Re: [Gretl-devel] c code question

On Mon, 16 Oct 2017, Berend Hasselman wrote: Thanks, Berend, this is very helpful. The complex-step derivative looks very cool. It can certainly be very useful in many cases. However, it requires the function to be differentiated to (i) make sense for complex values and (ii) to have an internal function that performes the evaluation of the complex function; this complicates things quite a bit for user-written functions. Besides, the quality of the result is comparable to what we already get via Richardson extrapolation. The complex-step technique performs a second-order approximation, which is what we get by setting fdjac_quality to 2. For example, try the following script (which uses the definition of rderiv as per Oleh's previous script): <hansl> set verbose off function scalar cube(matrix *x) return x[1]^3 end function g = rderiv("x^3", 0) printf "rderiv: %36.33f\n", g x = {0} set fdjac_quality 1 g = fdjac(x, cube(&x)) printf "fdjac(1): %36.33f\n", g set fdjac_quality 2 g = fdjac(x, cube(&x)) printf "fdjac(2): %36.33f\n", g </hansl> On my system I get <output> rderiv: -0.000000000000000000000000000000049 fdjac(1): 0.000000000000000888178419700125430 fdjac(2): 0.000000000000000000000000000000000 </output> ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------