228 lines
7.6 KiB
Python
228 lines
7.6 KiB
Python
# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# ==============================================================================
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"""The Laplace distribution class."""
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from __future__ import absolute_import
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from __future__ import division
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from __future__ import print_function
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import math
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import numpy as np
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from tensorflow.python.framework import constant_op
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from tensorflow.python.framework import dtypes
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from tensorflow.python.framework import ops
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from tensorflow.python.framework import tensor_shape
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from tensorflow.python.ops import array_ops
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from tensorflow.python.ops import check_ops
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from tensorflow.python.ops import math_ops
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from tensorflow.python.ops import nn
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from tensorflow.python.ops import random_ops
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from tensorflow.python.ops.distributions import distribution
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from tensorflow.python.ops.distributions import special_math
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from tensorflow.python.util.tf_export import tf_export
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__all__ = [
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"Laplace",
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"LaplaceWithSoftplusScale",
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]
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@tf_export("distributions.Laplace")
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class Laplace(distribution.Distribution):
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"""The Laplace distribution with location `loc` and `scale` parameters.
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#### Mathematical details
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The probability density function (pdf) of this distribution is,
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```none
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pdf(x; mu, sigma) = exp(-|x - mu| / sigma) / Z
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Z = 2 sigma
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```
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where `loc = mu`, `scale = sigma`, and `Z` is the normalization constant.
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Note that the Laplace distribution can be thought of two exponential
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distributions spliced together "back-to-back."
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The Lpalce distribution is a member of the [location-scale family](
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https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be
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constructed as,
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```none
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X ~ Laplace(loc=0, scale=1)
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Y = loc + scale * X
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```
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"""
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def __init__(self,
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loc,
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scale,
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validate_args=False,
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allow_nan_stats=True,
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name="Laplace"):
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"""Construct Laplace distribution with parameters `loc` and `scale`.
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The parameters `loc` and `scale` must be shaped in a way that supports
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broadcasting (e.g., `loc / scale` is a valid operation).
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Args:
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loc: Floating point tensor which characterizes the location (center)
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of the distribution.
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scale: Positive floating point tensor which characterizes the spread of
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the distribution.
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validate_args: Python `bool`, default `False`. When `True` distribution
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parameters are checked for validity despite possibly degrading runtime
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performance. When `False` invalid inputs may silently render incorrect
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outputs.
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allow_nan_stats: Python `bool`, default `True`. When `True`,
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statistics (e.g., mean, mode, variance) use the value "`NaN`" to
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indicate the result is undefined. When `False`, an exception is raised
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if one or more of the statistic's batch members are undefined.
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name: Python `str` name prefixed to Ops created by this class.
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Raises:
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TypeError: if `loc` and `scale` are of different dtype.
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"""
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parameters = dict(locals())
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with ops.name_scope(name, values=[loc, scale]) as name:
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with ops.control_dependencies([check_ops.assert_positive(scale)] if
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validate_args else []):
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self._loc = array_ops.identity(loc, name="loc")
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self._scale = array_ops.identity(scale, name="scale")
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check_ops.assert_same_float_dtype([self._loc, self._scale])
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super(Laplace, self).__init__(
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dtype=self._loc.dtype,
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reparameterization_type=distribution.FULLY_REPARAMETERIZED,
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validate_args=validate_args,
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allow_nan_stats=allow_nan_stats,
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parameters=parameters,
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graph_parents=[self._loc, self._scale],
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name=name)
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@staticmethod
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def _param_shapes(sample_shape):
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return dict(
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zip(("loc", "scale"), ([ops.convert_to_tensor(
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sample_shape, dtype=dtypes.int32)] * 2)))
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@property
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def loc(self):
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"""Distribution parameter for the location."""
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return self._loc
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@property
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def scale(self):
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"""Distribution parameter for scale."""
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return self._scale
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def _batch_shape_tensor(self):
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return array_ops.broadcast_dynamic_shape(
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array_ops.shape(self.loc), array_ops.shape(self.scale))
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def _batch_shape(self):
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return array_ops.broadcast_static_shape(
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self.loc.get_shape(), self.scale.get_shape())
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def _event_shape_tensor(self):
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return constant_op.constant([], dtype=dtypes.int32)
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def _event_shape(self):
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return tensor_shape.scalar()
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def _sample_n(self, n, seed=None):
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shape = array_ops.concat([[n], self.batch_shape_tensor()], 0)
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# Uniform variates must be sampled from the open-interval `(-1, 1)` rather
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# than `[-1, 1)`. In the case of `(0, 1)` we'd use
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# `np.finfo(self.dtype.as_numpy_dtype).tiny` because it is the smallest,
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# positive, "normal" number. However, the concept of subnormality exists
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# only at zero; here we need the smallest usable number larger than -1,
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# i.e., `-1 + eps/2`.
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uniform_samples = random_ops.random_uniform(
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shape=shape,
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minval=np.nextafter(self.dtype.as_numpy_dtype(-1.),
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self.dtype.as_numpy_dtype(0.)),
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maxval=1.,
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dtype=self.dtype,
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seed=seed)
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return (self.loc - self.scale * math_ops.sign(uniform_samples) *
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math_ops.log1p(-math_ops.abs(uniform_samples)))
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def _log_prob(self, x):
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return self._log_unnormalized_prob(x) - self._log_normalization()
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def _prob(self, x):
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return math_ops.exp(self._log_prob(x))
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def _log_cdf(self, x):
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return special_math.log_cdf_laplace(self._z(x))
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def _log_survival_function(self, x):
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return special_math.log_cdf_laplace(-self._z(x))
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def _cdf(self, x):
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z = self._z(x)
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return (0.5 + 0.5 * math_ops.sign(z) *
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(1. - math_ops.exp(-math_ops.abs(z))))
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def _log_unnormalized_prob(self, x):
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return -math_ops.abs(self._z(x))
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def _log_normalization(self):
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return math.log(2.) + math_ops.log(self.scale)
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def _entropy(self):
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# Use broadcasting rules to calculate the full broadcast scale.
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scale = self.scale + array_ops.zeros_like(self.loc)
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return math.log(2.) + 1. + math_ops.log(scale)
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def _mean(self):
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return self.loc + array_ops.zeros_like(self.scale)
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def _stddev(self):
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return math.sqrt(2.) * self.scale + array_ops.zeros_like(self.loc)
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def _median(self):
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return self._mean()
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def _mode(self):
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return self._mean()
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def _z(self, x):
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return (x - self.loc) / self.scale
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class LaplaceWithSoftplusScale(Laplace):
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"""Laplace with softplus applied to `scale`."""
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def __init__(self,
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loc,
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scale,
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validate_args=False,
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allow_nan_stats=True,
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name="LaplaceWithSoftplusScale"):
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parameters = dict(locals())
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with ops.name_scope(name, values=[loc, scale]) as name:
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super(LaplaceWithSoftplusScale, self).__init__(
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loc=loc,
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scale=nn.softplus(scale, name="softplus_scale"),
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validate_args=validate_args,
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allow_nan_stats=allow_nan_stats,
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name=name)
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self._parameters = parameters
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