On Mon, Jul 1, 2013 at 5:27 AM, David Ingerman <daviddavif...@gmail.com> wrote: > On Monday, July 1, 2013 2:06:54 AM UTC-7, Harald Schilly wrote: >> On Monday, July 1, 2013 10:45:36 AM UTC+2, David Ingerman wrote: The >> following matrix operation produces wrong answer in online Sage: >> M=matrix(RR,[[7,3,10,13],[1,1,2,2],[1,2,3,4],[1,3,5,7]]);det(M);invM=M^(-1);invM*M;det(invM) >> >> RR stands for the "real numbers" with the usual 53bits of precision, e.g. >> 5.123957322…. >> QQ are rational numbers where two large integers build up each number, >> e.g. 41000041/333000333000333000333000333000333000333 >> Therefore, QQ has a much higher precision … but is much slower and uses more >> memory. >> >> In your case, the lack of precision in RR causes you troubles and you have >> to find a way to pose the problem you want to solve differently. You cannot >> rely on QQ, because in bad cases, the expressions blow up and eat all your >> memory. More generally, this is not a Sage related problem, but related to >> all calculations your are doing "natively" with your CPU. >> >> To see in advance when this happens, you have to calculate the >> conditional number of the matrix. I think that's only in numpy (or I >> haven't found it). >> >> sage: M=matrix(RR,[[7,3,10,13],[1,1,2,2],[1,2,3,4],[1,3,5,7]]) >> sage: import numpy as np >> sage: np.linalg.cond(M) >> 104.85355762315329 >> >> http://en.wikipedia.org/wiki/Condition_number >> >> Here are some decomposition methods that might help: >> >> http://en.wikipedia.org/wiki/Matrix_decomposition >> >> H > > But this is a very small matrix and conditional number is not large...
Using RDF is better: sage: M=matrix(RDF,[[7,3,10,13],[1,1,2,2],[1,2,3,4],[1,3,5,7]]);det(M);invM=M^(-1);invM*M;det(invM) -7.0 [ 1.0 0.0 0.0 -8.881784197e-16] [ 0.0 1.0 0.0 -8.881784197e-16] [ 4.4408920985e-16 0.0 1.0 8.881784197e-16] [-5.55111512313e-17 -2.77555756156e-16 -1.66533453694e-16 1.0] -0.142857142857 > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/groups/opt_out. > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
