code: def _grass_opt(params, fun, grad, maxiter, gtol):
      """
      Minimize a function on a Grassmann manifold.
  
      Parameters
      ----------
      params : array_like
          Starting value for the optimization.
      fun : function
          The function to be minimized.
      grad : function
          The gradient of fun.
      maxiter : int
          The maximum number of iterations.
      gtol : float
          Convergence occurs when the gradient norm falls below this value.
  
      Returns
      -------
      params : array_like
          The minimizing value for the objective function.
      fval : float
          The smallest achieved value of the objective function.
      cnvrg : bool
          True if the algorithm converged to a limit point.
  
      Notes
      -----
      `params` is 2-d, but `fun` and `grad` should take 1-d arrays
      `params.ravel()` as arguments.
  
      Reference
      ---------
      A Edelman, TA Arias, ST Smith (1998).  The geometry of algorithms with
      orthogonality constraints. SIAM J Matrix Anal Appl.
      http://math.mit.edu/~edelman/publications/geometry_of_algorithms.pdf
      """
  
      p, d = params.shape
      params = params.ravel()
  
      f0 = fun(params)
      cnvrg = False
  
      for _ in range(maxiter):
          # Project the gradient to the tangent space
          g = grad(params)
          g -= np.dot(g, params) * params / np.dot(params, params)
  
          if np.sqrt(np.sum(g * g)) < gtol:
              cnvrg = True
              break
  
          gm = g.reshape((p, d))
          u, s, vt = np.linalg.svd(gm, 0)
  
          paramsm = params.reshape((p, d))
          pa0 = np.dot(paramsm, vt.T)
  
          def geo(t):
              # Parameterize the geodesic path in the direction
              # of the gradient as a function of a real value t.
              pa = pa0 * np.cos(s * t) + u * np.sin(s * t)
              return np.dot(pa, vt).ravel()
  
          # Try to find a downhill step along the geodesic path.
          step = 2.0
          while step > 1e-10:
              pa = geo(-step)
              f1 = fun(pa)
              if f1 < f0:
                  params = pa
                  f0 = f1
                  break
              step /= 2
  
      params = params.reshape((p, d))
      return params, f0, cnvrg
  
imports: import warnings
  import numpy
  import pandas
  from statsmodels.base import model
  import statsmodels.base.wrapper
  from statsmodels.tools.sm_exceptions import ConvergenceWarning
label_desc: Use image node_id 1 for calling a global function with example usage: _grass_opt(params, fun, grad, maxiter, gtol) and returns: params,  f0,  cnvrg, np