Mercurial > hg > octave-lyh

comparison scripts/linear-algebra/rref.m @ 11469:c776f063fefe

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Overhaul m-script files to use common variable name between code and documentation.
author Rik <octave@nomad.inbox5.com>
date Sun, 09 Jan 2011 12:41:21 -0800
parents 95c3e38098bf
children fd0a3ac60b0e
comparison
equal deleted inserted replaced
11468:e1edf0ba3bcb 11469:c776f063fefe
15 ## You should have received a copy of the GNU General Public License 15 ## You should have received a copy of the GNU General Public License
16 ## along with Octave; see the file COPYING. If not, see 16 ## along with Octave; see the file COPYING. If not, see
17 ## <http://www.gnu.org/licenses/>. 17 ## <http://www.gnu.org/licenses/>.
18 18
19 ## -*- texinfo -*- 19 ## -*- texinfo -*-
20 ## @deftypefn {Function File} {[@var{r}, @var{k}] =} rref (@var{a}, @var{tol}) 20 ## @deftypefn {Function File} {[@var{r}, @var{k}] =} rref (@var{A}, @var{tol})
21 ## 21 ##
22 ## Returns the reduced row echelon form of @var{a}. @var{tol} defaults 22 ## Returns the reduced row echelon form of @var{A}. @var{tol} defaults
23 ## to @code{eps * max (size (@var{a})) * norm (@var{a}, inf)}. 23 ## to @code{eps * max (size (@var{A})) * norm (@var{A}, inf)}.
24 ## 24 ##
25 ## Called with two return arguments, @var{k} returns the vector of 25 ## Called with two return arguments, @var{k} returns the vector of
26 ## "bound variables", which are those columns on which elimination 26 ## "bound variables", which are those columns on which elimination
27 ## has been performed. 27 ## has been performed.
28 ## 28 ##
29 ## @end deftypefn 29 ## @end deftypefn
30 30
31 ## Author: Paul Kienzle <pkienzle@users.sf.net> 31 ## Author: Paul Kienzle <pkienzle@users.sf.net>
32 ## (based on a anonymous source from the public domain) 32 ## (based on an anonymous source from the public domain)
33 33
34 function [A, k] = rref (A, tolerance) 34 function [A, k] = rref (A, tol)
35 35
36 if (nargin < 1 || nargin > 2) 36 if (nargin < 1 || nargin > 2)
37 print_usage (); 37 print_usage ();
38 endif 38 endif
39 39
43 43
44 [rows, cols] = size (A); 44 [rows, cols] = size (A);
45 45
46 if (nargin < 2) 46 if (nargin < 2)
47 if (isa (A, "single")) 47 if (isa (A, "single"))
48 tolerance = eps ("single") * max (rows, cols) * norm (A, inf ("single")); 48 tol = eps ("single") * max (rows, cols) * norm (A, inf ("single"));
49 else 49 else
50 tolerance = eps * max (rows, cols) * norm (A, inf); 50 tol = eps * max (rows, cols) * norm (A, inf);
51 endif 51 endif
52 endif 52 endif
53 53
54 used = zeros (1, cols); 54 used = zeros (1, cols);
55 r = 1; 55 r = 1;
56 for c = 1:cols 56 for c = 1:cols
57 ## Find the pivot row 57 ## Find the pivot row
58 [m, pivot] = max (abs (A(r:rows,c))); 58 [m, pivot] = max (abs (A(r:rows,c)));
59 pivot = r + pivot - 1; 59 pivot = r + pivot - 1;
60 60
61 if (m <= tolerance) 61 if (m <= tol)
62 ## Skip column c, making sure the approximately zero terms are 62 ## Skip column c, making sure the approximately zero terms are
63 ## actually zero. 63 ## actually zero.
64 A (r:rows, c) = zeros (rows-r+1, 1); 64 A (r:rows, c) = zeros (rows-r+1, 1);
65 else 65 else
66 ## keep track of bound variables 66 ## keep track of bound variables