eigenvalues problem
- Subject: eigenvalues problem
- From: Bernhard Stoevesandt
- Date: Tue, 25 Aug 2009 14:18:51 +0200
Hi, hm no. It doesn't work. Now i get:
(%i1)
A:2*matrix([(2*m1^2+2*m2*m4+2*m3*m7),m3*m8+m6*m7+m4*m5+m2*m5+m1*m4+m1*m2,m1*m3+m1*m7+m2*m6+m4*m8+m3*m9+m7*m9],[m3*m8+m6*m7+m4*m5+m2*m5+m1*m4+m1*m2,
2*m5^2+2*m2*m4+2*m6*m8,
m2*m7+m4*m3+m5*m6+m5*m8+m6*m9+m8*m9],[m1*m3+m1*m7+m2*m6+m4*m8+m3*m9+m7*m9,m2*m7+m4*m3+m5*m6+m5*m8+m6*m9+m8*m9,
2*m9^2+2*m3*m7+2*m6*m8]);
[ 2 ]
[ 2 (2 m3 m7 + 2 m2 m4 + 2 m1 ) ]
(%o1) Col 1 = [ ]
[ 2 (m3 m8 + m6 m7 + m4 m5 + m2 m5 + m1 m4 + m1 m2) ]
[ ]
[ 2 (m7 m9 + m3 m9 + m4 m8 + m1 m7 + m2 m6 + m1 m3) ]
[ 2 (m3 m8 + m6 m7 + m4 m5 + m2 m5 + m1 m4 + m1 m2) ]
[ ]
Col 2 = [ 2 ]
[ 2 (2 m6 m8 + 2 m5 + 2 m2 m4) ]
[ ]
[ 2 (m8 m9 + m6 m9 + m5 m8 + m2 m7 + m5 m6 + m3 m4) ]
[ 2 (m7 m9 + m3 m9 + m4 m8 + m1 m7 + m2 m6 + m1 m3) ]
[ ]
Col 3 = [ 2 (m8 m9 + m6 m9 + m5 m8 + m2 m7 + m5 m6 + m3 m4) ]
[ ]
[ 2 ]
[ 2 (2 m9 + 2 m6 m8 + 2 m3 m7) ]
(%i2) eigenvalues(A)$
Maxima encountered a Lisp error:
Error in CONDITIONS::CLCS-UNIVERSAL-ERROR-HANDLER [or a callee]:
Couldn't protect
Automatically continuing.
To reenable the Lisp debugger set *debugger-hook* to nil
The version is for Ubuntu 8.10
Maxima version: 5.13.0
Maxima build date: 3:56 12/15/2007
host type: x86_64-unknown-linux-gnu
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.8
Bernhard
Stefano Ferri schrieb:
> Hi, I've tryed with your matrix B and Maxima can compute eigenvalues,
> but results are really long expressions, so most of the time is spent
> printing the result. Only calculation took 16.8 seconds on an athlon
> 1900+, without printing the output. Output printing took about 4-5
> minutes. Try with
>
> eigenvalues(B)$
>
> instead of eigenvalues(B);
> I had no problem with your matrix C, no errors. Wich version of Maxima
> are you using? Now I'm with Maxima 5.18.1, compiled with CLISP.
> Stefano
>
>
>
> 2009/8/25 Bernhard Stoevesandt <bernhard.stoevesandt at uni-oldenburg.de>:
>> Hi everyone,
>>
>> well, i do have a rather complicated matrix of which i would like to
>> optain the eigenvalues. The problem is with maxima i don't get them.
