code: def make_augmented_matrix(endog, exog, penalty_matrix, weights):
      """augment endog, exog and weights with stochastic restriction matrix
  
      Parameters
      ----------
      endog : ndarray
          response or endogenous variable
      exog : ndarray
          design matrix, matrix of exogenous or explanatory variables
      penalty_matrix : ndarray, 2-Dim square
          penality matrix for quadratic penalization
      weights : ndarray
          weights for WLS
  
      Returns
      -------
      endog_aug : ndarray
          augmented response variable
      exog_aug : ndarray
          augmented design matrix
      weights_aug : ndarray
          augmented weights for WLS
      """
      (
          y,
          x,
          s,
      ) = (
          endog,
          exog,
          penalty_matrix,
      )
      nobs = x.shape[0]
  
      # TODO: needs full because of broadcasting with weights
      # check what weights should be doing
      rs = matrix_sqrt(s)
      x1 = np.vstack([x, rs])  # augmented x
      n_samp1es_x1 = x1.shape[0]
  
      y1 = np.array([0.0] * n_samp1es_x1)  # augmented y
      y1[:nobs] = y
  
      id1 = np.array([1.0] * rs.shape[0])
      w1 = np.concatenate([weights, id1])
  
      return y1, x1, w1
  
imports: from collections.abc import Iterable
  import copy
  import numpy
  from scipy import optimize
  import pandas
  import statsmodels.base.wrapper
  from statsmodels.discrete.discrete_model import Logit
  from statsmodels.genmod.generalized_linear_model import GLM, GLMResults, GLMResultsWrapper, _check_convergence
  import statsmodels.regression.linear_model
  from statsmodels.tools.sm_exceptions import PerfectSeparationError, ValueWarning
  from statsmodels.tools.decorators import cache_readonly
  from statsmodels.tools.data import _is_using_pandas
  from statsmodels.tools.linalg import matrix_sqrt
  from statsmodels.base._penalized import PenalizedMixin
  from statsmodels.gam.gam_penalties import MultivariateGamPenalty
  from statsmodels.gam.gam_cross_validation.gam_cross_validation import MultivariateGAMCVPath
  from statsmodels.gam.gam_cross_validation.cross_validators import KFold
label_desc: Use image node_id 3 for calling a global function with example usage: make_augmented_matrix(endog, exog, penalty_matrix, weights) and returns: y1,  x1,  w1