View source on GitHub
|
LinearOperator acting like a [batch] of permutation matrices.
Inherits From: LinearOperator
tf.linalg.LinearOperatorPermutation(
perm, dtype=tf.dtypes.float32, is_non_singular=None, is_self_adjoint=None,
is_positive_definite=None, is_square=None, name='LinearOperatorPermutation'
)
This operator acts like a [batch] of permutations with shape
[B1,...,Bb, N, N] for some b >= 0. The first b indices index a
batch member. For every batch index (i1,...,ib), A[i1,...,ib, : :] is
an N x N matrix. This matrix A is not materialized, but for
purposes of broadcasting this shape will be relevant.
LinearOperatorPermutation is initialized with a (batch) vector.
A permutation, is defined by an integer vector v whose values are unique
and are in the range [0, ... n]. Applying the permutation on an input
matrix has the folllowing meaning: the value of v at index i
says to move the v[i]-th row of the input matrix to the i-th row.
Because all values are unique, this will result in a permutation of the
rows the input matrix. Note, that the permutation vector v has the same
semantics as tf.transpose.
# Create a 3 x 3 permutation matrix that swaps the last two columns.
vec = [0, 2, 1]
operator = LinearOperatorPermutation(vec)
operator.to_dense()
==> [[1., 0., 0.]
[0., 0., 1.]
[0., 1., 0.]]
operator.shape
==> [3, 3]
# This will be zero.
operator.log_abs_determinant()
==> scalar Tensor
x = ... Shape [3, 4] Tensor
operator.matmul(x)
==> Shape [3, 4] Tensor
#### Shape compatibility
This operator acts on [batch] matrix with compatible shape.
`x` is a batch matrix with compatible shape for `matmul` and `solve` if
operator.shape = [B1,...,Bb] + [N, N], with b >= 0 x.shape = [C1,...,Cc] + [N, R], and [C1,...,Cc] broadcasts with [B1,...,Bb] to [D1,...,Dd]
#### Matrix property hints
This `LinearOperator` is initialized with boolean flags of the form `is_X`,
for `X = non_singular, self_adjoint, positive_definite, square`.
These have the following meaning:
* If `is_X == True`, callers should expect the operator to have the
property `X`. This is a promise that should be fulfilled, but is *not* a
runtime assert. For example, finite floating point precision may result
in these promises being violated.
* If `is_X == False`, callers should expect the operator to not have `X`.
* If `is_X == None` (the default), callers should have no expectation either
way.
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2"><h2 class="add-link">Args</h2></th></tr>
<tr>
<td>
`perm`
</td>
<td>
Shape `[B1,...,Bb, N]` Integer `Tensor` with `b >= 0`
`N >= 0`. An integer vector that represents the permutation to apply.
Note that this argument is same as <a href="../../tf/transpose"><code>tf.transpose</code></a>. However, this
permutation is applied on the rows, while the permutation in
<a href="../../tf/transpose"><code>tf.transpose</code></a> is applied on the dimensions of the `Tensor`. `perm`
is required to have unique entries from `{0, 1, ... N-1}`.
</td>
</tr><tr>
<td>
`dtype`
</td>
<td>
The `dtype` of arguments to this operator. Default: `float32`.
Allowed dtypes: `float16`, `float32`, `float64`, `complex64`,
`complex128`.
</td>
</tr><tr>
<td>
`is_non_singular`
</td>
<td>
Expect that this operator is non-singular.
</td>
</tr><tr>
<td>
`is_self_adjoint`
</td>
<td>
Expect that this operator is equal to its hermitian
transpose. This is autoset to true
</td>
</tr><tr>
<td>
`is_positive_definite`
</td>
<td>
Expect that this operator is positive definite,
meaning the quadratic form `x^H A x` has positive real part for all
nonzero `x`. Note that we do not require the operator to be
self-adjoint to be positive-definite. See:
https://en.wikipedia.org/wiki/Positive-definite_matrix#Extension_for_non-symmetric_matrices
This is autoset to false.
</td>
</tr><tr>
<td>
`is_square`
</td>
<td>
Expect that this operator acts like square [batch] matrices.
