From help-octave-request at bevo dot che dot wisc dot edu  Sun Jan 21 17:47:57 2001
Subject: Re: RREF (row reduce echelon form)
From: Paul Kienzle <pkienzle at kienzle dot powernet dot co dot uk>
To: "J. R. Miller" <millerjr at u dot washington dot edu>
Cc: help-octave at bevo dot che dot wisc dot edu
Date: Sun, 21 Jan 2001 16:49:58 +0000

And here is the version which comes with matcompat:
	http://users.powernet.co.uk/kienzle/octave/matcompat
Also, a number of different versions have been submitted to octave-sources
and help-octave over the years.  Perhaps you grabbed one of the them and
that's why you thought it was part of Octave?

Paul Kienzle
pkienzle at kienzle dot powernet dot co dot uk

## rref   Reduced row echelon form
##      R = rref (A, tol) returns the reduced row echelon form of a.
##      tol defaults to eps * max (size (A)) * norm (A, inf)
##
##      [R, k] = rref (...) returns the vector of "bound variables",
##      which are those columns on which elimination has been performed.

## Author: Paul Kienzle (based on a anonymous source from the public domain)

function [A, k] = rref (A, tolerance)

  ## Supress empty list warnings
  eleo = empty_list_elements_ok;
  unwind_protect
    empty_list_elements_ok = 1;
    
    [rows,cols] = size (A);

    if (nargin < 2)
      tolerance = eps * max (rows, cols) * norm (A, inf);
    endif

    used = zeros(1,cols);
    r = 1;
    for c=1:cols
      ## Find the pivot row
      [m, pivot] = max (abs (A (r:rows, c)));
      pivot = r + pivot - 1;
      
      if (m <= tolerance)
        ## Skip column c, making sure the approximately zero terms are
        ## actually zero.
        A (r:rows, c) = zeros (rows-r+1, 1);

      else
        ## keep track of bound variables
        used (1, c) = 1;

        ## Swap current row and pivot row
        A ([pivot, r], c:cols) = A ([r, pivot], c:cols);

        ## Normalize pivot row
        A (r, c:cols) = A (r, c:cols) / A (r, c);

        ## Eliminate the current column
        ridx = [1:r-1, r+1:rows];
        A (ridx, c:cols) = A (ridx, c:cols) - A (ridx, c) * A(r, c:cols);

        ## Check if done
        if (r++ == rows) break; endif
      endif
    endfor
    k = find(used);

  unwind_protect_cleanup
    ## Restore state
    empty_list_elements_ok = eleo;
  end_unwind_protect
endfunction

On Sat, Jan 20, 2001 at 09:46:43PM -0800, J. R. Miller wrote:
> Hi,
> 
> I seem to recall several years ago there was an octave command or function
> "RREF" (row reduce echelon form), for whatever version of Octave
> corresponded to Debian 1.2 or 1.3.  Returning, I can't find "RREF".  If
> I'm just not seeing it, please tell me where to look, or how to setup.
> 
> If it's not part of Octave, is there somewhere fellow users share this
> kind of code, so I don't have to reinvent the wheel?
> 
> Otherwise, please tell me where I can find pseudocode for the algorithm
> and whatever language reference is recommended for writing this code.  
> /This is not an area of strength for me, so please be specific./
> 
> Thanks,
> 
> JR
> millerjr at u dot washington dot edu
> 
> 
> 
> 
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Octave is freely available under the terms of the GNU GPL.

Octave's home on the web:  http://www.octave.org
How to fund new projects:  http://www.octave.org/funding.html
Subscription information:  http://www.octave.org/archive.html
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