code: def _compute_precision_cholesky_from_precisions(
      precisions, covariance_type
  ):
      r"""Compute the Cholesky decomposition of precisions using precisions themselves.
  
      As implemented in :func:`_compute_precision_cholesky`, the `precisions_cholesky_` is
      an upper-triangular matrix for each Gaussian component, which can be expressed as
      the $UU^T$ factorization of the precision matrix for each Gaussian component, where
      $U$ is an upper-triangular matrix.
  
      In order to use the Cholesky decomposition to get $UU^T$, the precision matrix
      $\Lambda$ needs to be permutated such that its rows and columns are reversed, which
      can be done by applying a similarity transformation with an exchange matrix $J$,
      where the 1 elements reside on the anti-diagonal and all other elements are 0. In
      particular, the Cholesky decomposition of the transformed precision matrix is
      $J\Lambda J=LL^T$, where $L$ is a lower-triangular matrix. Because $\Lambda=UU^T$
      and $J=J^{-1}=J^T$, the `precisions_cholesky_` for each Gaussian component can be
      expressed as $JLJ$.
  
      Refer to #26415 for details.
  
      Parameters
      ----------
      precisions : array-like
          The precision matrix of the current components.
          The shape depends on the covariance_type.
  
      covariance_type : {'full', 'tied', 'diag', 'spherical'}
          The type of precision matrices.
  
      Returns
      -------
      precisions_cholesky : array-like
          The cholesky decomposition of sample precisions of the current
          components. The shape depends on the covariance_type.
      """
      if covariance_type == "full":
          precisions_cholesky = np.array(
              [
                  _flipudlr(
                      linalg.cholesky(_flipudlr(precision), lower=True)
                  )
                  for precision in precisions
              ]
          )
      elif covariance_type == "tied":
          precisions_cholesky = _flipudlr(
              linalg.cholesky(_flipudlr(precisions), lower=True)
          )
      else:
          precisions_cholesky = np.sqrt(precisions)
      return precisions_cholesky
  
imports: import numpy
  from scipy import linalg
  from ..utils import check_array
  from ..utils._param_validation import StrOptions
  from ..utils.extmath import row_norms
  from ._base import BaseMixture, _check_shape
label_desc: Use image node_id 14 for calling a global function with example usage: _compute_precision_cholesky_from_precisions(precisions, covariance_type) and returns: precisions_cholesky