>> Here is what i do:
>>
>> (%i1) B:matrix([2*(m1*m1+m2*m4+m3*m7),m3*m8 + m6*m7 + m4*m5 + m2*m5 +
>> m1*m4 + m1*m2,m1*m3+m1*m7+m2*m6+m4*m8+m3*m9+m7*m9], [m3*m8 + m6*m7 +
>> m4*m5 + m2*m5 +
>> m1*m4+m1*m2,2*(m5*m5+m2*m4+m6*m8),m2*m7+m4*m3+m5*m6+m5*m8+m6*m9+m8*m9]
>> ,[m1*m3+m1*m7+m2*m6+m4*m8+m3*m9+m7*m9,m2*m7+m4*m3+m5*m6+m5*m8+m6*m9+m8*m9,2*(m9*m9+m3*m7+m6*m8)]);
>> [ 2 ]
>> [ 2 (m3 m7 + m2 m4 + m1 ) ]
>> (%o1) Col 1 = [ ]
>> [ m3 m8 + m6 m7 + m4 m5 + m2 m5 + m1 m4 + m1 m2 ]
>> [ ]
>> [ m7 m9 + m3 m9 + m4 m8 + m1 m7 + m2 m6 + m1 m3 ]
>> [ m3 m8 + m6 m7 + m4 m5 + m2 m5 + m1 m4 + m1 m2 ]
>> [ ]
>> Col 2 = [ 2 ]
>> [ 2 (m6 m8 + m5 + m2 m4) ]
>> [ ]
>> [ m8 m9 + m6 m9 + m5 m8 + m2 m7 + m5 m6 + m3 m4 ]
>> [ m7 m9 + m3 m9 + m4 m8 + m1 m7 + m2 m6 + m1 m3 ]
>> [ ]
>> Col 3 = [ m8 m9 + m6 m9 + m5 m8 + m2 m7 + m5 m6 + m3 m4 ]
>> [ ]
>> [ 2 ]
>> [ 2 (m9 + m6 m8 + m3 m7) ]
>>
>> if i type in:
>>
>> (%i2) eigenvalues(B);
>>
>> nothing happens. I mean nothing. I can still type, but i don't get any
>> output. I i want to kill the process, there is no process to kill. Also,
>> i cannot type in any new command. There is no promt. So i have to restart.
>> Now, maybe this is to complicated. So i did:
>>
>> (%i1) C:matrix([2*(m1*m1+m2*m4+m3*m7),2,3],[4,5,6],[7,8,9]);
>> (%i2) A:eigenvalues(C);
>>
>> i get:
>> sqrt(3) %i 1 - 3/2 4 4
>> (%o2) [[(- ---------- - -) expt(3 sqrt(- 3328 m3 m7
>> 2 2
>> 3 2 3 3
>> - (13312 m2 m3 m4 + (13312 m1 - 53184) m3 ) m7
>> 2 2 2 2 2
>> - (19968 m2 m3 m4 + (39936 m1 - 159552) m2 m3 m4
>> 4 2 2 2
>> + (19968 m1 - 159552 m1 + 351300) m3 ) m7
>> 3 3 2 2 2
>> - (13312 m2 m3 m4 + (39936 m1 - 159552) m2 m3 m4
>> 4 2
>> + (39936 m1 - 319104 m1 + 702600) m2 m3 m4
>> 6 4 2 4 4
>> + (13312 m1 - 159552 m1 + 702600 m1 - 519140) m3) m7 - 3328 m2 m4
>> 2 3 3 4 2 2 2
>> - (13312 m1 - 53184) m2 m4 - (19968 m1 - 159552 m1 + 351300) m2 m4
>> 6 4 2 8
>> 6
>> - (13312 m1 - 159552 m1 + 702600 m1 - 519140) m2 m4 - 3328 m1 +
>> 53184 m1
>> 4 2 3 3
>> - 351300 m1 + 519140 m1 - 274413)/2 + (16 m3 m7
>> 2 2
>> + m2 (48 m3 m4 m7 - 336 m3 m4 m7 - 762 m4)
>> 2 2 2 2 2
>> + m1 (48 m3 m7 + m2 (96 m3 m4 m7 - 336 m4) - 336 m3 m7 + 48 m2 m4
>> - 762)
>> 2 2 2 2 2 4
>> - 168 m3 m7 + m2 (48 m3 m4 m7 - 168 m4 ) + m1 (48 m3 m7 + 48 m2 m4
