• Home
  • Line#
  • Scopes#
  • Navigate#
  • Raw
  • Download
1# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
2#
3# Licensed under the Apache License, Version 2.0 (the "License");
4# you may not use this file except in compliance with the License.
5# You may obtain a copy of the License at
6#
7#     http://www.apache.org/licenses/LICENSE-2.0
8#
9# Unless required by applicable law or agreed to in writing, software
10# distributed under the License is distributed on an "AS IS" BASIS,
11# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12# See the License for the specific language governing permissions and
13# limitations under the License.
14# ==============================================================================
15"""`LinearOperator` acting like a diagonal matrix."""
16
17from __future__ import absolute_import
18from __future__ import division
19from __future__ import print_function
20
21from tensorflow.python.framework import dtypes
22from tensorflow.python.framework import ops
23from tensorflow.python.ops import array_ops
24from tensorflow.python.ops import check_ops
25from tensorflow.python.ops import math_ops
26from tensorflow.python.ops.linalg import linalg_impl as linalg
27from tensorflow.python.ops.linalg import linear_operator
28from tensorflow.python.ops.linalg import linear_operator_util
29from tensorflow.python.util.tf_export import tf_export
30
31__all__ = ["LinearOperatorDiag",]
32
33
34@tf_export("linalg.LinearOperatorDiag")
35class LinearOperatorDiag(linear_operator.LinearOperator):
36  """`LinearOperator` acting like a [batch] square diagonal matrix.
37
38  This operator acts like a [batch] diagonal matrix `A` with shape
39  `[B1,...,Bb, N, N]` for some `b >= 0`.  The first `b` indices index a
40  batch member.  For every batch index `(i1,...,ib)`, `A[i1,...,ib, : :]` is
41  an `N x N` matrix.  This matrix `A` is not materialized, but for
42  purposes of broadcasting this shape will be relevant.
43
44  `LinearOperatorDiag` is initialized with a (batch) vector.
45
46  ```python
47  # Create a 2 x 2 diagonal linear operator.
48  diag = [1., -1.]
49  operator = LinearOperatorDiag(diag)
50
51  operator.to_dense()
52  ==> [[1.,  0.]
53       [0., -1.]]
54
55  operator.shape
56  ==> [2, 2]
57
58  operator.log_abs_determinant()
59  ==> scalar Tensor
60
61  x = ... Shape [2, 4] Tensor
62  operator.matmul(x)
63  ==> Shape [2, 4] Tensor
64
65  # Create a [2, 3] batch of 4 x 4 linear operators.
66  diag = tf.random_normal(shape=[2, 3, 4])
67  operator = LinearOperatorDiag(diag)
68
69  # Create a shape [2, 1, 4, 2] vector.  Note that this shape is compatible
70  # since the batch dimensions, [2, 1], are broadcast to
71  # operator.batch_shape = [2, 3].
72  y = tf.random_normal(shape=[2, 1, 4, 2])
73  x = operator.solve(y)
74  ==> operator.matmul(x) = y
75  ```
76
77  #### Shape compatibility
78
79  This operator acts on [batch] matrix with compatible shape.
80  `x` is a batch matrix with compatible shape for `matmul` and `solve` if
81
82  ```
83  operator.shape = [B1,...,Bb] + [N, N],  with b >= 0
84  x.shape =   [C1,...,Cc] + [N, R],
85  and [C1,...,Cc] broadcasts with [B1,...,Bb] to [D1,...,Dd]
86  ```
87
88  #### Performance
89
90  Suppose `operator` is a `LinearOperatorDiag` of shape `[N, N]`,
91  and `x.shape = [N, R]`.  Then
92
93  * `operator.matmul(x)` involves `N * R` multiplications.
94  * `operator.solve(x)` involves `N` divisions and `N * R` multiplications.
95  * `operator.determinant()` involves a size `N` `reduce_prod`.
96
97  If instead `operator` and `x` have shape `[B1,...,Bb, N, N]` and
98  `[B1,...,Bb, N, R]`, every operation increases in complexity by `B1*...*Bb`.
99
100  #### Matrix property hints
101
102  This `LinearOperator` is initialized with boolean flags of the form `is_X`,
103  for `X = non_singular, self_adjoint, positive_definite, square`.
104  These have the following meaning:
105
106  * If `is_X == True`, callers should expect the operator to have the
107    property `X`.  This is a promise that should be fulfilled, but is *not* a
108    runtime assert.  For example, finite floating point precision may result
109    in these promises being violated.
110  * If `is_X == False`, callers should expect the operator to not have `X`.
111  * If `is_X == None` (the default), callers should have no expectation either
112    way.
113  """
114
115  def __init__(self,
116               diag,
117               is_non_singular=None,
118               is_self_adjoint=None,
119               is_positive_definite=None,
120               is_square=None,
121               name="LinearOperatorDiag"):
122    r"""Initialize a `LinearOperatorDiag`.
123
124    Args:
125      diag:  Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`.
126        The diagonal of the operator.  Allowed dtypes: `float16`, `float32`,
127          `float64`, `complex64`, `complex128`.
128      is_non_singular:  Expect that this operator is non-singular.
