class_docstr: `LinearOperator` acting like a [batch] of toeplitz matrices.
  
  This operator acts like a [batch] Toeplitz 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.
  
  #### Description in terms of toeplitz matrices
  
  Toeplitz means that `A` has constant diagonals. Hence, `A` can be generated
  with two vectors. One represents the first column of the matrix, and the
  other represents the first row.
  
  Below is a 4 x 4 example:
  
  ```
  A = |a b c d|
      |e a b c|
      |f e a b|
      |g f e a|
  ```
  
  #### Example of a Toeplitz operator.
  
  ```python
  # Create a 3 x 3 Toeplitz operator.
  col = [1., 2., 3.]
  row = [1., 4., -9.]
  operator = LinearOperatorToeplitz(col, row)
  
  operator.to_dense()
  ==> [[1., 4., -9.],
       [2., 1., 4.],
       [3., 2., 1.]]
  
  tensor_shape.TensorShape(operator.shape)
  ==> [3, 3]
  
  operator.log_abs_determinant()
  ==> scalar Tensor
  
  x = ... Shape [3, 4] Tensor
  operator.matmul(x)
  ==> Shape [3, 4] Tensor
  ```
  
  #### Shape compatibility
  
  This operator acts on [batch] matrix with compatible shape.
  `x` is a batch matrix with compatible shape for `matmul` and `solve` if
  
  ```
  tensor_shape.TensorShape(operator.shape) = [B1,...,Bb] + [N, N],  with b >= 0
  tensor_shape.TensorShape(x.shape) =   [C1,...,Cc] + [N, 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.
docstr: Initialize a `LinearOperatorToeplitz`.
  
  Args:
    col: Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`.
      The first column of the operator. Allowed dtypes: `float16`, `float32`,
        `float64`, `complex64`, `complex128`. Note that the first entry of
        `col` is assumed to be the same as the first entry of `row`.
    row: Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`.
      The first row of the operator. Allowed dtypes: `float16`, `float32`,
        `float64`, `complex64`, `complex128`. Note that the first entry of
        `row` is assumed to be the same as the first entry of `col`.
    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`.
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code: def __init__(
      self,
      col,
      row,
      is_non_singular=None,
      is_self_adjoint=None,
      is_positive_definite=None,
      is_square=None,
      name="LinearOperatorToeplitz",
  ):
      r"""Initialize a `LinearOperatorToeplitz`.
  
      Args:
        col: Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`.
          The first column of the operator. Allowed dtypes: `float16`, `float32`,
            `float64`, `complex64`, `complex128`. Note that the first entry of
            `col` is assumed to be the same as the first entry of `row`.
        row: Shape `[B1,...,Bb, N]` `Tensor` with `b >= 0` `N >= 0`.
          The first row of the operator. Allowed dtypes: `float16`, `float32`,
            `float64`, `complex64`, `complex128`. Note that the first entry of
            `row` is assumed to be the same as the first entry of `col`.
        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`.
      """
      parameters = dict(
          col=col,
          row=row,
          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=[row, col]):
          self._row = linear_operator_util.convert_nonref_to_tensor(
              row, name="row"
          )
          self._col = linear_operator_util.convert_nonref_to_tensor(
              col, name="col"
          )
          self._check_row_col(self._row, self._col)
  
          if is_square is False:  # pylint:disable=g-bool-id-comparison
              raise ValueError(
                  "Only square Toeplitz operators currently supported."
              )
          is_square = True
  
          super(LinearOperatorToeplitz, self).__init__(
              dtype=self._row.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_probability.python.internal.backend.numpy import dtype
  from tensorflow_probability.python.internal.backend.numpy import ops
  from tensorflow_probability.python.internal.backend.numpy import numpy_array
  from tensorflow_probability.python.internal.backend.numpy import debugging
  from tensorflow_probability.python.internal.backend.numpy import numpy_math
  from tensorflow_probability.python.internal.backend.numpy import linalg_impl
  from tensorflow_probability.python.internal.backend.numpy.gen import linear_operator
  from tensorflow_probability.python.internal.backend.numpy.gen import linear_operator_circulant
  from tensorflow_probability.python.internal.backend.numpy.gen import linear_operator_util
  from tensorflow_probability.python.internal.backend.numpy import numpy_signal
  import numpy
  from tensorflow_probability.python.internal.backend.numpy import linalg_impl
  from tensorflow_probability.python.internal.backend.numpy import ops
  from tensorflow_probability.python.internal.backend.numpy.gen import tensor_shape
  from tensorflow_probability.python.internal.backend.numpy import private
label_desc: Use image node_id 1 to create a new LinearOperatorToeplitz object from inherited base classes: linear_operator with example: obj = LinearOperatorToeplitz(col, row, is_non_singular, is__adjoint, is_positive_definite, is_square, name)