[Jprogramming] Golden Ratio (sqrt approach) ...

[Devon McCormick]

   (+`%)/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 <info at airkreuzer.com> 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 <rauldmiller at gmail.com> 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 <info at airkreuzer.com > <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 > >
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-- 

Devon McCormick, CFA

Quantitative Consultant