tf.linalg.LinearOperatorKronecker

Kronecker product between two LinearOperators.

Inherits From: LinearOperator

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])

operator.to_dense()
==> [[1., 0., 2., 0.],
     [2., 1., 4., 2.],
     [3., 0., 4., 0.],
     [6., 3., 8., 4.]]

operator.shape
==> [4, 4]

operator.log_abs_determinant()
==> scalar Tensor

x = ... Shape [4, 2] Tensor
operator.matmul(x)
==> 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])
operator_large.matmul(x)
==> Shape [2, 3, 30, 2] Tensor

Performance

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_s