[ADMB Users] Interpolation while optimising

[Richard Methot]

When I need to join two discontinuous functions in a differentiable way, 
I do something like:

   f1(x)  for x<X
  f2(x)  for x>=X
  steep=10.;  // or larger value depending on expected magnitude of x-X
  join(x) =1./(1.+mfexp(steep*(x-X))));  // so is steep and centered on X

 // composite function is then
   f(x) = f1(x)*join(x) + f2(x)*(1.-join(x));

  this is not perfect and depending on the slope of f1 and f2 near X may 
result in a small wrinkle in the composite function, but it has served 
my purposes.

Rick Methot

Mark Payne wrote:
> Hi,
>
> I have been wondering about this for quite some time. What is the "correct" way to do  interpolation in ADMB, so that you don't run into problems with discontinuous gradients? I see that there are a series of cubic spline interpolation functions in there, spine(), splint() but that they are also marked for replacement. Is there something else in the works or is this the best approach?
>
> Cheers,
>
> Mark
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