On Apr 23, 2009, at 12:09 AM, Stan Schymanski wrote: > Hi Jason, > > It think that find_root does use fast_float, but it compiles the > fast_float function every time it is called. This makes it very > slow if > I want to find the roots of f for all values of b between say -3 > and -1. > Therefore, I would like to be able to compile a fast_float function of > e.g. 'b' and 'x', then pluck in different values for b and call > find_root repeatedly to find the roots. > The partial trick did it, but it would be great if this could be made > more intuitively and part of fast_float, as you suggested.
Creating fast_float (or, now, fast_callable) objects should be much faster with the new symbolics. > Since fast_float can be defined for an arbitrary number of > variables, I > think that it should be possible to generate a fast_float > expression for > any symbolic equation, and if this was a callable function or even > worked with .subs() it would be a huge enhancement. A partial function application would be a great thing to add to this class, though I'm not sure how much effort should be put into simplification (probably just change inputs to constants). > > Thanks again, > > Stan > > Jason Grout wrote: >> Unfortunately, I don't that will ever work, as Python does not do >> automatic currying (did I use the right term?). The list >> comprehension >> in python is a special case, where the function is not evaluated >> until >> you have a value for x. However, in the case of plot, the >> function ff >> is evaluated first, and since x is missing, there is an error. >> >> However, in your case, it would probably make a lot more sense to >> do this: >> >> f = a*x^3+b*x^2+c*x+d >> plot(f.subs(a=1,b=2,c=3,d=4), (x, 0, 6)) >> >> This uses the fact that f is a symbolic expression, then the subs >> command substitutes in variables and returns another expression. >> fast_float is called by plot automatically. >> >> If find_root doesn't automatically use fast_float (it should!), >> then you >> could do something like: >> >> f = a*x^3+b*x^2+c*x+d >> find_root(fast_float(f.subs(a=1,b=2,c=3,d=4), 'x'), (x, 0, 6)) >> >> (or whatever the syntax is). >> >> Again, this only works for Sage symbolic expressions... >> >> Sorry I didn't think of this earlier. For general python >> functions, you >> could use the partial trick we talked about. >> >> It might make sense to have some sort of partial evaluation available >> for fast_float functions, so if a few arguments were given, it >> behaved >> like the partial trick above. >> >> Thanks, >> >> Jason >> >> >> >>> >> >> > > -- > ________________________________________ > > Stan Schymanski > Scientist > Max Planck Institute for Biogeochemistry > Postfach 10 01 64 > D-07701 Jena > > Phone: +49.3641.576264 > Fax: +49.3641.577274 > WWW: http://www.bgc-jena.mpg.de/~sschym > > Biospheric Theory and Modelling Group > http://www.bgc-jena.mpg.de/bgc-theory/ > _________________________________________ > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
