code: def test_projection(self):
      pc = PCA(self.x, ncomp=5)
      mu = self.x.mean(0)
      demean_x = self.x - mu
      coef = np.linalg.pinv(pc.factors).dot(demean_x)
      direct = pc.factors.dot(coef)
      assert_allclose(pc.projection, direct + mu)
  
      pc = PCA(self.x, standardize=False, ncomp=5)
      coef = np.linalg.pinv(pc.factors).dot(demean_x)
      direct = pc.factors.dot(coef)
      assert_allclose(pc.projection, direct + mu)
  
      pc = PCA(self.x, standardize=False, demean=False, ncomp=5)
      coef = np.linalg.pinv(pc.factors).dot(self.x)
      direct = pc.factors.dot(coef)
      assert_allclose(pc.projection, direct)
  
      pc = PCA(self.x, ncomp=5, gls=True)
      mu = self.x.mean(0)
      demean_x = self.x - mu
      coef = np.linalg.pinv(pc.factors).dot(demean_x)
      direct = pc.factors.dot(coef)
      assert_allclose(pc.projection, direct + mu)
  
      pc = PCA(self.x, standardize=False, ncomp=5)
      coef = np.linalg.pinv(pc.factors).dot(demean_x)
      direct = pc.factors.dot(coef)
      assert_allclose(pc.projection, direct + mu)
  
      pc = PCA(
          self.x, standardize=False, demean=False, ncomp=5, gls=True
      )
      coef = np.linalg.pinv(pc.factors).dot(self.x)
      direct = pc.factors.dot(coef)
      assert_allclose(pc.projection, direct)
  
      # Test error for too many factors
      project = pc.project
      assert_raises(ValueError, project, 6)
  
imports: from statsmodels.compat.platform import PLATFORM_WIN32
  import warnings
  import numpy
  import pandas
  import pytest
  from numpy.testing import assert_allclose, assert_equal, assert_raises
  from statsmodels.multivariate.pca import PCA, pca
  from statsmodels.multivariate.tests.results.datamlw import data, princomp1, princomp2
  from statsmodels.tools.sm_exceptions import EstimationWarning
label_desc: Use image node_id 10 for calling the TestPCA obj's underlying member method code with example usage: obj.test_projection() without return types