Dear R-listers
Is there anyone who knows why I get different eigenvectors when I run
MatLab and R? I run both programs in Windows Me. Can I make R to produce
the same vectors as MatLab?
#R Matrix
PA9900<-c(11/24 ,10/53 ,0/1 ,0/1 ,29/43 ,1/24 ,27/53 ,0/1 ,0/1 ,13/43
,14/24 ,178/53 ,146/244 ,17/23 ,15/43 ,2/24 ,4/53 ,0/1 ,2/23 ,2/43 ,4/24
,58/53 ,26/244 ,0/1 ,5/43)
#R-syntax
PA9900<-matrix(PA9900,nrow=5,byrow=T)
eigen(PA9900)
#R-output
$values
[1] 1.2352970 0.3901522 -0.2562860 0.2259411 0.1742592
$vectors
[,1] [,2] [,3] [,4] [,5]
[1,] -0.67795430 -1.70686496 -0.52613955 -8.675109 -0.8413826
[2,] -0.32621100 0.54611272 -0.21526356 -2.726193 -0.2876643
[3,] -2.83313878 -2.88801964 0.87388189 45.427935 4.5069361
[4,] -0.09857565 -0.33015962 0.09136359 -5.426254 -0.8201206
[5,] -0.68977432 0.01977374 0.61772506 3.751978 0.4348802
%Matlab Matrix
PA9900 =[11/24 10/53 0/1 0/1 29/43 ;1/24 27/53 0/1 0/1 13/43 ;14/24
178/53 146/244 17/23 15/43 ;2/24 4/53 0/1 2/23 2/43 ;4/24 58/53 26/244
0/1 5/43]
%MatLab-syntax
[wmat,dmat]=eig(mat)
%MatLab-output
wmat
-0.2250 0.4330 -0.4998 -0.1795 -0.1854
-0.1083 0.1771 0.1599 -0.0614 -0.0583
-0.9403 -0.7191 -0.8457 0.9617 0.9708
-0.0327 -0.0752 -0.0967 -0.1750 -0.1160
-0.2289 -0.5083 0.0058 0.0928 0.0802
dmat
1.2353 0 0 0 0
0 -0.2563 0 0 0
0 0 0.3902 0 0
0 0 0 0.1743 0
0 0 0 0 0.2259
Yours sincerely, Mikael Niva
********************************************
Mikael Niva
Avd. f?r V?xtekologi, Dept. of Plant Ecology
EvolutionsBiologiskt Centrum, Uppsala Universitet
Villav?gen 14
752 36 UPPSALA
E-post Mikael.Niva at EBC.UU.SE
Tel. +46 (0)18 471 28 65
Fax +46 (0)18 55 34 19
Mikael Niva <mikael.niva at ebc.uu.se> wrote:> Is there anyone who knows why I get different eigenvectors when I run > MatLab and R?R orders the eigenvalues by absolute value, which seems sensible; the MatLab eigenvalues you gave do not seem to be in any particular order. R does not normalize the eigenvectors (as MatLab does), but you can easily do so yourself: R> PA9900<-c(11/24 ,10/53 ,0/1 ,0/1 ,29/43 ,1/24 ,27/53 ,0/1 ,0/1 ,13/43 R> ,14/24 ,178/53 ,146/244 ,17/23 ,15/43 ,2/24 ,4/53 ,0/1 ,2/23 ,2/43 ,4/24 R> ,58/53 ,26/244 ,0/1 ,5/43) R> PA9900<-matrix(PA9900,nrow=5,byrow=T) R> eig <- eigen(PA9900) R> eig$values # Note they are in descending order of absolute value: [1] 1.2352970 0.3901522 -0.2562860 0.2259411 0.1742592 R> sweep(eig$vectors, 2, sqrt(colSums(eig$vectors^2)), "/") [,1] [,2] [,3] [,4] [,5] [1,] -0.22500913 -0.499825704 -0.43295788 -0.18537961 -0.17952679 [2,] -0.10826756 0.159919608 -0.17713941 -0.05825639 -0.06137926 [3,] -0.94030246 -0.845706299 0.71911349 0.97075584 0.96165016 [4,] -0.03271669 -0.096681499 0.07518268 -0.11595437 -0.17499009 [5,] -0.22893213 0.005790397 0.50832318 0.08017655 0.09279089 This is the same as the MatLab result you gave, except for 2 things: 1) The column order matches the eigenvalue order, so R's columns are in a different order than Matlab's. 2) The sign is different for one of the vectors (my column 3, your 2). The sign of an eigenvector is not well defined, even after normalization. MatLab> wmat MatLab> -0.2250 0.4330 -0.4998 -0.1795 -0.1854 MatLab> -0.1083 0.1771 0.1599 -0.0614 -0.0583 MatLab> -0.9403 -0.7191 -0.8457 0.9617 0.9708 MatLab> -0.0327 -0.0752 -0.0967 -0.1750 -0.1160 MatLab> -0.2289 -0.5083 0.0058 0.0928 0.0802 MatLab> MatLab> dmat MatLab> 1.2353 0 0 0 0 MatLab> 0 -0.2563 0 0 0 MatLab> 0 0 0.3902 0 0 MatLab> 0 0 0 0.1743 0 MatLab> 0 0 0 0 0.2259 Side note: there is some relation between eigenvectors and svd (singular value decomposition) which I have not fully grokked yet; if anyone has a simple explanation I'd be grateful. -- -- David Brahm (brahm at alum.mit.edu)
Mikael -
The matrix PA9900 is not a symmetric matrix. Eigen() will
automatically detect this. help("eigen") says explicitly:
"For `eigen( , symmetric = FALSE)' the choice of length of
the eigenvectors is not defined by LINPACK. In all other
cases the vectors are normalized to unit length."
