You are right, in the following sense,
ys=. [ * }.@:(% {.)@:(+/)@:(] ^/ i.@:>:@:[)
update=. ] ,~ -/@:(] * [ {.~ #@:]) % #@:]
simple=. -@:|.@:>@:{:@:p.@:(ys update ^: (#@:[) 1:)f.
mean=. +/ % #
std =: mean &.: *: @: (- mean)
Y=. 1 2 3 7
(mean ; std) Y
┌────┬───────┐
│3.25│2.27761│
└────┴───────┘
( S0=. 3 simple Y )
1.6084j0.550768 1.6084j_0.550768 6.53321
(mean ; std) S0
┌────┬───────┐
│3.25│2.27761│
└────┴───────┘
However, if complex results are allowed (and I do not see why should not be
allowed) then the statement: " The vector 'A simplify B' has the same A
moments as the vector B" does not provide a (full) characterization of the
result since,
( S1=. (3&simple + 2*(mean - 3&simple)) Y)
4.8916j_0.550768 4.8916j0.550768 _0.0332088
(mean ; std) S1
┌────┬───────┐
│3.25│2.27761│
└────┴───────┘
and clearly,
S0 -: S1
0
Yet, S0 seems to be a better result compared to S1 in following context:
(mean ; std) *: Y
┌─────┬───────┐
│15.75│19.4084│
└─────┴───────┘
(mean ; std) *: S0
┌─────┬───────┐
│15.75│18.9894│
└─────┴───────┘
(mean ; std) *: S1
┌─────┬───────┐
│15.75│10.2303│
└─────┴───────┘
That is, under *: apparently, S0 as opposed to S1, preserves better the
mean and the std, and under other some other transformations as well, for
example,
(mean ; std) %: Y
┌─────┬────────┐
│1.698│0.605626│
└─────┴────────┘
(mean ; std) %: S0
┌───────┬────────┐
│1.70945│0.572513│
└───────┴────────┘
(mean ; std) %: S1
┌─────────────────┬──────────────────┐
│1.47679j0.0607443│1.03934j_0.0863113│
└─────────────────┴──────────────────┘
(mean ; std) ^ Y
┌───────┬───────┐
│281.707│470.541│
└───────┴───────┘
(mean ; std) ^ S0
┌───────┬───────┐
│232.038│322.125│
└───────┴───────┘
(mean ; std) ^ S1
┌───────┬────────┐
│75.9723│0j20.618│
└───────┴────────┘
(mean ; std) ^. Y
┌────────┬────────┐
│0.934417│0.703815│
└────────┴────────┘
(mean ; std) ^. S0
┌────────┬────────┐
│0.979417│0.574606│
└────────┴────────┘
(mean ; std) ^. S1
┌─────────────────┬────────────────┐
│_0.0724338j1.0472│2.35516j_1.48176│
└─────────────────┴────────────────┘
Of course, the simplification might not work well when there is some
variation within the range; but, even then S0 seems to make more sense than
S1,
(mean ; std) 2 o. Y
┌──────────┬────────┐
│_0.0279837│0.708947│
└──────────┴────────┘
(mean ; std) 2 o. S0
┌────────┬─────────┐
│0.294011│0.0673377│
└────────┴─────────┘
(mean ; std) 2 o. S1
┌────────┬──────────┐
│0.470473│0j0.276611│
└────────┴──────────┘
In any case, I find symplify quite interesting but it seems that your
definition is incomplete. Perhaps, A&simplify should also be required to
be analytic?
On Fri, Jun 26, 2015 at 4:54 AM, 'Bo Jacoby' via Programming <
[email protected]> wrote:
> datatype 1 2 3 7integer datatype 2 simplify 1 2 3 7floating
> datatype 3 simplify 1 2 3 7complex (2&simplify=[:2&simplify 3&simplify)
> 1 2 3 71 1A correct result may be non-real!
