code: def barycentric_interpolate(xi, yi, x, axis=0):
      """
      Convenience function for polynomial interpolation.
  
      Constructs a polynomial that passes through a given set of points,
      then evaluates the polynomial. For reasons of numerical stability,
      this function does not compute the coefficients of the polynomial.
  
      This function uses a "barycentric interpolation" method that treats
      the problem as a special case of rational function interpolation.
      This algorithm is quite stable, numerically, but even in a world of
      exact computation, unless the `x` coordinates are chosen very
      carefully - Chebyshev zeros (e.g. cos(i*pi/n)) are a good choice -
      polynomial interpolation itself is a very ill-conditioned process
      due to the Runge phenomenon.
  
      Parameters
      ----------
      xi : array_like
          1-d array of x coordinates of the points the polynomial should
          pass through
      yi : array_like
          The y coordinates of the points the polynomial should pass through.
      x : scalar or array_like
          Points to evaluate the interpolator at.
      axis : int, optional
          Axis in the yi array corresponding to the x-coordinate values.
  
      Returns
      -------
      y : scalar or array_like
          Interpolated values. Shape is determined by replacing
          the interpolation axis in the original array with the shape of x.
  
      See Also
      --------
      BarycentricInterpolator
  
      Notes
      -----
      Construction of the interpolation weights is a relatively slow process.
      If you want to call this many times with the same xi (but possibly
      varying yi or x) you should use the class `BarycentricInterpolator`.
      This is what this function uses internally.
  
      """
      return BarycentricInterpolator(xi, yi, axis=axis)(x)
  
imports: from __future__ import division, print_function, absolute_import
  import warnings
  import numpy
  from scipy.special import factorial
  from scipy._lib.six import xrange
  from scipy._lib._util import _asarray_validated
label_desc: Use image node_id 4 for calling a global function with example usage: barycentric_interpolate(xi, yi, x, axis) and returns: BarycentricInterpolator