code: def components_from_metric(metric, tol=None):
      """Returns the transformation matrix from the Mahalanobis matrix.
  
      Returns the transformation matrix from the Mahalanobis matrix, i.e. the
      matrix L such that metric=L.T.dot(L).
  
      Parameters
      ----------
      metric : symmetric `np.ndarray`, shape=(d x d)
        The input metric, from which we want to extract a transformation matrix.
  
      tol : positive `float`, optional
        Eigenvalues of `metric` between 0 and - tol are considered zero. If tol is
        None, and w_max is `metric`'s largest eigenvalue, and eps is the epsilon
        value for datatype of w, then tol is set to w_max * metric.shape[0] * eps.
  
      Returns
      -------
      L : np.ndarray, shape=(d x d)
        The transformation matrix, such that L.T.dot(L) == metric.
      """
      if not np.allclose(metric, metric.T):
          raise ValueError("The input metric should be symmetric.")
      # If M is diagonal, we will just return the elementwise square root:
      if np.array_equal(metric, np.diag(np.diag(metric))):
          _check_sdp_from_eigen(np.diag(metric), tol)
          return np.diag(np.sqrt(np.maximum(0, np.diag(metric))))
      else:
          try:
              # if `M` is positive semi-definite, it will admit a Cholesky
              # decomposition: L = cholesky(M).T
              return np.linalg.cholesky(metric).T
          except LinAlgError:
              # However, currently np.linalg.cholesky does not support indefinite
              # matrices. So if the latter does not work we will return L = V.T w^(
              # -1/2), with M = V*w*V.T being the eigenvector decomposition of M with
              # the eigenvalues in the diagonal matrix w and the columns of V being the
              # eigenvectors.
              w, V = np.linalg.eigh(metric)
              _check_sdp_from_eigen(w, tol)
              return V.T * np.sqrt(np.maximum(0, w[:, None]))
  
imports: import numpy
  from numpy.linalg import LinAlgError
  from sklearn.datasets import make_spd_matrix
  from sklearn.decomposition import PCA
  from sklearn.utils import check_array
  from sklearn.utils.validation import check_X_y, check_random_state
  from .exceptions import PreprocessorError, NonPSDError
  from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
  from scipy.linalg import pinvh, eigh
  import sys
  import time
  import warnings
label_desc: Use image node_id 13 for calling a global function with example usage: components_from_metric(metric, tol) and returns: np, np, unknown