拉格朗日插值法及python实现

python 实现

方法一：

#bao
from scipy.interpolate import lagrange
x=[1,3,5]
y=[2,10,1]
print(lagrange(x,y))#拟合曲线
print(lagrange(x,y)(10))#估值`

结果：

        2
-2.125 x + 12.5 x - 8.375
-95.875

方法二：

#python
import numpy
import matplotlib
from matplotlib import pyplot
x=[1,3,5]
y=[2,10,1]
def lagrange_interploate(x1):
    P=[]
    L_n=0
    for i in range(len(x)):
        numerator=1
        denominator=1
        for j in range(len(x)):
            if j!=i:
                numerator*=(x1-x[j])
                denominator*=(x[i]-x[j])
        P.append(numerator/denominator)

    for i in range(len(x)):
        L_n+=y[i]*P[i]

    return round(L_n,3)

print(lagrange_interploate(10))

结果：

-95.875

拟合曲线图像：

x2=numpy.linspace(-10,10,20,endpoint=False)
print(x2)
y2=[]
for i in range(len(x2)):
    y2.append(lagrange_interploate(x2[i]))
print(y2)

pyplot.plot(x2,y2)
pyplot.scatter(x,y,marker='.')
pyplot.show()