class_docstr: Constructs a multi-output multivariate Normal random variable, based on mean and covariance
  Can be multi-output multivariate, or a batch of multi-output multivariate Normal
  
  Passing a matrix mean corresponds to a multi-output multivariate Normal
  Passing a matrix mean corresponds to a batch of multivariate Normals
  
  :param torch.Tensor mean:  An `n x t` or batch `b x n x t` matrix of means for the MVN distribution.
  :param ~linear_operator.operators.LinearOperator covar: An `... x NT x NT` (batch) matrix.
      covariance matrix of MVN distribution.
  :param bool validate_args: (default=False) If True, validate `mean` and `covariance_matrix` arguments.
  :param bool interleaved: (default=True) If True, covariance matrix is interpreted as block-diagonal w.r.t.
      inter-task covariances for each observation. If False, it is interpreted as block-diagonal
      w.r.t. inter-observation covariance for each task.
docstr: Constructs a new MultivariateNormal that represents a random variable
  modified by an indexing operation.
  
  The mean and covariance matrix arguments are indexed accordingly.
  
  :param Any idx: Index to apply to the mean. The covariance matrix is indexed accordingly.
  :returns: If indices specify a slice for samples and tasks, returns a
      MultitaskMultivariateNormal, else returns a MultivariateNormal.
docstr_tok: ["Constructs","a","new","MultivariateNormal","that","represents","a","random","variable","modified","by","an","indexing","operation",".","The","mean","and","covariance","matrix","arguments","are","indexed","accordingly",".",":","param","Any","idx",":","Index","to","apply","to","the","mean",".","The","covariance","matrix","is","indexed","accordingly",".",":","returns",":","If","indices","specify","a","slice","for","samples","and","tasks",",","returns","a","MultitaskMultivariateNormal",",","else","returns","a","MultivariateNormal","."]
code: def __getitem__(self, idx) -> MultivariateNormal:
      """
      Constructs a new MultivariateNormal that represents a random variable
      modified by an indexing operation.
  
      The mean and covariance matrix arguments are indexed accordingly.
  
      :param Any idx: Index to apply to the mean. The covariance matrix is indexed accordingly.
      :returns: If indices specify a slice for samples and tasks, returns a
          MultitaskMultivariateNormal, else returns a MultivariateNormal.
      """
  
      # Normalize index to a tuple
      if not isinstance(idx, tuple):
          idx = (idx,)
  
      if ... in idx:
          # Replace ellipsis '...' with explicit indices
          ellipsis_location = idx.index(...)
          if ... in idx[ellipsis_location + 1 :]:
              raise IndexError("Only one ellipsis '...' is supported!")
          prefix = idx[:ellipsis_location]
          suffix = idx[ellipsis_location + 1 :]
          infix_length = self.mean.dim() - len(prefix) - len(suffix)
          if infix_length < 0:
              raise IndexError(f"Index {idx} has too many dimensions")
          idx = prefix + (slice(None),) * infix_length + suffix
      elif len(idx) == self.mean.dim() - 1:
          # Normalize indices ignoring the task-index to include it
          idx = idx + (slice(None),)
  
      new_mean = self.mean[idx]
  
      # We now create a covariance matrix appropriate for new_mean
      if len(idx) <= self.mean.dim() - 2:
          # We are only indexing the batch dimensions in this case
          return MultitaskMultivariateNormal(
              mean=new_mean,
              covariance_matrix=self.lazy_covariance_matrix[idx],
              interleaved=self._interleaved,
          )
      elif len(idx) > self.mean.dim():
          raise IndexError(f"Index {idx} has too many dimensions")
      else:
          # We have an index that extends over all dimensions
          batch_idx = idx[:-2]
          if self._interleaved:
              row_idx = idx[-2]
              col_idx = idx[-1]
              num_rows = self._output_shape[-2]
              num_cols = self._output_shape[-1]
          else:
              row_idx = idx[-1]
              col_idx = idx[-2]
              num_rows = self._output_shape[-1]
              num_cols = self._output_shape[-2]
  
