Re: [Gretl-devel] fdjac: a better example

Of course, my exp(100) example is incorrect: relative precision is better than 10^-12 even on 32-bit system. Also, ways to determine h should be different for qualities 0,1, and 2 Quality 0 requires much lesser h: for x from (0,1) sqrt($macheps) even 10^-1* sqrt($macheps) works OK And of course if x==0 should be changed to something like abs(x)< 10^-1* sqrt($macheps) for quality 0 Currently, I can't tell about quality 1 Oleh I'll write my impression on the tests later 30 грудня 2015, 12:48:19, від "Riccardo (Jack) Lucchetti" < r.lucchetti(a)univpm.it >: On Wed, 30 Dec 2015, oleg_komashko(a)ukr.net wrote: Of course ANY numerical approximation to a derivative is a ratio; therefore, what is crucial to its precision is the relative order of magnitude of numerator and denominator. It's easy to contruct pathological cases and there's no silver bullet that works in all cases. That said, the following settings seem to work reasonably well in a decently-sized array of cases (diff against git HEAD --- not applied yet). <diff> diff --git a/minpack/fdjac2.c b/minpack/fdjac2.c index 9e9676a..54e64ec 100644 --- a/minpack/fdjac2.c +++ b/minpack/fdjac2.c @@ -144,10 +144,10 @@ int fdjac2_(S_fp fcn, int m, int n, int quality, for (j = 0; j < n; j++) { temp = x[j]; if (quality == 2) { - if (fabs(temp) > 1000) { - h = 1000 * sqrt(fabs(temp/1000)) * eps; + if (fabs(temp) > 128) { + h = 128* sqrt(fabs(temp/128)) * eps / sqrt(6); } else { - h = 1000 * eps; + h = 128 * eps / sqrt(6); } } else { h = eps * fabs(temp); </diff> I'm attaching a battery of tests. ------------------------------------------------------- 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 -------------------------------------------------------