>> I'm using fractions.Fraction as entries in a matrix because I need to >> have very high precision and fractions.Fraction provides infinite >> precision . . . >> >> Probably it doesn't matter but the matrix has all components non-zero >> and is about a thousand by thousand in size. > > I wonder how big the numerators and denominators in those > fractions are going to get during the matrix inversion. Would > it be surprising if the elements of the inverse matrix had > numerators and denominators a million times longer than the > original matrix?
I've checked this with Maple for matrix size 150 x 150 and the numerators and denominators do get pretty long. But that's okay as long as it is kept exact. The whole story is that I have a matrix A and matrix B both of which have rational entries and they both have pretty crazy entries too. Their magnitude spans many orders of magnitude, but inverse(A)*B is an okay matrix and I can deal with it using floating point numbers. I only need this exact fraction business for inverse(A)*B (yes, a preconditioner would be useful :)) And I wouldn't want to write the whole matrix into a file, call Maple on it, parse the result, etc. So after all I might just code the inversion via Gauss elimination myself in a way that can deal with fractions, shouldn't be that hard. Cheers, Daniel -- Psss, psss, put it down! - http://www.cafepress.com/putitdown -- http://mail.python.org/mailman/listinfo/python-list
