# [SciPy-user] [Fwd: Re: Computing eigenvalues by trace minimization]

dmitrey openopt@ukr....
Fri Jun 29 07:11:16 CDT 2007

```Nils Wagner wrote:
> dmitrey wrote:
>
>> As for your code, I didn't make any changes. You need just specify
>> desired contol and then make funtol, xtol, gradtol small enough. Maybe,
>> in future I'll implement something more appropriate for to have exitflag
>> positive.
>>
>> BTW for small-scaled problem using df, dh didn't yields any benefits
>> only for nVars = 100 I've got ~6 sec with df, dh provided and 11 sec
>> without the ones.
>> for your nVars=10 time elapsed is almost the same.
>>
>> HTH, D.
>>
>> Nils Wagner wrote:
>>
>>
>>
>>>
>>>
>>>
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>>
>  Hi Dmitrey,
>
> Thank you for your help. BTW, have you managed the installation of symeig ?
> http://mdp-toolkit.sourceforge.net/symeig.html
>
I have installed symeig ok
As for pysparse, 1st of all I went to sandbox/pysparse, run
sudo python setup.py install,
then
from pysparse import *
all works ok
HTH, D

> 1) you don't need to use .T in dot, it's executing automatically:
> f = lambda x: dot(x.T,dot(A,x)) # => dot(x,dot(A,x))
> h = lambda x: dot(x.T,dot(B,x))-1.0 # => dot(x,dot(B,x))-1.0
>
>
> Let us assume that we are interested in the smallest m eigenvalues
> instead of the smallest eigenvalue.
> Then you will need .T in case of rectangular matrices x. Therefore I
> an extension.
> #f = lambda x: trace(dot(x.T,dot(A,x))) # Version for m > 1
> #h = lambda x: dot(x.T,dot(B,x))-identity(m)
>
> from scipy import dot, rand
>
> n = 10
> m = 3
> A = rand(n,n)
> x = rand(n,m)
> res = dot(x.T,dot(A,x))
>
> Nils
>
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>
>
>

```