In the example you give, the eigenvectors from R are clearly
NOT normalized to unit length, while those from Matlab are.
Even after normalizing them, the R eigenvectors will differ
by order and sign from the Matlab ones. (Compare R column 3
with Matlab column 2.) Have to look at the EISPACK source
documentation to see whether it's returning right eigenvectors
or left eigenvectors for an asymmetric matix.
- tom blackwell - u michigan medical school - ann arbor -
On Thu, 3 Apr 2003, Mikael Niva wrote:
> Dear R-listers
>
> Is there anyone who knows why I get different eigenvectors when I run
> MatLab and R? I run both programs in Windows Me. Can I make R to produce
> the same vectors as MatLab?
>
> #R Matrix
> PA9900<-c(11/24 ,10/53 ,0/1 ,0/1 ,29/43 ,1/24 ,27/53 ,0/1 ,0/1 ,13/43
> ,14/24 ,178/53 ,146/244 ,17/23 ,15/43 ,2/24 ,4/53 ,0/1 ,2/23 ,2/43 ,4/24
> ,58/53 ,26/244 ,0/1 ,5/43)
>
> #R-syntax
> PA9900<-matrix(PA9900,nrow=5,byrow=T)
> eigen(PA9900)
>
> #R-output
> $values
> [1] 1.2352970 0.3901522 -0.2562860 0.2259411 0.1742592
>
> $vectors
> [,1] [,2] [,3] [,4] [,5]
> [1,] -0.67795430 -1.70686496 -0.52613955 -8.675109 -0.8413826
> [2,] -0.32621100 0.54611272 -0.21526356 -2.726193 -0.2876643
> [3,] -2.83313878 -2.88801964 0.87388189 45.427935 4.5069361
> [4,] -0.09857565 -0.33015962 0.09136359 -5.426254 -0.8201206
> [5,] -0.68977432 0.01977374 0.61772506 3.751978 0.4348802
>
> %Matlab Matrix
> PA9900 =[11/24 10/53 0/1 0/1 29/43 ;1/24 27/53 0/1 0/1 13/43 ;14/24
> 178/53 146/244 17/23 15/43 ;2/24 4/53 0/1 2/23 2/43 ;4/24 58/53 26/244
> 0/1 5/43]
>
> %MatLab-syntax
> [wmat,dmat]=eig(mat)
>
> %MatLab-output
> wmat > -0.2250 0.4330 -0.4998 -0.1795 -0.1854
> -0.1083 0.1771 0.1599 -0.0614 -0.0583
> -0.9403 -0.7191 -0.8457 0.9617 0.9708
> -0.0327 -0.0752 -0.0967 -0.1750 -0.1160
> -0.2289 -0.5083 0.0058 0.0928 0.0802
>
> dmat > 1.2353 0 0 0 0
> 0 -0.2563 0 0 0
> 0 0 0.3902 0 0
> 0 0 0 0.1743 0
> 0 0 0 0 0.2259
>
> Yours sincerely, Mikael Niva
>
> ********************************************
> Mikael Niva
> Avd. för Växtekologi, Dept. of Plant Ecology
> EvolutionsBiologiskt Centrum, Uppsala Universitet
> Villavägen 14
> 752 36 UPPSALA
> E-post Mikael.Niva at EBC.UU.SE
> Tel. +46 (0)18 471 28 65
> Fax +46 (0)18 55 34 19