Hello. Thank you for showing me the equivalent process in PARI/GP. I
think this implies I need to transfer the complex Hermitian matrix
into gp_console() to find eigenvectors, then transfer them back to
Sage. I'll update this post when I figure out how to do that.
In the mean time, if someone has a simple way of doing that please let
me know. My updated Sage code lacks the last step.
precision_digits=30
nop=5 # rank of matrix
MS_nop_comp=MatrixSpace(ComplexField(precision_digits),nop,nop)
tmat=MS_nop_comp(0) # zero-ize the values
ttdag=MS_nop_comp(0)
for a in range(nop):
for b in range(nop):
tmat[a,b]=random()+I*random()
ttdag=tmat*tmat.conjugate().transpose() # get a Hermitian matrix
# Find eigenvectors of ttdag in PARI/GP, pass results back to sage
Thanks for the help,
On Mar 30, 2:45 pm, achrzesz <[email protected]> wrote:
> sage: gp_console()
> ? \p 100
> realprecision = 115 significant digits (100 digits displayed)
> ? a=matrix(3,3,k,m,random(1.0))+I*matrix(3,3,k,m,random(1.0));
> ? m=a*conj(a)~;
> ? mateigen(m)
>
> On 30 Mar, 18:20, Jason Grout <[email protected]> wrote:
>
>
>
>
>
>
>
> > On 3/30/11 10:44 AM, Ben123 wrote:
>
> > > Hello. I've written a sage program which produces a complex matrix. I
> > > want to find the eigenvalues and associated eigenvectors. I also want
> > > to use arbitrary precision. I don't care about speed. I've read old
> > > posts to this group on this topic, but am unsure how to proceed.
> > > Currently I'm using the following method and using sage 4.6.1
>
> > > precision_digits=30
> > > nop=5 # rank of matrix
> > > MS_nop_comp=MatrixSpace(ComplexField(precision_digits),nop,nop)
> > > tmat=MS_nop_comp(0) # zero-ize the values
> > > ttdag=MS_nop_comp(0)
>
> > > # I realize there are more efficient methods of getting a random
> > > matrix, but this is explicit
> > > for a in range(nop):
> > > for b in range(nop):
> > > tmat[a,b]=random()+I*random()
>
> > > ttdag=tmat*tmat.conjugate().transpose() # get a Hermitian matrix
> > > print 'ttdag is'
> > > print ttdag
> > > print 'eigenvalues of ttdag are '
> > > print ttdag.eigenvalues() # eigenvalues of Hermitian matrix should be
> > > real. Imaginary component is due to finite precision.
> > > # I can get better precision here by increasing precision_digits
>
> > > #print ttdag.eigenmatrix_right()
> > > # IndexError: list index out of range
>
> > > print ttdag.eigenvectors_right()
> > > # this is not returning the eigenvectors, even when precision is
> > > increased to 500
>
> > > How can I find the eigenvectors of a complex Hermitian matrix with
> > > arbitrary precision?
>
> > One option: you might look at using the alglib library; at one time, the
> > author was writing a Sage interface, but that work has stalled for
> > several months. Alglib appears to have a python interface, though.
>
> > Alglib:http://www.alglib.net/
>
> > Rob Beezer's been doing some work on the numerical linear algebra in
> > Sage, so he also might have something to add...
>
> > Thanks,
>
> > Jason
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