Perhaps you could be more specific on what f90 tools in Maxima you could use. (Converting to python/ cython may be educational etc, but maybe not so likely to pay off soon.)
It is also possible to generate functions in Maxima itself that are compiled to machine language. If you declare variables to be fixnums, floats, etc, the code may be acceptably fast, though unlikely to be as fast as a good Fortran program. You can find some possibly useful papers by search on google for Galerkin Macsyma. A paper by Miola goes back to 1974. Good luck. RJF On Sep 4, 6:40 am, Guilherme <guito...@gmail.com> wrote: > Hello, > > I am using Sage for a while, but I am still a newbie. > > I am an engineer studying nonlinear dynamical systems. I do the > modeling by means of symbolic manipulation (Galerkin approximation) > but I need a numerical solver to time integrate the model. On another > tread I mentioned a spkg I made for Assimulo so that I can use the > Sundials suite of numerical solvers, particularly IDA. > > Everything is working fine, but slow. > > The size of the symbolic system can be changed as the order of > approximation goes higher. But the symbolic system remains static > during integration, just the variables are substituted at every time- > step. > > The bottleneck is the substitution of state-variables into the > symbolic system to turn it into floats which is consumed by the solver > at every time-step. > > The solver needs a residual (and a Jacobian) functions having > numpy.array as input and output. > > I made some experiment streaming out the symbolic system into a > Fortran file. I used Maxima's f90 function, but it is very limited. I > had to to plenty of vim substitutions to shape it into a usable code. > > By using this approach on the residual and jacobian functions I has > able to cut the run-time from 30min to 30sec on a complicated enough > model. Every entry on my symbolic matrices are very long products of > polynomials over the state-variables and floating-point > coefficients... The Fortran files easily fills a bunch of pages... I > am not sure how Cython could help here. > > I think fast_float and fast_callable cannot handle SR matrices and > vectors. Right? > > Hoping to make the case a bit clearer, I made a quick example on this > worksheet:http://www.sagenb.org/home/pub/3115/ > > I think that having an automated symbolic(matrix/vector)-to-Fortran > (f2py) translator for such numerical intensive evaluations wouldn't > hurt. > > Therefore I am looking for instructions on how you guys would proceed > do write such translator... if not yet available. > Any thoughts or alternatives? > > Regards, > Guilherme -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
