NB. tacit
run=: upd rec
upd=: [ ((({~ 0{::]) + 1{::])`(0{::])`[} - 2{::]) ~.@] ; ] (+//. ; ]) 1 <: [
NB. explicit
RUN=: UPD rec
UPD=: 4 : 0
b -~ x u}~ (x {~ u=. ~.y) + y +//. b=. x >: 1
)
rec=: ((] + ] >: i.@[) (?@$ <:))@#
Slower on short vectors, faster on larger ones (j805):
1e2 ts 'tick^:1e4#~20'
0.0408952 3840
1e2 ts 'run^:1e4#~20'
0.0802917 4864
1e2 ts 'RUN^:1e4#~20'
0.0636084 7040
10 ts 'tick^:1e4#~100'
0.243663 23552
10 ts 'run^:1e4#~100'
0.12502 11904
10 ts 'RUN^:1e4#~100'
0.104644 14848
Probably because of =/.
Louis
> On 19 Jul 2017, at 18:37, Rob Hodgkinson <[email protected]> wrote:
>
> Thanks Mike it formats and reads perfectly… nice job, Rob
>
>> On 20 Jul 2017, at 8:02 am, 'Mike Day' via Programming
>> <[email protected]> wrote:
>>
>> This took me much longer than a lunch-break, partly because we
>> were away in France, and I was experimenting with J701 on my
>> iPad when Liz would let me.
>>
>> I came up with a number of variants, of which the following is best.
>> It's slower and uses more space than Raul's for small problem-sizes,
>> but is perhaps better for larger problems, eg n > 100 or so.
>>
>> NB. a Boolean verb for whether a player donates, which,
>> NB. of course, depends on whether he has any money:
>>
>> donation =: 1 & <.
>>
>> NB. This verb lists the indexes of the random donee (? player donated to)
>> NB. for each player, whether of not that player CAN donate.
>> NB. It assumes that its single argument is i.n where n is the number
>> NB. of players, which is why its name ends in i (!):
>>
>> idoneei=:(#|(+?&.<:@#~@#))
>>
>> NB. The idea is to concatenate
>> NB. (the old state minus donation) and (donation), namely
>> NB. ((-, ])donation)
>> NB. and sum them as ordered with this left-hand key:
>> NB. (i.n) concatenated with (idonee), namely
>> NB. (, idoneei)@(i.@#)
>>
>> NB. Here it is, with a fix, f.
>>
>> new =: ((,idoneei)@(i.@#) +//. ((-, ])donation )) f.
>>
>> NB. time & space:
>> ts =: 6!:2 , 7!:2@]
>>
>> NB. where my version is ok:
>> ts'orig ^:5000 #~200' NB. Xiao-Yong Jin's original suggestion
>> 5.72563 22912
>> ts'tick ^:5000 #~200' NB. Raul's revised version
>> 1.57339 77824
>> ts'new ^:5000 #~200' NB. The best I could manage
>> 0.922963 20992
>>
>> NB. and where it isn't so good:
>> ts'orig ^:5000 #~10' NB. Xiao-Yong Jin
>> 0.341718 6272
>> ts'tick ^:5000 #~10' NB. Raul M
>> 0.0445439 3840
>> ts'new ^:5000 #~10' NB. Mike D
>> 0.0676198 4864
>>
>> Sorry for this late posting, but it wasn't convenient to
>> write up and send until home and with laptop to hand.
>>
>> Thanks,
>> Mike
>>
>> NB. prepared in notepad, copied to Thunderbird, and trying
>> to force fixed width - hope it displays reasonably.
>>
>>
>>
>> On 11/07/2017 19:33, Devon McCormick wrote:
>>> Reading the page referenced, I see where I was confused. The problem
>>> starts out as 100 people each with $100, but then solves a variant of it
>>> for 45 people with $45 each, possibly so the animation is legible. It's
>>> not clear why they even mention the first set of numbers.
>>>
>>> On Mon, Jul 10, 2017 at 8:37 PM, Raul Miller <[email protected]> wrote:
>>>
>>>> Oops, I did not think about that "reflexive giving" wart.
>>>>
>>>> Here's a fix for my version:
>>>>
>>>> tick=: (0 >. <:) + i.@# +/@:(=/)~ I.@:* (] + <:) +/@:* ?@# <:@#
>>>> require 'stats'
>>>> stddev"1 tick^:(i.10) 45#45
>>>> 0 0.977008 1.18705 1.73205 2.01133 2.15322 2.46798 2.86832 2.97719 3.1334
>>>> tick^:10000]20#20
>>>> 3 20 1 15 10 38 6 8 23 24 11 90 33 67 5 13 7 20 1 5
>>>>
>>>> Thanks,
>>>>
>>>> --
>>>> Raul
>>>>
>>>> On Mon, Jul 10, 2017 at 7:50 PM, 'Pascal Jasmin' via Programming
>>>> <[email protected]> wrote:
>>>>>
>>>>> The number of $ available each round is the number of people with >&0.
>>>> The number of potential recipients is the population. This simplification
>>>> though means its possible for someone to pay himself.
>>>>>
>>>>> A correction to your version,
>>>>>
>>>>> /:~@(-&1`]@.(=&0)"0 (#/.~@] + ~.@]{[)`(~.@])`[} >&0 # (?@#~@#@]`]`[} ]
>>>> I.@:= i.@#)@?@#~@#)^:21000 #~10
>>>>> That assumption would increase the likelihood of eventual
>>>> "superconcntration" but that doesn't seem to happen.
>>>>> As soon as some have 0, the rest have a "negative return" expectation
>>>> each turn.
