[sage-support] Re: Completely confused about simple Sage matrix operation error
On Monday, July 1, 2013 1:45:36 AM UTC-7, 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) If one changes RR to QQ the answers turn correct. Or it is enough to change one corner matrix entry to: M=matrix(RR,[[8,3,10,13],[1,1,2,2],[1,2,3,4],[1,3,5,7]]);det(M);invM=M^(-1);invM*M;det(invM) to get right answers. How can one be sure about Sage linear algebra w/this problem? Am I missing something obvious? It took me several hours to zero in on this bug from a large program. Ant feedback will be appreciated. 'Sage Version 5.4, Release Date: 2012-11-09' -- 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.
[sage-support] Re: Completely confused about simple Sage matrix operation error
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. 4141/333000333000333000333000333000333000333 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 -- 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.
[sage-support] Re: Completely confused about simple Sage matrix operation error
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. 4141/333000333000333000333000333000333000333 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... -- 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.
Re: [sage-support] Re: Completely confused about simple Sage matrix operation error
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. 4141/333000333000333000333000333000333000333 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 [ 1.00.00.0 -8.881784197e-16] [ 0.01.00.0 -8.881784197e-16] [ 4.4408920985e-160.01.08.881784197e-16] [-5.55111512313e-17 -2.77555756156e-16 -1.66533453694e-161.0] -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.
Re: [sage-support] Re: Completely confused about simple Sage matrix operation error
I think problem is actually due to the inverse using a non-numerically stable echelon form algorithm for inexact fields. For example, if you using matrices over RDF: 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) you don't get this problem. My guess is that if we implemented something like partial pivoting for inexact fields. --Mike --Mike On Mon, Jul 1, 2013 at 10:06 AM, Harald Schilly harald.schi...@gmail.com 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. 4141/333000333000333000333000333000333000333 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 -- 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.
