﻿功能:对矩阵进行左极分解(Left Polar Decomposition)

格式:

[V,R]=LPD(A)
A:为方阵变量

说明:任何一个可逆方阵A都可以唯一的表示为A=V*R,其中R为一个正交矩阵,V为正定对称矩阵.

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 ]

[r,u]=Lpd(a)//回车得到如下结果
u =
[ 209.343313381690   -2.2945173681E-55   -8.4278629422E-21   -1.7055795446E-21
  7.7699923441E-41    15.0499987675216   -4.2178263343E-32    1.0222532997E-17
 -8.4278629422E-21   -6.1091922775E-33    70.5364453227561    3.0198225184E-13
 -1.7055795446E-21   -3.5234688853E-47    3.0198225184E-13    31.4440471226690 ]
r =
[ 0.44868448376715    0.32410435452631    0.18624400845863    0.05335857368910
  3.05892279706310    4.95171590192609    3.61273275658245    3.26030866246705
  0.47641327498066    0.81375857897298    1.10053546529152    1.06002981188486
  1.09006044049564    0.95228976285772    0.54980283700073    1.88040476893838 ]