class_docstr: `LinearOperator` acting like a [batch] square diagonal matrix.
  
  This operator acts like a [batch] diagonal 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
  an `N x N` matrix.  This matrix `A` is not materialized, but for
  purposes of broadcasting this shape will be relevant.
  
  `LinearOperatorDiag` is initialized with a (batch) vector.
  
  ```python
  # Create a 2 x 2 diagonal linear operator.
  diag = [1., -1.]
  operator = LinearOperatorDiag(diag)
  
  operator.to_dense()
  ==> [[1.,  0.]
       [0., -1.]]
  
  operator.shape
  ==> [2, 2]
  
  operator.log_abs_determinant()
  ==> scalar Tensor
  
  x = ... Shape [2, 4] Tensor
  operator.matmul(x)
  ==> Shape [2, 4] Tensor
  
  # Create a [2, 3] batch of 4 x 4 linear operators.
  diag = tf.random.normal(shape=[2, 3, 4])
  operator = LinearOperatorDiag(diag)
  
  # Create a shape [2, 1, 4, 2] vector.  Note that this shape is compatible
  # since the batch dimensions, [2, 1], are broadcast to
  # operator.batch_shape = [2, 3].
  y = tf.random.normal(shape=[2, 1, 4, 2])
  x = operator.solve(y)
  ==> operator.matmul(x) = y
  ```
  
  #### 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, N],  with b >= 0
  x.shape =   [C1,...,Cc] + [N, R],
  and [C1,...,Cc] broadcasts with [B1,...,Bb] to [D1,...,Dd]
  ```
  
  #### Performance
  
  Suppose `operator` is a `LinearOperatorDiag` of shape `[N, N]`,
  and `x.shape = [N, R]`.  Then
  
  * `operator.matmul(x)` involves `N * R` multiplications.
  * `operator.solve(x)` involves `N` divisions and `N * R` multiplications.
  * `operator.determinant()` involves a size `N` `reduce_prod`.
  
  If instead `operator` and `x` have shape `[B1,...,Bb, N, N]` and
  `[B1,...,Bb, N, R]`, every operation increases in complexity by `B1*...*Bb`.
  
  #### 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.
docstr: Initialize a `LinearOperatorDiag`.
  
  Args:
    diag:  Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`.
      The diagonal of the operator.  Allowed dtypes: `float16`, `float32`,
        `float64`, `complex64`, `complex128`.
    is_non_singular:  Expect that this operator is non-singular.
    is_self_adjoint:  Expect that this operator is equal to its hermitian
      transpose.  If `diag.dtype` is real, this is auto-set to `True`.
    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.
    name: A name for this `LinearOperator`.
  
  Raises:
    TypeError:  If `diag.dtype` is not an allowed type.
    ValueError:  If `diag.dtype` is real, and `is_self_adjoint` is not `True`.
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code: def __init__(
      self,
      diag,
      is_non_singular=None,
      is_self_adjoint=None,
      is_positive_definite=None,
      is_square=None,
      name="LinearOperatorDiag",
  ):
      r"""Initialize a `LinearOperatorDiag`.
  
      Args:
        diag:  Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`.
          The diagonal of the operator.  Allowed dtypes: `float16`, `float32`,
            `float64`, `complex64`, `complex128`.
        is_non_singular:  Expect that this operator is non-singular.
        is_self_adjoint:  Expect that this operator is equal to its hermitian
          transpose.  If `diag.dtype` is real, this is auto-set to `True`.
        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.
        name: A name for this `LinearOperator`.
  
      Raises:
        TypeError:  If `diag.dtype` is not an allowed type.
        ValueError:  If `diag.dtype` is real, and `is_self_adjoint` is not `True`.
      """
      parameters = dict(
          diag=diag,
          is_non_singular=is_non_singular,
          is_self_adjoint=is_self_adjoint,
          is_positive_definite=is_positive_definite,
          is_square=is_square,
          name=name,
      )
  
      with ops.name_scope(name, values=[diag]):
          self._diag = linear_operator_util.convert_nonref_to_tensor(
              diag, name="diag"
          )
          self._check_diag(self._diag)
  
          # Check and auto-set hints.
          if not self._diag.dtype.is_complex:
              if is_self_adjoint is False:
                  raise ValueError(
                      "A real diagonal operator is always self adjoint."
                  )
              else:
                  is_self_adjoint = True
  
          if is_square is False:
              raise ValueError(
                  "Only square diagonal operators currently supported."
              )
          is_square = True
  
          super(LinearOperatorDiag, self).__init__(
              dtype=self._diag.dtype,
              is_non_singular=is_non_singular,
              is_self_adjoint=is_self_adjoint,
              is_positive_definite=is_positive_definite,
              is_square=is_square,
              parameters=parameters,
              name=name,
          )
  
imports: from tensorflow.python.framework import ops
  from tensorflow.python.framework import tensor_conversion
  from tensorflow.python.ops import array_ops
  from tensorflow.python.ops import check_ops
  from tensorflow.python.ops import math_ops
  from tensorflow.python.ops.linalg import linalg_impl
  from tensorflow.python.ops.linalg import linear_operator
  from tensorflow.python.ops.linalg import linear_operator_lower_triangular
  from tensorflow.python.ops.linalg import linear_operator_util
  from tensorflow.python.ops.linalg import property_hint_util
  from tensorflow.python.util.tf_export import tf_export
label_desc: Use image node_id 1 to create a new LinearOperatorDiag object from inherited base classes: linear_operator with example: obj = LinearOperatorDiag(diag, is_non_singular, is__adjoint, is_positive_definite, is_square, name)