This is autoset to true.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
A name for this `LinearOperator`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2"><h2 class="add-link">Raises</h2></th></tr>
<tr>
<td>
`ValueError`
</td>
<td>
`is_self_adjoint` is not `True`, `is_positive_definite` is
not `False` or `is_square` is not `True`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2"><h2 class="add-link">Attributes</h2></th></tr>
<tr>
<td>
`H`
</td>
<td>
Returns the adjoint of the current `LinearOperator`.
Given `A` representing this `LinearOperator`, return `A*`.
Note that calling `self.adjoint()` and `self.H` are equivalent.
</td>
</tr><tr>
<td>
`batch_shape`
</td>
<td>
`TensorShape` of batch dimensions of this `LinearOperator`.
If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns
`TensorShape([B1,...,Bb])`, equivalent to `A.shape[:-2]`
</td>
</tr><tr>
<td>
`domain_dimension`
</td>
<td>
Dimension (in the sense of vector spaces) of the domain of this operator.
If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns `N`.
</td>
</tr><tr>
<td>
`dtype`
</td>
<td>
The `DType` of `Tensor`s handled by this `LinearOperator`.
</td>
</tr><tr>
<td>
`graph_parents`
</td>
<td>
List of graph dependencies of this `LinearOperator`. (deprecated)
Warning: THIS FUNCTION IS DEPRECATED. It will be removed in a future version.
Instructions for updating:
Do not call `graph_parents`.
</td>
</tr><tr>
<td>
`is_non_singular`
</td>
<td>
</td>
</tr><tr>
<td>
`is_positive_definite`
</td>
<td>
</td>
</tr><tr>
<td>
`is_self_adjoint`
</td>
<td>
</td>
</tr><tr>
<td>
`is_square`
</td>
<td>
Return `True/False` depending on if this operator is square.
</td>
</tr><tr>
<td>
`perm`
</td>
<td>
</td>
</tr><tr>
<td>
`range_dimension`
</td>
<td>
Dimension (in the sense of vector spaces) of the range of this operator.
If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns `M`.
</td>
</tr><tr>
<td>
`shape`
</td>
<td>
`TensorShape` of this `LinearOperator`.
If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns
`TensorShape([B1,...,Bb, M, N])`, equivalent to `A.shape`.
</td>
</tr><tr>
<td>
`tensor_rank`
</td>
<td>
Rank (in the sense of tensors) of matrix corresponding to this operator.
If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns `b + 2`.
</td>
</tr>
</table>
## Methods
<h3 id="add_to_tensor"><code>add_to_tensor</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L1046-L1059">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>add_to_tensor(
x, name='add_to_tensor'
)
</code></pre>
Add matrix represented by this operator to `x`. Equivalent to `A + x`.
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`x`
</td>
<td>
`Tensor` with same `dtype` and shape broadcastable to `self.shape`.
</td>
</tr><tr>
<td>
`name`
</td>
<td>
A name to give this `Op`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
A `Tensor` with broadcast shape and same `dtype` as `self`.
</td>
</tr>
</table>
<h3 id="adjoint"><code>adjoint</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L902-L917">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>adjoint(
name='adjoint'
)
</code></pre>
Returns the adjoint of the current `LinearOperator`.
Given `A` representing this `LinearOperator`, return `A*`.
Note that calling `self.adjoint()` and `self.H` are equivalent.
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`name`
</td>
<td>
A name for this `Op`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
`LinearOperator` which represents the adjoint of this `LinearOperator`.
</td>
</tr>
</table>
<h3 id="assert_non_singular"><code>assert_non_singular</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L510-L528">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>assert_non_singular(
name='assert_non_singular'
)
</code></pre>
Returns an `Op` that asserts this operator is non singular.
This operator is considered non-singular if
ConditionNumber < max{100, range_dimension, domain_dimension} * eps, eps := np.finfo(self.dtype.as_numpy_dtype).eps
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`name`
</td>
<td>
A string name to prepend to created ops.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
An `Assert` `Op`, that, when run, will raise an `InvalidArgumentError` if
the operator is singular.
</td>
</tr>
</table>
<h3 id="assert_positive_definite"><code>assert_positive_definite</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L546-L561">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>assert_positive_definite(
name='assert_positive_definite'
)
</code></pre>
Returns an `Op` that asserts this operator is positive definite.
