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 -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