>>>>>
>>>>> ________________________________
>>>>>
>>>>>
>>>>> From: Xiao-Yong Jin <[email protected]>
>>>>>
>>>>> To: "[email protected]" <[email protected]>
>>>>>
>>>>> Sent: Monday, July 10, 2017 3:43 PM
>>>>>
>>>>> Subject: [Jprogramming] Everyone giving dollars to random others
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> I thought this is a good lunch break exercise.
>>>>>
>>>>>
>>>>>
>>>>> http://www.decisionsciencenews.com/2017/06/19/counterintuitive-
>>>> problem-everyone-room-keeps-giving-dollars-random-others-
>>>> youll-never-guess-happens-next/
>>>>>
>>>>>
>>>>> Quote: “Imagine a room full of 100 people with 100 dollars each. With
>>>> every tick of the clock, every person with money gives a dollar to one
>>>> randomly chosen other person. After some time progresses, how will the
>>>> money be distributed?”
>>>>>
>>>>>
>>>>> And I came up with this simulation. (45 people with 45 dollars each,
>>>> same as on the webpage.)
>>>>>
>>>>>
>>>>> /:~@(-&1`]@.(=&0)"0 (#/.~@] + ~.@]{[)`(~.@])`[} >&0 # (?@#~@#@]`]`[} ]
>>>> I.@:= i.@#)^:_@?@#~@#)^:5000 #~45
>>>>>
>>>>>
>>>>> And I really like to see the mean expectations and the standard
>>>> deviation of the mean, I ended up doing this. (Make sure the J sentence is
>>>> one long line if you want to try it out.)
>>>>>
>>>>>
>>>>> ((],.[:(+/%#*<:@#)&.:*: -"1)+/%#)}.(/:~@(-&1`]@.(=&0)"0 (#/.~@] +
>>>> ~.@]{[)`(~.@])`[} >&0 # (?@#~@#@]`]`[}
>>>> ]I.@:=i.@#)^:_@?@#~@#)^:10000)^:(<65)
>>>> #~45
>>>>>
>>>>> 0.984375 0.124984
>>>>>
>>>>>
>>>>> 2.01562 0.170335
>>>>>
>>>>>
>>>>> 3.0625 0.180765
>>>>>
>>>>>
>>>>> 4.15625 0.230616
>>>>>
>>>>>
>>>>> 5.21875 0.248476
>>>>>
>>>>>
>>>>> 6.1875 0.306894
>>>>>
>>>>>
>>>>> 7.35938 0.332862
>>>>>
>>>>>
>>>>> 8.64062 0.362809
>>>>>
>>>>>
>>>>> 9.84375 0.380723
>>>>>
>>>>>
>>>>> 10.9688 0.383805
>>>>>
>>>>>
>>>>> 12.125 0.407944
>>>>>
>>>>>
>>>>> 13.6406 0.423964
>>>>>
>>>>>
>>>>> 15.0625 0.457453
>>>>>
>>>>>
>>>>> 16.5312 0.462893
>>>>>
>>>>>
>>>>> 18.1875 0.480717
>>>>>
>>>>>
>>>>> 19.7031 0.464877
>>>>>
>>>>>
>>>>> 21.1562 0.475709
>>>>>
>>>>>
>>>>> 22.7031 0.483702
>>>>>
>>>>>
>>>>> 24.4062 0.516935
>>>>>
>>>>>
>>>>> 26.4062 0.5768
>>>>>
>>>>>
>>>>> 28.1094 0.604266
>>>>>
>>>>>
>>>>> 29.8281 0.617838
>>>>>
>>>>>
>>>>> 31.875 0.61942
>>>>>
>>>>>
>>>>> 33.9375 0.603345
>>>>>
>>>>>
>>>>> 35.7812 0.642211
>>>>>
>>>>>
>>>>> 37.9844 0.647987
>>>>>
>>>>>
>>>>> 40.6562 0.731321
>>>>>
>>>>>
>>>>> 43 0.739342
>>>>>
>>>>>
>>>>> 45.3906 0.723616
>>>>>
>>>>>
>>>>> 48.0469 0.7613
>>>>>
>>>>>
>>>>> 51.6094 0.823639
>>>>>
>>>>>
>>>>> 54.7656 0.873934
>>>>>
>>>>>
>>>>> 57.1406 0.815544
>>>>>
>>>>>
>>>>> 60 0.866598
>>>>>
>>>>>
>>>>> 63.8594 0.898319
>>>>>
>>>>>
>>>>> 68.75 0.918018
>>>>>
>>>>>
>>>>> 73.5781 1.00736
>>>>>
>>>>>
>>>>> 78.3281 1.08128
>>>>>
>>>>>
>>>>> 84.9688 1.25534
>>>>>
>>>>>
>>>>> 93.4688 1.29731
>>>>>
>>>>>
>>>>> 104.578 1.73274
>>>>>
>>>>>
>>>>> 114.922 2.07574
>>>>>
>>>>>
>>>>> 131.938 2.7357
>>>>>
>>>>>
>>>>> 159.359 4.40899
>>>>>
>>>>>
>>>>> 204.766 7.24239
>>>>>
>>>>>
>>>>>
>>>>> So, how do I make a fancy animation (like the one in the webpage I
>>>> linked in the beginning of this message) with J?
>>>>>
>>>>> ----------------------------------------------------------------------
>>>>>
>>>>>
>>>>> For information about J forums see http://www.jsoftware.com/forums.htm
>>>>> ----------------------------------------------------------------------
>>>>> For information about J forums see http://www.jsoftware.com/forums.htm
>>>> ----------------------------------------------------------------------
>>>> For information about J forums see http://www.jsoftware.com/forums.htm
>>>>
>>>
>>>
>>
>>
>> ---
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>> https://www.avast.com/antivirus
>>
>> ----------------------------------------------------------------------
>> For information about J forums see http://www.jsoftware.com/forums.htm
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
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