Mercurial > octave-antonio
annotate scripts/linear-algebra/rank.m @ 11523:fd0a3ac60b0e
update copyright notices
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Fri, 14 Jan 2011 05:47:45 -0500 |
| parents | eb9e0b597d61 |
| children | 7ef7e20057fa |
| rev | line source |
|---|---|
| 11523 | 1 ## Copyright (C) 1993-2011 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/>. | |
| 245 | 18 |
| 3372 | 19 ## -*- texinfo -*- |
|
11470
eb9e0b597d61
Use common names for variables in documentation and code for a few more m-script files.
Rik <octave@nomad.inbox5.com>
parents:
10549
diff
changeset
|
20 ## @deftypefn {Function File} {} rank (@var{A}, @var{tol}) |
|
eb9e0b597d61
Use common names for variables in documentation and code for a few more m-script files.
Rik <octave@nomad.inbox5.com>
parents:
10549
diff
changeset
|
21 ## Compute the rank of @var{A}, using the singular value decomposition. |
|
eb9e0b597d61
Use common names for variables in documentation and code for a few more m-script files.
Rik <octave@nomad.inbox5.com>
parents:
10549
diff
changeset
|
22 ## The rank is taken to be the number of singular values of @var{A} that |
| 3372 | 23 ## are greater than the specified tolerance @var{tol}. If the second |
| 24 ## argument is omitted, it is taken to be | |
| 3426 | 25 ## |
| 3372 | 26 ## @example |
|
11470
eb9e0b597d61
Use common names for variables in documentation and code for a few more m-script files.
Rik <octave@nomad.inbox5.com>
parents:
10549
diff
changeset
|
27 ## tol = max (size (@var{A})) * sigma(1) * eps; |
| 3372 | 28 ## @end example |
| 3426 | 29 ## |
| 3372 | 30 ## @noindent |
| 3600 | 31 ## where @code{eps} is machine precision and @code{sigma(1)} is the largest |
|
11470
eb9e0b597d61
Use common names for variables in documentation and code for a few more m-script files.
Rik <octave@nomad.inbox5.com>
parents:
10549
diff
changeset
|
32 ## singular value of @var{A}. |
| 3372 | 33 ## @end deftypefn |
| 4 | 34 |
| 2314 | 35 ## Author: jwe |
| 36 | |
| 2311 | 37 function retval = rank (A, tol) |
| 4 | 38 |
| 39 if (nargin == 1) | |
| 40 sigma = svd (A); | |
| 4706 | 41 if (isempty (sigma)) |
| 42 tolerance = 0; | |
| 43 else | |
|
7795
df9519e9990c
Handle single precision eps values
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
44 if (isa (A, "single")) |
| 10549 | 45 tolerance = max (size (A)) * sigma (1) * eps ("single"); |
|
7795
df9519e9990c
Handle single precision eps values
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
46 else |
| 10549 | 47 tolerance = max (size (A)) * sigma (1) * eps; |
|
7795
df9519e9990c
Handle single precision eps values
David Bateman <dbateman@free.fr>
parents:
7017
diff
changeset
|
48 endif |
| 4706 | 49 endif |
| 4 | 50 elseif (nargin == 2) |
| 262 | 51 sigma = svd (A); |
| 4 | 52 tolerance = tol; |
| 53 else | |
| 6046 | 54 print_usage (); |
| 4 | 55 endif |
| 4706 | 56 |
| 4 | 57 retval = sum (sigma > tolerance); |
| 58 | |
| 59 endfunction |