[Jprogramming] applying >1 gerunds to a set of items

[Devon McCormick]

   (i.10) corr i.10      NB. Perfectly correlated
1
   (i.10) corr |.i.10    NB. Perfectly anti-correlated (inversely
correlated)
_1
   (i.10) corr *:i.10    NB. Highly correlated
0.962691
   (i.10) corr 10?@$100  NB. No significant correlation
0.0442917



On Wed, Feb 20, 2013 at 11:37 AM, Dan Bron <j at bron.us> wrote:

> I wrote:
> > corr =: (+/@:* % *&(+/)&.:*:)&(- +/%#)
>
> Linda asked for:
> > some sample data for corr with your expected result
>
> I'll just short-circuit this discussion and rephrase corr in Simplistic J
> for you.
>
>     avg =:  +/ % #
>     sumSqrs =:  13 : '+/ *: y'
>     simplisticCorr =:  13 : '(x - avg x) ( ([: +/ *) % [: %: ([: sumSqrs [)
> * [: sumSqrs ]) (y - avg y)'
>     simplisticCorrSpelledOut =: simplisticCorr f.
>
>     simplisticCorr
>  ([ - [: avg [) (([: +/ *) % [: %: ([: sumSqrs [) * [: sumSqrs ]) ] - [:
> avg
> ]
>
>     simplisticCorrSpelledOut
>  ([ - [: (+/ % #) [) (([: +/ *) % [: %: ([: ([: +/ *:) [) * [: ([: +/ *:)
> ])
> ] - [: (+/ % #) ]
>
> Of course, defining it this way defeats the entire purpose for which I
> introduced corr (elegance, simplicity, symmetry, brevity) but I know you
> have other purposes (avoiding conjunctions at all costs).
>
> So if you want to play with it for these purposes, any standard textbook
> example of calculating the correlation coefficient will do:
>
>    gnp1955   =:   91  51  58  359 134   70  129 515 70  707  468  749   998
> 2334
>    trade1955 =: 2729 407 349 1169 923 2689 1601 415 83 5395 1852 6530 18677
> 26836
>
>     gnp1955 corr trade1955  NB. GNP/capita highly correlated with trade in
> 1955
>  0.925343
>     gnp1955 simplisticCorr trade1955
>  0.925343
>     gnp1955 simplisticCorrSpelledOut trade1955
>  0.925343
>
> However, for those are interested in the verb's form, rather than its
> function, and want to know why I introduced it as a beautiful example of J,
> some explanations can be in the original thread:
>
> http://www.jsoftware.com/pipermail/programming/2007-June/007179.html
>
> [I should have noted yesterday that Oleg Kobchenko was the original author
> of corr (which I was somewhat disappointed to discover when I independently
> developed it some years later....)]
>
> -Dan
>
> PS:  Because I know you want to see it:
>
>    5!:4<'simplisticCorr'
>     +- [
>     +- -
>   +-+   +- [:
>   | +---+- avg
>   |     +- [
>   |
>   |     +- [:
>   | +---+- / --- +
>   | |   +- *
>   | +- %
>   +-+   +- [:
>   | |   +- %:
> --+ |   |         +- [:
>   | +---+     +---+- sumSqrs
>   |     |     |   +- [
>   |     +-----+- *
>   |           |   +- [:
>   |           +---+- sumSqrs
>   |               +- ]
>   | +- ]
>   | +- -
>   +-+   +- [:
>     +---+- avg
>         +- ]
>
>    5!:4<'simplisticCorrSpelledOut'
>     +- [
>     +- -
>   +-+   +- [:
>   | |   |     +- / --- +
>   | +---+-----+- %
>   |     |     +- #
>   |     +- [
>   |
>   |     +- [:
>   | +---+- / --- +
>   | |   +- *
>   | +- %
>   | |   +- [:
>   +-+   +- %:
>   | |   |           +- [:
> --+ |   |           |    +- [:
>   | +---+     +-----+----+- / --- +
>   |     |     |     |    +- *:
>   |     |     |     +- [
>   |     +-----+- *
>   |           |     +- [:
>   |           |     |    +- [:
>   |           +-----+----+- / --- +
>   |                 |    +- *:
>   |                 +- ]
>   | +- ]
>   | +- -
>   +-+   +- [:
>     |   |     +- / --- +
>     +---+-----+- %
>         |     +- #
>         +- ]
>
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>



-- 
Devon McCormick, CFA
^me^ at acm.
org is my
preferred e-mail