code: def checkApproxEigs(self, example_name, dtype):
      fn, eigs, n, m = _callable_generators(dtype)[example_name]
  
      k = len(eigs)
      X = self.rng().standard_normal(size=(n, k)).astype(dtype)
  
      theta, U, iters = linalg.lobpcg_standard(fn, X, m, tol=0.0)
  
      # Given tolerance is zero all iters should be used.
      self.assertEqual(iters, m)
  
      # Evaluate in f64.
      as64 = functools.partial(np.array, dtype=np.float64)
      theta, eigs, U = (as64(x) for x in (theta, eigs, U))
  
      relerr = np.abs(theta - eigs) / eigs
      UTU = U.T.dot(U)
  
      tol = np.sqrt(jnp.finfo(dtype).eps) * 100
      if example_name == "ring laplacian":
          tol = 1e-2
  
      for i in range(k):
          self.assertLessEqual(
              relerr[i],
              tol,
              msg=f"eigenvalue {i} (actual {theta[i]} expected {eigs[i]})",
          )
          self.assertAllClose(UTU[i, i], 1.0, rtol=tol)
          UTU[i, i] = 0
          self.assertArraysAllClose(
              UTU[i], np.zeros_like(UTU[i]), atol=tol
          )
  
      self._possibly_plot(fn, eigs, X, m, "callable_" + example_name)
  
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 5 for calling the LobpcgTest obj's underlying member method code with example usage: obj.checkApproxEigs(example_name, dtype) without return types