code: def check_gradient(fcn, Dfcn, x0, args=(), col_deriv=0):
      """Perform a simple check on the gradient for correctness."""
  
      x = atleast_1d(x0)
      n = len(x)
      x = x.reshape((n,))
      fvec = atleast_1d(fcn(x, *args))
      m = len(fvec)
      fvec = fvec.reshape((m,))
      ldfjac = m
      fjac = atleast_1d(Dfcn(x, *args))
      fjac = fjac.reshape((m, n))
      if col_deriv == 0:
          fjac = transpose(fjac)
  
      xp = zeros((n,), float)
      err = zeros((m,), float)
      fvecp = None
      _minpack._chkder(m, n, x, fvec, fjac, ldfjac, xp, fvecp, 1, err)
  
      fvecp = atleast_1d(fcn(xp, *args))
      fvecp = fvecp.reshape((m,))
      _minpack._chkder(m, n, x, fvec, fjac, ldfjac, xp, fvecp, 2, err)
  
      good = prod(greater(err, 0.5), axis=0)
  
      return (good, err)
  
imports: import warnings
  from .None import _minpack
  import numpy
  from numpy import atleast_1d, triu, shape, transpose, zeros, prod, greater, asarray, inf, finfo, inexact, issubdtype, dtype
  from scipy import linalg
  from scipy.linalg import svd, cholesky, solve_triangular, LinAlgError
  from scipy._lib._util import _asarray_validated, _lazywhere, _contains_nan
  from scipy._lib._util import getfullargspec_no_self
  from ._optimize import OptimizeResult, _check_unknown_options, OptimizeWarning
  from ._lsq import least_squares
  from ._lsq.least_squares import prepare_bounds
  from scipy.optimize._minimize import Bounds
  from numpy import dot, eye, take
  from numpy.linalg import inv
label_desc: Use image node_id 10 for calling a global function with example usage: check_gradient(fcn, Dfcn, x0, args, col_deriv) and returns: good,  err