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Kronecker product between two LinearOperators.

Inherits From: LinearOperator, Module

This operator composes one or more linear operators [op1,...,opJ], building a new LinearOperator representing the Kronecker product: op1 x op2 x .. opJ (we omit parentheses as the Kronecker product is associative).

If opj has shape batch_shape_j + [M_j, N_j], then the composed operator will have shape equal to broadcast_batch_shape + [prod M_j, prod N_j], where the product is over all operators.

# Create a 4 x 4 linear operator composed of two 2 x 2 operators.
operator_1 = LinearOperatorFullMatrix([[1., 2.], [3., 4.]])
operator_2 = LinearOperatorFullMatrix([[1., 0.], [2., 1.]])
operator = LinearOperatorKronecker([operator_1, operator_2])

==> [[1., 0., 2., 0.],
     [2., 1., 4., 2.],
     [3., 0., 4., 0.],
     [6., 3., 8., 4.]]

==> [4, 4]

==> scalar Tensor

x = ... Shape [4, 2] Tensor
==> Shape [4, 2] Tensor

# Create a [2, 3] batch of 4 x 5 linear operators.
matrix_45 = tf.random.normal(shape=[2, 3, 4, 5])
operator_45 = LinearOperatorFullMatrix(matrix)

# Create a [2, 3] batch of 5 x 6 linear operators.
matrix_56 = tf.random.normal(shape=[2, 3, 5, 6])
operator_56 = LinearOperatorFullMatrix(matrix_56)

# Compose to create a [2, 3] batch of 20 x 30 operators.
operator_large = LinearOperatorKronecker([operator_45, operator_56])

# Create a shape [2, 3, 20, 2] vector.
x = tf.random.normal(shape=[2, 3, 6, 2])
==> Shape [2, 3, 30, 2] Tensor


The performance of LinearOperatorKronecker 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.

operators Iterable of LinearOperator objects, each with the same dtype and composable shape, representing the Kronecker factors.
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, 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:
is_square Expect that this operator acts like square [batch] matrices.
name A name for this LinearOperator. Default is the individual operators names joined with _x_.

TypeError If all operators do not have the same dtype.
ValueError If operators is empty.

H Returns the adjoint of the current LinearOperator.