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
>>
>>
>> ---
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>> https://www.avast.com/antivirus
>>
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