class_docstr: Similar to :class:`~gpytorch.variational.VariationalStrategy`,
  except the whitening operation is performed using Contour Integral Quadrature
  rather than Cholesky (see `Pleiss et al. (2020)`_ for more info).
  See the `CIQ-SVGP tutorial`_ for an example.
  
  Contour Integral Quadrature uses iterative matrix-vector multiplication to approximate
  the :math:`\mathbf K_{\mathbf Z \mathbf Z}^{-1/2}` matrix used for the whitening operation.
  This can be more efficient than the standard variational strategy for large numbers
  of inducing points (e.g. :math:`M > 1000`) or when the inducing points have structure
  (e.g. they lie on an evenly-spaced grid).
  
  .. note::
  
      It is recommended that this object is used in conjunction with
      :obj:`~gpytorch.variational.NaturalVariationalDistribution` and
      `natural gradient descent`_.
  
  :param model: Model this strategy is applied to.
      Typically passed in when the VariationalStrategy is created in the
      __init__ method of the user defined model.
  :param inducing_points: Tensor containing a set of inducing
      points to use for variational inference.
  :param variational_distribution: A
      VariationalDistribution object that represents the form of the variational distribution :math:`q(\mathbf u)`
  :param learn_inducing_locations: (Default True): Whether or not
      the inducing point locations :math:`\mathbf Z` should be learned (i.e. are they
      parameters of the model).
  :param jitter_val: Amount of diagonal jitter to add for Cholesky factorization numerical stability
  
  .. _Pleiss et al. (2020):
      https://arxiv.org/pdf/2006.11267.pdf
  .. _CIQ-SVGP tutorial:
      examples/04_Variational_and_Approximate_GPs/SVGP_CIQ.html
  .. _natural gradient descent:
      examples/04_Variational_and_Approximate_GPs/Natural_Gradient_Descent.html
code: def __call__(
      self, x: torch.Tensor, prior: bool = False, *params, **kwargs
  ) -> MultivariateNormal:
      # This is mostly the same as _VariationalStrategy.__call__()
      # but with special rules for natural gradient descent (to prevent O(M^3) computation)
  
      # If we're in prior mode, then we're done!
      if prior:
          return self.model.forward(x)
  
      # Delete previously cached items from the training distribution
      if self.training:
          self._clear_cache()
  
      # (Maybe) initialize variational distribution
      if not self.variational_params_initialized.item():
          if self._ngd():
              noise = torch.randn_like(
                  self.prior_distribution.mean
              ).mul_(1e-3)
              eye = torch.eye(
                  noise.size(-1), dtype=noise.dtype, device=noise.device
              ).mul(-0.5)
              self._variational_distribution.natural_vec.data.copy_(
                  noise
              )
              self._variational_distribution.natural_mat.data.copy_(eye)
              self.variational_params_initialized.fill_(1)
          else:
              prior_dist = self.prior_distribution
              self._variational_distribution.initialize_variational_distribution(
                  prior_dist
              )
              self.variational_params_initialized.fill_(1)
  
      # Ensure inducing_points and x are the same size
      inducing_points = self.inducing_points
      if inducing_points.shape[:-2] != x.shape[:-2]:
          x, inducing_points = self._expand_inputs(x, inducing_points)
  
      # Get q(f)
      if self._ngd():
          return Module.__call__(
              self,
              x,
              inducing_points,
              inducing_values=None,
              variational_inducing_covar=None,
              *params,
              **kwargs,
          )
      else:
          # Get p(u)/q(u)
          variational_dist_u = self.variational_distribution
  
          if isinstance(variational_dist_u, MultivariateNormal):
              return Module.__call__(
                  self,
                  x,
                  inducing_points,
                  inducing_values=variational_dist_u.mean,
                  variational_inducing_covar=variational_dist_u.lazy_covariance_matrix,
                  **kwargs,
              )
          elif isinstance(variational_dist_u, Delta):
              return Module.__call__(
                  self,
                  x,
                  inducing_points,
                  inducing_values=variational_dist_u.mean,
                  variational_inducing_covar=None,
                  **kwargs,
              )
          else:
              raise RuntimeError(
                  f"Invalid variational distribuition ({type(variational_dist_u)}). "
                  "Expected a multivariate normal or a delta distribution."
              )
  
imports: from typing import Optional, Tuple
  import torch
  from linear_operator import to_linear_operator
  from linear_operator.operators import DiagLinearOperator, LinearOperator, MatmulLinearOperator, SumLinearOperator
  from linear_operator.utils import linear_cg
  from torch import Tensor
  from torch.autograd.function import FunctionCtx
  from ..None import settings
  from ..distributions import Delta, Distribution, MultivariateNormal
  from ..module import Module
  from ..utils.memoize import cached
  from ._variational_strategy import _VariationalStrategy
  from .natural_variational_distribution import NaturalVariationalDistribution
label_desc: Use image node_id 6 for calling the CiqVariationalStrategy obj's underlying member method code with example usage: obj.__call__(x, prior) and returns: self, Module, Module, Module