ex7-4

1.代码实现

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import numpy as np
from scipy.interpolate import interp1d
from scipy.interpolate import lagrange
import pylab as plt
a=np.loadtxt('data7_4.txt')
x0=a[0]
y0=a[1]
x=np.linspace(0,15,151)
yx1=interp1d(x0,y0)
y1=yx1(x)
p2=lagrange(x0,y0)
y2=np.polyval(p2,x)
yx3=interp1d(x0,y0,'cubic')
y3=yx3(x)
dx=np.diff(x)
dy=np.diff(y3)
dyx=dy/dx
dyx0=dyx[0]
xt=x[130:]
yt=y3[130:]
ymin=min(yt)
xmin=[xt[ind]for ind,v in enumerate(yt) if v==ymin]
print('x=0处斜率的数值解为：',dyx0)
print('xmin=',xmin)
print('ymin=',ymin)
plt.rc('font',family='SimHei')
plt.rc('axes',unicode_minus=False)
plt.subplots_adjust(wspace=0.5)
plt.subplot(131)
plt.plot(x,y2)
plt.title('分段线性插值')
plt.subplot(132)
plt.plot(x,y2)
plt.title('拉格朗日插值')
plt.subplot(133)
plt.plot(x,y3)
plt.title('三次样条插值')
plt.show()

2.