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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 ] )
# 计算Newton插值法所需的差商
def divided_diff ( t_values , v_values ) :
# 用给定的数值初始化差商数组
differences = v_values . copy ( )
# 遍历每个数据点，计算差商
for i in range ( 1 , len ( t_values ) ) :
for j in range ( len ( t_values ) - 1 , i - 1 , - 1 ) :
differences [ j ] = ( differences [ j ] - differences [ j - 1 ] ) / ( t_values [ j ] - t_values [ j - i ] )
return differences
# 使用Newton插值法寻找 t=16 时的速度
def newton_interpolation ( t_values , v_values , target_t ) :
differences = divided_diff ( t_values , v_values )
p = differences [ 0 ]
for i in range ( 1 , len ( t_values ) ) :
term = differences [ i ]
for j in range ( i ) :
term * = ( target_t - t_values [ j ] )
p + = term
return p
t_target = 16
velocity_at_16 = newton_interpolation ( t_values , v_values , t_target )
print ( f " 使用Newton插值法， { velocity_at_16 : .2f } m/s " )
