[Maxima-bugs] [ maxima-Bugs-3337674 ] Symmetric matrix yields complex eigenvalues

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Bugs item #3337674, was opened at 2011-06-27 08:46
Message generated for change (Settings changed) made by rtoy
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Category: None
Group: None
>Status: Closed
Resolution: Wont Fix
Priority: 5
Private: No
Submitted By: Dženan Zukić (dzenanz)
Assigned to: Nobody/Anonymous (nobody)
Summary: Symmetric matrix yields complex eigenvalues

Initial Comment:
When using eigenvectors command in wxMaxima, the following symmetric matrix yields complex eigenvalues:
matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722])

All eigenvalues of a symmetric matrix should be real: http://en.wikipedia.org/wiki/Symmetric_matrix

Maxima version: 5.24.0
Maxima build date: 20:39 4/5/2011
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8

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Comment By: Raymond Toy (rtoy)
Date: 2012-08-18 16:52

Message:
In addition, I think algorithms for symmetric matrices should be used,
instead of a general eigen solver.

I don't consider this a bug in maxima.

Marking as pending/wontfix.


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Comment By: Barton Willis (willisbl)
Date: 2011-06-28 21:00

Message:
For a floating point evaluation of eigenvalues, you should use a purely
numeric
method, not a symbolic method. One (not the only) option is
eigens_by_jacobi 
(symmetric and either binary64 or bigfloat entries). 

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Comment By: Dženan Zukić (dzenanz)
Date: 2011-06-28 05:37

Message:
Thanks for suggestions, but I was using Maxima trying to verify some
results obtained using numeric library. However after getting this
nonsensical result from Maxima I used another numeric library and obtained
similar results (difference was after some decimal points).

I am not a frequent user of Maxima, and this problem has significantly
lowered my faith in it.

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Comment By: Barton Willis (willisbl)
Date: 2011-06-28 05:23

Message:
I think the problem is that the default value of ratepsilon is too small;
try this:
(also do this same with ratepsilon : 1.0e-8)

(%i1) load(hypergeometric)$
(%i2) ratepsilon : 1.0e-18$
(%i3) m :
matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722])$
(%i4) first(eigenvalues(m)), ratprint : false$
(%i5) nfloat(% - conjugate(%),[],100);
(%o5) [8.0266455652163197256568351091[46
digits]5913348171925384517960952b-197*%i-1.3377742608693866209428058515[46
digits]0985558028654230752993492b-197,-5.3510970434775464837712234061[46
digits]3942232114616923011973968b-197*%i-1.3377742608693866209428058515[46
digits]0985558028654230752993492b-197,-1.9934389902195135071021405630[46
digits]0374693317196116973450023b-205*%i-2.6755485217387732418856117030[46
digits]1971116057308461505986984b-197]

See also http://en.wikipedia.org/wiki/Casus_irreducibilis

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