Mercurial > hg > octave-lyh
annotate scripts/linear-algebra/cond.m @ 14138:72c96de7a403 stable
maint: update copyright notices for 2012
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Mon, 02 Jan 2012 14:25:41 -0500 |
| parents | f96b9b9f141b |
| children | f3d52523cde1 |
| rev | line source |
|---|---|
|
14138
72c96de7a403
maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
parents:
12642
diff
changeset
|
1 ## Copyright (C) 1993-2012 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 -*- |
|
11471
994e2a93a8e2
Use uppercase 'A' to refer to matrix inputs in m-files.
Rik <octave@nomad.inbox5.com>
parents:
10793
diff
changeset
|
20 ## @deftypefn {Function File} {} cond (@var{A}) |
|
11563
3c6e8aaa9555
Grammarcheck m-files before 3.4 release.
Rik <octave@nomad.inbox5.com>
parents:
11523
diff
changeset
|
21 ## @deftypefnx {Function File} {} cond (@var{A}, @var{p}) |
|
12584
7ef7e20057fa
Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
22 ## Compute the @var{p}-norm condition number of a matrix. |
|
12642
f96b9b9f141b
doc: Periodic grammarcheck and spellcheck of documentation.
Rik <octave@nomad.inbox5.com>
parents:
12584
diff
changeset
|
23 ## |
|
12584
7ef7e20057fa
Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents:
11587
diff
changeset
|
24 ## @code{cond (@var{A})} is ## defined as |
|
10602
38eae0c3a003
Add TeX equation to cond.m documentation
Rik <octave@nomad.inbox5.com>
parents:
9307
diff
changeset
|
25 ## @tex |
|
11471
994e2a93a8e2
Use uppercase 'A' to refer to matrix inputs in m-files.
Rik <octave@nomad.inbox5.com>
parents:
10793
diff
changeset
|
26 ## $ {\parallel A \parallel_p * \parallel A^{-1} \parallel_p .} $ |
|
10602
38eae0c3a003
Add TeX equation to cond.m documentation
Rik <octave@nomad.inbox5.com>
parents:
9307
diff
changeset
|
27 ## @end tex |
|
38eae0c3a003
Add TeX equation to cond.m documentation
Rik <octave@nomad.inbox5.com>
parents:
9307
diff
changeset
|
28 ## @ifnottex |
|
11471
994e2a93a8e2
Use uppercase 'A' to refer to matrix inputs in m-files.
Rik <octave@nomad.inbox5.com>
parents:
10793
diff
changeset
|
29 ## @code{norm (@var{A}, @var{p}) * norm (inv (@var{A}), @var{p})}. |
|
10602
38eae0c3a003
Add TeX equation to cond.m documentation
Rik <octave@nomad.inbox5.com>
parents:
9307
diff
changeset
|
30 ## @end ifnottex |
|
38eae0c3a003
Add TeX equation to cond.m documentation
Rik <octave@nomad.inbox5.com>
parents:
9307
diff
changeset
|
31 ## |
|
38eae0c3a003
Add TeX equation to cond.m documentation
Rik <octave@nomad.inbox5.com>
parents:
9307
diff
changeset
|
32 ## By default @code{@var{p} = 2} is used which implies a (relatively slow) |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11563
diff
changeset
|
33 ## singular value decomposition. Other possible selections are |
|
10687
a8ce6bdecce5
Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents:
10602
diff
changeset
|
34 ## @code{@var{p} = 1, Inf, "fro"} which are generally faster. See |
|
10602
38eae0c3a003
Add TeX equation to cond.m documentation
Rik <octave@nomad.inbox5.com>
parents:
9307
diff
changeset
|
35 ## @code{norm} for a full discussion of possible @var{p} values. |
|
9307
c2923c27c877
Various documentation improvements
Rik <rdrider0-list@yahoo.com>
parents:
9051
diff
changeset
|
36 ## @seealso{condest, rcond, norm, svd} |
| 3372 | 37 ## @end deftypefn |
| 4 | 38 |
| 2314 | 39 ## Author: jwe |
| 40 | |
|
11471
994e2a93a8e2
Use uppercase 'A' to refer to matrix inputs in m-files.
Rik <octave@nomad.inbox5.com>
parents:
10793
diff
changeset
|
41 function retval = cond (A, p) |
| 4 | 42 |
| 7484 | 43 if (nargin && nargin < 3) |
|
11471
994e2a93a8e2
Use uppercase 'A' to refer to matrix inputs in m-files.
Rik <octave@nomad.inbox5.com>
parents:
10793
diff
changeset
|
44 if (ndims (A) > 2) |
| 8664 | 45 error ("cond: only valid on 2-D objects"); |
| 7484 | 46 endif |
| 47 | |
| 48 if (nargin <2) | |
| 49 p = 2; | |
| 4890 | 50 endif |
| 51 | |
|
7768
a2d9f325b65a
Use isschar instead of deprecated isstr
Rafael Laboissiere <rafael@debian.org>
parents:
7484
diff
changeset
|
52 if (! ischar (p) && p == 2) |
|
11471
994e2a93a8e2
Use uppercase 'A' to refer to matrix inputs in m-files.
Rik <octave@nomad.inbox5.com>
parents:
10793
diff
changeset
|
53 [nr, nc] = size (A); |
| 7484 | 54 if (nr == 0 || nc == 0) |
| 55 retval = 0.0; | |
|
11471
994e2a93a8e2
Use uppercase 'A' to refer to matrix inputs in m-files.
Rik <octave@nomad.inbox5.com>
parents:
10793
diff
changeset
|
56 elseif (any (any (isinf (A) | isnan (A)))) |
| 7484 | 57 error ("cond: argument must not contain Inf or NaN values"); |
| 58 else | |
|
11471
994e2a93a8e2
Use uppercase 'A' to refer to matrix inputs in m-files.
Rik <octave@nomad.inbox5.com>
parents:
10793
diff
changeset
|
59 sigma = svd (A); |
| 7484 | 60 sigma_1 = sigma(1); |
| 61 sigma_n = sigma(end); | |
| 62 if (sigma_1 == 0 || sigma_n == 0) | |
| 63 retval = Inf; | |
| 64 else | |
| 65 retval = sigma_1 / sigma_n; | |
| 66 endif | |
| 67 endif | |
| 3250 | 68 else |
|
11587
c792872f8942
all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents:
11563
diff
changeset
|
69 retval = norm (A, p) * norm (inv (A), p); |
| 3250 | 70 endif |
| 4 | 71 else |
| 6046 | 72 print_usage (); |
| 4 | 73 endif |
| 74 | |
| 75 endfunction | |
| 7411 | 76 |
| 7484 | 77 %!test |
| 78 %! y= [7, 2, 3; 1, 3, 4; 6, 4, 5]; | |
| 79 %! tol = 1e-6; | |
| 80 %! type = {1, 2, 'fro', 'inf', inf}; | |
| 81 %! for n = 1:numel(type) | |
| 82 %! rcondition(n) = 1 / cond (y, type{n}); | |
| 83 %! endfor | |
| 84 %! assert (rcondition, [0.017460, 0.019597, 0.018714, 0.012022, 0.012022], tol); | |
| 7411 | 85 |
| 7484 | 86 %!assert (abs (cond ([1, 2; 2, 1]) - 3) < sqrt (eps)); |
| 87 | |
| 88 %!assert (cond ([1, 2, 3; 4, 5, 6; 7, 8, 9]) > 1.0e+16); | |
| 7411 | 89 |
| 90 %!error cond (); | |
| 91 | |
| 7484 | 92 %!error cond (1, 2, 3); |
| 7411 | 93 |