Daniel Fetchinson wrote: >>> I guess this is a question to folks with some numpy background (but >>> not necessarily). >>> >>> I'm using fractions.Fraction as entries in a matrix because I need to >>> have very high precision and fractions.Fraction provides infinite >>> precision (as I've learned from advice from this list). >> >> "Infinite" precision only for values that can be expressed as a fraction: >> >>>>> Fraction(2)**Fraction(1, 2) >> 1.4142135623730951 >>>>> type(_) >> <type 'float'> > > True, but I only need to add, multiply and divide my fractions in > order to end up with the entries in the matrix. > >>> Now I need to >>> calculate its inverse. Can numpy help in this regard? Can I tell numpy >>> that the inverse matrix should also have entries in >>> fractions.Fraction? Or numpy can only do floating point calculations? >> >> I tried it, and numpy.linalg.inv() converted the Fraction values to >> float. If you aren't concerned about efficiency it should be easy to do >> it yourself, in pure python. > > If there is no other way, that's what I'll try to do. > >> You could also ask on the numpy mailing list. >> >>> Probably it doesn't matter but the matrix has all components non-zero >>> and is about a thousand by thousand in size. >> >> Hmm, where did you get that million of exact fractions from? > > The million of exact fractions are coming from a recursion relation. > This recursion relation only adds, multiplies and divides numbers so > the end result is always a rational number. > >> If some real >> world data is involved the error introduced by the floating point >> calculation may be negligable in comparison with the initial measurement >> uncertainty. > > It's a mathematical problem so no uncertainty is present in the > initial values. And even if there was, if there are many orders of > magnitude differences between the entries in the matrix floating point > does not suffice for various things like eigenvalue calculation and > stuff like that.
It may be worthwhile to have a look at http://www.sagemath.org/ sage: Matrix([[1,2],[3,4]])**-1 [ -2 1] [ 3/2 -1/2] sage: a = Matrix([[1,2],[3,4]]) sage: b = Matrix([[1,2],[3,4]])**-1 sage: a*b [1 0] [0 1] sage: type(b[1,1]) <type 'sage.rings.rational.Rational'> Peter -- http://mail.python.org/mailman/listinfo/python-list
