The function might be much more complicated than that so that symbolic differentiation won't scale unlike automatic differentiation.
It might also be that I can't write down the function as a symbolic expression without going through a lot of extra work. The application I have in mind is applying a bunch of functions, additions and multiplications on intervals assigned to vertices and edges of a triangulation. This would be really easy to do with automatic differentiation (in fact, I already did an ad-hoc implementation). Symbolic integration and automatic differentiation are two different things! And there really are applications for the latter. On Friday, June 22, 2018 at 1:14:17 PM UTC-7, Matthias Goerner wrote: > > I have a function such as cos(x/y) and values for x and y and want to use > automatic differentiation (a la wikipedia article > <https://en.wikipedia.org/wiki/Automatic_differentiation#Automatic_differentiation_using_dual_numbers>) > > to find the value and derivatives with respect to x and y. Can this be done > easily in Sage, preferably using interval arithmetic? > > I was hoping for an object that I could use something like this: > > sage: A.<dx, dy> = AutomaticDifferentiationField(RDF, 2) > sage: x = 2.0 + dx > sage: y = 3.0 + dy > sage: f = cos(x,y) > sage: f > 0.785887260776948 -0.303099142275227 * dx + 0.137415511793275 * dy > sage: f.value() > 0.785887260776948 > sage: f.derivatives() > [-0.303099142275227, 0.137415511793275] > > And replacing RDF by RIF and setting x = RIF(1.99, 2.01) + dx, y = ... > would do it over interval arithmetic then. > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
