Thanks for the implementation. It would have taken me a long time to
figure that out. It appears the "ev" (eigenvectors) are returned, with
the last one being normalized to have entries of unity.
On Mar 31, 5:32 am, achrzesz <achrz...@wp.pl> wrote:
> Compare such version
>
> precision_digits=100
> nop=5 # rank of matrix
> MS_nop_comp=MatrixSpace(ComplexField(precision_digits),nop,nop)
> tmat=MS_nop_comp.random_element()
> ttdag=tmat*tmat.conjugate().transpose()
> m=gp(ttdag)
> gp('default(realprecision,100)')
> ev=gp.mateigen(m).sage()
> print ev[:-1]
>
> On 31 Mar, 12:14, achrzesz <achrz...@wp.pl> wrote:
>
>
>
>
>
>
>
> > #NOT CHECKED
> > precision_digits=100
> > 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()
> > m=gp(ttdag)
> > gp('default(realprecision,100)')
> > ev=gp.mateigen(m).sage()
> > print ev[:-1]
>
> > On 31 Mar, 11:47, achrzesz <achrz...@wp.pl> wrote:
>
> > > Since GP/PARI default precision is 38 (on my system)
> > > (and I dont know how to set \p 100 from sage)
> > > it would be probably better to replace
> > > precision_digits=30
> > > by
> > > precision_digits=38
>
> > > On 30 Mar, 23:03, achrzesz <achrz...@wp.pl> wrote:
>
> > > > # NO WARRANTY
> > > > 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()
> > > > m=gp(ttdag)
> > > > ev=gp.mateigen(m).sage()
> > > > print ev[:-1]
>
> > > > On 30 Mar, 22:34, Ben123 <ben.is.loca...@gmail.com> wrote:
>
> > > > > 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 <achrz...@wp.pl> 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 <jason-s...@creativetrax.com> 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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