On Tuesday, August 25, 2015 08:37:34 AM Spencer Lyon wrote: > That’s right. The ODE solver does give me the first derivative. The problem > is that I need the first two derivatives!
If the ODE solver support DualNumbers, you may be able to extract the derivative-of-the-derivative from epsilon(derivative). --Tim > > > > // Spencer > > From: Mauro <[email protected]> > Reply: [email protected] <[email protected]>> > Date: August 25, 2015 at 8:31:50 AM > To: [email protected] <[email protected]>> > Subject: Re: [julia-users] Re: ANN: JuliaDiff -- differentiation tools in > Julia > > About the data, it should be pretty smooth. It is generated as the output > > of applying a stiff ODE solver where the domain is covered by 10,000 > > points > > on the unit interval. I've tried using all 10,000 (x, y) points. I was > > concerned about overfitting, so I also tried thinning the data by taking > > every `n`th point, but that didn't help. > > The ODE solver should, at least internally, have an estimate of the > derivative. Maybe there is a way to get at that? Otherwise, if the ODE > is in the form dx/dt = F(x,t) then just plug your x and t into that. If > it is of the form 0=F(dx/dt,x,t) then you could solve the system of > equations for dx/dt for all x,t. > > > That's a good point regarding regression or Bayesean techniques. I'll > > definitely consider that. > > > > Thanks again for the comments! > > > > On Tuesday, August 25, 2015 at 5:45:08 AM UTC-4, Christoph Ortner wrote: > >> P.S.: I think your problem is unrelated to `julia-diff` which deals with > >> a > >> completely different class of differentiation algorithms.
