code: def approx_copula_pdf(
      copula, k_bins=10, force_uniform=True, use_pdf=False
  ):
      """Histogram probabilities as approximation to a copula density.
  
      Parameters
      ----------
      copula : instance
          Instance of a copula class. Only the ``pdf`` method is used.
      k_bins : int
          Number of bins along each dimension in the approximating histogram.
      force_uniform : bool
          If true, then the pdf grid will be adjusted to have uniform margins
          using `nearest_matrix_margin`.
          If false, then no adjustment is done and the margins may not be exactly
          uniform.
      use_pdf : bool
          If false, then the grid cell probabilities will be computed from the
          copula cdf.
          If true, then the density, ``pdf``, is used and cell probabilities
          are approximated by averaging the pdf of the cell corners. This is
          only useful if the cdf is not available.
  
      Returns
      -------
      bin probabilites : ndarray
          Probability that random variable falls in given bin. This corresponds
          to a discrete distribution, and is not scaled to bin size to form a
          piecewise uniform, histogram density.
          Bin probabilities are a k-dim array with k_bins segments in each
          dimensionrows.
  
      Notes
      -----
      This function is intended for internal use and will be generalized in
      future. API will change.
      """
      k_dim = copula.k_dim
      k = k_bins + 1
      ks = tuple([k] * k_dim)
  
      if use_pdf:
          g = _Grid([k] * k_dim, eps=0.1 / k_bins)
          pdfg = copula.pdf(g.x_flat).reshape(*ks)
          # correct for bin size
          pdfg *= 1 / k**k_dim
          ag = average_grid(pdfg)
          if force_uniform:
              pdf_grid = nearest_matrix_margins(
                  ag, maxiter=100, tol=1e-8
              )
          else:
              pdf_grid = ag / ag.sum()
      else:
          g = _Grid([k] * k_dim, eps=1e-6)
          cdfg = copula.cdf(g.x_flat).reshape(*ks)
          # correct for bin size
          pdf_grid = cdf2prob_grid(cdfg, prepend=None)
          # TODO: check boundary approximation, eg. undefined at zero
          # for now just normalize
          pdf_grid /= pdf_grid.sum()
  
      return pdf_grid
  
file_path: statsmodels/statsmodels/distributions/tools.py
imports: import warnings
  import numpy
  from scipy import interpolate, stats
label_desc: Use image node_id 7 for calling a global function with example usage: approx_copula_pdf(copula, k_bins, force_uniform, use_pdf) and returns: pdf_grid