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

[Nils Wagner]

dmitrey wrote:
> So, please update svn
> 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

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
have asked for
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