>>>> 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'>
This sounds like a good idea! Cheers, Daniel -- Psss, psss, put it down! - http://www.cafepress.com/putitdown -- http://mail.python.org/mailman/listinfo/python-list
