python7.3

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d, CubicSpline

T = np.array([700, 720, 740, 760, 780])
V = np.array([0.0977, 0.1218, 0.1406, 0.1551, 0.1664])

T_interp = np.array([750, 770])

f_linear = interp1d(T, V, kind='linear')
V_linear_interp = f_linear(T_interp)

cs = CubicSpline(T, V)
V_cubic_interp = cs(T_interp)

print(f"线性插值结果:T={T_interp}对应的V={V_linear_interp}")
print(f"三次样条插值结果:T={T_interp}对应的V={V_cubic_interp}")

x = np.linspace(700, 780, 400)

plt.figure(figsize=(10, 6))
plt.plot(T, V,'o',label='原始数据点')
plt.plot(x,f_linear(x),'-',label='线性插值')
plt.plot(x,cs(x),' -- ',label='三次样条插值')
plt.scatter(T_interp,V_linear_interp,color='red',label='线性插值点')
plt.scatter(T_interp,V_cubic_interp,color='green',label='三次样条插值点')
plt.xlabel('温度T')
plt.ylabel('体积V')
plt.title('过热蒸汽体积随温度变化的插值')
plt.legend()
plt.grid(True)
plt.show()