Bill -
I calculated eigenvalues in both J and Matlab and got the same results you
did.
I also picked one of his other examples ("Predicition of Dynamics" on page
7) and
got a completely different answer than the one he shows.
This might be one of those "Well, everyone knows you first have foo the
matrix
before you take the eigenvalue." I notice, for instance, that all his
eigenvectors
sum to 1.
FYI the text of my two sessions follows.
Devon
+.--------- J session -----------+.
]m=: >1 0.333333 5 1; 3 1 5 1; 0.2 0.2 1 0.2; 1 1 5 1
1 0.333333 5 1
3 1 5 1
0.2 0.2 1 0.2
1 1 5 1
'leigv eigv reigv'=. dgeev_jlapack_ m
eigv
4.1545007 _0.077250375j0.79743768 _0.077250375j_0.79743768 _5.5511151e_17
+.--------- Matlab session -----------+.
>> m= [1 0.333333 5 1; 3 1 5 1; 0.2 0.2 1 0.2; 1 1 5 1]
m =
1.0000 0.3333 5.0000 1.0000
3.0000 1.0000 5.0000 1.0000
0.2000 0.2000 1.0000 0.2000
1.0000 1.0000 5.0000 1.0000
>> eig(m)
ans =
4.1545
-0.0773 + 0.7974i
-0.0773 - 0.7974i
-0.0000
On 3/1/06, Bill Harris <[EMAIL PROTECTED]> wrote:
>
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> It's been a while since I've done much linear algebra stuff, and I don't
> think I've ever used LAPACK before.
>
> Recently, I was trying to duplicate the results in
> http://actifeld.com/A%20Possible%20Method.doc. In particular, Geoff
> Coyle gives a matrix on p. 6 and then shows the eigenvector (presumably
> the principal eigenvector) as (0.232, 0.402, 0.061, 0.305).
>
> I tried using dgeev_jlapack_ as in the lab (J5.04). Here are snippets
> of my work:
>
> ,----[ His Client Preference Matrix ]
> | m
> | 1 0.333333 5 1
> | 3 1 5 1
> | 0.2 0.2 1 0.2
> | 1 1 5 1
> `----
>
> ,----[ Eigenvalues; the first is presumably the principal eigenvalues ]
> | > 1{ dgeev_jlapack_ m
> | 4.1545007 _0.077250375j0.79743768 _0.077250375j_0.79743768_5.5511151e_17
> `----
>
> ,----[ Left eigenvectors; the first is presumably the principal ]
> | > 0{ dgeev_jlapack_ m
> | 0.25760047 0.25043806j0.32061757 0.25043806j_0.32061757
> 0
> | 0.14598546 0.11143426j_0.18169805 0.11143426j0.18169805
> 1.0965318e_17
> | 0.93661124 _0.87103684 _0.87103684
> _0.98058068
> | 0.18732225 _0.17420737j_2.3592239e_16 _0.17420737j2.3592239e_16
> 0.19611614
> |
> `----
>
> ,----[ Right eigenvectors; the first is presumably the principal ]
> | > 2{ dgeev_jlapack_ m
> | 0.41429869 0.15147845j_0.40545658 0.15147845j0.40545658
> 4.86865e_17
> | 0.73105594 _0.82614212 _0.82614212
> _1.2962781e_15
> | 0.10632205 0.043552657j0.055757287 0.043552657j_0.055757287
> _0.19611614
> | 0.53161023 0.21776329j0.27878644 0.21776329j_0.27878644
> 0.98058068
> `----
>
> ,----[ Principle left eigenvector, with components converted to magnitudes
> ]
> | {. | > 0{ dgeev_jlapack_ m
> | 0.25760047 0.40683516 0.40683516 0
> `----
>
> ,----[ Principal right eigenvector, with components converted to
> magnitudes ]
> | {. | > 2{ dgeev_jlapack_ m
> | 0.41429869 0.43282878 0.43282878 4.86865e_17
> `----
>
> None of those match his (0.232, 0.402, 0.061, 0.305). While I'm waiting
> on an answer from him, does anyone here see anything I'm doing dumb?
> Can anyone reproduce his result, perhaps using LAPACK? I do read that
> people tend to find principal eigenvectors using a power method, which
> only returns the principal eigenvector, but I neither see that in my
> skimming of the LAPACK docs nor do I (yet) know why it's better to go
> that way than to find them all, assuming it's not computationally costly
> to find them all.
>
> TIA,
>
> Bill
> - --
> Bill Harris http://facilitatedsystems.com/weblog/
> Facilitated Systems Everett, WA 98208 USA
> http://facilitatedsystems.com/ phone: +1 425 337-5541
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--
Devon McCormick
^me^ at acm.
org is my
preferred e-mail
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