Mercurial > hg > octave-nkf
annotate scripts/linear-algebra/rank.m @ 10023:73fc43e01f4c
allow issquare on arbitrary data
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Fri, 25 Dec 2009 22:20:33 +0100 |
| parents | 16f53d29049f |
| children | 95c3e38098bf |
| rev | line source |
|---|---|
| 7017 | 1 ## Copyright (C) 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2004, 2005, |
| 9245 | 2 ## 2006, 2007, 2008, 2009 John W. Eaton |
| 2313 | 3 ## |
| 4 ## This file is part of Octave. | |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 2313 | 10 ## |
| 11 ## Octave is distributed in the hope that it will be useful, but | |
| 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 14 ## General Public License for more details. | |
| 15 ## | |
| 16 ## You should have received a copy of the GNU General Public License | |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 245 | 19 |
| 3372 | 20 ## -*- texinfo -*- |
| 21 ## @deftypefn {Function File} {} rank (@var{a}, @var{tol}) | |
| 22 ## Compute the rank of @var{a}, using the singular value decomposition. | |
|
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23 ## The rank is taken to be the number of singular values of @var{a} that |
| 3372 | 24 ## are greater than the specified tolerance @var{tol}. If the second |
| 25 ## argument is omitted, it is taken to be | |
| 3426 | 26 ## |
| 3372 | 27 ## @example |
| 3600 | 28 ## tol = max (size (@var{a})) * sigma(1) * eps; |
| 3372 | 29 ## @end example |
| 3426 | 30 ## |
| 3372 | 31 ## @noindent |
| 3600 | 32 ## where @code{eps} is machine precision and @code{sigma(1)} is the largest |
| 3372 | 33 ## singular value of @var{a}. |
| 34 ## @end deftypefn | |
| 4 | 35 |
| 2314 | 36 ## Author: jwe |
| 37 | |
| 2311 | 38 function retval = rank (A, tol) |
| 4 | 39 |
| 40 if (nargin == 1) | |
| 41 sigma = svd (A); | |
| 4706 | 42 if (isempty (sigma)) |
| 43 tolerance = 0; | |
| 44 else | |
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45 if (isa (A, "single")) |
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46 tolerance = max (size (A)) * sigma (1) * eps ("single"); |
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47 else |
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48 tolerance = max (size (A)) * sigma (1) * eps; |
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49 endif |
| 4706 | 50 endif |
| 4 | 51 elseif (nargin == 2) |
| 262 | 52 sigma = svd (A); |
| 4 | 53 tolerance = tol; |
| 54 else | |
| 6046 | 55 print_usage (); |
| 4 | 56 endif |
| 4706 | 57 |
| 4 | 58 retval = sum (sigma > tolerance); |
| 59 | |
| 60 endfunction |