Ahti:
The current versions of LAPACK work differently on Windows and Linux. I
also erroneously assumed a sort order on the returned eigenvalues, which
appears true for Linux and false for Windows.
I did post a followup on this, but it seems not to have made it to the
archives.
To calculate the principal eigenvalue you need:
require '~addons/lapack/lapack.ijs'
require '~addons/lapack/dgeev.ijs'
la=:3 : 0
'l c r'=.dgeev_jlapack_ y.
({. \: c){"1 r
)
With your example, this gives
(%+/)la m2
0.0935079 0.152629 0.174427 0.166814 0.154946 0.257677
(%+/) power m2
0.0935079 0.152629 0.174427 0.166814 0.154946 0.257677
Please let me know if this works for you.
Best wishes,
John
Ahti Kitsik wrote:
> Most of the matrices produce similar results with LAPACK dgeev and power
> method J-implementation proposed by Mr. John Randall.
>
> However, few of the AHP matrices have LAPACK-produced eigenvector
> half-negative (e.g. _0.685 0.406 _0.414 0.310 0.331 0.043).
> Could someone provide a hint what could be the logical meaning behind
> this? How should one normalize such weight-lists?
>
> Anyway, to the point.
> Following example demonstrates a matrice where powermethod and LAPACK
> dgeev give very different results.
> Am I missing something?
>
> Ahti.
>
> require jpath '~addons\lapack\lapack.ijs'
> require jpath '~addons\lapack\dgeev.ijs'
>
> NB. The power method for calculating the principal eigenvector
> mp=:+/ . *
> normalize=:%(>./@:|)
> iterate=:normalize@:mp
> init=:[: ? # # 0:
> power=:13 : 'y.&iterate^:_ init y.'
>
> m2=: 6 6$1,(%6),(%5),6,(%2),(%2),6 1,(%8),5 4,(%8),5 8
> 1,(%7),4,(%8),(%6),(%5),7 1 6,(%4),2,(%4),(%4),(%6),1 7 2 8 8 4,(%7),1
> m2
> 1 0.166667 0.2 6 0.5 0.5
> 6 1 0.125 5 4 0.125
> 5 8 1 0.142857 4 0.125
> 0.166667 0.2 7 1 6 0.25
> 2 0.25 0.25 0.166667 1 7
> 2 8 8 4 0.142857 1
> ]v=:{."1 (2{::dgeev_jlapack_ m2) NB. LAPACK right eigenvector
> _0.675103 0.40594 _0.414364 0.309959 0.331358 0.043336
> \:v NB. Order
> 1 4 3 5 2 0
>
> ]p=:power m2
> 0.362889 0.592327 0.676923 0.647377 0.601319 1
> \:p NB. Order
> 5 2 3 4 1 0
>
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