The type of the this LinearOperator. Arguments to matmul and
solve will have to be this type.
graph_parents
(Deprecated) Python list of graph prerequisites of this
LinearOperator Typically tensors that are passed during initialization
is_non_singular
Expect that this operator is non-singular.
is_self_adjoint
Expect that this operator is equal to its hermitian
transpose. If dtype is real, this is equivalent to being symmetric.
is_positive_definite
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
is_square
Expect that this operator acts like square [batch] matrices.
name
A name for this LinearOperator.
parameters
Python dict of parameters used to instantiate this
LinearOperator.
Raises
ValueError
If any member of graph_parents is None or not a Tensor.
ValueError
If hints are set incorrectly.
Attributes
H
Returns the adjoint of the current LinearOperator.
Given A representing this LinearOperator, return A*.
Note that calling self.adjoint() and self.H are equivalent.
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.shape[:-2]
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.
dtype
The DType of Tensors handled by this LinearOperator.
graph_parents
List of graph dependencies of this LinearOperator. (deprecated)
is_non_singular
is_positive_definite
is_self_adjoint
is_square
Return True/False depending on if this operator is square.
name
Name prepended to all ops created by this LinearOperator.
Sequence of non-trainable variables owned by this module and its submodules.
operators
parameters
Dictionary of parameters used to instantiate 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.
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.shape.
submodules
Sequence of all sub-modules.
Submodules are modules which are properties of this module, or found as
properties of modules which are properties of this module (and so on).
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.
Args
name
A name to give this Op.
Returns
An AssertOp, that, when run, will raise an InvalidArgumentError if
the operator is not positive definite.
assert_self_adjoint
assert_self_adjoint(name='assert_self_adjoint')
Returns an Op that asserts this operator is self-adjoint.
Here we check that this operator is exactly equal to its hermitian
transpose.
Args
name
A string name to prepend to created ops.
Returns
An AssertOp, that, when run, will raise an InvalidArgumentError if
the operator is not self-adjoint.
batch_shape_tensor
batch_shape_tensor(name='batch_shape_tensor')
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].
Args
name
A name for this Op.
Returns
int32Tensor
cholesky
cholesky(name:str='cholesky')->'LinearOperator'
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.
Args
name
A name for this Op.
Returns
LinearOperator which represents the lower triangular matrix
in the Cholesky decomposition.
Raises
ValueError
When the LinearOperator is not hinted to be positive
definite and self adjoint.
cond
cond(name='cond')
Returns the condition number of this linear operator.
Args
name
A name for this Op.
Returns
Shape [B1,...,Bb]Tensor of same dtype as self.
determinant
determinant(name='det')
Determinant for every batch member.
Args
name
A name for this Op.
Returns
Tensor with shape self.batch_shape and same dtype as self.
Raises
NotImplementedError
If self.is_square is False.
diag_part
diag_part(name='diag_part')
Efficiently get the [batch] diagonal part of this operator.
If this operator has shape [B1,...,Bb, M, N], this returns a
Tensordiagonal, 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 diagonalmy_operator.diag_part()==> [1.,2.]# Equivalent, but inefficient methodtf.linalg.diag_part(my_operator.to_dense())==> [1.,2.]
Transform [batch] matrix x with left multiplication: x --> Ax.
# 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_jA[...,:,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 matrix A. Assume A.shape = [..., M, N]operator=LinearOperator(...)X=...# shape [..., N], batch vectorY=operator.matvec(X)Y.shape==> [...,M]Y[...,:]=sum_jA[...,:,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.
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
int32Tensor
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).
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
int32Tensor, 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.
with_name_scope
@classmethodwith_name_scope(method)
Decorator to automatically enter the module name scope.
[[["Easy to understand","easyToUnderstand","thumb-up"],["Solved my problem","solvedMyProblem","thumb-up"],["Other","otherUp","thumb-up"]],[["Missing the information I need","missingTheInformationINeed","thumb-down"],["Too complicated / too many steps","tooComplicatedTooManySteps","thumb-down"],["Out of date","outOfDate","thumb-down"],["Samples / code issue","samplesCodeIssue","thumb-down"],["Other","otherDown","thumb-down"]],["Last updated 2023-11-21 UTC."],[],[]]