code: def jitter_cholesky_eig(
      F,
      matrix: Tensor,
      num_data_points: Optional[int] = None,
      float_type: Type = np.float64,
      diag_weight: float = 1e-6,
  ) -> Tensor:
      """
      This function applies the jitter method using the eigenvalue decomposition.
      The eigenvalues are bound below by the jitter, which is proportional to the
      mean of the diagonal elements.
  
      Parameters
      ----------
      F
          A module that can either refer to the Symbol API or the NDArray
          API in MXNet.
      matrix
          Matrix of shape (batch_size, num_data_points, num_data_points).
      num_data_points
          Number of rows in the kernel_matrix.
      float_type
          Determines whether to use single or double precision.
  
      Returns
      -------
      Tensor
          Returns the approximate lower triangular Cholesky factor `L`
          of shape (batch_size, num_data_points, num_data_points)
      """
      diag = batch_diagonal(
          F, matrix, num_data_points, float_type
      )  # shape (batch_size, num_data_points, 1)
      diag_mean = diag.mean(axis=1).expand_dims(
          axis=2
      )  # shape (batch_size, 1, 1)
      U, Lambda = F.linalg.syevd(matrix)
      jitter = (
          F.broadcast_mul(diag_mean, F.ones_like(diag)) * diag_weight
      )
      # `K = U^TLambdaU`, where the rows of `U` are the eigenvectors of `K`.
      # The eigendecomposition :math:`U^TLambdaU` is used instead of
      # :math: ULambdaU^T, sine to utilize row-based computation
      # (see Section 4, Seeger et al., 2018)
      return F.linalg.potrf(
          F.linalg.gemm2(
              U,
              F.linalg.gemm2(
                  F.broadcast_mul(
                      F.eye(num_data_points, dtype=float_type),
                      F.maximum(jitter, Lambda.expand_dims(axis=2)),
                  ),
                  U,
              ),
              transpose_a=True,
          )
      )
  
imports: from typing import Optional, Type
  import mxnet
  import numpy
  from gluonts.mx import Tensor
label_desc: Use image node_id 3 for calling a global function with example usage: jitter_cholesky_eig(F, matrix, num_data_points, float_type, diag_weight) and returns: F