On Thursday, June 2, 2011, John Cremona <john.crem...@gmail.com> wrote: > 1. Are the matrices in these tests dense?
Yes, very. > 2. How do the timings grow with the dimension? I do not know. > > 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 > -- 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
