code: def krogh_interpolate(xi, yi, x, der=0, axis=0):
      """
      Convenience function for polynomial interpolation.
  
      See `KroghInterpolator` for more details.
  
      Parameters
      ----------
      xi : array_like
          Known x-coordinates.
      yi : array_like
          Known y-coordinates, of shape ``(xi.size, R)``.  Interpreted as
          vectors of length R, or scalars if R=1.
      x : array_like
          Point or points at which to evaluate the derivatives.
      der : int or list, optional
          How many derivatives to extract; None for all potentially
          nonzero derivatives (that is a number equal to the number
          of points), or a list of derivatives to extract. This number
          includes the function value as 0th derivative.
      axis : int, optional
          Axis in the yi array corresponding to the x-coordinate values.
  
      Returns
      -------
      d : ndarray
          If the interpolator's values are R-dimensional then the
          returned array will be the number of derivatives by N by R.
          If `x` is a scalar, the middle dimension will be dropped; if
          the `yi` are scalars then the last dimension will be dropped.
  
      See Also
      --------
      KroghInterpolator
  
      Notes
      -----
      Construction of the interpolating polynomial is a relatively expensive
      process. If you want to evaluate it repeatedly consider using the class
      KroghInterpolator (which is what this function uses).
  
      """
      P = KroghInterpolator(xi, yi, axis=axis)
      if der == 0:
          return P(x)
      elif _isscalar(der):
          return P.derivative(x, der=der)
      else:
          return P.derivatives(x, der=np.amax(der) + 1)[der]
  
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 2 for calling a global function with example usage: krogh_interpolate(xi, yi, x, der, axis) and returns: P, P, P