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
