Python插值法(1)————拉格朗日插值多项式

代码

from sympy import *
import math
from matplotlib import pyplot as plt


def lagrange(x, y):
    p, la = symbols('p  la')
    n = len(x)
    s = 0
    for k in range(n):
        la = y[k]
        for j in range(k):
            la = la * (p - x[j]) / (x[k] - x[j])
        for j in range(k+1, n):
            la = la * (p - x[j]) / (x[k] - x[j])
        s = s + la
    print(expand(simplify(s)))
    return s


p = symbols('p')
x = [i*math.pi/6 for i in range(6)]
print(x)
y = [math.cos(i) for i in x]
t = lagrange(x, y)
chazhi = [i*math.pi/18 for i in range(18)]
chazhiy = []
for i in chazhi:
    chazhiy.append(t.subs(p, i))
plt.figure(figsize=(15, 8), dpi=80)
plt.plot(x, y, 'r1', markersize=25, label='original')
plt.plot(chazhi, chazhiy, 'kD:', markersize=8, label='lagrange')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.savefig('lagrange.jpg')
plt.show()

计算结果如下图所示