python计算对角线有理函数插值

"""
皮蛋编程(https://www.pidancode.com)
创建日期：2022/3/29
功能描述：python计算对角线有理函数插值
"""
''' 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]