Re: RREF (row reduce echelon form)

[Paul Kienzle]

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
address@hidden

## 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
> address@hidden
> 
> 
> 
> 
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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
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