>
>
>
>
> Den 9:53 fredag den 26. juni 2015 skrev 'Bo Jacoby' via Programming <
> [email protected]>:
>
>
>
> Explanation: The vector 'A simplify B' has the same A moments as the
> vector B.Examples: 1 simplify 0 21 2 simplify 0 20 2 3 simplify 0
> 2_0.224745 1 2.22474 2 simplify 3 simplify 0 20 2 1 simplify 3 simplify
> 0 21
>
>
>
>
> Den 0:04 fredag den 26. juni 2015 skrev Kip Murray <
> [email protected]>:
>
>
>
> 1 X
>
> 2 X X
>
> 3
>
> 4 X
>
> 5
>
> 6 X
>
>
> 1 X
>
> 2
>
> 3 X
>
> 4
>
> 5 X
>
> 6
>
>
> 1
> X
> 2 X
>
> 3
>
> 4
>
> 5 X
>
> 6
>
>
> Above I have attempted three histograms. The first shows the data set 1 2
> 2 4 6 which has mean 3 and standard deviation 2, median 2 and fourths (not
> quartiles) 1.5 and 5 . The second histogram shows the mean and the mean
> plus or minus a standard deviation, and the third histogram shows the
> median and fourths. (The fourths are respectively the median of the
> numbers below the median, and the median of the numbers above the median.)
>
> --Kip Murray
>
>
> On Thursday, June 25, 2015, Devon McCormick <[email protected]> wrote:
>
> > I put together this J based on the "fivenum" routine in R mentioned in
> the
> > Wikipedia link:
> >
> > fivenum=: 3 : 0
> > if. 0=#y=. /:~y do. 5#_.
> > else. n4=. -:<.-:3+#y
> > d=. <:1,n4,(-:>:#y),(n4-~>:#y),#y
> > -:(y{~<.d)+y{~>.d
> > end.
> > )
> >
> > It returns the minimum, the quartile points, and the maximum of a series.
> > The first branch of the "if" roughly replicates some of the R function's
> > NA-handling.
> >
> > On Thu, Jun 25, 2015 at 10:14 AM, David Lambert <[email protected]
> > <javascript:;>>
> > wrote:
> >
> > > Is simplify supposed to report the i.x moments of the data? Would be
> > > useful.
> > > When I removed the question marks from simplify to make valid j
> > > 1 simplify DATA NB. does report the mean
> > > Otherwise I haven't made sense of the results for the verb I created.
> > >
> > > datatype N
> > > integer
> > >
> > > 3 simplify N
> > > _951.236j1533.8 _951.236j_1533.8 2658.39
> > >
> > > Date: Thu, 25 Jun 2015 08:39:51 +0000 (UTC)
> > >> From: "'Bo Jacoby' via Programming"<[email protected]
> > <javascript:;>>
> > >> To: Programming Forum<[email protected] <javascript:;>>
> > >> Subject: [Jprogramming] simplify
> > >> Message-ID:
> > >> <
> [email protected]
> > <javascript:;>>
> > >> Content-Type: text/plain; charset=UTF-8
> > >>
> > >> NB.?If you have got a bunch of numbers? ? ? ]n=.?20#10035 32 66 37 94
> 56
> > >> 44 30 25 70 27 68 49 92 96 79 74 99 72 22NB. and you want to simplify,
> > then
> > >> take the mean value
> > >>
> > >
> > > <unreadable cut>
> > >>
> > >
> > > )NB.?If you can simplify the programming, the please let me know.
> > >> ThanksBo
> > >>
> > >
> > > ----------------------------------------------------------------------
> > > For information about J forums see http://www.jsoftware.com/forums.htm
> > >
> >
> >
> >
> > --
> > Devon McCormick, CFA
> > ----------------------------------------------------------------------
> > For information about J forums see http://www.jsoftware.com/forums.htm
> >
>
>
> --
> Sent from Gmail Mobile
> ----------------------------------------------------------------------
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>
>
>
>
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>
>
>
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