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From: rockwell@socrates.umd.edu (Raul Rockwell)
Newsgroups: comp.lang.apl
Subject: Re: Grade Down Columns of An Array
Message-ID: <ROCKWELL.91Jun21080548@socrates.umd.edu>
Date: 21 Jun 91 13:05:48 GMT
References: <33789@usc.edu>
Sender: rockwell@socrates.umd.edu (Raul Rockwell)
Organization: Traveller
Lines: 63
In-Reply-To: ann@neuro.usc.edu's message of 21 Jun 91 03: 57:51 GMT

Ann Simpson Chapin:
   Does anyone know how to grade down the columns of an array (rank 2)
   so that each column of the array is graded down as if it is a
   separate vector?  I do not want to have to create an interactive
   function ..
  
   I am using APL Plus II on a 386 with plenty on memory and a math
   coprocessor.....

Well, if you were using J, I'd recommend something like  
   \:~ "1  &.|: array

But since you're not, I'll try and describe a way to do this in
vanilla APL.  Basically, you coerce the array to a vector, sort the
vector in a way which preserves the original column order, then
reshape back to the original shape.

First off, you'll need the array in vector form.  You'll want all
members of a single column adjacent to each other, so you need to
transpose the array before you ravel it.  I'm going to give each
sentence twice -- once in psuedo-apl puns, and once in J.

   vec <- , (\) array
   vec =. , |:  array

Second off, you'll need to grade the array.  You want the grade to
preserve the original column ordering, so you need to normalize the
array, and add numbers to force the proper static ordering.

  normalized <- /|\  /|\ array
  normalized =. /:   /:  array

  colHorder <- - (R vec) x (R array)[0] / i (R array)[1]
  col_order =. - (# vec) * (0{$array)   # i. 1{$array

  grade <- \|/ colHorder + normalized
  grade =. \:  col_order + normalized

Finally, you need to restore the original shape of the array.  Note
that you need to do a transpose as well, which means that you need to
reshape using transposed dimensions.  (I'll just reverse the
dimensions here).

  sorted <- (\) ( (|) R array)R vec[grade]
  sorted =. |:  ( |.  $ array)$ grade{vec

voila.

As an aside, I haven't tested this code yet, but the basic concept is
sound.  I hope you can read it.  Also note that I've assumed origin 0
for the APL session -- I trust conversion to origin 1 is obvious, if
that is desired.

puns used here:
  <-   assignment
  (\)  transpose
  (|)  rotate
  R    rho
  H    delta
  x    times

-- 
Raul <rockwell@socrates.umd.edu>