Mercurial > octave-nkf
annotate scripts/linear-algebra/orth.m @ 12312:b10ea6efdc58 release-3-4-x ss-3-3-91
version is now 3.3.91
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Mon, 31 Jan 2011 08:36:58 -0500 |
| parents | fd0a3ac60b0e |
| children | 7ef7e20057fa |
| rev | line source |
|---|---|
| 11523 | 1 ## Copyright (C) 1994-2011 John W. Eaton |
| 2313 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 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 | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 2313 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 1026 | 18 |
| 3372 | 19 ## -*- texinfo -*- |
|
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20 ## @deftypefn {Function File} {} orth (@var{A}, @var{tol}) |
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eb9e0b597d61
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Rik <octave@nomad.inbox5.com>
parents:
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21 ## Return an orthonormal basis of the range space of @var{A}. |
| 3426 | 22 ## |
| 2311 | 23 ## The dimension of the range space is taken as the number of singular |
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Rik <octave@nomad.inbox5.com>
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24 ## values of @var{A} greater than @var{tol}. If the argument @var{tol} is |
| 3372 | 25 ## missing, it is computed as |
| 3426 | 26 ## |
| 3372 | 27 ## @example |
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28 ## max (size (@var{A})) * max (svd (@var{A})) * eps |
| 3372 | 29 ## @end example |
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30 ## @seealso{null} |
| 3372 | 31 ## @end deftypefn |
| 557 | 32 |
| 5428 | 33 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 2312 | 34 ## Created: 24 December 1993. |
| 35 ## Adapted-By: jwe | |
| 557 | 36 |
| 2312 | 37 function retval = orth (A, tol) |
| 557 | 38 |
| 3141 | 39 if (nargin == 1 || nargin == 2) |
| 557 | 40 |
| 3141 | 41 [U, S, V] = svd (A); |
| 557 | 42 |
| 3141 | 43 [rows, cols] = size (A); |
| 1065 | 44 |
| 3141 | 45 [S_nr, S_nc] = size (S); |
| 46 | |
| 47 if (S_nr == 1 || S_nc == 1) | |
| 48 s = S(1); | |
| 49 else | |
| 50 s = diag (S); | |
| 51 endif | |
| 557 | 52 |
| 3141 | 53 if (nargin == 1) |
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54 if (isa (A, "single")) |
| 10549 | 55 tol = max (size (A)) * s (1) * eps ("single"); |
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56 else |
| 10549 | 57 tol = max (size (A)) * s (1) * eps; |
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58 endif |
| 3141 | 59 endif |
| 60 | |
| 61 rank = sum (s > tol); | |
| 557 | 62 |
| 3141 | 63 if (rank > 0) |
| 64 retval = -U (:, 1:rank); | |
| 65 else | |
| 66 retval = zeros (rows, 0); | |
| 67 endif | |
| 557 | 68 |
| 69 else | |
| 3141 | 70 |
| 6046 | 71 print_usage (); |
| 3141 | 72 |
| 557 | 73 endif |
| 74 | |
| 75 endfunction |