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# Copyright 2018 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.
# ==============================================================================
"""FillTriangular bijector."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from tensorflow.python.framework import ops
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.distributions import bijector
from tensorflow.python.ops.distributions import util as dist_util
from tensorflow.python.util import deprecation
__all__ = [
"FillTriangular",
]
class FillTriangular(bijector.Bijector):
"""Transforms vectors to triangular.
Triangular matrix elements are filled in a clockwise spiral.
Given input with shape `batch_shape + [d]`, produces output with
shape `batch_shape + [n, n]`, where
`n = (-1 + sqrt(1 + 8 * d))/2`.
This follows by solving the quadratic equation
`d = 1 + 2 + ... + n = n * (n + 1)/2`.
#### Example
```python
b = tfb.FillTriangular(upper=False)
b.forward([1, 2, 3, 4, 5, 6])
# ==> [[4, 0, 0],
# [6, 5, 0],
# [3, 2, 1]]
b = tfb.FillTriangular(upper=True)
b.forward([1, 2, 3, 4, 5, 6])
# ==> [[1, 2, 3],
# [0, 5, 6],
# [0, 0, 4]]
```
"""
@deprecation.deprecated(
"2018-10-01",
"The TensorFlow Distributions library has moved to "
"TensorFlow Probability "
"(https://github.com/tensorflow/probability). You "
"should update all references to use `tfp.distributions` "
"instead of `tf.contrib.distributions`.",
warn_once=True)
def __init__(self,
upper=False,
validate_args=False,
name="fill_triangular"):
"""Instantiates the `FillTriangular` bijector.
Args:
upper: Python `bool` representing whether output matrix should be upper
triangular (`True`) or lower triangular (`False`, default).
validate_args: Python `bool` indicating whether arguments should be
checked for correctness.
name: Python `str` name given to ops managed by this object.
"""
self._upper = upper
super(FillTriangular, self).__init__(
forward_min_event_ndims=1,
inverse_min_event_ndims=2,
validate_args=validate_args,
name=name)
def _forward(self, x):
return dist_util.fill_triangular(x, upper=self._upper)
def _inverse(self, y):
return dist_util.fill_triangular_inverse(y, upper=self._upper)
def _forward_log_det_jacobian(self, x):
return array_ops.zeros_like(x[..., 0])
def _inverse_log_det_jacobian(self, y):
return array_ops.zeros_like(y[..., 0, 0])
def _forward_event_shape(self, input_shape):
batch_shape, d = input_shape[:-1], input_shape[-1].value
if d is None:
n = None
else:
n = vector_size_to_square_matrix_size(d, self.validate_args)
return batch_shape.concatenate([n, n])
def _inverse_event_shape(self, output_shape):
batch_shape, n1, n2 = (output_shape[:-2],
output_shape[-2].value,
output_shape[-1].value)
if n1 is None or n2 is None:
m = None
elif n1 != n2:
raise ValueError("Matrix must be square. (saw [{}, {}])".format(n1, n2))
else:
m = n1 * (n1 + 1) / 2
return batch_shape.concatenate([m])
def _forward_event_shape_tensor(self, input_shape_tensor):
batch_shape, d = input_shape_tensor[:-1], input_shape_tensor[-1]
n = vector_size_to_square_matrix_size(d, self.validate_args)
return array_ops.concat([batch_shape, [n, n]], axis=0)
def _inverse_event_shape_tensor(self, output_shape_tensor):
batch_shape, n = output_shape_tensor[:-2], output_shape_tensor[-1]
if self.validate_args:
is_square_matrix = check_ops.assert_equal(
n, output_shape_tensor[-2], message="Matrix must be square.")
with ops.control_dependencies([is_square_matrix]):
n = array_ops.identity(n)
d = math_ops.cast(n * (n + 1) / 2, output_shape_tensor.dtype)
return array_ops.concat([batch_shape, [d]], axis=0)
@deprecation.deprecated(
"2018-10-01",
"The TensorFlow Distributions library has moved to "
"TensorFlow Probability "
"(https://github.com/tensorflow/probability). You "
"should update all references to use `tfp.distributions` "
"instead of `tf.contrib.distributions`.",
warn_once=True)
def vector_size_to_square_matrix_size(d, validate_args, name=None):
"""Convert a vector size to a matrix size."""
if isinstance(d, (float, int, np.generic, np.ndarray)):
n = (-1 + np.sqrt(1 + 8 * d)) / 2.
if float(int(n)) != n:
raise ValueError("Vector length is not a triangular number.")
return int(n)
else:
with ops.name_scope(name, "vector_size_to_square_matrix_size", [d]) as name:
n = (-1. + math_ops.sqrt(1 + 8. * math_ops.to_float(d))) / 2.
if validate_args:
with ops.control_dependencies([check_ops.assert_equal(
math_ops.to_float(math_ops.to_int32(n)), n,
message="Vector length is not a triangular number")]):
n = array_ops.identity(n)
return math_ops.cast(n, d.dtype)
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