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import numpy as np
# 给定数据
t_values = np . array ( [ 0 , 10 , 15 , 20 , 22.5 , 30 ] )
v_values = np . array ( [ 0 , 227.04 , 362.78 , 517.35 , 602.97 , 901.67 ] )
# 确定插值区间，选择包含 t=16 的四个数据点
t0 = t_values [ 1 ] # 10
t1 = t_values [ 2 ] # 15
t2 = t_values [ 3 ] # 20
t3 = t_values [ 4 ] # 22.5
v0 = v_values [ 1 ] # 227.04
v1 = v_values [ 2 ] # 362.78
v2 = v_values [ 3 ] # 517.35
v3 = v_values [ 4 ] # 602.97
# 构造Lagrange插值多项式
p = v0 * ( ( 16 - t1 ) * ( 16 - t2 ) * ( 16 - t3 ) ) / ( ( t0 - t1 ) * ( t0 - t2 ) * ( t0 - t3 ) ) + \
v1 * ( ( 16 - t0 ) * ( 16 - t2 ) * ( 16 - t3 ) ) / ( ( t1 - t0 ) * ( t1 - t2 ) * ( t1 - t3 ) ) + \
v2 * ( ( 16 - t0 ) * ( 16 - t1 ) * ( 16 - t3 ) ) / ( ( t2 - t0 ) * ( t2 - t1 ) * ( t2 - t3 ) ) + \
v3 * ( ( 16 - t0 ) * ( 16 - t1 ) * ( 16 - t2 ) ) / ( ( t3 - t0 ) * ( t3 - t1 ) * ( t3 - t2 ) )
# 计算 t=16 时的速度
velocity_at_16 = p
print ( f " 使用Lagrange插值法， { velocity_at_16 : .2f } m/s " )
