code: def _check_eigen(M, w, V, rtol=1e-8, atol=1e-14):
      mult_wV = np.multiply(w, V)
      dot_MV = M.dot(V)
      assert_allclose(mult_wV, dot_MV, rtol=rtol, atol=atol)
  
imports: from __future__ import division, print_function, absolute_import
  import itertools
  import numpy
  from numpy.testing import assert_almost_equal, assert_equal, assert_allclose, assert_array_less
  from scipy import ones, rand, r_, diag, linalg, eye
  from scipy.linalg import eig, eigh, toeplitz
  import scipy.sparse
  from scipy.sparse.linalg.eigen.lobpcg import lobpcg
  from scipy.sparse.linalg import eigs
  from scipy.sparse import spdiags
  import pytest
label_desc: Use image node_id 10 for calling a global function with example usage: _check_eigen(M, w, V, rtol, atol) without return types