LostTech.TensorFlow : API Documentation

Type LinearOperatorBlockDiag

Namespace tensorflow.linalg

Parent LinearOperator

Interfaces ILinearOperatorBlockDiag

Combines one or more `LinearOperators` in to a Block Diagonal matrix.

This operator combines one or more linear operators `[op1,...,opJ]`, building a new `LinearOperator`, whose underlying matrix representation is square and has each operator `opi` on the main diagonal, and zero's elsewhere.

#### Shape compatibility

If `opj` acts like a [batch] square matrix `Aj`, then `op_combined` acts like the [batch] square matrix formed by having each matrix `Aj` on the main diagonal.

Each `opj` is required to represent a square matrix, and hence will have shape `batch_shape_j + [M_j, M_j]`.

If `opj` has shape `batch_shape_j + [M_j, M_j]`, then the combined operator has shape `broadcast_batch_shape + [sum M_j, sum M_j]`, where `broadcast_batch_shape` is the mutual broadcast of `batch_shape_j`, `j = 1,...,J`, assuming the intermediate batch shapes broadcast. Even if the combined shape is well defined, the combined operator's methods may fail due to lack of broadcasting ability in the defining operators' methods. #### Performance

The performance of `LinearOperatorBlockDiag` on any operation is equal to the sum of the individual operators' operations.

#### 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 4 x 4 linear operator combined of two 2 x 2 operators.
            operator_1 = LinearOperatorFullMatrix([[1., 2.], [3., 4.]])
            operator_2 = LinearOperatorFullMatrix([[1., 0.], [0., 1.]])
            operator = LinearOperatorBlockDiag([operator_1, operator_2]) 
 operator.to_dense()
==> [[1., 2., 0., 0.],
     [3., 4., 0., 0.],
     [0., 0., 1., 0.],
     [0., 0., 0., 1.]] 
 operator.shape
==> [4, 4] 
 operator.log_abs_determinant()
==> scalar Tensor 
 x1 =... # Shape [2, 2] Tensor
x2 =... # Shape [2, 2] Tensor
x = tf.concat([x1, x2], 0)  # Shape [2, 4] Tensor
operator.matmul(x)
==> tf.concat([operator_1.matmul(x1), operator_2.matmul(x2)]) 
 # Create a [2, 3] batch of 4 x 4 linear operators.
matrix_44 = tf.random.normal(shape=[2, 3, 4, 4])
operator_44 = LinearOperatorFullMatrix(matrix) 
 # Create a [1, 3] batch of 5 x 5 linear operators.
matrix_55 = tf.random.normal(shape=[1, 3, 5, 5])
operator_55 = LinearOperatorFullMatrix(matrix_55) 
 # Combine to create a [2, 3] batch of 9 x 9 operators.
operator_99 = LinearOperatorBlockDiag([operator_44, operator_55]) 
 # Create a shape [2, 3, 9] vector.
x = tf.random.normal(shape=[2, 3, 9])
operator_99.matmul(x)
==> Shape [2, 3, 9] Tensor

Methods

Properties

Public instance methods

object determinant(string name)

Determinant for every batch member.
Parameters
string name
A name for this `Op`.
Returns
object
`Tensor` with shape `self.batch_shape` and same `dtype` as `self`.

object determinant_dyn(ImplicitContainer<T> name)

Determinant for every batch member.
Parameters
ImplicitContainer<T> name
A name for this `Op`.
Returns
object
`Tensor` with shape `self.batch_shape` and same `dtype` as `self`.

object log_abs_determinant(string name)

Log absolute value of determinant for every batch member.
Parameters
string name
A name for this `Op`.
Returns
object
`Tensor` with shape `self.batch_shape` and same `dtype` as `self`.

object log_abs_determinant_dyn(ImplicitContainer<T> name)

Log absolute value of determinant for every batch member.
Parameters
ImplicitContainer<T> name
A name for this `Op`.
Returns
object
`Tensor` with shape `self.batch_shape` and same `dtype` as `self`.

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;

IList<object> operators get;

object operators_dyn get;

object PythonObject get;

Dimension range_dimension get;

object range_dimension_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;