On Thu, Jan 26, 2012 at 6:12 AM, Jason Grout <jason-s...@creativetrax.com> wrote: > On 1/26/12 7:54 AM, Marco Streng wrote: >> >> 2012/1/26 Jason Grout<jason-s...@creativetrax.com>: >>> >>> That's part of the problem pointed out in an earlier message---our RR >>> matrices really are pretty bad for numerical things, but RDF matrices are >>> the way to go (the RDF matrices use standard numerical algorithms for the >>> most part, whereas RR matrices use naive algorithms that can be really >>> bad >>> and slow). This should be fixed, but for right now, RR matrices don't >>> seem >>> to be all that useful compared to RDF matrices. >> >> >> Is RDF always better than 53-bit RR in this way? If so, perhaps >> "RealNumber" or the preparser could be changed to use RDF if the >> precision is sufficiently small. Most users typing 12.345 will want >> the fastest implementation and not something generic. > > > No, this is a linear algebra problem, not a general problem in Sage. Usually > RR is better mathematically than RDF.
For example, with RDF the largest allowed number is actually pretty tiny: sage: a = 10.0^1000; a 1.00000000000000e1000 sage: type(a) <type 'sage.rings.real_mpfr.RealNumber'> sage: float(a) inf I've been hit by this many times when developing algorithms. For example, for some exact linear algebra work I was doing with Clement Pernet, we developed an algorithm, and it wasn't possible to compute the relevant bounds for big input using machine doubles, i.e., using RDF. I found it easy to implement that part of the algorithm, because Sage has mpfr (i.e., RR), but Clement had to redesign that whole part of the algorithm in order to properly implement it in Linbox, because Linbox does (or didn't) depend on mpfr. -- William > > Thanks, > > Jason > > > > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