>> - 168)
>> 3 3 6 1
>> - 762 m3 m7 + 16 m2 m4 + 16 m1 + 9601)/54, -)
>> 3
>> sqrt(3) %i 1 2 2
>> + (---------- - -) (4 m3 m7 + m2 (8 m3 m4 m7 - 28 m4)
>> 2 2
>> 2 2 2 4
>> + m1 (8 m3 m7 + 8 m2 m4 - 28) - 28 m3 m7 + 4 m2 m4 + 4 m1 + 292)
>> - 3/2 4 4 3
>> /(9 expt(3 sqrt(- 3328 m3 m7 - (13312 m2 m3 m4
>> 2 3 3 2 2 2
>> + (13312 m1 - 53184) m3 ) m7 - (19968 m2 m3 m4
>> 2 2 4 2
>> 2 2
>> + (39936 m1 - 159552) m2 m3 m4 + (19968 m1 - 159552 m1 + 351300) m3
>> ) m7
>> 3 3 2 2 2
>> - (13312 m2 m3 m4 + (39936 m1 - 159552) m2 m3 m4
>> 4 2
>> + (39936 m1 - 319104 m1 + 702600) m2 m3 m4
>> 6 4 2 4 4
>> + (13312 m1 - 159552 m1 + 702600 m1 - 519140) m3) m7 - 3328 m2 m4
>> 2 3 3 4 2 2 2
>> - (13312 m1 - 53184) m2 m4 - (19968 m1 - 159552 m1 + 351300) m2 m4
>> 6 4 2 8
>> 6
>> - (13312 m1 - 159552 m1 + 702600 m1 - 519140) m2 m4 - 3328 m1 +
>> 53184 m1
>> 4 2 3 3
>> - 351300 m1 + 519140 m1 - 274413)/2 + (16 m3 m7
>> 2 2
>> + m2 (48 m3 m4 m7 - 336 m3 m4 m7 - 762 m4)
>> 2 2 2 2 2
>> + m1 (48 m3 m7 + m2 (96 m3 m4 m7 - 336 m4) - 336 m3 m7 + 48 m2 m4
>> - 762)
>> 2 2 2 2 2 4
>> - 168 m3 m7 + m2 (48 m3 m4 m7 - 168 m4 ) + m1 (48 m3 m7 + 48 m2 m4
>> - 168)
>> 3 3 6 1
>> - 762 m3 m7 + 16 m2 m4 + 16 m1 + 9601)/54, -))
>> 3
>> Universal error handler called recursively (:ERROR NIL
>>
>> CONDITIONS::CLCS-UNIVERSAL-ERROR-HANDLER
>> "" "Couldn't protect")
>> Universal error handler called recursively (:ERROR NIL
>>
>> CONDITIONS::CLCS-UNIVERSAL-ERROR-HANDLER
>> "" "Couldn't protect")
>> Maxima encountered a Lisp error:
>>
>> Error in CONDITIONS::CLCS-UNIVERSAL-ERROR-HANDLER [or a callee]: Caught
>> fatal error [memory may be damaged]
>>
>> Automatically continuing.
>> To reenable the Lisp debugger set *debugger-hook* to nil.
>>
>> So what are the problems?
>>
>> Bernhard
>> _______________________________________________
>> Maxima mailing list
>> Maxima at math.utexas.edu
>> http://www.math.utexas.edu/mailman/listinfo/maxima
>>
>
--
---------------------------------------------------------------------------------------
Dipl. Phys. Bernhard Stoevesandt
ForWind + AG TWiSt
Fakult?t V
Carl-von-Ossietzky Universit?t Oldenburg
Carl-von-Ossietzky-Str.9
26111 Oldenburg
Tel: 0441/798-3577 Fax:0441/798-3579
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