例題1-2 Lagrange內插法 已知 平面上3點 求x=1.5 , f(x)= ?

例題1-2 Lagrange內插法

已知　平面上3點

   x                  y=f(x)
===================
 1.0                 0.0
 2.0                 0.693
 3.0                 1.099

求x=1.5 ,  f(x)= ?

#/********** Lagrange's interpolation ***************/
n=3
x= [0.0 for i in range(n+1)]     #x [n] 矩陣
y= [0.0 for i in range(n+1)]     #f [n] 矩陣
x=[1.0 , 2.0  ,3.0]
y=[0.0 , 0.693 , 1.099 ]

a=1.5   #x=1.5 求 f(1.5)= ?

print("\nEnter the number of the terms of the table: ",n)
print("\nEnter the respective values of the variables x and y: \n")
print("The values of x =")
for i  in range (0,n) :     # 
    print( round( x[i],4),"\t",end='')
print()
print("The values of y =")
for i  in range (0,n) :     # 
    print( round( y[i],4),"\t",end='')

print("\n\nEnter the value of the x to find the respective value of y ",a)

k=0.0
for i in range(0, n):
    s=1.0
    t=1.0
    for j in range(0,n):
        if(j!=i):
            s=s*(a-x[j]);
            t=t*(x[i]-x[j]);
    k=k+((s/t)*y[i]);

print("\nThe respective value of the variable y is: {%f}" %(k))




輸出畫面
======== RESTART: F:/2018-09勤益科大數值分析/數值分析/PYTHON/EX1-2.py ============

Enter the number of the terms of the table:  3

Enter the respective values of the variables x and y: 

The values of x =
1.0 2.0 3.0
The values of y =
0.0 0.693 1.099

Enter the value of the x to find the respective value of y  1.5

The respective value of the variable y is: {0.382375}
>>>