The tacit form does not help with my anti-derivative attempt: (^.@-. % ]) deriv_jcalculus_ _1 |domain error: deriv_jcalculus_ | 13!:8(3) |deriv_jcalculus_[:16]
On Fri, Jan 15, 2021 at 2:16 PM Henry Rich <[email protected]> wrote: > Right, you'll never get a closed-form derivative for an explicit > function. Make it tacit: > > (^.@-. % ]) deriv_jcalculus_ 1 > (((_1 * %@-.) * ]) - ^.@-. * 1"0) % *:@] > > The cases that are Lebesgue-integrable but not Riemann-integrable have > discontinuities or infinities that are inconsistent with digital > approximation, IIUC. > > Henry Rich > > On 1/15/2021 1:58 PM, Devon McCormick wrote: > > The Lebesgue method is supposed to handle cases Riemann cannot. > > I tried using the anti-derivatives from the calculus add-ons but cannot > > make them work for an arbitrary user-defined function like "f3=: ] %~ [: > ^. > > -.". > > > > On Fri, Jan 15, 2021 at 9:16 AM 'Pascal Jasmin' via Programming < > > [email protected]> wrote: > > > >> The Riemann–Darboux approach seems so much easier. Just take a range > and > >> a step interval (resolution) (all as y) to iterate the function (adverb > >> argument) and add all the results up divided by number of intervals > times > >> range. > >> > >> > >> > >> > >> > >> > >> On Thursday, January 14, 2021, 04:21:19 p.m. EST, Devon McCormick < > >> [email protected]> wrote: > >> > >> > >> > >> > >> > >> Has anyone looked into implementing a Lebesgue integration adverb in J? > >> This looks like a good explanation of it: > >> https://en.m.wikipedia.org/wiki/Lebesgue_integration . > >> > >> -- > >> > >> Devon McCormick, CFA > >> > >> Quantitative Consultant > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > > > > > -- > This email has been checked for viruses by AVG. > https://www.avg.com > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > -- Devon McCormick, CFA Quantitative Consultant ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
