code: def _check_sdp_from_eigen(w, tol=None):
      """Checks if some of the eigenvalues given are negative, up to a tolerance
      level, with a default value of the tolerance depending on the eigenvalues.
      It also returns whether the matrix is positive definite, up to the above
      tolerance.
  
      Parameters
      ----------
      w : array-like, shape=(n_eigenvalues,)
        Eigenvalues to check for non semidefinite positiveness.
  
      tol : positive `float`, optional
        Absolute eigenvalues below tol are considered zero. If
        tol is None, and eps is the epsilon value for datatype of w, then tol
        is set to abs(w).max() * len(w) * eps.
  
      Returns
      -------
      is_definite : bool
        Whether the matrix is positive definite or not.
  
      See Also
      --------
      np.linalg.matrix_rank for more details on the choice of tolerance (the same
        strategy is applied here)
      """
      if tol is None:
          tol = np.abs(w).max() * len(w) * np.finfo(w.dtype).eps
      if tol < 0:
          raise ValueError("tol should be positive.")
      if any(w < -tol):
          raise NonPSDError()
      if any(abs(w) < tol):
          return False
      return True
  
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 12 for calling a global function with example usage: _check_sdp_from_eigen(w, tol) and returns: True, False