I don't really follow what you are doing here -- for example, I look at stuff like 11 summary@hist i.11 and do not understand how that result corresponds to "size of the dataset" -- but even without knowing your intentions, I can point out that you can simplify tomb:
tomb=:(^/ i.@>:)~ , It sort of smells like you were working with matrices designed for inversion and polynomial fitting, but that doesn't tell me much (if anything) about your destination. Good luck, -- Raul On Sat, Aug 22, 2020 at 5:35 AM 'Bo Jacoby' via Programming <[email protected]> wrote: > > Thanks to Michael and to ethiejiesa! > The program is now: > > tomb=.[ (^/ i.@>:)~ ,@] NB. Powers of a tombola > > hist=.]* ((^/&i. >:)~ #) NB. Powers of a histogram > s=.(*#)@(}.%{.)@(+/) NB. summation > f1=.$~2 # # NB. n*n matrix > f2=.>:@i.@#,}: NB. insert S0, remove Sn > f3=.*_1^i.@# NB. change signs > f4=.|:|.!.0"0 1~-@i.@# NB. shift in zeroes > m=.|:@f4@(f3"1@f2@|:@f1) NB. Matrix > e=.1,(%.m) NB. solve lin.eqns. > pol=._1 x: -@|.@>@{:@p.@|. NB. solve alg.eqn. > hp=.x: :: ] NB. high precision > summary=.pol@e@s@hp f. NB. complete program > (I need the comma in tomb, so now it is smelly again.) > Michael wrote: "Any clue as to the input to summary, or what you're > summarising? Sorry if it's obvious!" > No sir, it is not obvious if it is not obvious to you. > Left input to summary@tomb and summary@hist is the size of the output dataset. > Right input to summary@tomb is the input dataset described as a tombola. The > same number may occur on many tickets. The order of the tickets is immaterial. > Right input to summary@hist is the input dataset described as a histogram. > the number of zeroes, the number of ones, the number og twos &c. > Examples: > > 11 summary@tomb i.11 > > > 0 1 2 3 4 5 6 7 8 9 10 > > 11 summary@tomb 11 NB. this wouldn't work without the comma in tomb > 11 11 11 11 11 11 11 11 11 11 11 > > 1 summary@tomb i.11 NB. mean value > 5 > > 2 summary@tomb i.11 NB. mean plus/minus std.dev. > 1.83772 8.16228 > > > 3 summary@tomb i.11 NB. generalized into 3 numbers > > 1.12702 5 8.87298 > > > > Explanations: > > > > 5 tomb i.11 > > 1 0 0 0 0 0 > > 1 1 1 1 1 1 > > 1 2 4 8 16 32 > > 1 3 9 27 81 243 > > 1 4 16 64 256 1024 > > 1 5 25 125 625 3125 > > 1 6 36 216 1296 7776 > > 1 7 49 343 2401 16807 > > 1 8 64 512 4096 32768 > > 1 9 81 729 6561 59049 > > 1 10 100 1000 10000 100000 > > +/ hp 5 tomb i.11 > 11 55 385 3025 25333 220825 > > (}.%{.) +/ hp 5 tomb i.11 > 5 35 275 2303 20075 > > (*#) (}.%{.) +/ hp 5 tomb i.11 > 25 175 1375 11515 100375 > > s hp 5 tomb i.11 > 25 175 1375 11515 100375 > > f1 s hp 5 tomb i.11 > 25 175 1375 11515 100375 > > 25 175 1375 11515 100375 > > 25 175 1375 11515 100375 > > 25 175 1375 11515 100375 > > 25 175 1375 11515 100375 > > |: f1 s hp 5 tomb i.11 > 25 25 25 25 25 > > 175 175 175 175 175 > > 1375 1375 1375 1375 1375 > > 11515 11515 11515 11515 11515 > > 100375 100375 100375 100375 100375 > > f2 |: f1 s hp 5 tomb i.11 > 1 2 3 4 5 > > 25 25 