From octave-sources-request at bevo dot che dot wisc dot edu Thu Dec  6 11:30:51 2001
Subject: Echelon form m-files
From: Jason Karcz <nozai at yahoo dot com>
To: octave-sources at bevo dot che dot wisc dot edu
Date: Thu, 6 Dec 2001 11:29:53 -0600


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Content-Type: text/plain; charset=us-ascii
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Attached are two m-files that can be put in the
/usr/share/octave/x.x.x/m/linear-algebra/ directory to
add the functionality of row echelon and reduced row
echelon form.  These are an incredibly large part of
linear algebra, and these files have been tested on
matricies large and small (including empty).  They
work.

Thanks for looking at them!

Jason Karcz

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Content-Type: text/plain; name="rref.m"
Content-Description: rref.m
Content-Disposition: inline; filename="rref.m"

## Copyright (C) 2001 Jason E. Karcz
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this file.  If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

## -*- texinfo -*-
##  at deftypefn {Function File} {} rref (@var{x})
## Computes the reduced row echelon form of a matrix.
##  at end deftypefn

## Author: jek

function z = rref (x)

  if (nargin != 1)
	  
    usage ("rref (x)");
    
  endif

  x = ref (x);
  
  [nr, nc] = size (x);

  pivr = 1;
  
  for i = 1:nc

	if (pivr <= nr)
	  
		if (x(pivr,i) != 0)

			x(pivr,:) = x(pivr,:) / x(pivr,i);
		  
			if (norm (x(1:pivr-1,i)) != 0 && pivr != 1)

				tmp = pivr - 1;

				while (tmp != 0)

					x(tmp,:) = x(tmp,:) - x(tmp,i) * x(pivr,:);

					tmp = tmp - 1;

				endwhile

			endif

			pivr = pivr + 1;

		endif
		
	endif

  endfor
		
  z = x;
  
endfunction

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Content-Type: text/plain; name="ref.m"
Content-Description: ref.m
Content-Disposition: inline; filename="ref.m"

## Copyright (C) 2001 Jason E. Karcz
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this file.  If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

## -*- texinfo -*-
##  at deftypefn {Function File} {} ref (@var{x})
## Computes the row echelon form of a matrix.
##  at end deftypefn

## Author: jek

function z = ref (x)

  if (nargin != 1)

    usage ("ref (x)");

  endif

  [nr, nc] = size (x);

  pivr = 1;
  
  for i = 1:nc

	if (norm (x(pivr:nr,i)) != 0 && pivr < nr)

		if (x(pivr,i) == 0)

			tmp = pivr+1;
		
			while (x(pivr,i) == 0)

				if (x(tmp,i) != 0)

					tmpv = x(tmp,:);
					x(tmp,:) = x(pivr,:);
					x(pivr,:) = tmpv;

				endif

				tmp = tmp + 1;
				
			endwhile

		endif

		for j = pivr+1:nr

			x(j,:) = x(j,:) - (x(j,i) / x(pivr,i)) * x(pivr,:);

		endfor

		pivr = pivr + 1;

	endif

  endfor

  z = x;
  
endfunction

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