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
