Harald Schilly wrote: > This is from the notebook's "report a problem" bugtracker, there are > *two* different problems reported. Machine is Linux/32bit on Sage > 4.0.2. > > > Quote: > > different formatting of output of eigenvectors_left depending on which > space the matrix is over A = matrix(QQ,3,3,range(9)) > B = matrix(RDF,3,3,range(9)) > > A.eigenvectors_left() > [(0, [ > (1, -2, 1) > ], 1), (-1.348469228349535?, [(1, 0.3101020514433644?, > -0.3797958971132713?)], 1), (13.34846922834954?, [(1, > 1.289897948556636?, 1.579795897113272?)], 1)] > i.e. a list (eigenvalue, [corresponding eigenspace], multiplicity) > > whereas > B.eigenvectors_left() > ([13.3484692283, -1.34846922835, -1.1327908706e-15], [ 0.440242867236 > 0.567868371314 0.695493875393] > [ 0.897878732262 0.278434036822 -0.341010658618] > [ 0.408248290464 -0.816496580928 0.408248290464]) > i.e. a list of eigenvalues and then a matrix whose rows are the > eigenvectors > > this is a bit confusing and it would be nicer if the output formatting > was the same in both cases.
Yep, I agree. That's been on my TODO list for a while. The difference is that scipy computes the RDF eigenvectors, and its format is not massaged into the more normal Sage format. Similar observations apply to the other RDF eigen functions. I hope someone beats me to it :). > > ******************* > second one: > ******************* > > Also, I noticed that the eigenvalues for the matrix over RDF are a bit > inaccurate, leading to very different eigenvectors. Using > B.charpoly.roots() > [(-1.34846922835, 1), (0.0, 1), (13.3484692283, 1)] > the zero eigenvalue is actually zero > > could the output of the eigenvectors_left method be standardised over > the different fields? (same goes for eigenvectors_right, of course) > > About the values of eigenvalues and -vectors, is that an intrinsic > problem with using RDF or can it be improved? The RDF uses scipy, which in turn uses the standard fortran libraries to compute these things. We could maybe make a bigger cutoff for deciding when the returned value is zero. But I think we still ought to call scipy/fortran for the RDF functions. In general, RDF things are machine-precision things, and that is what scipy/fortran specializes in. Note that there is also a speed difference: sage: %timeit B.charpoly().roots() 1000 loops, best of 3: 764 µs per loop sage: %timeit B.eigenvalues() 1000 loops, best of 3: 382 µs per loop sage: C = random_matrix(RDF,100) sage: %timeit d=C.eigenvalues() 10 loops, best of 3: 126 ms per loop sage: %timeit d=C.charpoly().roots() 10 loops, best of 3: 180 ms per loop Interestingly, it also goes the other way for certain matrices: sage: D = matrix(RDF,100,range(100^2)) sage: %timeit d=D.eigenvalues() 10 loops, best of 3: 111 ms per loop sage: %timeit d=D.charpoly().roots() 10 loops, best of 3: 2.84 ms per loop Thanks, Jason --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
