1. Are the matrices in these tests dense? 2. How do the timings grow with the dimension?
John On Thu, Jun 2, 2011 at 1:14 AM, William Stein <wst...@gmail.com> wrote: > 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 > -- 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
