(+`%)/10$1 1.625 (+`%)/100$1 1.61803 (+`%)/100$1x 32951280099r20365011074 0j25":(+`%)/100$1x 1.6180339887498948482035085 0j25":(+`%)/1000$1x 1.6180339887498948482045868 0j55":(+`%)/1000$1x 1.6180339887498948482045868343656381177203091798057628621 0j55":(+`%)/2000$1x 1.6180339887498948482045868343656381177203091798057628621
On Thu, Apr 14, 2016 at 7:02 PM, Martin Kreuzer <[email protected]> wrote: > Thanks Raul, Kip -- > > (1) Am now comfortable (again) with foreign print precision; just for the > record: > > def=. 6 > ext=. 13 > 9!:10 '' NB. check > 6 > 9!:11 (ext) NB. set > > 9!:10 '' NB. check > 13 > 9!:11 ] def NB. reset > > 9!:10 '' > 6 > > (2) The tacit version looks pretty straight forward (and works fine). > > (3) Will follow up your ideas/suggestions on "injection" and verb (cr) -- > fodder for the weekend perhaps (no chance to stay with it on a regular > basis yet, at least there's the habit of reading through the posts). > > (4) Meanwhile, looking at your parameters of the (a cr b) call, I did this > small modification, getting rid of the "cleanup" (1-~): > > ] v=. 0 ,13#1 > 0 1 1 1 1 1 1 1 1 1 1 1 1 1 > (+&%:)/ v > 1.618033473928 > > -M > > At 2016-04-14 21:43, you wrote: > >> The following is not simpler but invents a "continued root" in which >> dyadic root %: plays the role dyadic % plays in a continued fraction. >> Here is the picture of a "continued root": a1 b0 + %: >> b1 + a2 %: b2 + a3 >> %: b3 + . >> . . Verb cr >> below produces "convergents" which stop with a "diagonal" element. The >> basic idea in verb cr belongs to Raul Miller. cr =: {.@] , {.@] + [: ([: >> %:`+/ ,)\ [: |: [ ,: }.@] NB. Usage a cr b (13#2) cr 0,13#1 NB. The 2 >> means square roots are used 0 1 1.414213562 1.553773974 1.598053182 >> 1.611847754 1.616121207 1.617442799 1.617851291 1.617977531 1.618016542 >> 1.618028597 1.618032323 1.618033474 --Kip Murray On Thursday, April 14, >> 2016, Raul Miller <[email protected]> wrote: > One thing you could >> do is get rid of the intermediate names in gr: > > gr=: monad define > >> 1-~ (+&%:)/ y$1 > ) > > And you might want to make this tacit, for example: >> > > 13 :'1-~ (+&%:)/ y$1' > 1 -~ [: +&%:/ 1 $~ ] > > Or, depending on >> your preferences, you might want to use induction > rather than insertion: >> > > gri=: 1-~(1+%:@])^:([-1:)&1 > > I guess it's really a matter of >> what your idea of "elegance" is... > > Personally, when I am fiddling with >> small expressions, I like to set > up a line that evaluates and then tweak >> the expression and watch to > make sure the result does not change. For >> this example, I'd have lines > like: > > gr 10 > 1.61798 > >> 1-~(1+%:)^:9]1 > 1.61798 > 13 :'((+&%:)/ y$1) - 1' 10 > 1.61798 > >> (1-~(1+%:@])^:([-1:)&1) 10 > 1.61798 > > (with lots of other lines, >> including some errors, mixed in) > > But the precision issue you are seeing >> is really the print precision > global parameter. See > >> http://www.jsoftware.com/help/dictionary/dx009.htm for how to change > >> that. > > I hope this helps. > > -- > Raul > > On Thu, Apr 14, 2016 at 3:13 >> PM, Martin Kreuzer <[email protected] > <javascript:;>> wrote: > > >> Moving from continued fraction to continued square root, I arrived at > >> this: > > > > NB. modelling gr=. rt(1+rt(1+rt(1+rt(1+...)))) > > > > >> gr=. monad define > > ps=. + > > rt=. %: > > v=. y $ 1 > > r=. 1-~ (ps&rt)/ >> v > > ) > > gr 10 > > 1.61798 > > gr 13 > > 1.61803 > > > > Q1: > > >> What would be (more elegant and/or concise) ways to do this, especially > >> the > > line with the return value (r)..? > > Q2: > > What should I do to >> get higher precision (more digits) in the result (and > > still having a >> floating point number); does that need a "foreign"..? > > (I'm sure that I >> have seen this before, but can't remember where.) > > > > Thanks > > -M > > >> > > ---------------------------------------------------------------------- >> > > For information about J forums see >> http://www.jsoftware.com/forums.htm > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm >> -- Sent from Gmail Mobile >> ---------------------------------------------------------------------- For >> information about J forums see http://www.jsoftware.com/forums.htm >> > > ---------------------------------------------------------------------- > 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
