已知 x=1:10,y=exp(x),使用 python 计算 x=1: 10处的导数一阶中心差分与拉格朗日插值函数
时间: 2024-03-21 21:15:54 浏览: 17
首先,我们需要导入必要的库:
```python
import numpy as np
from scipy.interpolate import lagrange
```
然后,计算一阶中心差分:
```python
x = np.arange(1, 11)
y = np.exp(x)
dx = x[1] - x[0]
dy = np.zeros_like(y)
dy[0] = (y[1] - y[0]) / dx
dy[-1] = (y[-1] - y[-2]) / dx
dy[1:-1] = (y[2:] - y[:-2]) / (2*dx)
```
最后,计算拉格朗日插值函数:
```python
poly = lagrange(x, y)
d_poly = np.polyder(poly)
d_lagrange = d_poly(x)
```
完整代码如下:
```python
import numpy as np
from scipy.interpolate import lagrange
x = np.arange(1, 11)
y = np.exp(x)
dx = x[1] - x[0]
dy = np.zeros_like(y)
dy[0] = (y[1] - y[0]) / dx
dy[-1] = (y[-1] - y[-2]) / dx
dy[1:-1] = (y[2:] - y[:-2]) / (2*dx)
poly = lagrange(x, y)
d_poly = np.polyder(poly)
d_lagrange = d_poly(x)
print("一阶中心差分:", dy)
print("拉格朗日插值函数:", d_lagrange)
```