Louis is correct that there is no simpler way to explain this. At least not from anything in this email thread so far. Perhaps it would make it easier to point out that the following w=: (+/ .*~ |:) - (#%~[:*/~+/) gives the same as u and v.
If this generates more confusion, perhaps going back to a tautology on a list of numbers would make it clearer. t0=: ( (+/%#)@:*: - *:@:(+/%#) ) -: (+/%#)@:*:@:(- +/%#) t1=: ( +/ @:*: - *:@:(+/)%# ) -: +/ @:*:@:(- +/%#) check t0?10#0 t1?10#0 > On Feb 13, 2017, at 10:39 AM, Louis de Forcrand <[email protected]> wrote: > > I'm afraid that what is happenning here is not simple. > > u=: (mp~ |:) (-"1 mean) > v=: (mp~ |:)@(-"1 mean) > > u A > A mp~ |: (-"1 mean) A > (|: A -"1 mean A) mp A > > v A > (mp~ |:) A -"1 mean A > (|: A -"1 mean A) mp A -"1 mean A > > It is not obvious that these two verbs are mathematically equivalent. That is > why my post may be hard to follow. > > Louis > >> On 13 Feb 2017, at 17:25, Raul Miller <[email protected]> wrote: >> >> Eh... ok, but that's pretty hard to follow, and there's much simpler >> ways of recognizing what's going on here. >> >> -- >> Raul >> >> >>> On Mon, Feb 13, 2017 at 10:15 AM, Louis de Forcrand <[email protected]> >>> wrote: >>> I forgot to divide by m, see my correction. >>> >>> Louis >>> >>>> On 13 Feb 2017, at 15:24, Raul Miller <[email protected]> wrote: >>>> >>>> I'm having problems following your reasoning here. >>>> >>>> Consider: >>>> >>>> A=: 5 3 $ 90 60 90 90 90 30 60 60 60 60 60 90 30 30 30 >>>> mean=: +/%# >>>> mp=: +/ . * >>>> C=: A - B=: (E=: (m,m) $ 1) mp A % m=: #A >>>> u=: ((mp~ |:) (-"1 mean)) % # >>>> v=: (mp~ |:)@(-"1 mean) % # >>>> u A >>>> 504 360 180 >>>> 360 360 0 >>>> 180 0 720 >>>> (|:C) mp A >>>> 2520 1800 900 >>>> 1800 1800 0 >>>> 900 0 3600 >>>> >>>> If I understand your presentation, those two results should have been >>>> the same. But they are not... >>>> >>>> Can you run through your work with some example values and see whether >>>> you think it's the presentation or my understanding of it that needs >>>> to change? >>>> >>>> Thanks, >>>> >>>> -- >>>> Raul >>>> >>>> >>>> >>>>> On Mon, Feb 13, 2017 at 6:36 AM, Louis de Forcrand <[email protected]> >>>>> wrote: >>>>> A few corrections: >>>>> >>>>> u is >>>>> (|:C) mp A % m >>>>> and v is >>>>> (|:C) mp C % m >>>>> but we can multiply both by m when showing that they are equal. >>>>> >>>>> In addition, I forgot a division by m here: >>>>>> +/ (i{Et) * j {"1 E >>>>> that should read >>>>> +/ (i{Et) * j {"1 E % m. >>>>> >>>>> Louis >>>>> >>>>>> On 13 Feb 2017, at 01:35, Louis de Forcrand <[email protected]> wrote: >>>>>> >>>>>> The two statements are executing two different procedures which happen >>>>>> to be mathematically equivalent: >>>>>> >>>>>> u=: ((mp~ |:) (-"1 mean)) % # >>>>>> v=: (mp~ |:)@(-"1 mean) % # >>>>>> >>>>>> If (u -: v) A for a matrix A, then >>>>>> (((mp~ |:) (-"1 mean)) -: (mp~ |:)@(-"1 mean)) A. >>>>>> >>>>>> Let >>>>>> C=: A - B=: (E=: (m,m) $ 1) mp A % m=: #A >>>>>> then u is >>>>>> (|:C) mp A >>>>>> and v is >>>>>> (|:C) mp C. >>>>>> >>>>>> Let's look at u: >>>>>> (|:C) mp A >>>>>> (|:A-B) mp A >>>>>> ((At=: |:A) - Bt=: |:B) mp A >>>>>> (At mp A) - Bt mp A >>>>>> >>>>>> Now for v: >>>>>> (|:C) mp C >>>>>> (At - Bt) mp A - B >>>>>> (At mp A) - (At mp B) - (Bt mp A) + Bt mp B >>>>>> >>>>>> We can see that if >>>>>> (Bt mp B) -: At mp B >>>>>> then (u -: v) A. >>>>>> >>>>>> At mp B >>>>>> At mp E mp A % m >>>>>> >>>>>> Bt mp B >>>>>> (|: E mp A % m) mp E mp A % m >>>>>> At mp (Et=: |:E) mp E mp A % *:m >>>>>> At mp (E mp E % m) mp A % m >>>>>> >>>>>> Now (and for the coup de grace): >>>>>> (<i,j) { E mp E % m >>>>>> +/ (i{Et) * j {"1 E >>>>>> +/ (m$1) * m $ 1 % m >>>>>> 1 for all i and j between 0 and m. >>>>>> Therefor >>>>>> E -: E mp E % m. >>>>>> >>>>>> And thus >>>>>> Bt mp B >>>>>> At mp E mp A % m >>>>>> At mp B >>>>>> >>>>>> (u -: v) A for all matrices A. # >>>>>> >>>>>> Cheers, >>>>>> Louis >>>>>> >>>>>> PS: I hope I didn't make and mistakes, but I might have. Thanks for >>>>>> checking! >>>>>> >>>>>>> On 12 Feb 2017, at 18:54, Raul Miller <[email protected]> wrote: >>>>>>> >>>>>>> It's not so much that it's of no use, but that it's redundant. >>>>>>> >>>>>>> When your hook is a train where the first verb is a hook, you can >>>>>>> restructure either of them so that the other of those two hooks takes >>>>>>> over the responsibility of obtaining the hook's "left argument" >>>>>>> (presumably, this would eliminate the other hook). >>>>>>> >>>>>>> I hope this helps, >>>>>>> >>>>>>> -- >>>>>>> Raul >>>>>>> >>>>>>> >>>>>>>> On Sun, Feb 12, 2017 at 10:18 AM, R.E. Boss <[email protected]> >>>>>>>> wrote: >>>>>>>> I think the problem is that the big hook is of no use, that's what >>>>>>>> creates confusion. >>>>>>>> >>>>>>>> (data mp1 mn data)% # data >>>>>>>> 504 360 180 >>>>>>>> 360 360 0 >>>>>>>> 180 0 720 >>>>>>>> >>>>>>>> data mp1 mn data >>>>>>>> 2520 1800 900 >>>>>>>> 1800 1800 0 >>>>>>>> 900 0 3600 >>>>>>>> >>>>>>>> mp1 mn data >>>>>>>> 2520 1800 900 >>>>>>>> 1800 1800 0 >>>>>>>> 900 0 3600 >>>>>>>> >>>>>>>> >>>>>>>> R.E. Boss >>>>>>>> >>>>>>>> >>>>>>>> -----Original Message----- >>>>>>>> From: Programming [mailto:[email protected]] On >>>>>>>> Behalf Of 'Mike Day' via Programming >>>>>>>> Sent: zondag 12 februari 2017 12:02 >>>>>>>> To: [email protected] >>>>>>>> Subject: Re: [Jprogramming] Hooked again >>>>>>>> >>>>>>>> It looks to me as if the two left hooks form one big left hook, not >>>>>>>> that I'm into boxing: >>>>>>>> >>>>>>>> mn =: -"1 mean >>>>>>>> mp1=: mp~|: >>>>>>>> >>>>>>>> ((mp1 mn)%#)data NB. big "hook" >>>>>>>> 504 360 180 >>>>>>>> 360 360 0 >>>>>>>> 180 0 720 >>>>>>>> >>>>>>>> ((mp1 @: mn)%#)data NB. mp1 after mn using @: >>>>>>>> 504 360 180 >>>>>>>> 360 360 0 >>>>>>>> 180 0 720 >>>>>>>> >>>>>>>> (([: mp1 mn)%#)data NB. mp1 after mn using [: >>>>>>>> 504 360 180 >>>>>>>> 360 360 0 >>>>>>>> 180 0 720 >>>>>>>> >>>>>>>> Any use? >>>>>>>> >>>>>>>> Mike >>>>>>>> >>>>>>>> >>>>>>>>> On 12/02/2017 08:06, Lippu Esa wrote: >>>>>>>>> ]data=. 5 3 $ 90 60 90 90 90 30 60 60 60 60 60 90 30 30 30 >>>>>>>>> >>>>>>>>> mean=: +/%# >>>>>>>>> mp=: +/ . * >>>>>>>>> covmat=: ((mp~|:)(-"1 mean))%# NB. divede by n not n-1 to comply with >>>>>>>>> the example >>>>>>>> >>>>>>>> >>>>>>>> --- >>>>>>>> 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 >>>>>> >>>>>> ---------------------------------------------------------------------- >>>>>> 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 >>> >>> ---------------------------------------------------------------------- >>> 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
