of the distribution(s)."""
return self._dim
def _batch_shape_tensor(self):
return constant_op.constant([self._dim + 1], dtype=dtypes.int32)
def _batch_shape(self):
return TensorShape(self._dim + 1)
def _event_shape_tensor(self):
return constant_op.constant([], dtype=dtypes.int32)
def _event_shape(self):
return tensor_shape.scalar()
def _sample_n(self, n, seed=None):
return nn_impl.l2_normalize(random_ops.random_normal(shape=array_ops.concat(([n], [self._dim + 1]), 0),
dtype=self.dtype, seed=seed), axis=-1)
def _log_prob(self, x):
return - array_ops.ones(shape=array_ops.shape(x)[:-1], dtype=self.dtype) * self.__log_surface_area()
def _prob(self, x):
return math_ops.exp(self._log_prob(x))
def _entropy(self):
return self.__log_surface_area()
def __log_surface_area(self):
return math.log(2) + ((self._dim + 1) / 2) * math.log(math.pi) - gen_math_ops.lgamma(
math_ops.cast((self._dim + 1) / 2, dtype=self.dtype))
