code: def _initialize_metric_mahalanobis(
      input,
      init="identity",
      random_state=None,
      return_inverse=False,
      strict_pd=False,
      matrix_name="matrix",
  ):
      """Returns a PSD matrix that can be used as a prior or an initialization
      for the Mahalanobis distance
  
      Parameters
      ----------
      input : array-like
        The input samples (can be tuples or regular samples).
  
      init : string or numpy array, optional (default='identity')
        Specification for the matrix to initialize. Possible options are
        'identity', 'covariance', 'random', and a numpy array of shape
        (n_features, n_features).
  
        'identity'
          An identity matrix of shape (n_features, n_features).
  
        'covariance'
          The (pseudo-)inverse covariance matrix (raises an error if the
          covariance matrix is not definite and `strict_pd == True`)
  
        'random'
          A random positive definite (PD) matrix of shape
          `(n_features, n_features)`, generated using
          `sklearn.datasets.make_spd_matrix`.
  
        numpy array
          A PSD matrix (or strictly PD if strict_pd==True) of
          shape (n_features, n_features), that will be used as such to
          initialize the metric, or set the prior.
  
      random_state : int or `numpy.RandomState` or None, optional (default=None)
        A pseudo random number generator object or a seed for it if int. If
        ``init='random'``, ``random_state`` is used to set the random Mahalanobis
        matrix. If ``init='pca'``, ``random_state`` is passed as an
        argument to PCA when initializing the matrix.
  
      return_inverse : bool, optional (default=False)
        Whether to return the inverse of the specified matrix. This
        can be sometimes useful. It will return the pseudo-inverse (which is the
        same as the inverse if the matrix is definite (i.e. invertible)). If
        `strict_pd == True` and the matrix is not definite, it will return an
        error.
  
      strict_pd : bool, optional (default=False)
        Whether to enforce that the provided matrix is definite (in addition to
        being PSD).
  
      param_name : str, optional (default='matrix')
        The name of the matrix used (example: 'init', 'prior'). Will be used in
        error messages.
  
      Returns
      -------
      M, or (M, M_inv) : `numpy.ndarray`
        The initial matrix to use M, and its inverse if `return_inverse=True`.
      """
      n_features = input.shape[-1]
      if isinstance(init, np.ndarray):
          # we copy the array, so that if we update the metric, we don't want to
          # update the init
          init = check_array(init, copy=True)
  
          # Assert that init.shape[1] = n_features
          if init.shape != (n_features,) * 2:
              raise ValueError(
                  "The input dimensionality {} of the given "
                  "mahalanobis matrix `{}` must match the "
                  "dimensionality of the given inputs ({}).".format(
                      init.shape, matrix_name, n_features
                  )
              )
  
          # Assert that the matrix is symmetric
          if not np.allclose(init, init.T):
              raise ValueError(
                  "`{}` is not symmetric.".format(matrix_name)
              )
  
      elif init not in ["identity", "covariance", "random"]:
          raise ValueError(
              "`{}` must be 'identity', 'covariance', 'random' "
              "or a numpy array of shape (n_features, n_features).".format(
                  matrix_name
              )
          )
  
      random_state = check_random_state(random_state)
      M = init
      if isinstance(M, np.ndarray):
          w, V = eigh(M, check_finite=False)
          init_is_definite = _check_sdp_from_eigen(w)
          if strict_pd and not init_is_definite:
              raise LinAlgError(
                  "You should provide a strictly positive definite "
                  "matrix as `{}`. This one is not definite. Try another"
                  " {}, or an algorithm that does not "
                  "require the {} to be strictly positive definite.".format(
                      *((matrix_name,) * 3)
                  )
              )
          elif return_inverse and not init_is_definite:
              warnings.warn(
                  "The initialization matrix is not invertible: "
                  "using the pseudo-inverse instead."
              )
          if return_inverse:
              M_inv = _pseudo_inverse_from_eig(w, V)
              return M, M_inv
          else:
              return M
      elif init == "identity":
          M = np.eye(n_features, n_features)
          if return_inverse:
              M_inv = M.copy()
              return M, M_inv
          else:
              return M
      elif init == "covariance":
          if input.ndim == 3:
              # if the input are tuples, we need to form an X by deduplication
              X = np.unique(np.vstack(input), axis=0)
          else:
              X = input
          # atleast2d is necessary to deal with scalar covariance matrices
          M_inv = np.atleast_2d(np.cov(X, rowvar=False))
          w, V = eigh(M_inv, check_finite=False)
          cov_is_definite = _check_sdp_from_eigen(w)
          if strict_pd and not cov_is_definite:
              raise LinAlgError(
                  "Unable to get a true inverse of the covariance "
                  "matrix since it is not definite. Try another "
                  "`{}`, or an algorithm that does not "
                  "require the `{}` to be strictly positive definite.".format(
                      *((matrix_name,) * 2)
                  )
              )
          elif not cov_is_definite:
              warnings.warn(
                  "The covariance matrix is not invertible: "
                  "using the pseudo-inverse instead."
                  "To make the covariance matrix invertible"
                  " you can remove any linearly dependent features and/or "
                  "reduce the dimensionality of your input, "
                  "for instance using `sklearn.decomposition.PCA` as a "
                  "preprocessing step."
              )
          M = _pseudo_inverse_from_eig(w, V)
          if return_inverse:
              return M, M_inv
          else:
              return M
      elif init == "random":
          # we need to create a random symmetric matrix
          M = make_spd_matrix(n_features, random_state=random_state)
          if return_inverse:
              # we use pinvh even if we know the matrix is definite, just because
              # we need the returned matrix to be symmetric (and sometimes
              # np.linalg.inv returns not symmetric inverses of symmetric matrices)
              # TODO: there might be a more efficient method to do so
              M_inv = pinvh(M)
              return M, M_inv
          else:
              return M
  
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 17 for calling a global function with example usage: _initialize_metric_mahalanobis(input, init, random_state, return_inverse, strict_pd, matrix_name) and returns: M,  M_inv, M, M,  M_inv, M, M,  M_inv, M, M,  M_inv, M