25 25 25 > > 175 175 175 175 175 > > 1375 1375 1375 1375 1375 > > 11515 11515 11515 11515 11515 > > f3"1 f2 |: f1 s hp 5 tomb i.11 > 1 _2 3 _4 5 > > 25 _25 25 _25 25 > > 175 _175 175 _175 175 > > 1375 _1375 1375 _1375 1375 > > 11515 _11515 11515 _11515 11515 > > f4 f3"1 f2 |: f1 s hp 5 tomb i.11 > 1 25 175 1375 11515 > > 0 _2 _25 _175 _1375 > > 0 0 3 25 175 > > 0 0 0 _4 _25 > > 0 0 0 0 5 > > |: f4 f3"1 f2 |: f1 s hp 5 tomb i.11 > 1 0 0 0 0 > > 25 _2 0 0 0 > > 175 _25 3 0 0 > > 1375 _175 25 _4 0 > > 11515 _1375 175 _25 5 > > m s hp 5 tomb i.11 > 1 0 0 0 0 > > 25 _2 0 0 0 > > 175 _25 3 0 0 > > 1375 _175 25 _4 0 > > 11515 _1375 175 _25 5 > > (%.m) s hp 5 tomb i.11 > 25 225 875 1340 450 > > |.1,(%.m) s 5 tomb i.11 > 450 1340 875 225 25 1 > > p.|.1,(%.m) s hp 5 tomb i.11 > ┌─┬─────────────────────────────────────┐ > > │1│_9.54306 _7.0882 _5 _2.9118 _0.456938│ > > └─┴─────────────────────────────────────┘ > > _1 x: - |. > {: p.|.1,(%.m) s hp 5 tomb i.11 > 0.456938 2.9118 5 7.0882 9.54306 > > 5 summary@tomb i.11 > 0.456938 2.9118 5 7.0882 9.54306 > > > > Thanks! > Bo. Den fredag den 21. august 2020 17.01.49 CEST skrev 'Michael Day' via > Programming <[email protected]>: > > Any clue as to the input to summary, or what you're summarising? > > Sorry if it's obvious! > > Note these (display ?) errors: > > pol =. _1 [space] x: ... > > hp =. x [space] :: ] ... > > Cheers, > > Mike > > > On 21/08/2020 15:41, 'Bo Jacoby' via Programming wrote: > > > > tomb=.(^/i.@>:)~ NB. tombola lottery powers > > hist=.({."1~>:)~(*[:^/~i.@#@,)NB. histogram powers > > s=.(*#)@ (}.%{.) @ (+/) NB. summation > > f1=.$~2# # NB. n*n matrix > > f2=.>:@i.@#, }: NB. insert S0, remove Sn > > f3=.*_1^i.@# NB. change sign > > f4=.|:|.!.0"01~-@i.@# NB. shift zeroes in > > m=.|:@f4@(f3"1@f2@|:@f1) NB. matrix > > e=.1,(%.m) NB. solve linear equations > > pol=._1x: -@|.@>@{:@p.@|. NB.solve alg.eqn. > > hp=.x::: ] NB. high precision > > summary=.pol@e@s@hp f. NB. complete program > > sorry for the still missing carriage returns. > > Den fredag den 21. august 2020 16.37.19 CEST skrev Bo Jacoby > > <[email protected]>: > > > > tomb=.(^/i.@>:)~ NB. tombola lottery > > powershist=.({."1~>:)~(*[:^/~i.@#@,)NB. histogram powerss=.(*#)@ (}.%{.) @ > > (+/) NB. summationf1=.$~2# # NB. n*n matrixf2=.>:@i.@#, }: NB. insert S0, > > remove Snf3=.*_1^i.@# NB. change signf4=.|:|.!.0"01~-@i.@# NB. shift zeroes > > inm=.|:@f4@(f3"1@f2@|:@f1) NB. matrixe=.1,(%.m) NB. solve linear > > equationspol=._1x: -@|.@>@{:@p.@|. NB.solve alg.eqn.hp=.x::: ] NB. high > > precisionsummary=.pol@e@s@hp f. NB. complete program > > This should be better. Sorry. > > Bo. Den fredag den 21. august 2020 16.29.35 CEST skrev 'Bo Jacoby' via > > Programming <[email protected]>: > > > > Thank you! > > I was trying to accomplish this > > tomb=.(^/i.@>:)~ NB. tombola lottery > > powershist=.({."1~>:)~(*[:^/~i.@#@,)NB. histogram powerss=.(*#)@ (}.%{.) @ > > (+/) NB. summationf1=.$~2# # NB. n*n matrixf2=.>:@i.