Re: [sage-devel] Re: Automatic Differentiation - Taylor Arithmetics

(Apologies for reviving this old thread, but since I saw a couple of mentions of ODE integration via Taylor's method in the mailing list archive, I thought that some people might be interested) We just released the latest version of our Taylor integrator heyoka.py: https://github.com/bluescarni/h

[sage-devel] Re: Automatic Differentiation - Taylor Arithmetics

Hi all, Yet another open source alternative: Taylor models are implemented in Julia (see TaylorModels.jl ), and this library offers validated integration of ODEs (disclaimer: i also contribute to this and related projects that use other methods

[sage-devel] Re: Automatic Differentiation - Taylor Arithmetics

Nisoli Isaia wrote: > I've seen that you wrote a sage interface for sollya, which > seems to take already take care of Taylor models. Indeed, though the Taylor models in Sollya may be a bit limited, and (if I understood right, but I'm really no expert here) have some performance issues. > Is So

[sage-devel] Re: Automatic Differentiation - Taylor Arithmetics

Dear Marc, I've seen that you wrote a sage interface for sollya, which seems to take already take care of Taylor models. Is Sollya already a part of Sage? Are there any plans of Sollya entering sage? Best wishes Isaia On Saturday, April 20, 2019 at 5:36:46 AM UTC-3, Marc Mezzarobba wrote: > > N

[sage-devel] Re: Automatic Differentiation - Taylor Arithmetics

You might be interested in this .. https://people.eecs.berkeley.edu/~fateman/papers/ADIL.pdf which is algorithm differentiation written in Lisp. Sage includes Lisp (underneath Maxima, for example) Manipulation of program source to produce other program source is routinely supported in Lisp, and

[sage-devel] Re: Automatic Differentiation - Taylor Arithmetics

You might be interested in taking a look at tides [1]. It is a library for integration of ODE's in high precission using precisely automatic differentiation and Taylor arithmetic. It doesn't use interval arithemtic (so, no certified computation), but maybe some ideas could be useful. The way it

Re: [sage-devel] Re: Automatic Differentiation - Taylor Arithmetics

Do you know how this (forward automatic differentiation implementation) will compare to autograd [1] or ForwardDiff.jl [2]? Can for example autograd be used as some sort of a backend? There is also the "tutorial implementation" autodidact [3] which seems relevant. Regards, TB [1] https://gi

[sage-devel] Re: Automatic Differentiation - Taylor Arithmetics

Thank you! I think I could start by exposing these ARB functions to SAGE, so that the interface is more complete, and then try to do the same for Real Interval. Best wishes Isaia On Monday, April 22, 2019 at 4:59:36 AM UTC-3, Marc Mezzarobba wrote: > > Nisoli Isaia wrote: > > P.=CBF[] > > x._s

[sage-devel] Re: Automatic Differentiation - Taylor Arithmetics

Nisoli Isaia wrote: > P.=CBF[] > x._sin_series(4) Indeed, I remembered wrong. Only a few of these arb functions are accessible from sage at this point. It is trivial to add more, though. The relevant files are src/sage/libs/arb/acb_poly.pxd src/sage/rings/polynomial/polynomial_complex_arb.pyx

[sage-devel] Re: Automatic Differentiation - Taylor Arithmetics

On Saturday, April 20, 2019 at 5:36:46 AM UTC-3, Marc Mezzarobba wrote: > > Nisoli Isaia wrote: > > I was planning in doing a Cython implementation of Forward automatic > > differentiation and > > Taylor arithmetics as in > > https://press.princeton.edu/titles/9488.html > > to use to implem

[sage-devel] Re: Automatic Differentiation - Taylor Arithmetics

Nisoli Isaia wrote: > I was planning in doing a Cython implementation of Forward automatic > differentiation and > Taylor arithmetics as in > https://press.princeton.edu/titles/9488.html > to use to implement a library for Sage with rigorous quadrature and > integration of ODE. This is very inter