# TEST
def PCA_test():
  iris = datasets.load_iris()
  p = iris.data.shape[1]
  k = p
  X_reduced = PCA(n_components=k).fit(iris.data)
  X_reduced_eig = PCA_eig(iris.data, k)
  comp_diff = np.round(np.absolute(X_reduced.components_) - np.absolute(X_reduced_eig['components'].transpose()),3)
  print('Equal Components: ', np.array_equal(comp_diff,np.zeros([p,p])))
  var_diff = np.round(X_reduced.explained_variance_ - X_reduced_eig['explained_variance'], 3)
  print('Equal Explained Variance:', np.array_equal(var_diff, np.zeros(k)))
  return

PCA_test()
# Output
# Equal Components:  True
# Equal Explained Variance: True