[Scilab-users] The numderivative function

[Samuel Gougeon]

Le 18/11/2017 à 22:01, Hermes a écrit :
> Hi;
> The numderivative function consumes a lot of time in the calculations.
> In the following script I show two options for my "odes" function
> In one of them I use the numderivative function; and the calculation is
> extended by 9 minutes. And in the other I use the Jacobian determinant of
> the function, for each variable, obtained in wxMaxima. And the calculation
> is a few, few, seconds.
> I am interested in using the function with numderivative, and very similar
> to how I have developed it, since it allows me to use it for systems of more
> equations.

Your script makes Scilab 6.0.0 crashing every time it is run => trials 
done only on 5.5.2

  * I get *145 s* by default when numderivative() is called as usual
    from its library.
    Without numderivative(), i get *1.97 s*.
  * After exec(SCI+"/modules/optimization/macros/numderivative.sci",-1),
    this time decreases down to *45 s *only. This is unlikely proper to
    numderivative(). 5.5.2 looks to miss an optimization. For the time
    being, no way to test this on 6.0.0.
  * Your script calls numderivative() ~57000 times.
  * Profiling  numderivative() and its dependencies shows that
    numderivative_evalf() spends a lot of time.
  * Replacing execstr(.., "errcatch") in numderivative_evalf() with
    try/catch, we get***38 s*
  * Then, mainly, vectorizing the function to derivate in order to
    accept x with N columns instead of only 1, and changing
    numderivative() in order to be able to work with this new vectorized
    profile, we get *29 s*.

Improving numderivative() in order to be fully able to work with 
vectorized functions should be possible, but then

  * at first sight it will be less easy to keep it able to run with
    functions that are NOT vectorized (=> back-compatibility issue)
  * The jacobian would become an hypermatrix (OK)
  * The hessian would get up to 4 dimensions

You may post a report on bugzilla in order to point numderivative 
slowness() (if it is not already reported)(Bugzilla is currently off, 
taking its week-end).

Regards

Samuel Gougeon


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