﻿功能:全选主元三角分解

格式:
[P,Q,L,U]=LUPQ(A)
A:方阵变量

说明:函数执行成功后返回转换矩阵P和Q,返回下三角矩阵L，返回对角线为1的上三角矩阵U.其含义即为:P*A*Q=L*U

例子:

a =
[ 93.9290964947683    67.8490794579727    38.9889378282190    11.1702606133978
  46.0367843257435    74.5233182211049    54.3716235339509    49.0676413518692
  33.6044989217094    57.3996375116518    77.6278596732895    74.7707348665086
  34.2759118575025    29.9438441777340    17.2880263148286    59.1275361641904 ]

[p,q,l,u]=lupq(a)
p =
[ 1.00000000000000    0.00000000000000    0.00000000000000    0.00000000000000
  0.00000000000000    1.00000000000000    0.00000000000000    0.00000000000000
  0.00000000000000    0.00000000000000    1.00000000000000    0.00000000000000
  0.00000000000000    0.00000000000000    0.00000000000000    1.00000000000000 ]
q =
[ 1.00000000000000    0.00000000000000    0.00000000000000    0.00000000000000
  0.00000000000000    1.00000000000000    0.00000000000000    0.00000000000000
  0.00000000000000    0.00000000000000    1.00000000000000    0.00000000000000
  0.00000000000000    0.00000000000000    0.00000000000000    1.00000000000000 ]
l =
[ 93.9290964947683    0.00000000000000    0.00000000000000    0.00000000000000
  46.0367843257435    41.2689428010145    0.00000000000000    0.00000000000000
  33.6044989217094    33.1256435888910    35.3747856614996    0.00000000000000
  34.2759118575025    5.18485943392049   -1.36973332539647    50.9600987139459 ]
u =
[ 1.00000000000000    0.00000000000000    0.00000000000000    0.00000000000000
  0.00000000000000    1.00000000000000    0.00000000000000    0.00000000000000
  0.00000000000000    0.00000000000000    1.00000000000000    0.00000000000000
  0.00000000000000    0.00000000000000    0.00000000000000    1.00000000000000 ]