Here, positive definite means that the quadratic form `x^H A x` has positive
real part for all nonzero `x`. Note that we do not require the operator to
be self-adjoint to be positive definite.
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`name`
</td>
<td>
A name to give this `Op`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
An `Assert` `Op`, that, when run, will raise an `InvalidArgumentError` if
the operator is not positive definite.
</td>
</tr>
</table>
<h3 id="assert_self_adjoint"><code>assert_self_adjoint</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L573-L587">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>assert_self_adjoint(
name='assert_self_adjoint'
)
</code></pre>
Returns an `Op` that asserts this operator is self-adjoint.
Here we check that this operator is *exactly* equal to its hermitian
transpose.
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`name`
</td>
<td>
A string name to prepend to created ops.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
An `Assert` `Op`, that, when run, will raise an `InvalidArgumentError` if
the operator is not self-adjoint.
</td>
</tr>
</table>
<h3 id="batch_shape_tensor"><code>batch_shape_tensor</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L324-L339">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>batch_shape_tensor(
name='batch_shape_tensor'
)
</code></pre>
Shape of batch dimensions of this operator, determined at runtime.
If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns a `Tensor` holding
`[B1,...,Bb]`.
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`name`
</td>
<td>
A name for this `Op`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
`int32` `Tensor`
</td>
</tr>
</table>
<h3 id="cholesky"><code>cholesky</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L947-L970">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>cholesky(
name='cholesky'
)
</code></pre>
Returns a Cholesky factor as a `LinearOperator`.
Given `A` representing this `LinearOperator`, if `A` is positive definite
self-adjoint, return `L`, where `A = L L^T`, i.e. the cholesky
decomposition.
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`name`
</td>
<td>
A name for this `Op`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
`LinearOperator` which represents the lower triangular matrix
in the Cholesky decomposition.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Raises</th></tr>
<tr>
<td>
`ValueError`
</td>
<td>
When the `LinearOperator` is not hinted to be positive
definite and self adjoint.
</td>
</tr>
</table>
<h3 id="cond"><code>cond</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L1096-L1106">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>cond(
name='cond'
)
</code></pre>
Returns the condition number of this linear operator.
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`name`
</td>
<td>
A name for this `Op`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
Shape `[B1,...,Bb]` `Tensor` of same `dtype` as `self`.
</td>
</tr>
</table>
<h3 id="determinant"><code>determinant</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L706-L723">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>determinant(
name='det'
)
</code></pre>
Determinant for every batch member.
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`name`
</td>
<td>
A name for this `Op`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
`Tensor` with shape `self.batch_shape` and same `dtype` as `self`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Raises</th></tr>
<tr>
<td>
`NotImplementedError`
</td>
<td>
If `self.is_square` is `False`.
</td>
</tr>
</table>
<h3 id="diag_part"><code>diag_part</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L997-L1023">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>diag_part(
name='diag_part'
)
</code></pre>
Efficiently get the [batch] diagonal part of this operator.
If this operator has shape `[B1,...,Bb, M, N]`, this returns a
`Tensor` `diagonal`, of shape `[B1,...,Bb, min(M, N)]`, where
`diagonal[b1,...,bb, i] = self.to_dense()[b1,...,bb, i, i]`.
my_operator = LinearOperatorDiag([1., 2.])
Efficiently get the diagonal
my_operator.diag_part() ==> [1., 2.]
Equivalent, but inefficient method
tf.linalg.diag_part(my_operator.to_dense()) ==> [1., 2.]
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`name`
</td>
<td>
A name for this `Op`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr>
<td>
`diag_part`
</td>
<td>
A `Tensor` of same `dtype` as self.
</td>
</tr>
</table>
<h3 id="domain_dimension_tensor"><code>domain_dimension_tensor</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L409-L425">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>domain_dimension_tensor(
name='domain_dimension_tensor'
)
</code></pre>
Dimension (in the sense of vector spaces) of the domain of this operator.
Determined at runtime.
If this operator acts like the batch matrix `A` with
`A.shape = [B1,...,Bb, M, N]`, then this returns `N`.
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`name`
</td>
<td>
A name for this `Op`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
`int32` `Tensor`
</td>
</tr>
</table>
<h3 id="eigvals"><code>eigvals</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L1064-L1081">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>eigvals(
name='eigvals'
)
</code></pre>
Returns the eigenvalues of this linear operator.
