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tf.linalg.LinearOperatorZeros

LinearOperator acting like a [batch] zero matrix.

Inherits From: LinearOperator, Module

This operator acts like a [batch] zero matrix A with shape [B1,...,Bb, N, M] 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 M matrix. This matrix A is not materialized, but for purposes of broadcasting this shape will be relevant.

LinearOperatorZeros is initialized with num_rows, and optionally num_columns,batch_shape, anddtypearguments. Ifnum_columnsisNone, then this operator will be initialized as a square matrix. Ifbatch_shapeisNone, this operator efficiently passes through all arguments. Ifbatch_shape` is provided, broadcasting may occur, which will require making copies.

# Create a 2 x 2 zero matrix.
operator = LinearOperatorZero(num_rows=2, dtype=tf.float32)

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

operator.shape
==> [2, 2]

operator.determinant()
==> 0.

x = ... Shape [2, 4] Tensor
operator.matmul(x)
==> Shape [2, 4] Tensor, same as x.

# Create a 2-batch of 2x2 zero matrices
operator = LinearOperatorZeros(num_rows=2, batch_shape=[2])
operator.to_dense()
==> [[[0., 0.]
      [0., 0.]],
     [[0., 0.]
      [0., 0.]]]

# Here, even though the operator has a batch shape, the input is the same as
# the output, so x can be passed through without a copy.  The operator is able
# to detect that no broadcast is necessary because both x and the operator
# have statically defined shape.
x = ... Shape [2, 2, 3]
operator.matmul(x)
==> Shape [2, 2, 3] Tensor, same as tf.zeros_like(x)

# Here the operator and x have different batch_shape, and are broadcast.
# This requires a copy, since the output is different size than the input.
x = ... Shape [1, 2, 3]
operator.matmul(x)
==> Shape [2, 2, 3] Tensor, equal to tf.zeros_like([x, x])

Shape compatibility

This operator acts on [batch] matrix with compatible shape. x is a batch matrix with compatible shape for matmul and solve if

operator.shape = [B1,...,Bb] + [N, M],  with b >= 0
x.shape =   [C1,...,Cc] + [M, 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.

num_rows Scalar non-negative integer Tensor. Number of rows in the corresponding zero matrix.
num_columns Scalar non-negative integer Tensor. Number of columns in the corresponding zero matrix. If None, defaults to the value of num_rows.
batch_shape Optional 1-D integer Tensor. The shape of the leading dimensions. If None, this operator has no leading dimensions.
dtype Data type of the matrix that this operator represents.
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