[Scilab-users] The numderivative function

[Samuel Gougeon]

Le 18/11/2017 à 22:38, Samuel Gougeon a écrit :
> 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
>

This is assuming that the architecture of the current numderivative() 
implementation is kept.
A complete refactoring would be possible. But used for ode(), IMO this 
would not save much of the time spent, since anyway ode() calls the 
function for a single point.

Beside the lack of vectorization, the order is not free. For instance, 
order=3 needs to call numderivative() twice, for instance with order=2 
then with order=1. This limitation is a bit strange.

SG

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