[Jprogramming] Matrix inverse query

[robert therriault]

Hey Raul,

The subject of my conference talk was going to be jsoftware.com as a learning ecology and labs are a big part of that (and could become bigger). I have not seen a specific lab author since J602. Do you know of one or are we following the "use any text editor" advice?  

http://www.jsoftware.com/jwiki/Labs

Cheers, bob

On Apr 23, 2014, at 11:23 AM, Raul Miller <rauldmiller at gmail.com> wrote:

> If you are interested, you might consider putting together a J lab on the
> subject.
> 
> This would:
> 
> (a) Help you retain the concepts for yourself, and expand your
> understanding of them, and
> (b) Help convey them to other people, also.
> 
> If this interests you, we can help point you at lab authoring
> documentation. We need some people interested in writing some labs because
> the new platforms (especially phones) have UI adaptations which need some
> fixing, for labs.
> 
> Meanwhile, one of the more important issues for an author is finding a good
> reviewing audience to work with. (Even more important, of course, is
> writing stuff.)
> 
> Thanks,
> 
> -- 
> Raul
> 
> 
> On Wed, Apr 23, 2014 at 1:52 PM, alexgian <alexgian at blueyonder.co.uk> wrote:
> 
>>> The information and more are in the vocabulary page for %.
>> 
>> Well, yes, but so tersely and compactly expressed that you have to know the
>> long answer before you understand it!  I did look at the Vocab page, but
>> didn't "get it", that's why I posted.
>> 
>> It needed Roger's somewhat more expanded explanation for those of us that
>> are somewhat slower on the uptake.  That's why I said the Vocab could use a
>> touch up.  It is NOT user friendly, more of an ultra-coded reference.  Of
>> course, you might not see it this way, but I'd bet most newcomers would.
>> 
>> And it's not as if there is a longer explanation somewhere else, is there?
>> Well, other than this thread, I mean...    :)
>> 
>> 
>> 
>> On 23 April 2014 18:17, Roger Hui <rogerhui.canada at gmail.com> wrote:
>> 
>>> The information and more are in the vocabulary page for %.
>>> http://www.jsoftware.com/help/dictionary/d131.htm .
>>> 
>>> 
>>> On Wed, Apr 23, 2014 at 10:02 AM, alexgian <alexgian at blueyonder.co.uk
>>>> wrote:
>>> 
>>>> Great info, thanks Roger.
>>>> If it was up to me, I'd DEFINITELY include that in the Vocabulary, is
>> it
>>>> even documented anywhere else?
>>>> 
>>>> 
>>>> On 23 April 2014 17:33, Roger Hui <rogerhui.canada at gmail.com> wrote:
>>>> 
>>>>> %. x for a vector x is the same as ($x)$%.,.x, and the key expression
>>> is
>>>>> %.,.x, the "matrix inverse" of a 1-column matrix.  b=.y%.x on a tall
>>>> matrix
>>>>> x is solving a least-squares problem, the coefficients b that
>> minimizes
>>>> the
>>>>> sum of squares of y - x +/ .* b .
>>>>> 
>>>>> In addition, for a non-zero vector x, (%.x) +/ .* x is 1, a special
>>> case
>>>> of
>>>>> that (%.x)+/ .* x is an identity matrix, whence one can deduce that
>> for
>>>>> vector x, %.x is x%+/x^2.
>>>>> 
>>>>>   ] x=: 7 ?.@$ 100
>>>>> 94 56 8 6 85 48 66
>>>>>   %. x
>>>>> 0.00362137 0.00215741 0.000308202 0.000231152 0.00327465 0.00184921
>>>>> 0.00254267
>>>>>   (%.x) +/ .* x
>>>>> 1
>>>>>   x % +/x^2
>>>>> 0.00362137 0.00215741 0.000308202 0.000231152 0.00327465 0.00184921
>>>>> 0.00254267
>>>>> 
>>>>>   M=: 7 3 ?.@$ 100
>>>>>   (%.M) +/ .* M
>>>>>           1 5.55112e_17 _2.77556e_17
>>>>> _1.21431e_16           1  1.11022e_16
>>>>> _4.85723e_17 1.94289e_16            1
>>>>> 
>>>>> 
>>>>> 
>>>>> On Wed, Apr 23, 2014 at 9:13 AM, alexgian <alexgian at blueyonder.co.uk
>>> 
>>>>> wrote:
>>>>> 
>>>>>> Just wondering:
>>>>>> %. 2 3 4
>>>>>>   0.0689655 0.103448 0.137931
>>>>>> 
>>>>>> Which is fair enough enough at one level, I suppose, since the dot
>>>>> product
>>>>>> of the two arrays IS 1, but what system/equation is being solved
>>> here?
>>>>>> Obviously, there are infinite solutions.  Why that one?
>>>>>> IOW, which "matrix" is being inverted here?
>>>>>> 
>>>>>> Thanks
>>>>>> 
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