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# tf.linalg.LinearOperatorZeros

`LinearOperator` acting like a [batch] zero matrix.

Inherits From: `LinearOperator`

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`, and`dtype`arguments. If`num_columns`is`None`, then this operator will be initialized as a square matrix. If`batch_shape`is`None```, this operator efficiently passes through all arguments. If```batch_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 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: https://en.wikipedia.org/wiki/Positive-definite_matrix#Extension_for_non-symmetric_matrices
`is_square` Expect that this operator acts like square [batch] matrices.
`assert_proper_shapes` Python `bool`. If `False`, only perform static checks that initialization and method arguments have proper shape. If `True`, and static checks are inconclusive, add asserts to the graph.
`name` A name for this `LinearOperator`

`ValueError` If `num_rows` is determined statically to be non-scalar, or negative.
`ValueError` If `num_columns` is determined statically to be non-scalar, or negative.
`ValueError` If `batch_shape` is determined statically to not be 1-D, or negative.
`ValueError` If any of the following is not `True`: `{is_self_adjoint, is_non_singular, is_positive_definite}`.

`H` Returns the adjoint of the current `LinearOperator`.

Given `A` representing this `LinearOperator`, return `A*`. Note that calling `self.adjoint()` and `self.H` are equivalent.

`batch_shape` `TensorShape` of batch dimensions of this `LinearOperator`.

If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `TensorShape([B1,...,Bb])`, equivalent to `A.shape[:-2]`

`domain_dimension` Dimension (in the sense of vector spaces) of the domain of this operator.

If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `N`.

`dtype` The `DType` of `Tensor`s handled by this `LinearOperator`.
`graph_parents` List of graph dependencies of this `LinearOperator`.
`is_non_singular`

`is_positive_definite`

`is_self_adjoint`

`is_square` Return `True/False` depending on if this operator is square.
`range_dimension` Dimension (in the sense of vector spaces) of the range of this operator.

If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `M`.

`shape` `TensorShape` of this `LinearOperator`.

If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `TensorShape([B1,...,Bb, M, N])`, equivalent to `A.shape`.

`tensor_rank` Rank (in the sense of tensors) of matrix corresponding to this operator.

If this operator acts like the batch matrix `A` with `A.shape = [B1,...,Bb, M, N]`, then this returns `b + 2`.

## Methods

### `add_to_tensor`

View source

Add matrix represented by this operator to `mat`. Equiv to `I + mat`.

Args
`mat` `Tensor` with same `dtype` and shape broadcastable to `self`.
`name` A name to give this `Op`.

Returns
A `Tensor` with broadcast shape and same `dtype` as `self`.

### `adjoint`

View source

Returns the adjoint of the current `LinearOperator`.

Given `A` representing this `LinearOperator`, return `A*`. Note that calling `self.adjoint()` and `self.H` are equivalent.

Args
`name` A name for this `Op`.

Returns
`LinearOperator` which represents the adjoint of this `LinearOperator`.

### `assert_non_singular`

View source

Returns an `Op` that asserts this operator is non singular.

This operator is considered non-singular if

``````ConditionNumber < max{100, range_dimension, domain_dimension} * eps,
eps := np.finfo(self.dtype.as_numpy_dtype).eps
``````

Args
`name` A string name to prepend to created ops.

Returns
An `Assert` `Op`, that, when run, will raise an `InvalidArgumentError` if the operator is singular.

### `assert_positive_definite`

View source

Returns an `Op` that asserts this operator is positive definite.

Here, positive definite means that 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.

Args
`name` A name to give this `Op`.

Returns
An `Assert` `Op`, that, when run, will raise an `InvalidArgumentError` if the operator is not positive definite.

### `assert_self_adjoint`

View source

Returns an `Op` that asserts this operator is self-adjoint.

Here we check that this operator is exactly equal to its hermitian transpose.

Args
`name` A string name to prepend to created ops.

Returns
An