If the operator is marked as self-adjoint (via `is_self_adjoint`)
this computation can be more efficient.
Note: This currently only supports self-adjoint operators.
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`name`
</td>
<td>
A name for this `Op`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
Shape `[B1,...,Bb, N]` `Tensor` of same `dtype` as `self`.
</td>
</tr>
</table>
<h3 id="inverse"><code>inverse</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L922-L945">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>inverse(
name='inverse'
)
</code></pre>
Returns the Inverse of this `LinearOperator`.
Given `A` representing this `LinearOperator`, return a `LinearOperator`
representing `A^-1`.
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`name`
</td>
<td>
A name scope to use for ops added by this method.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
`LinearOperator` representing inverse of this matrix.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Raises</th></tr>
<tr>
<td>
`ValueError`
</td>
<td>
When the `LinearOperator` is not hinted to be `non_singular`.
</td>
</tr>
</table>
<h3 id="log_abs_determinant"><code>log_abs_determinant</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L735-L752">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>log_abs_determinant(
name='log_abs_det'
)
</code></pre>
Log absolute value of determinant for every batch member.
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Args</th></tr>
<tr>
<td>
`name`
</td>
<td>
A name for this `Op`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Returns</th></tr>
<tr class="alt">
<td colspan="2">
`Tensor` with shape `self.batch_shape` and same `dtype` as `self`.
</td>
</tr>
</table>
<!-- Tabular view -->
<table class="responsive fixed orange">
<colgroup><col width="214px"><col></colgroup>
<tr><th colspan="2">Raises</th></tr>
<tr>
<td>
`NotImplementedError`
</td>
<td>
If `self.is_square` is `False`.
</td>
</tr>
</table>
<h3 id="matmul"><code>matmul</code></h3>
<a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v2.2.0/tensorflow/python/ops/linalg/linear_operator.py#L600-L653">View source</a>
<pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
<code>matmul(
x, adjoint=False, adjoint_arg=False, name='matmul'
)
</code></pre>
Transform [batch] matrix `x` with left multiplication: `x --> Ax`.
```python
# Make an operator acting like batch matrix A. Assume A.shape = [..., M, N]
operator = LinearOperator(...)
operator.shape = [..., M, N]
X = ... # shape [..., N, R], batch matrix, R > 0.
Y = operator.matmul(X)
Y.shape
==> [..., M, R]
Y[..., :, r] = sum_j A[..., :, j] X[j, r]
| Args | |
|---|---|
x
|
LinearOperator or Tensor with compatible shape and same dtype as
self. See class docstring for definition of compatibility.
|
adjoint
|
Python bool. If True, left multiply by the adjoint: A^H x.
|
adjoint_arg
|
Python bool. If True, compute A x^H where x^H is
the hermitian transpose (transposition and complex conjugation).
|
name
|
A name for this Op.
|
| Returns | |
|---|---|
A LinearOperator or Tensor with shape [..., M, R] and same dtype
as self.
|
matvec
matvec(
x, adjoint=False, name='matvec'
)
Transform [batch] vector x with left multiplication: x --> Ax.
# Make an operator acting like batch matric A. Assume A.shape = [..., M, N]
operator = LinearOperator(...)
X = ... # shape [..., N], batch vector
Y = operator.matvec(X)
Y.shape
==> [..., M]
Y[..., :] = sum_j A[..., :, j] X[..., j]
| Args | |
|---|---|
x
|
Tensor with compatible shape and same dtype as self.
x is treated as a [batch] vector meaning for every set of leading
dimensions, the last dimension defines a vector.
See class docstring for definition of compatibility.
|
adjoint
|
Python bool. If True, left multiply by the adjoint: A^H x.
|
name
|
A name for this Op.
|
| Returns | |
|---|---|
A Tensor with shape [..., M] and same dtype as self.
|
range_dimension_tensor
range_dimension_tensor(
name='range_dimension_tensor'
)
Dimension (in the sense of vector spaces) of the range of this operator.
Determined at runtime.
