On 10/26/2012 09:17 PM, Jason Grout wrote:
On 10/26/12 6:25 AM, Volker Braun wrote:
The matrix is over RR (MPFR software floats). M.change_ring(RDF).det()
gives the right answer.
There is no special det() implementation for RR, we compute the
Hessenberg form and from that characteristic polynomial. Sage uses
Gaussian elimination to compute the Hessenberg form, and this is known
to be numerically unstable in unfavorable cases
(http://www.jstor.org/stable/2004967). I guess your matrix is one of
these cases; there is no overflow, its a numerical instability.
Yep. If you're doing computations with numerical matrices, you should
always use RDF or CDF matrices. In this case, RDF/CDF matrices use LU
factorization and then compute the determinant from that, using the
scipy.linalg.determinant function (which in turn uses LAPACK).
Thanks,
Jason
That raises a problem that I see with the current use of RR. What is the
reason behind using RR instead of RDF/CDF by default? I have been going
through the various methods available when doing M.<tab>. A lot more
methods have been implemented for RDF compared to RR. Although a huge
range of methods seem "available", most of the interesting ones don't
work for RR. Quite a number of them, but less than RR, also don't work
for RDF.
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