code: def test_corr_nearest_factor(self, dm):
      objvals = [
          np.array([6241.8, 6241.8, 579.4, 264.6, 264.3]),
          np.array([2104.9, 2104.9, 710.5, 266.3, 286.1]),
      ]
  
      d = 100
  
      # Construct a test matrix with exact factor structure
      X = np.zeros((d, dm), dtype=np.float64)
      x = np.linspace(0, 2 * np.pi, d)
      np.random.seed(10)
      for j in range(dm):
          X[:, j] = np.sin(x * (j + 1)) + 1e-10 * np.random.randn(d)
  
      _project_correlation_factors(X)
      assert np.isfinite(X).all()
      X *= 0.7
      mat = np.dot(X, X.T)
      np.fill_diagonal(mat, 1.0)
  
      # Try to recover the structure
      rslt = corr_nearest_factor(mat, dm, maxiter=10000)
      err_msg = "rank=%d, niter=%d" % (dm, len(rslt.objective_values))
      assert_allclose(
          rslt.objective_values[:5],
          objvals[dm - 1],
          rtol=0.5,
          err_msg=err_msg,
      )
      assert rslt.Converged
  
      mat1 = rslt.corr.to_matrix()
      assert_allclose(mat, mat1, rtol=0.25, atol=1e-3, err_msg=err_msg)
  
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 2 for calling the Test_Factor obj's underlying member method code with example usage: obj.test_corr_nearest_factor(dm) without return types