code: def _constraints_factor(
      encoding_matrix,
      comparison="pairwise",
      k_params=None,
      idx_start=None,
  ):
      """helper function to create constraints based on encoding matrix
  
      Parameters
      ----------
      encoding_matrix : ndarray
          contrast matrix for the encoding of a factor as defined by patsy.
          The number of rows should be equal to the number of levels or categories
          of the factor, the number of columns should be equal to the number
          of parameters for this factor.
      comparison : str
          Currently only 'pairwise' is implemented. The restriction matrix
          can be used for testing the hypothesis that all pairwise differences
          are zero.
      k_params : int
          number of parameters
      idx_start : int
          Index of the first parameter of this factor. The restrictions on the
          factor are inserted as a block in the full restriction matrix starting
          at column with index `idx_start`.
  
      Returns
      -------
      contrast : ndarray
          Contrast or restriction matrix that can be used in hypothesis test
          of model results. The number of columns is k_params.
      """
  
      cm = encoding_matrix
      k_level, k_p = cm.shape
  
      import statsmodels.sandbox.stats.multicomp as mc
  
      if comparison in ["pairwise", "pw", "pairs"]:
          c_all = -mc.contrast_allpairs(k_level)
      else:
          raise NotImplementedError("currentlyonly pairwise comparison")
  
      contrasts = c_all.dot(cm)
      if k_params is not None:
          if idx_start is None:
              raise ValueError(
                  "if k_params is not None, then idx_start is "
                  "required"
              )
          contrasts = _embed_constraints(contrasts, k_params, idx_start)
      return contrasts
  
imports: import numpy
  from scipy.stats import f
  from scipy.stats import t
  from scipy import stats
  from statsmodels.tools.tools import clean0, fullrank
  from statsmodels.stats.multitest import multipletests
label_desc: Use image node_id 6 for calling a global function with example usage: _constraints_factor(encoding_matrix, comparison, k_params, idx_start) and returns: contrasts