/usr/share/freemat/toolbox/matrix/rref.m is in freemat-data 4.0-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 | % RREF RREF Reduced Row Echelon Form of a Matrix
%
% Usage
%
% Calculates the reduced row echelon form of a matrix using Gauss
% Jordan elimination with partial pivoting. The generic syntax
% for rref is
%
% R = rref(A)
%
% A default tolerance of max(size(A))*eps*norm(A,inf) is used to
% detect negligible column elements. The second form of rref
% returns a vector k as well as R
%
% [R,k] = rref(A)
%
% where k is a vector that correponds to the columns of A
% used as pivot columns. If you want to control the tolerance
% used to identify negligible elements, you can use the form
%
% [R,k] = rref(A, tolerance)
%
% This implementation of rref is based on the one from
% the matcompat lib for octave. It is copyright Paul Kienzle,
% and distributed under the GNU GPL.
function [A,k] = rref(A, tolerance)
% Original notice for rref from
% http://users.powernet.co.uk/kienzle/octave/matcompat/rref.m
% Copyright (C) 2000 Paul Kienzle
%
% 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 of the License, 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 program; if not, write to the Free Software
% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
% 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)
[rows,cols] = size (A);
if (nargin < 2)
tolerance = eps * max (rows, cols) * norm (A, inf);
end
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; end
r = r + 1;
end
end
k = find(used);
end
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