code: def test_spg_optim(self, reset_randomstate):
      dm = 100
  
      ind = np.arange(dm)
      indmat = np.abs(ind[:, None] - ind[None, :])
      M = 0.8**indmat
  
      def obj(x):
          return np.dot(x, np.dot(M, x))
  
      def grad(x):
          return 2 * np.dot(M, x)
  
      def project(x):
          return x
  
      x = np.random.normal(size=dm)
      rslt = _spg_optim(obj, grad, x, project)
      xnew = rslt.params
      assert rslt.Converged is True
      assert_almost_equal(obj(xnew), 0, decimal=3)
  
imports: import warnings
  import numpy
  from numpy.testing import assert_almost_equal, assert_allclose
  import scipy.sparse
  import pytest
  from statsmodels.stats.correlation_tools import corr_nearest, corr_clipped, cov_nearest, _project_correlation_factors, corr_nearest_factor, _spg_optim, corr_thresholded, cov_nearest_factor_homog, FactoredPSDMatrix
  from statsmodels.tools.testing import Holder
label_desc: Use image node_id 4 for calling the Test_Factor obj's underlying member method code with example usage: obj.test_spg_optim(reset_randomstate) and returns: np, unknown, x