          if isinstance(row_idx, int) and isinstance(col_idx, int):
              # Single sample with single task
              row_idx = _normalize_index(row_idx, num_rows)
              col_idx = _normalize_index(col_idx, num_cols)
              new_cov = DiagLinearOperator(
                  self.lazy_covariance_matrix.diagonal()[
                      batch_idx + (row_idx * num_cols + col_idx,)
                  ]
              )
              return MultivariateNormal(
                  mean=new_mean, covariance_matrix=new_cov
              )
          elif isinstance(row_idx, int) and isinstance(col_idx, slice):
              # A block of the covariance matrix
              row_idx = _normalize_index(row_idx, num_rows)
              col_idx = _normalize_slice(col_idx, num_cols)
              new_slice = slice(
                  col_idx.start + row_idx * num_cols,
                  col_idx.stop + row_idx * num_cols,
                  col_idx.step,
              )
              new_cov = self.lazy_covariance_matrix[
                  batch_idx + (new_slice, new_slice)
              ]
              return MultivariateNormal(
                  mean=new_mean, covariance_matrix=new_cov
              )
          elif isinstance(row_idx, slice) and isinstance(col_idx, int):
              # A block of the reversely interleaved covariance matrix
              row_idx = _normalize_slice(row_idx, num_rows)
              col_idx = _normalize_index(col_idx, num_cols)
              new_slice = slice(
                  row_idx.start + col_idx,
                  row_idx.stop * num_cols + col_idx,
                  row_idx.step * num_cols,
              )
              new_cov = self.lazy_covariance_matrix[
                  batch_idx + (new_slice, new_slice)
              ]
              return MultivariateNormal(
                  mean=new_mean, covariance_matrix=new_cov
              )
          elif (
              isinstance(row_idx, slice)
              and isinstance(col_idx, slice)
              and row_idx == col_idx == slice(None, None, None)
          ):
              new_cov = self.lazy_covariance_matrix[batch_idx]
              return MultitaskMultivariateNormal(
                  mean=new_mean,
                  covariance_matrix=new_cov,
                  interleaved=self._interleaved,
                  validate_args=False,
              )
          elif isinstance(row_idx, slice) or isinstance(col_idx, slice):
              # slice x slice or indices x slice or slice x indices
              if isinstance(row_idx, slice):
                  row_idx = torch.arange(num_rows)[row_idx]
              if isinstance(col_idx, slice):
                  col_idx = torch.arange(num_cols)[col_idx]
              row_grid, col_grid = torch.meshgrid(
                  row_idx, col_idx, indexing="ij"
              )
              indices = (row_grid * num_cols + col_grid).reshape(-1)
              new_cov = self.lazy_covariance_matrix[
                  batch_idx + (indices,)
              ][..., indices]
              return MultitaskMultivariateNormal(
                  mean=new_mean,
                  covariance_matrix=new_cov,
                  interleaved=self._interleaved,
                  validate_args=False,
              )
          else:
              # row_idx and col_idx have pairs of indices
              indices = row_idx * num_cols + col_idx
              new_cov = self.lazy_covariance_matrix[
                  batch_idx + (indices,)
              ][..., indices]
              return MultivariateNormal(
                  mean=new_mean,
                  covariance_matrix=new_cov,
              )
  
imports: import torch
  from linear_operator import LinearOperator, to_linear_operator
  from linear_operator.operators import BlockDiagLinearOperator, BlockInterleavedLinearOperator, CatLinearOperator, DiagLinearOperator
  from .multivariate_normal import MultivariateNormal
label_desc: Use image node_id 15 for calling the MultitaskMultivariateNormal obj's underlying member method code with example usage: obj.__getitem__(idx) and returns: MultitaskMultivariateNormal, MultivariateNormal, MultivariateNormal, MultivariateNormal, MultitaskMultivariateNormal, MultitaskMultivariateNormal, MultivariateNormal