code: def fit_l1_cvxopt_cp(
      f,
      score,
      start_params,
      args,
      kwargs,
      disp=False,
      maxiter=100,
      callback=None,
      retall=False,
      full_output=False,
      hess=None,
  ):
      """
      Solve the l1 regularized problem using cvxopt.solvers.cp
  
      Specifically:  We convert the convex but non-smooth problem
  
      .. math:: \\min_\\beta f(\\beta) + \\sum_k\\alpha_k |\\beta_k|
  
      via the transformation to the smooth, convex, constrained problem in twice
      as many variables (adding the "added variables" :math:`u_k`)
  
      .. math:: \\min_{\\beta,u} f(\\beta) + \\sum_k\\alpha_k u_k,
  
      subject to
  
      .. math:: -u_k \\leq \\beta_k \\leq u_k.
  
      Parameters
      ----------
      All the usual parameters from LikelhoodModel.fit
      alpha : non-negative scalar or numpy array (same size as parameters)
          The weight multiplying the l1 penalty term
      trim_mode : 'auto, 'size', or 'off'
          If not 'off', trim (set to zero) parameters that would have been zero
              if the solver reached the theoretical minimum.
          If 'auto', trim params using the Theory above.
          If 'size', trim params if they have very small absolute value
      size_trim_tol : float or 'auto' (default = 'auto')
          For use when trim_mode === 'size'
      auto_trim_tol : float
          For sue when trim_mode == 'auto'.  Use
      qc_tol : float
          Print warning and do not allow auto trim when (ii) in "Theory" (above)
          is violated by this much.
      qc_verbose : bool
          If true, print out a full QC report upon failure
      abstol : float
          absolute accuracy (default: 1e-7).
      reltol : float
          relative accuracy (default: 1e-6).
      feastol : float
          tolerance for feasibility conditions (default: 1e-7).
      refinement : int
          number of iterative refinement steps when solving KKT equations
          (default: 1).
      """
      from cvxopt import solvers, matrix
  
      start_params = np.array(start_params).ravel("F")
  
      ## Extract arguments
      # k_params is total number of covariates, possibly including a leading constant.
      k_params = len(start_params)
      # The start point
      x0 = np.append(start_params, np.fabs(start_params))
      x0 = matrix(x0, (2 * k_params, 1))
      # The regularization parameter
      alpha = np.array(kwargs["alpha_rescaled"]).ravel("F")
      # Make sure it's a vector
      alpha = alpha * np.ones(k_params)
      assert alpha.min() >= 0
  
      ## Wrap up functions for cvxopt
      f_0 = lambda x: _objective_func(f, x, k_params, alpha, *args)
      Df = lambda x: _fprime(score, x, k_params, alpha)
      G = _get_G(k_params)  # Inequality constraint matrix, Gx \leq h
      h = matrix(0.0, (2 * k_params, 1))  # RHS in inequality constraint
      H = lambda x, z: _hessian_wrapper(hess, x, z, k_params)
  
      ## Define the optimization function
      def F(x=None, z=None):
          if x is None:
              return 0, x0
          elif z is None:
              return f_0(x), Df(x)
          else:
              return f_0(x), Df(x), H(x, z)
  
      ## Convert optimization settings to cvxopt form
      solvers.options["show_progress"] = disp
      solvers.options["maxiters"] = maxiter
      if "abstol" in kwargs:
          solvers.options["abstol"] = kwargs["abstol"]
      if "reltol" in kwargs:
          solvers.options["reltol"] = kwargs["reltol"]
      if "feastol" in kwargs:
          solvers.options["feastol"] = kwargs["feastol"]
      if "refinement" in kwargs:
          solvers.options["refinement"] = kwargs["refinement"]
  
      ### Call the optimizer
      results = solvers.cp(F, G, h)
      x = np.asarray(results["x"]).ravel()
      params = x[:k_params]
  
      ### Post-process
      # QC
      qc_tol = kwargs["qc_tol"]
      qc_verbose = kwargs["qc_verbose"]
      passed = l1_solvers_common.qc_results(
          params, alpha, score, qc_tol, qc_verbose
      )
      # Possibly trim
      trim_mode = kwargs["trim_mode"]
      size_trim_tol = kwargs["size_trim_tol"]
      auto_trim_tol = kwargs["auto_trim_tol"]
      params, trimmed = l1_solvers_common.do_trim_params(
          params,
          k_params,
          alpha,
          score,
          passed,
          trim_mode,
          size_trim_tol,
          auto_trim_tol,
      )
  
      ### Pack up return values for statsmodels
      # TODO These retvals are returned as mle_retvals...but the fit was not ML
      if full_output:
          fopt = f_0(x)
          gopt = float("nan")  # Objective is non-differentiable
          hopt = float("nan")
          iterations = float("nan")
          converged = results["status"] == "optimal"
          warnflag = results["status"]
          retvals = {
              "fopt": fopt,
              "converged": converged,
              "iterations": iterations,
              "gopt": gopt,
              "hopt": hopt,
              "trimmed": trimmed,
              "warnflag": warnflag,
          }
      else:
          x = np.array(results["x"]).ravel()
          params = x[:k_params]
  
      ### Return results
      if full_output:
          return params, retvals
      else:
          return params
  
imports: import numpy
  import statsmodels.base.l1_solvers_common
label_desc: Use image node_id 1 for calling a global function with example usage: fit_l1_cvxopt_cp(f, score, start_params, args, kwargs, disp, maxiter, callback, retall, full_output, hess) and returns: params,  retvals, params, int,  x0, f_0,  Df, f_0,  Df,  H