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comparison scripts/linear-algebra/rank.m @ 2303:5cffc4b8de57

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[project @ 1996-06-24 09:15:24 by jwe]
author jwe
date Mon, 24 Jun 1996 09:15:24 +0000
parents 5d29638dd524
children 2b5788792cad
comparison
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2302:470c856bf55a 2303:5cffc4b8de57
1 # Copyright (C) 1996 John W. Eaton 1 ### Copyright (C) 1996 John W. Eaton
2 # 2 ###
3 # This file is part of Octave. 3 ### This file is part of Octave.
4 # 4 ###
5 # Octave is free software; you can redistribute it and/or modify it 5 ### Octave is free software; you can redistribute it and/or modify it
6 # under the terms of the GNU General Public License as published by the 6 ### under the terms of the GNU General Public License as published by
7 # Free Software Foundation; either version 2, or (at your option) any 7 ### the Free Software Foundation; either version 2, or (at your option)
8 # later version. 8 ### any later version.
9 # 9 ###
10 # Octave is distributed in the hope that it will be useful, but WITHOUT 10 ### Octave is distributed in the hope that it will be useful, but
11 # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 11 ### WITHOUT ANY WARRANTY; without even the implied warranty of
12 # FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 12 ### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 # for more details. 13 ### General Public License for more details.
14 # 14 ###
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, write to the Free 16 ### along with Octave; see the file COPYING. If not, write to the Free
17 # Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. 17 ### Software Foundation, 59 Temple Place - Suite 330, Boston, MA
18 ### 02111-1307, USA.
18 19
19 function retval = rank (A, tol) 20 function retval = rank (A, tol)
20 21
21 # usage: rank (a, tol) 22 ## usage: rank (a, tol)
22 # 23 ##
23 # Return the rank of the matrix a. The rank is taken to be the number 24 ## Return the rank of the matrix a. The rank is taken to be the number
24 # of singular values of a that are greater than tol. 25 ## of singular values of a that are greater than tol.
25 # 26 ##
26 # If the second argument is omitted, it is taken to be 27 ## If the second argument is omitted, it is taken to be
27 # 28 ##
28 # tol = max (size (a)) * sigma (1) * eps; 29 ## tol = max (size (a)) * sigma (1) * eps;
29 # 30 ##
30 # where eps is machine precision and sigma is the largest singular 31 ## where eps is machine precision and sigma is the largest singular
31 # value of a. 32 ## value of a.
32 33
33 if (nargin == 1) 34 if (nargin == 1)
34 sigma = svd (A); 35 sigma = svd (A);
35 tolerance = max (size (A)) * sigma (1) * eps; 36 tolerance = max (size (A)) * sigma (1) * eps;
36 elseif (nargin == 2) 37 elseif (nargin == 2)