class_docstr: Base test for this type of operator.
code: def operator_and_matrix(
      self,
      shape_info,
      dtype,
      use_placeholder,
      ensure_self_adjoint_and_pd=False,
  ):
      # Recall A = L + UDV^H
      shape = list(shape_info.shape)
      diag_shape = shape[:-1]
      k = shape[-2] // 2 + 1
      u_perturbation_shape = shape[:-1] + [k]
      diag_update_shape = shape[:-2] + [k]
  
      # base_operator L will be a symmetric positive definite diagonal linear
      # operator, with condition number as high as 1e4.
      base_diag = self._gen_positive_diag(dtype, diag_shape)
      lin_op_base_diag = base_diag
  
      # U
      u = linear_operator_test_util.random_normal_correlated_columns(
          u_perturbation_shape, dtype=dtype
      )
      lin_op_u = u
  
      # V
      v = linear_operator_test_util.random_normal_correlated_columns(
          u_perturbation_shape, dtype=dtype
      )
      lin_op_v = v
  
      # D
      if self._is_diag_update_positive or ensure_self_adjoint_and_pd:
          diag_update = self._gen_positive_diag(
              dtype, diag_update_shape
          )
      else:
          diag_update = linear_operator_test_util.random_normal(
              diag_update_shape, stddev=1e-4, dtype=dtype
          )
      lin_op_diag_update = diag_update
  
      if use_placeholder:
          lin_op_base_diag = array_ops.placeholder_with_default(
              base_diag, shape=None
          )
          lin_op_u = array_ops.placeholder_with_default(u, shape=None)
          lin_op_v = array_ops.placeholder_with_default(v, shape=None)
          lin_op_diag_update = array_ops.placeholder_with_default(
              diag_update, shape=None
          )
  
      base_operator = linalg.LinearOperatorDiag(
          lin_op_base_diag,
          is_positive_definite=True,
          is_self_adjoint=True,
      )
  
      operator = linalg.LinearOperatorLowRankUpdate(
          base_operator,
          lin_op_u,
          v=lin_op_v if self._use_v else None,
          diag_update=lin_op_diag_update
          if self._use_diag_update
          else None,
          is_diag_update_positive=self._is_diag_update_positive,
      )
  
      # The matrix representing L
      base_diag_mat = array_ops.matrix_diag(base_diag)
  
      # The matrix representing D
      diag_update_mat = array_ops.matrix_diag(diag_update)
  
      # Set up mat as some variant of A = L + UDV^H
      if self._use_v and self._use_diag_update:
          # In this case, we have L + UDV^H and it isn't symmetric.
          expect_use_cholesky = False
          matrix = base_diag_mat + math_ops.matmul(
              u, math_ops.matmul(diag_update_mat, v, adjoint_b=True)
          )
      elif self._use_v:
          # In this case, we have L + UDV^H and it isn't symmetric.
          expect_use_cholesky = False
          matrix = base_diag_mat + math_ops.matmul(u, v, adjoint_b=True)
      elif self._use_diag_update:
          # In this case, we have L + UDU^H, which is PD if D > 0, since L > 0.
          expect_use_cholesky = self._is_diag_update_positive
          matrix = base_diag_mat + math_ops.matmul(
              u, math_ops.matmul(diag_update_mat, u, adjoint_b=True)
          )
      else:
          # In this case, we have L + UU^H, which is PD since L > 0.
          expect_use_cholesky = True
          matrix = base_diag_mat + math_ops.matmul(u, u, adjoint_b=True)
  
      if expect_use_cholesky:
          self.assertTrue(operator._use_cholesky)
      else:
          self.assertFalse(operator._use_cholesky)
  
      return operator, matrix
  
imports: import numpy
  from tensorflow.python.framework import config
  from tensorflow.python.framework import dtypes
  from tensorflow.python.framework import test_util
  from tensorflow.python.ops import array_ops
  from tensorflow.python.ops import math_ops
  from tensorflow.python.ops import variables
  from tensorflow.python.ops.linalg import linalg
  from tensorflow.python.ops.linalg import linear_operator_test_util
  from tensorflow.python.platform import test
label_desc: Use image node_id 3 for calling the BaseLinearOperatorLowRankUpdatetest obj's underlying member method code with example usage: obj.operator_and_matrix(shape_info, dtype, use_placeholder, ensure__adjoint_and_pd) and returns: operator,  matrix