LostTech.TensorFlow : API Documentation

Type LinearOperatorToeplitz

Namespace tensorflow.linalg

Parent LinearOperator

Interfaces ILinearOperatorToeplitz

`LinearOperator` acting like a [batch] of toeplitz matrices.

This operator acts like a [batch] Toeplitz 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 an `N x N` matrix. This matrix `A` is not materialized, but for purposes of broadcasting this shape will be relevant.

#### Description in terms of toeplitz matrices

Toeplitz means that `A` has constant diagonals. Hence, `A` can be generated with two vectors. One represents the first column of the matrix, and the other represents the first row.

Below is a 4 x 4 example:

``` A = |a b c d| |e a b c| |f e a b| |g f e a| ```

#### Example of a Toeplitz operator. 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.
Show Example 
# Create a 3 x 3 Toeplitz operator.
            col = [1., 2., 3.]
            row = [1., 4., -9.]
            operator = LinearOperatorToeplitz(col, row) 
 operator.to_dense()
==> [[1., 4., -9.],
     [2., 1., 4.],
     [3., 2., 1.]] 
 operator.shape
==> [3, 3] 
 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

Methods

Properties

Public static methods

LinearOperatorToeplitz NewDyn(object col, object row, object is_non_singular, object is_self_adjoint, object is_positive_definite, object is_square, ImplicitContainer<T> name)

Initialize a `LinearOperatorToeplitz`.
Parameters
object col
Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`. The first column of the operator. Allowed dtypes: `float16`, `float32`, `float64`, `complex64`, `complex128`. Note that the first entry of `col` is assumed to be the same as the first entry of `row`.
object row
Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`. The first row of the operator. Allowed dtypes: `float16`, `float32`, `float64`, `complex64`, `complex128`. Note that the first entry of `row` is assumed to be the same as the first entry of `col`.
object is_non_singular
Expect that this operator is non-singular.
object is_self_adjoint
Expect that this operator is equal to its hermitian transpose. If `diag.dtype` is real, this is auto-set to `True`.
object 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
object is_square
Expect that this operator acts like square [batch] matrices.
ImplicitContainer<T> name
A name for this `LinearOperator`.

Public properties

object batch_shape get;

object batch_shape_dyn get;

Tensor col get;

object col_dyn get;

Dimension domain_dimension get;

object domain_dimension_dyn get;

object dtype get;

object dtype_dyn get;

IList<object> graph_parents get;

object graph_parents_dyn get;

Nullable<bool> is_non_singular get;

object is_non_singular_dyn get;

object is_positive_definite get;

object is_positive_definite_dyn get;

object is_self_adjoint get;

object is_self_adjoint_dyn get;

Nullable<bool> is_square get;

object is_square_dyn get;

object name get;

object name_dyn get;

object name_scope get;

object name_scope_dyn get;

object PythonObject get;

Dimension range_dimension get;

object range_dimension_dyn get;

Tensor row get;

object row_dyn get;

TensorShape shape get;

object shape_dyn get;

ValueTuple<object> submodules get;

object submodules_dyn get;

Nullable<int> tensor_rank get;

object tensor_rank_dyn get;

object trainable_variables get;

object trainable_variables_dyn get;

object variables get;

object variables_dyn get;