R和MATLAB返回不同的特征向量 [英] R and MATLAB returning different eigenvectors

问题描述

我遗漏了一些明显的东西，但是这里有:

I'm missing something obvious, but here goes:

在R中，

dput(M)
structure(c(-2.77555756156289e-16, 9.63770703841896e-16, 0, 9.63770703841896e-16, 
10.6543192562307, 4.11228781751498e-14, 0, 4.11228781751498e-14, 
275.591724761168), .Dim = c(3L, 3L), .Dimnames = list(c("", "", 
""), c("", "", "")))

#thus M is

 -2.775558e-16 9.637707e-16 0.000000e+00
  9.637707e-16 1.065432e+01 4.112288e-14
  0.000000e+00 4.112288e-14 2.755917e+02

eig(M)
$values
[1]  2.755917e+02  1.065432e+01 -2.775558e-16

$vectors
             [,1]         [,2] [,3]
[1,] 5.428099e-34 9.045822e-17    1
[2,] 1.552173e-16 1.000000e+00    0
[3,] 1.000000e+00 0.000000e+00    0

但在MATLAB

[vv,ee] = eig(M)
% hand-copied so ignore the precision)
vv = 
   1.0    -0.    -0.
   0      0      -1
   0      -1     0

ee = 
 %diagonals only
0.0    275.59   10.6543

特征值与abs(vv) == 1的位置匹配，但是我不明白的是为什么某些特征向量在MATLAB中是负数，而在R中却不是. 差异很大，因为我正尝试移植此MATLAB包(尤其是parabolafit_direct.m和`parabolafit_directm.m')以及后续算法对值的符号敏感.我检查了一下，由于这些符号差异，MATLAB程序包确实产生了正确的拟合输出(到数据集的抛物线)，而我的R端口却没有.

The eigenvalues match up with the locations where abs(vv) == 1 , but the thing I don't understand is why some eigenvectors are negative one in MATLAB but not in R. It makes a big difference, as I'm trying to port this MATLAB package, (in particular, parabolafit_direct.m and `parabolafit_directm.m' ) and the subsequent algorithms are sensitive to the sign of the values. I checked, and the MATLAB package does produce the correct fitted output (parabolic curve to dataset), while my R-port does not, because of these sign differences.

那么，为什么会有所不同，我该怎么做才能修改我的R代码以获得所需的数据符号?

So, why the difference, and what can I do to modify my R code to get the desired signs of the data?

我继续研究代码，看看这两个负一个"值是否在下一组方程式中被抵消，但是还没有看到.

I continue to dig into the code to see if these two "negative one" values cancel out in the next set of equations, but haven't seen that yet.

推荐答案

大多数重要信息在Andras Deak的评论中.总结一下:众所周知，本征值和本征向量仅在乘积常数之前是唯一的.尽管在这种特殊情况下，R和MATLAB碰巧以不同的符号结尾，但是所有随后对本征矢量进行的矩阵运算将产生相同的结果(同样，在符号或常数值之内).

Most of the important info is in the comments by Andras Deak. To summarize: as we all (should) know, eigenvalues and eigenvectors are only unique up to a multiplicative constant. While in this particular case R and MATLAB happened to end up with differing signs, all subsequent matrix operations on the eigenvectors will yield the same result (again,to within sign or constant value).

在我的特定情况下，最终结果实质上是:一个答案是a*x -b =0，另一个是-a*x + b = 0.

In my particular case, the final result essentially was: one answer was a*x -b =0 and the other was -a*x + b = 0 .

这篇关于R和MATLAB返回不同的特征向量的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！