On Dec 9, 2008, at 5:19 PM, Tim Lahey wrote: > On Dec 9, 2008, at 7:55 PM, William Stein wrote: > >>> I ran across this in some timestepping code I wrote for a ODE solver >>> for systems of second order ODEs. The general trick I used is to set >>> the first n-1 terms based upon the formula and set the final one to >>> the endpoint. It means that the final one may be shorter, but that >>> way >>> it always ends at the set endpoint. >> >> Any chance you could dive in and fixe srange? It's a pure Python >> function in >> sage/misc/misc.py >> > > That's an awfully complicated function for what should be fairly > simple. > I'm not entirely sure what is being done is some of that code so I > don't > know if I want to touch it.
Go for it, go off the docstring and examples rather than the code. > What about the other similar functions? They should probably be fixed too. > From my MATLAB code, the timestep loop looks like (using MATLAB > syntax): > > % Iterate over timesteps > while (t<tfinal) & (t + h >t) > > % Ensure we end at tfinal, this may shorten the last timestep > if t + h > tfinal, h = tfinal - t; end > t = t + h; > > end > > Note the trick is checking that that t+h > tfinal. That checks to > see if > we pass the endpoint. Also, with the loop, we're also checking to make > sure that the step increases t. This is to prevent looping through if > we're exactly at the endpoint. There is probably a better way of doing > this, > but with floats checking equality is problematic. Yeah. It's unclear exactly how "include endpoint" is supposed to behave in the inexact case. Sometimes step*k == (b-a) - epsilon, and sometimes step*k == (b-a) + epsilon. For example sage: RR(1/49) * 49 < 1 True so should srange(0, 1, RR(1/49)) return the RR(1/49)*49 as the last value? Should srange(0, 1, RR(1/49), include_endpoint=True) return RR (1/49)*49 and then 1? This is all assuming that a+n*b == a + b + ... + b, which is often false (but it's almost certainly not worth the speed penalty to compute it via multiplication). - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
