code: def wrap_functions(fun, bc, fun_jac, bc_jac, k, a, S, D, dtype):
      """Wrap functions for unified usage in the solver."""
      if fun_jac is None:
          fun_jac_wrapped = None
  
      if bc_jac is None:
          bc_jac_wrapped = None
  
      if k == 0:
  
          def fun_p(x, y, _):
              return np.asarray(fun(x, y), dtype)
  
          def bc_wrapped(ya, yb, _):
              return np.asarray(bc(ya, yb), dtype)
  
          if fun_jac is not None:
  
              def fun_jac_p(x, y, _):
                  return np.asarray(fun_jac(x, y), dtype), None
  
          if bc_jac is not None:
  
              def bc_jac_wrapped(ya, yb, _):
                  dbc_dya, dbc_dyb = bc_jac(ya, yb)
                  return (
                      np.asarray(dbc_dya, dtype),
                      np.asarray(dbc_dyb, dtype),
                      None,
                  )
  
      else:
  
          def fun_p(x, y, p):
              return np.asarray(fun(x, y, p), dtype)
  
          def bc_wrapped(x, y, p):
              return np.asarray(bc(x, y, p), dtype)
  
          if fun_jac is not None:
  
              def fun_jac_p(x, y, p):
                  df_dy, df_dp = fun_jac(x, y, p)
                  return np.asarray(df_dy, dtype), np.asarray(
                      df_dp, dtype
                  )
  
          if bc_jac is not None:
  
              def bc_jac_wrapped(ya, yb, p):
                  dbc_dya, dbc_dyb, dbc_dp = bc_jac(ya, yb, p)
                  return (
                      np.asarray(dbc_dya, dtype),
                      np.asarray(dbc_dyb, dtype),
                      np.asarray(dbc_dp, dtype),
                  )
  
      if S is None:
          fun_wrapped = fun_p
      else:
  
          def fun_wrapped(x, y, p):
              f = fun_p(x, y, p)
              if x[0] == a:
                  f[:, 0] = np.dot(D, f[:, 0])
                  f[:, 1:] += np.dot(S, y[:, 1:]) / (x[1:] - a)
              else:
                  f += np.dot(S, y) / (x - a)
              return f
  
      if fun_jac is not None:
          if S is None:
              fun_jac_wrapped = fun_jac_p
          else:
              Sr = S[:, :, np.newaxis]
  
              def fun_jac_wrapped(x, y, p):
                  df_dy, df_dp = fun_jac_p(x, y, p)
                  if x[0] == a:
                      df_dy[:, :, 0] = np.dot(D, df_dy[:, :, 0])
                      df_dy[:, :, 1:] += Sr / (x[1:] - a)
                  else:
                      df_dy += Sr / (x - a)
  
                  return df_dy, df_dp
  
      return fun_wrapped, bc_wrapped, fun_jac_wrapped, bc_jac_wrapped
  
imports: from __future__ import division, print_function, absolute_import
  from warnings import warn
  import numpy
  from numpy.linalg import norm, pinv
  from scipy.sparse import coo_matrix, csc_matrix
  from scipy.sparse.linalg import splu
  from scipy.optimize import OptimizeResult
label_desc: Use image node_id 14 for calling a global function with example usage: wrap_functions(fun, bc, fun_jac, bc_jac, k, a, S, D, dtype) and returns: fun_wrapped,  bc_wrapped,  fun_jac_wrapped,  bc_jac_wrapped, np, np, np, np, f, np,  None, np,  np,  None, np,  np, np,  np,  np, df_dy,  df_dp