code: def value_and_jacobian(
      f,
      x,
      unconnected_gradients=None,
      name=None,
      parallel_iterations=None,
      experimental_use_pfor=True,
  ):
      """Computes `f(x)` and its jacobian wrt to `x`.
  
      Args:
        f: Python `callable` to be differentiated. If `f` returns a scalar, this
          scalar will be differentiated. If `f` returns a tensor or list of
          tensors, by default a scalar will be computed by adding all their values
          to produce a single scalar. If desired, the tensors can be elementwise
          multiplied by the tensors passed as the `dy` keyword argument to the
          returned jacobian function.
        x: A `Tensor` with respect to which the gradient is to be computed.
        unconnected_gradients: An enum `tf.UnconnectedGradients` which specifies
          the gradient value returned when the given input tensors are
          unconnected. Default value: `None`, which maps to
          `tf.UnconnectedGradients.NONE`.
        name: Python `str` name prefixed to ops created by this function.
          Default value: `None` (i.e., `'value_and_jacobian'`).
        parallel_iterations: A knob to control how many iterations are dispatched
          in parallel. This knob can be used to control the total memory usage.
        experimental_use_pfor: If true, uses pfor for computing the Jacobian.
          Else uses a tf.while_loop.
  
      Returns:
        A tuple of two elements. The first one is a `Tensor` representing the value
        of the function at `x` and the second one is a `Tensor` representing
        jacobian of `f(x)` wrt `x`.
        y: `y = f(x)`.
        dydx: Jacobian of `y` wrt `x_i`, where `x_i` is the i-th parameter in
        `x`.
      """
      unconnected_gradients = (
          unconnected_gradients or tf.UnconnectedGradients.NONE
      )
      x, is_x_batch_size = _prepare_args(x)
      with tf.name_scope(name or "value_and_jacobian"):
          with tf.GradientTape() as tape:
              tape.watch(x)
              y = f(x)
          jac = tape.batch_jacobian(
              y,
              x,
              unconnected_gradients=unconnected_gradients,
              parallel_iterations=parallel_iterations,
              experimental_use_pfor=experimental_use_pfor,
          )
  
          if is_x_batch_size:
              return y, jac
  
          return y[0], jac[0]
  
imports: import tensorflow.compat.v2
label_desc: Use image node_id 2 for calling a global function with example usage: value_and_jacobian(f, x, unconnected_gradients, name, parallel_iterations, experimental_use_pfor) and returns: y,  jac, y,  jac