﻿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 ]

[v,r] = Lpd(a)//回车得到如下结果
v =
[ 103.392551686058    52.1444810974814    33.4971733123496    23.2369850403258
  52.1444810974814    73.0808928008774    63.1340856730138    31.4839763693533
  33.4971733123496    63.1340856730138    96.9565969931872    39.1429818741177
  23.2369850403258    31.4839763693533    39.1429818741177    52.9437631145135 ]
r =
[ 0.92015234614012    0.20444337865811    0.16283980737483   -0.29155747623717
 -0.18243018489556    0.97324931054764    0.04541428309340    0.13207024664420
  0.00764400550222   -0.10093879907231    0.88770633619968    0.44914406229253
  0.34638195205822   -0.02828503638451   -0.42825016134983    0.83415903717990 ]