Mercurial > hg > octave-nkf
annotate scripts/linear-algebra/orth.m @ 10687:a8ce6bdecce5
Improve documentation strings.
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Tue, 08 Jun 2010 20:22:38 -0700 |
| parents | 95c3e38098bf |
| children | eb9e0b597d61 |
| rev | line source |
|---|---|
| 7017 | 1 ## Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2005, 2006, |
| 8920 | 2 ## 2007, 2008 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/>. | |
| 1026 | 19 |
| 3372 | 20 ## -*- texinfo -*- |
| 21 ## @deftypefn {Function File} {} orth (@var{a}, @var{tol}) | |
| 22 ## Return an orthonormal basis of the range space of @var{a}. | |
| 3426 | 23 ## |
| 2311 | 24 ## The dimension of the range space is taken as the number of singular |
| 3372 | 25 ## values of @var{a} greater than @var{tol}. If the argument @var{tol} is |
| 26 ## missing, it is computed as | |
| 3426 | 27 ## |
| 3372 | 28 ## @example |
| 29 ## max (size (@var{a})) * max (svd (@var{a})) * eps | |
| 30 ## @end example | |
|
10687
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Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
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31 ## @seealso{null} |
| 3372 | 32 ## @end deftypefn |
| 557 | 33 |
| 5428 | 34 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 2312 | 35 ## Created: 24 December 1993. |
| 36 ## Adapted-By: jwe | |
| 557 | 37 |
| 2312 | 38 function retval = orth (A, tol) |
| 557 | 39 |
| 3141 | 40 if (nargin == 1 || nargin == 2) |
| 557 | 41 |
| 3141 | 42 [U, S, V] = svd (A); |
| 557 | 43 |
| 3141 | 44 [rows, cols] = size (A); |
| 1065 | 45 |
| 3141 | 46 [S_nr, S_nc] = size (S); |
| 47 | |
| 48 if (S_nr == 1 || S_nc == 1) | |
| 49 s = S(1); | |
| 50 else | |
| 51 s = diag (S); | |
| 52 endif | |
| 557 | 53 |
| 3141 | 54 if (nargin == 1) |
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55 if (isa (A, "single")) |
| 10549 | 56 tol = max (size (A)) * s (1) * eps ("single"); |
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57 else |
| 10549 | 58 tol = max (size (A)) * s (1) * eps; |
|
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parents:
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changeset
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59 endif |
| 3141 | 60 endif |
| 61 | |
| 62 rank = sum (s > tol); | |
| 557 | 63 |
| 3141 | 64 if (rank > 0) |
| 65 retval = -U (:, 1:rank); | |
| 66 else | |
| 67 retval = zeros (rows, 0); | |
| 68 endif | |
| 557 | 69 |
| 70 else | |
| 3141 | 71 |
| 6046 | 72 print_usage (); |
| 3141 | 73 |
| 557 | 74 endif |
| 75 | |
| 76 endfunction |