[Jprogramming] Hermitian from triangular

[Dan Bron]

Put another way, in the abstract,  &.%  is an identity transformation and (f -: f&.%) a tautology.  So negative zero is -0 is -&.% 0 (only J is wise to the first trick, but not the second, sneakier one).

-Dan

Please excuse typos; composed on a handheld device.

On Jan 16, 2013, at 8:31 AM, Dan Bron <j at bron.us> wrote:

> In J, the reciprocal of zero is infinity.  Correspondingly, the reciprocal of negative zero is negative infinity. Ergo, the reciprocal of negative infinity is negative zero.
> 
>   %0
> _
>   %_
> 0
>   %__
> 0
>   % %_ NB. The two zeros look identical
> _
>   % %__ NB. But J knows their "signs"
> __
> 
> 
> So, you can produce a negative zero by inverting negative infinity, and you can identify a negative zero by inverting it.  If __=%x then x is negative zero (the only value whose reciprocal is negative infinity).
> 
> -Dan
> 
> Please excuse typos; composed on a handheld device.
> 
> On Jan 16, 2013, at 7:49 AM, Raul Miller <rauldmiller at gmail.com> wrote:
> 
>> I thought that J did not represent negative zero?
>> 
>> Is it possible to trick J into revealing a negative zero?  If so, does
>> it involve foreigns or is there some native calculations that lead
>> here?
>> 
>> Thanks,
>> 
>> -- 
>> Raul
>> 
>> On Wed, Jan 16, 2013 at 7:26 AM, Henry Rich <HenryHRich at nc.rr.com> wrote:
>>> On my awaking, there was a whiff of sulfur in the air, and a greenish
>>> haze... and somehow in my mind the idea that that last program won't work,
>>> because of the possibility of negative zero.  I'll stay relegated to imp
>>> status.
>>> 
>>> Henry Rich
>>> 
>>> 
>>> On 1/15/2013 6:20 PM, Henry Rich wrote:
>>>> 
>>>> Nah, that's not beyond impish.  The devilish solution is to take the
>>>> bitwise OR of the matrix with its conjugate transpose (but that's easier
>>>> in assembler language than in J:
>>>> (23 b.&.(a.&i.)&.(2&(3!:5))&.+. +@|:))
>>>> ).  And you need to be sure that the zeros on the lower diagonal and
>>>> below are true zeros!
>>>> 
>>>> Henry Rich
>>>> 
>>>> On 1/15/2013 6:03 PM, km wrote:
>>>>> 
>>>>> Oh, boy!  (v1`v2) } y <--> (v1 y) } (v2 y)
>>>>> 
>>>>> Brief and devilish, take care for your soul, Henry!
>>>>> 
>>>>> --Kip
>>>>> 
>>>>> Sent from my iPad
>>>>> 
>>>>> 
>>>>> On Jan 15, 2013, at 3:39 PM, Henry Rich <HenryHRich at nc.rr.com> wrote:
>>>>> 
>>>>>> hft =: 0&=`(,: +@|:)}
>>>>>> 
>>>>>> Henry Rich
>>>>>> 
>>>>>> On 1/15/2013 5:25 AM, km wrote:
>>>>>>> 
>>>>>>> This is an easy one.  A Hermitian matrix matches its conjugate
>>>>>>> transpose.  Write a verb hft that creates a Hermitian matrix from a
>>>>>>> triangular one that has a real diagonal.
>>>>>>> 
>>>>>>>   ishermitian =: -: +@|:
>>>>>>>   ]A =: 2 2 $ 1 2j3 0 4
>>>>>>> 1 2j3
>>>>>>> 0   4
>>>>>>>   ]B =: hft A
>>>>>>>   1 2j3
>>>>>>> 2j_3   4
>>>>>>>   ishermitian A
>>>>>>> 0
>>>>>>>   ishermitian B
>>>>>>> 1
>>>>>>> 
>>>>>>> Kip Murray
>>>>>>> 
>>>>>>> Sent from my iPad
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