@#, }: NB. indsæt S0, > > fjern Snf3=.*_1^i.@# NB. change signf4=.|:|.!.0"01~-@i.@# NB. shift zeroes > > inm=.|:@f4@(f3"1@f2@|:@f1) NB. matrixe=.1,(%.m) NB. solve linear > > equationspol=._1x: -@|.@>@{:@p.@|. NB.solve alg.eqn.hp=.x::: ] NB. high > > precisionsummary=.pol@e@s@hpf. NB. complete program > > 1&(summary@tomb) computes the mean value of a dataset. > > > > 1 summary@tomb i.11 > > 5 > > > > > > The mean value of 99 zeroes and 1 one is > > > > 1 summary@hist 99 1 > > > > 0.01 > > > > > > > > The mean value plus/minus the standard deviation is computed like this > > > > 2 summary@tomb i.11 > > > > 1.83772 8.16228 > > > > 2 summary@hist 99 1 > > _0.0894987 0.109499 > > > > > > > > Of course these two numbers have the correct mean value > > > > 1 summary@tomb 2 summary@tomb i.11 > > > > 5 > > > > 1 summary@tomb 2 summary@hist 99 1 > > 0.01 > > > > > > > > The computation is generalized to 3 numbers > > > > 3 summary@tomb i.11 > > > > 1.12702 5 8.87298 > > > > 3 summary@hist 99 1 > > _0.108204j0.16452 _0.108204j_0.16452 0.246409 > > > > having the correct mean values and standarddeviations. > > > > 2 summary@tomb 3 summary@tomb i.11 > > > > 1.83772 8.16228 > > > > 2 summary@tomb 3 summary@hist 99 1 > > _0.0894987 0.109499 > > > > > > > > Thus complicated probability distributions functions are summarized by a > > few numbers. That is what I accomplished! > > Thanks! > > Bo. > > Den fredag den 21. august 2020 15.33.50 CEST skrev ethiejiesa via > > Programming <[email protected]>: > > > > Bo Jacoby <[email protected]> wrote: > >> How to de-smell this: > >> 3([* i.@#@,@[ ^/ i.@>:@])~ 0 0 1 1 1 > > 3 (]* ((^/&i. >:)~ #)) 0 0 1 1 1 > > > > Maybe? That comes from just a little mechanical algebra: > > > >> 3([* i.@#@,@[ ^/ i.@>:@])~ 0 0 1 1 1 > > First notice the repeated (i.) on either argument of (^/). There is a > > general > > pattern, (f@u v f@w <--> u v&f w), which in this case specializes to > > > > 3([* #@,@[ ^/&i. >:@])~ 0 0 1 1 1 > > > > Then, at least in this example the (@,) is superfluous, so we elide it: > > > > 3([* #@[ ^/&i. >:@])~ 0 0 1 1 1 > > > > Finally, here is an idiom: ( (u@[ v w@]) <--> ((v w)~ u)~ ), and since > > (x v~~ y <--> x v y), we have > > > > 3 (]* ((^/&i. >:)~ #)) 0 0 1 1 1 > > > > The last idiom is really a matter of preference. I like the bare verbs, but > > code golf-wise it doesn't win. > > > > More importantly, however, I really have no idea what you are trying to > > accomplish. The above just performs some J syntax manipulations; however, > > this > > doesn't at all demonstrate the main point of avoiding code smell as I see > > it, > > which is more about finding places to improve the *algorithm* rather than > > only > > cleaning up the syntax. > > ---------------------------------------------------------------------- > > 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 > > -- > This email has been checked for viruses by Avast antivirus software. > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
