Julia語言 例題1-8 已知5點的座標值 使用牛頓內插法求差除表？

Julia語言 例題1-8 已知5點的座標值 使用牛頓內插法求差除表？

x       f(x)
===========
0        0
1        -3
2        0
3        15
4        48
===========


程式
using Printf
x= [0.0 , 1.0  ,2.0 , 3.0 , 4.0 ]
f= [[ 0.0     ,     0.0   ,0.0  ,0.0 ,0.0 ,0.0 ],
    [-3.0     ,     0.0   ,0.0  ,0.0 ,0.0 ,0.0 ],
    [0.0      ,     0.0   ,0.0  ,0.0 ,0.0 ,0.0 ],
    [15.0     ,     0.0   ,0.0  ,0.0 ,0.0 ,0.0 ],
    [48.0     ,     0.0   ,0.0  ,0.0 ,0.0 ,0.0 ]]

n=length(x)
println("  Divided Difference Table: ")
println("=============================")
for j=2:n
    for i=1:n-j+1
        f[i][j]=(f[i+1][j-1]-f[i][j-1])/(x[i+j-1]-x[i])
    end
end   

print("i\tx(i)\t\tf(i)\t\tf(i,i+1)\tf(i,i+1.i+2),  ......................\n")
for i=1:n
    s=@sprintf("%d\t%8.5f",i,x[i])
    print(s)
    for j=1:n-i+1
        s=@sprintf("\t%8.5f",f[i][j])
        print(s)
    end
    println()
 
end


輸出畫面

  Divided Difference Table: 
=============================
i x(i)  f(i)  f(i,i+1) f(i,i+1.i+2),  ......................
1  0.00000  0.00000 -3.00000  3.00000  1.00000  0.00000
2  1.00000 -3.00000  3.00000  6.00000  1.00000
3  2.00000  0.00000 15.00000  9.00000
4  3.00000 15.00000 33.00000
5  4.00000 48.00000

i=1 到 5 
Pn(x)= 0.0 + -3.0 (x-0.0) + 3.0 (x -0.0)(x -1.0) + 1.0 (x -0.0)(x -1.0) ()x -2.0) + 0.0 (x -0.0)(x -1.0) ()x -2.0)(x -3.0) 

i=3 到 5 
Pn(x)= 0.0 + 15 (x-2.0) + 9.0 (x -2.0)(x -3.0)