code: def fit_l1_slsqp(
      f,
      score,
      start_params,
      args,
      kwargs,
      disp=False,
      maxiter=1000,
      callback=None,
      retall=False,
      full_output=False,
      hess=None,
  ):
      """
      Solve the l1 regularized problem using scipy.optimize.fmin_slsqp().
  
      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
      acc : float (default 1e-6)
          Requested accuracy as used by slsqp
      """
      start_params = np.array(start_params).ravel("F")
  
      ### Extract values
      # 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))
      # alpha is 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
      # Convert display parameters to scipy.optimize form
      disp_slsqp = _get_disp_slsqp(disp, retall)
      # Set/retrieve the desired accuracy
      acc = kwargs.setdefault("acc", 1e-10)
  
      ### Wrap up for use in fmin_slsqp
      func = lambda x_full: _objective_func(
          f, x_full, k_params, alpha, *args
      )
      f_ieqcons_wrap = lambda x_full: _f_ieqcons(x_full, k_params)
      fprime_wrap = lambda x_full: _fprime(
          score, x_full, k_params, alpha
      )
      fprime_ieqcons_wrap = lambda x_full: _fprime_ieqcons(
          x_full, k_params
      )
  
      ### Call the solver
      results = fmin_slsqp(
          func,
          x0,
          f_ieqcons=f_ieqcons_wrap,
          fprime=fprime_wrap,
          acc=acc,
          iter=maxiter,
          disp=disp_slsqp,
          full_output=full_output,
          fprime_ieqcons=fprime_ieqcons_wrap,
      )
      params = np.asarray(results[0][: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 optimizers
      # TODO These retvals are returned as mle_retvals...but the fit was not ML.
      # This could be confusing someday.
      if full_output:
          x_full, fx, its, imode, smode = results
          fopt = func(np.asarray(x_full))
          converged = imode == 0
          warnflag = str(imode) + " " + smode
          iterations = its
          gopt = float("nan")  # Objective is non-differentiable
          hopt = float("nan")
          retvals = {
              "fopt": fopt,
              "converged": converged,
              "iterations": iterations,
              "gopt": gopt,
              "hopt": hopt,
              "trimmed": trimmed,
              "warnflag": warnflag,
          }
  
      ### Return
      if full_output:
          return params, retvals
      else:
          return params
  
file_path: statsmodels/statsmodels/base/l1_slsqp.py
imports: import numpy
  from scipy.optimize import fmin_slsqp
  import statsmodels.base.l1_solvers_common
label_desc: Use image node_id 1 for calling a global function with example usage: fit_l1_slsqp(f, score, start_params, args, kwargs, disp, maxiter, callback, retall, full_output, hess) and returns: params,  retvals, params