On Wed, Jun 1, 2011 at 11:32 AM, B Saunders <saund...@udel.edu> wrote: > >> >> When I wrote this code in 2007, for some range of matrix sizes and >> bitsizes it was the fastest code in the world (even solidly beating >> Magma, which was the fastest before)... mainly since IML is so damned >> good. I don't know what the current situation is. >> >> -- William >> >> > LinBox now has a Dixon based solver that I understand to be substantially > similar to IML (including copy of key ideas in the IML implementation). > Also, we have just reworked Wan's numeric-symbolic solver so that it is much > more robust. Some example timings are given in [1]. For example, on a full > row rank 500 by 501 integer matrix with entries random in (-100, 100), a > null space vector is computed in 1.09 sec using Dixon and 0.931 sec using > numeric-symbolic iteration.
I'm really glad that Linbox now has a Dixon solver! For completeness of this thread, I'll try the same benchmark with Sage (=IML). On my OS X core i7 2.6Ghz laptop (which uses the system ATLAS), this benchmark takes 0.74 seconds. sage: A = random_matrix(ZZ,500,501,x=-100,y=100) sage: time V = A.right_kernel() CPU times: user 0.82 s, sys: 0.04 s, total: 0.86 s Wall time: 0.74 s sage: V.dimension() 1 On my Intel Xeon 2.6Ghz Linux server (single threaded ATLAS): sage: A = random_matrix(ZZ,500,501,x=-100,y=100) sage: time V = A.right_kernel() CPU times: user 2.47 s, sys: 0.03 s, total: 2.50 s Wall time: 2.53 s On my Opteron 2.6Ghz Linux server (single threaded ATLAS): sage: A = random_matrix(ZZ,500,501,x=-100,y=100) sage: time V = A.right_kernel() CPU times: user 0.87 s, sys: 0.02 s, total: 0.89 s Wall time: 0.98 s This is all really just timing IML, plus conversions, plus IML's use of ATLAS. Here's a bigger one (on the 2.6Ghz opteron): sage: A = random_matrix(ZZ,1000,1001,x=-100,y=100) sage: time V = A.right_kernel() CPU times: user 5.59 s, sys: 0.07 s, total: 5.66 s Wall time: 5.66 s -- William > > -dave > > [1] S, Wood, and Youse, Symbolic-Numeric Exact Rational Linear System > Solver, to appear in ISSAC'11 next week. > > -- > You received this message because you are subscribed to the Google Groups > "linbox-use" group. > To post to this group, send email to linbox-...@googlegroups.com. > To unsubscribe from this group, send email to > linbox-use+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/linbox-use?hl=en. > -- 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
