''' p = rational(xData,yData,x)
  Evaluates the diagonal rational function interpolant p(x)
  that passes through he data points
'''  
from numpy import zeros
def rational(xData,yData,x):
  m = len(xData)
  r = yData.copy()
  rOld = zeros(m)
  for k in range(m-1):
    for i in range(m-k-1):
      if abs(x - xData[i+k+1]) < 1.0e-9:
        return yData[i+k+1]
      else:
        c1 = r[i+1] - r[i]
        c2 = r[i+1] - rOld[i+1]
        c3 = (x - xData[i])/(x - xData[i+k+1])
        r[i] = r[i+1] + c1/(c3*(1.0 - c1/c2) - 1.0)
        rOld[i+1] = r[i+1]
  return r[0]