（十七）LU分解

 #encoding=utf-8
 import numpy as np
 # 输入数据
 # a用来记录x的系数
 a=[[2.0,2.0,3.0],[4.0,7.0,7.0],[-2.0,4.0,5.0]]
 # b用来记录 y
 b=[3.0,1.0,-7.0]
 # n用来记录方程的个数
 n=len(b)
 # 定义x
 x=[0.0 for i in range(n)]
 l=[[0.0 for i in range(n)] for j in range(n)]
 u=[[0.0 for i in range(n)] for j in range(n)]
 #  为 u[1][i]赋值
 for i in range(0,n):
     u[0][i]=a[0][i]
 #  为 l[i][1]赋值
 for i in range(0,n):
     l[i][0]=a[i][0]/u[0][0]
 # 求 u[r][i] l[i][r]
 for r in range(1,n):
     for i in  range(r,n):
         p=0.0
         for j in range(0,r):
             p=p+l[r][j]*u[j][i]
         u[r][i]=a[r][i]-p
         q=0.0
         for j in range(0,r):
             q=q+l[i][j]*u[j][r]
         l[i][r]=(a[i][r]-q)/u[r][r]

 # 输出 l
 print "l:"
 for i in range(0,n):
     for j in range(0,n):
         print str(l[i][j])+" \t",
     print ""
 # 输出 u
 print  "u:"
 for i in range(0,n):
     for j in range(0,n):
         print str(u[i][j])+" \t",
     print ""