If this operator acts like the batch matrix A with
A.shape = [B1,...,Bb, M, N], then this returns M.
| Args | |
|---|---|
name
|
A name for this Op.
|
| Returns | |
|---|---|
int32 Tensor
|
shape_tensor
shape_tensor(
name='shape_tensor'
)
Shape of this LinearOperator, determined at runtime.
If this operator acts like the batch matrix A with
A.shape = [B1,...,Bb, M, N], then this returns a Tensor holding
[B1,...,Bb, M, N], equivalent to tf.shape(A).
| Args | |
|---|---|
name
|
A name for this Op.
|
| Returns | |
|---|---|
int32 Tensor
|
solve
solve(
rhs, adjoint=False, adjoint_arg=False, name='solve'
)
Solve (exact or approx) R (batch) systems of equations: A X = rhs.
The returned Tensor will be close to an exact solution if A is well
conditioned. Otherwise closeness will vary. See class docstring for details.
Examples:
# Make an operator acting like batch matrix A. Assume A.shape = [..., M, N]
operator = LinearOperator(...)
operator.shape = [..., M, N]
# Solve R > 0 linear systems for every member of the batch.
RHS = ... # shape [..., M, R]
X = operator.solve(RHS)
# X[..., :, r] is the solution to the r'th linear system
# sum_j A[..., :, j] X[..., j, r] = RHS[..., :, r]
operator.matmul(X)
==> RHS
| Args | |
|---|---|
rhs
|
Tensor with same dtype as this operator and compatible shape.
rhs is treated like a [batch] matrix meaning for every set of leading
dimensions, the last two dimensions defines a matrix.
See class docstring for definition of compatibility.
|
adjoint
|
Python bool. If True, solve the system involving the adjoint
of this LinearOperator: A^H X = rhs.
|
adjoint_arg
|
Python bool. If True, solve A X = rhs^H where rhs^H
is the hermitian transpose (transposition and complex conjugation).
|
name
|
A name scope to use for ops added by this method. |
| Returns | |
|---|---|
Tensor with shape [...,N, R] and same dtype as rhs.
|
| Raises | |
|---|---|
NotImplementedError
|
If self.is_non_singular or is_square is False.
|
solvevec
solvevec(
rhs, adjoint=False, name='solve'
)
Solve single equation with best effort: A X = rhs.
The returned Tensor will be close to an exact solution if A is well
conditioned. Otherwise closeness will vary. See class docstring for details.
Examples:
# Make an operator acting like batch matrix A. Assume A.shape = [..., M, N]
operator = LinearOperator(...)
operator.shape = [..., M, N]
# Solve one linear system for every member of the batch.
RHS = ... # shape [..., M]
X = operator.solvevec(RHS)
# X is the solution to the linear system
# sum_j A[..., :, j] X[..., j] = RHS[..., :]
operator.matvec(X)
==> RHS
| Args | |
|---|---|
rhs
|
Tensor with same dtype as this operator.
rhs is treated like a [batch] vector meaning for every set of leading
dimensions, the last dimension defines a vector. See class docstring
for definition of compatibility regarding batch dimensions.
|
adjoint
|
Python bool. If True, solve the system involving the adjoint
of this LinearOperator: A^H X = rhs.
|
name
|
A name scope to use for ops added by this method. |
| Returns | |
|---|---|
Tensor with shape [...,N] and same dtype as rhs.
|
| Raises | |
|---|---|
NotImplementedError
|
If self.is_non_singular or is_square is False.
|
tensor_rank_tensor
tensor_rank_tensor(
name='tensor_rank_tensor'
)
Rank (in the sense of tensors) of matrix corresponding to this operator.
If this operator acts like the batch matrix A with
A.shape = [B1,...,Bb, M, N], then this returns b + 2.
| Args | |
|---|---|
name
|
A name for this Op.
|
| Returns | |
|---|---|
int32 Tensor, determined at runtime.
|
to_dense
to_dense(
name='to_dense'
)
Return a dense (batch) matrix representing this operator.
trace
trace(
name='trace'
)
Trace of the linear operator, equal to sum of self.diag_part().
If the operator is square, this is also the sum of the eigenvalues.
| Args | |
|---|---|
name
|
A name for this Op.
|
| Returns | |
|---|---|
Shape [B1,...,Bb] Tensor of same dtype as self.
|
__matmul__
__matmul__(
other
)