code: def checkLobpcgConsistency(self, matrix_name, n, k, m, tol, dtype):
      A, eigs = _concrete_generators(dtype)[matrix_name](n, k)
      X = self.rng().standard_normal(size=(n, k)).astype(dtype)
  
      A, X = (jnp.array(i, dtype=dtype) for i in (A, X))
      theta, U, i = linalg.lobpcg_standard(A, X, m, tol)
  
      self.assertDtypesMatch(theta, A)
      self.assertDtypesMatch(U, A)
  
      self.assertLess(
          i,
          m,
          msg=f"expected early convergence iters {int(i)} < max {m}",
      )
  
      issorted = theta[:-1] >= theta[1:]
      all_true = np.ones_like(issorted).astype(bool)
      self.assertArraysEqual(issorted, all_true)
  
      k = X.shape[1]
      relerr = np.abs(theta - eigs[:k]) / eigs[:k]
      for i in range(k):
          # The self-consistency property should be ensured.
          u = np.asarray(U[:, i], dtype=A.dtype)
          t = float(theta[i])
          Au = A.dot(u)
          resid = Au - t * u
          resid_norm = np.linalg.norm(resid)
          vector_norm = np.linalg.norm(Au)
          adjusted_error = resid_norm / n / (t + vector_norm) / 10
  
          eps = float(jnp.finfo(dtype).eps) if tol is None else tol
          self.assertLessEqual(
              adjusted_error,
              eps,
              msg=f"convergence criterion for eigenvalue {i} not satisfied, "
              f"floating point error {adjusted_error} not <= {eps}",
          )
  
          # There's no real guarantee we can be within x% of the true eigenvalue.
          # However, for these simple unit test examples this should be met.
          tol = float(np.sqrt(eps)) * 10
          self.assertLessEqual(
              relerr[i],
              tol,
              msg=f"expected relative error within {tol}, was {float(relerr[i])}"
              f" for eigenvalue {i} (actual {float(theta[i])}, "
              f"expected {float(eigs[i])})",
          )
  
imports: import functools
  import re
  import os
  import unittest
  from absl.testing import absltest
  from absl.testing import parameterized
  import numpy
  import scipy.linalg
  import scipy.sparse
  import jax
  from jax import config
  from jax._src import test_util
  from jax.experimental.sparse import linalg, bcoo
  import jax.numpy
label_desc: Use image node_id 1 for calling the LobpcgTest obj's underlying member method code with example usage: obj.checkLobpcgConsistency(matrix_name, n, k, m, tol, dtype) without return types