class tf.contrib.linalg.LinearOperatorScaledIdentity
See the guide: Linear Algebra (contrib) > LinearOperator
LinearOperator
acting like a scaled [batch] identity matrix A = c I
.
This operator acts like a scaled [batch] identity matrix A
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 a scaled version of the N x N
identity matrix.
LinearOperatorIdentity
is initialized with num_rows
, and a multiplier
(a Tensor
) of shape [B1,...,Bb]
. N
is set to num_rows
, and the multiplier
determines the scale for each batch member.
# Create a 2 x 2 scaled identity matrix. operator = LinearOperatorIdentity(num_rows=2, multiplier=3.) operator.to_dense() ==> [[3., 0.] [0., 3.]] operator.shape ==> [2, 2] operator.log_determinant() ==> 2 * Log[3] x = ... Shape [2, 4] Tensor operator.apply(x) ==> 3 * x y = tf.random_normal(shape=[3, 2, 4]) # Note that y.shape is compatible with operator.shape because operator.shape # is broadcast to [3, 2, 2]. x = operator.solve(y) ==> 3 * x # Create a 2-batch of 2x2 identity matrices operator = LinearOperatorIdentity(num_rows=2, multiplier=5.) operator.to_dense() ==> [[[5., 0.] [0., 5.]], [[5., 0.] [0., 5.]]] x = ... Shape [2, 2, 3] operator.apply(x) ==> 5 * x # Here the operator and x have different batch_shape, and are broadcast. x = ... Shape [1, 2, 3] operator.apply(x) ==> 5 * x
This operator acts on [batch] matrix with compatible shape. x
is a batch matrix with compatible shape for apply
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]
operator.apply(x)
is O(D1*...*Dd*N*R)
operator.solve(x)
is O(D1*...*Dd*N*R)
operator.determinant()
is O(D1*...*Dd)
This LinearOperator
is initialized with boolean flags of the form is_X
, for X = non_singular, self_adjoint, positive_definite
. 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.
batch_shape
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.get_shape()[:-2]
TensorShape
, statically determined, may be undefined.
domain_dimension
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
.
Dimension
object.
dtype
The DType
of Tensor
s handled by this LinearOperator
.
graph_parents
List of graph dependencies of this LinearOperator
.
is_non_singular
is_positive_definite
is_self_adjoint
multiplier
The [batch] scalar Tensor
, c
in cI
.
name
Name prepended to all ops created by this LinearOperator
.
range_dimension
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
.
Dimension
object.
shape
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.get_shape()
.
TensorShape
, statically determined, may be undefined.
tensor_rank
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
.
name
: A name for this `Op.Python integer, or None if the tensor rank is undefined.
__init__(num_rows, multiplier, is_non_singular=None, is_self_adjoint=None, is_positive_definite=None, assert_proper_shapes=False, name='LinearOperatorScaledIdentity')
Initialize a LinearOperatorScaledIdentity
.
The LinearOperatorScaledIdentity
is initialized with num_rows
, which determines the size of each identity matrix, and a multiplier
, which defines dtype
, batch shape, and scale of each matrix.
This operator is able to broadcast the leading (batch) dimensions.
num_rows
: Scalar non-negative integer Tensor
. Number of rows in the corresponding identity matrix.multiplier
: Tensor
of shape [B1,...,Bb]
, or []
(a scalar).is_non_singular
: Expect that this operator is non-singular.is_self_adjoint
: Expect that this operator is equal to its hermitian transpose.is_positive_definite
: Expect that this operator is positive definite.assert_proper_shapes
: Python bool
. If False
, only perform static checks that initialization and method arguments have proper shape. If True
, and static checks are inconclusive, add asserts to the graph.name
: A name for this LinearOperator
ValueError
: If num_rows
is determined statically to be non-scalar, or negative.add_to_tensor(mat, name='add_to_tensor')
Add matrix represented by this operator to mat
. Equiv to I + mat
.
mat
: Tensor
with same dtype
and shape broadcastable to self
.name
: A name to give this Op
.A Tensor
with broadcast shape and same dtype
as self
.
apply(x, adjoint=False, name='apply')
Transform x
with left multiplication: x --> Ax
.
x
: 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.name
: A name for this `Op.A Tensor
with shape [..., M, R]
and same dtype
as self
.
assert_non_singular(name='assert_non_singular')
Returns an Op
that asserts this operator is non singular.
assert_positive_definite(name='assert_positive_definite')
Returns an Op
that asserts this operator is positive definite.
Here, positive definite means the real part of all eigenvalues is positive. We do not require the operator to be self-adjoint.
name
: A name to give this Op
.An Op
that asserts this operator is positive definite.
assert_self_adjoint(name='assert_self_adjoint')
Returns an Op
that asserts this operator is self-adjoint.
batch_shape_dynamic(name='batch_shape_dynamic')
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]
.
name
: A name for this `Op.int32
Tensor
determinant(name='det')
Determinant for every batch member.
name
: A name for this `Op.Tensor
with shape self.batch_shape
and same dtype
as self
.
domain_dimension_dynamic(name='domain_dimension_dynamic')
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
.
name
: A name for this Op
.int32
Tensor
log_abs_determinant(name='log_abs_det')
Log absolute value of determinant for every batch member.
name
: A name for this `Op.Tensor
with shape self.batch_shape
and same dtype
as self
.
range_dimension_dynamic(name='range_dimension_dynamic')
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
.
name
: A name for this Op
.int32
Tensor
shape_dynamic(name='shape_dynamic')
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)
.
name
: A name for this `Op.int32
Tensor
solve(rhs, adjoint=False, name='solve')
Solve R
(batch) systems of equations exactly: A X = rhs
.
Examples:
# Create an operator acting like a 10 x 2 x 2 matrix. operator = LinearOperator(...) operator.shape # = 10 x 2 x 2 # Solve one linear system (R = 1) for every member of the length 10 batch. RHS = ... # shape 10 x 2 x 1 X = operator.solve(RHS) # shape 10 x 2 x 1 # Solve five linear systems (R = 5) for every member of the length 10 batch. RHS = ... # shape 10 x 2 x 5 X = operator.solve(RHS) X[3, :, 2] # Solution to the linear system A[3, :, :] X = RHS[3, :, 2]
rhs
: Tensor
with same dtype
as this operator and compatible shape. See class docstring for definition of compatibility.adjoint
: Python bool
. If True
, solve the system involving the adjoint of this LinearOperator
.name
: A name scope to use for ops added by this method.Tensor
with shape [...,N, R]
and same dtype
as rhs
.
ValueError
: If self.is_non_singular is False.tensor_rank_dynamic(name='tensor_rank_dynamic')
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
.
name
: A name for this `Op.int32
Tensor
, determined at runtime.
to_dense(name='to_dense')
Return a dense (batch) matrix representing this operator.
Defined in tensorflow/contrib/linalg/python/ops/linear_operator_identity.py
.
© 2017 The TensorFlow Authors. All rights reserved.
Licensed under the Creative Commons Attribution License 3.0.
Code samples licensed under the Apache 2.0 License.
https://www.tensorflow.org/api_docs/python/tf/contrib/linalg/LinearOperatorScaledIdentity