tf.linalg.LinearOperatorScaledIdentity

LinearOperator acting like a scaled [batch] identity matrix A = c I.

Inherits From: LinearOperator, Module

This operator acts like a scaled [batch] identity 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 a scaled version of the N x N identity matrix.

LinearOperatorIdentity is initialized with num_rows, and a multiplier (a Tensor) of shape [B1,...,Bb]. N is set to num_rows, and the multiplier determines the scale for each batch member.

# Create a 2 x 2 scaled identity matrix.
operator = LinearOperatorIdentity(num_rows=2, multiplier=3.)

operator.to_dense()
==> [[3., 0.]
     [0., 3.]]

operator.shape
==> [2, 2]

operator.log_abs_determinant()
==> 2 * Log[3]

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

y = tf.random.normal(shape=[3, 2, 4])
# Note that y.shape is compatible with operator.shape because operator.shape
# is broadcast to [3, 2, 2].
x = operator.solve(y)
==> 3 * x

# Create a 2-batch of 2x2 identity matrices
operator = LinearOperatorIdentity(num_rows=2, multiplier=5.)
operator.to_dense()
==> [[[5., 0.]
      [0., 5.]],
     [[5., 0.]
      [0., 5.]]]

x = ... Shape [2, 2, 3]
operator.matmul(x)
==> 5 * x

# Here the operator and x have different batch_shape, and are broadcast.
x = ... Shape [1, 2, 3]
operator.matmul(x)
==> 5 * x

Shape compatibility

This operator acts on [batch] matrix with compatible shape.