# [R] buggy eigen function

Peter Dalgaard BSA p.dalgaard at biostat.ku.dk
Tue Mar 21 22:03:13 CET 2000

```Chong Gu <chong at stat.purdue.edu> writes:

> It was a real surprise, but a student in my class found that the
> function eigen is buggy.  He traced to the problem from his inability
> of getting principal component analysis to work on his data.

..
> Here is a matrix I generated through X'X, where X is 2x3.
>
> > jj
>            [,1]      [,2]       [,3]
> [1,]  0.8288469 -1.269783 -0.7533517
> [2,] -1.2697829  2.162132  2.0262917
> [3,] -0.7533517  2.026292  4.1927134
>
>
> Here are the 0.90.1 eigen results.
>
> > eigen(jj)
> \$values
> [1]  3.06206547  0.20492432 -0.04955518
>
> \$vectors
>            [,1]        [,2]        [,3]
> [1,] -0.2316032  0.05778620  0.06998513
> [2,]  0.4932735 -0.04951172  0.06919350
> [3,]  0.8489300  0.06527175 -0.01966568
>
>
> Here are the 1.0.0 eigen results.
>
> > eigen(jj)
> \$values
> [1]  2.765885782  0.008839573 -0.122630879
>
> \$vectors
>            [,1]       [,2]       [,3]
> [1,] -0.2236327  0.6670340  0.7106715
> [2,]  0.4693452 -0.5653355  0.6783147
> [3,]  0.8542268  0.4852437 -0.1866417

I get this on an i386 (well, k6-III):

> eigen(jj)
\$values
[1]  5.795187e+00  1.388505e+00 -2.006855e-07

\$vectors
[,1]       [,2]       [,3]
[1,] -0.3417893 -0.4739218  0.7067794
[2,]  0.7093264  0.4978512  0.5411749
[3,]  1.0576086 -0.4870615 -0.1345489

this is the same as S-PLUS 3.4 on a Sun SPARC, except that the sign of
the last two columns is reversed, and it also makes sense that one
eigenvalue should be zero for a rank-2 p.s.d. matrix. What hardware
are you working on?

--
O__  ---- Peter Dalgaard             Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics     2200 Cph. N
(*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
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```