129      is_self_adjoint:  Expect that this operator is equal to its hermitian
130        transpose.  If `diag.dtype` is real, this is auto-set to `True`.
131      is_positive_definite:  Expect that this operator is positive definite,
132        meaning the quadratic form `x^H A x` has positive real part for all
133        nonzero `x`.  Note that we do not require the operator to be
134        self-adjoint to be positive-definite.  See:
135        https://en.wikipedia.org/wiki/Positive-definite_matrix#Extension_for_non-symmetric_matrices
136      is_square:  Expect that this operator acts like square [batch] matrices.
137      name: A name for this `LinearOperator`.
138
139    Raises:
140      TypeError:  If `diag.dtype` is not an allowed type.
141      ValueError:  If `diag.dtype` is real, and `is_self_adjoint` is not `True`.
142    """
143
144    with ops.name_scope(name, values=[diag]):
145      self._diag = ops.convert_to_tensor(diag, name="diag")
146      self._check_diag(self._diag)
147
148      # Check and auto-set hints.
149      if not self._diag.dtype.is_complex:
150        if is_self_adjoint is False:
151          raise ValueError("A real diagonal operator is always self adjoint.")
152        else:
153          is_self_adjoint = True
154
155      if is_square is False:
156        raise ValueError("Only square diagonal operators currently supported.")
157      is_square = True
158
159      super(LinearOperatorDiag, self).__init__(
160          dtype=self._diag.dtype,
161          graph_parents=[self._diag],
162          is_non_singular=is_non_singular,
163          is_self_adjoint=is_self_adjoint,
164          is_positive_definite=is_positive_definite,
165          is_square=is_square,
166          name=name)
167
168  def _check_diag(self, diag):
169    """Static check of diag."""
170    allowed_dtypes = [
171        dtypes.float16,
172        dtypes.float32,
173        dtypes.float64,
174        dtypes.complex64,
175        dtypes.complex128,
176    ]
177
178    dtype = diag.dtype
179    if dtype not in allowed_dtypes:
180      raise TypeError(
181          "Argument diag must have dtype in %s.  Found: %s"
182          % (allowed_dtypes, dtype))
183
184    if diag.get_shape().ndims is not None and diag.get_shape().ndims < 1:
185      raise ValueError("Argument diag must have at least 1 dimension.  "
186                       "Found: %s" % diag)
187
188  def _shape(self):
189    # If d_shape = [5, 3], we return [5, 3, 3].
190    d_shape = self._diag.get_shape()
191    return d_shape.concatenate(d_shape[-1:])
192
193  def _shape_tensor(self):
194    d_shape = array_ops.shape(self._diag)
195    k = d_shape[-1]
196    return array_ops.concat((d_shape, [k]), 0)
197
198  def _assert_non_singular(self):
199    return linear_operator_util.assert_no_entries_with_modulus_zero(
200        self._diag,
201        message="Singular operator:  Diagonal contained zero values.")
202
203  def _assert_positive_definite(self):
204    if self.dtype.is_complex:
205      message = (
206          "Diagonal operator had diagonal entries with non-positive real part, "
207          "thus was not positive definite.")
208    else:
209      message = (
210          "Real diagonal operator had non-positive diagonal entries, "
211          "thus was not positive definite.")
212
213    return check_ops.assert_positive(
214        math_ops.real(self._diag),
215        message=message)
216
217  def _assert_self_adjoint(self):
218    return linear_operator_util.assert_zero_imag_part(
219        self._diag,
220        message=(
221            "This diagonal operator contained non-zero imaginary values.  "
222            " Thus it was not self-adjoint."))
223
224  def _matmul(self, x, adjoint=False, adjoint_arg=False):
225    diag_term = math_ops.conj(self._diag) if adjoint else self._diag
226    x = linalg.adjoint(x) if adjoint_arg else x
227    diag_mat = array_ops.expand_dims(diag_term, -1)
228    return diag_mat * x
229
230  def _determinant(self):
231    return math_ops.reduce_prod(self._diag, axis=[-1])
232
233  def _log_abs_determinant(self):
234    log_det = math_ops.reduce_sum(
235        math_ops.log(math_ops.abs(self._diag)), axis=[-1])
236    if self.dtype.is_complex:
237      log_det = math_ops.cast(log_det, dtype=self.dtype)
238    return log_det
239
240  def _solve(self, rhs, adjoint=False, adjoint_arg=False):
241    diag_term = math_ops.conj(self._diag) if adjoint else self._diag
242    rhs = linalg.adjoint(rhs) if adjoint_arg else rhs
243    inv_diag_mat = array_ops.expand_dims(1. / diag_term, -1)
244    return rhs * inv_diag_mat
245
246  def _to_dense(self):
247    return array_ops.matrix_diag(self._diag)
248
249  def _diag_part(self):
250    return self.diag
251
252  def _add_to_tensor(self, x):
253    x_diag = array_ops.matrix_diag_part(x)
254    new_diag = self._diag + x_diag
255    return array_ops.matrix_set_diag(x, new_diag)
256
257  @property
258  def diag(self):
259    return self._diag
260