LostTech.TensorFlow : API Documentation

Type LinearOperatorHouseholder

Namespace tensorflow.linalg

Parent LinearOperator

Interfaces ILinearOperatorHouseholder

`LinearOperator` acting like a [batch] of Householder transformations.

This operator acts like a [batch] of householder reflections 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.

`LinearOperatorHouseholder` is initialized with a (batch) vector.

A Householder reflection, defined via a vector `v`, which reflects points in `R^n` about the hyperplane orthogonal to `v` and through the origin. 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 2 x 2 householder transform.
            vec = [1 / np.sqrt(2), 1. / np.sqrt(2)]
            operator = LinearOperatorHouseholder(vec) 
 operator.to_dense()
==> [[0.,  -1.]
     [-1., -0.]] 
 operator.shape
==> [2, 2] 
 operator.log_abs_determinant()
==> scalar Tensor 
 x =... Shape [2, 4] Tensor
operator.matmul(x)
==> Shape [2, 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

Properties

Public properties

object batch_shape get;

object batch_shape_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;

object reflection_axis get;

object reflection_axis_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;