Mercurial > hg > octave-lyh
annotate scripts/linear-algebra/cond.m @ 10687:a8ce6bdecce5
Improve documentation strings.
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Tue, 08 Jun 2010 20:22:38 -0700 |
| parents | 38eae0c3a003 |
| children | be55736a0783 |
| rev | line source |
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| 7017 | 1 ## Copyright (C) 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2003, 2004, |
| 8920 | 2 ## 2005, 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 -*- |
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21 ## @deftypefn {Function File} {} cond (@var{a}) |
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22 ## @deftypefnx {Function File} {} cond (@var{a},@var{p}) |
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23 ## Compute the @var{p}-norm condition number of a matrix. @code{cond (@var{a})} is |
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24 ## defined as |
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25 ## @tex |
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26 ## $ {\parallel a \parallel_p * \parallel a^{-1} \parallel_p .} $ |
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27 ## @end tex |
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28 ## @ifnottex |
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29 ## @code{norm (@var{a}, @var{p}) * norm (inv (@var{a}), @var{p})}. |
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Rik <octave@nomad.inbox5.com>
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30 ## @end ifnottex |
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31 ## |
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32 ## By default @code{@var{p} = 2} is used which implies a (relatively slow) |
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33 ## singular value decomposition. Other possible selections are |
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34 ## @code{@var{p} = 1, Inf, "fro"} which are generally faster. See |
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35 ## @code{norm} for a full discussion of possible @var{p} values. |
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36 ## @seealso{condest, rcond, norm, svd} |
| 3372 | 37 ## @end deftypefn |
| 4 | 38 |
| 2314 | 39 ## Author: jwe |
| 40 | |
| 7484 | 41 function retval = cond (a, p) |
| 4 | 42 |
| 7484 | 43 if (nargin && nargin < 3) |
| 4891 | 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 | |
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52 if (! ischar (p) && p == 2) |
| 7484 | 53 [nr, nc] = size (a); |
| 54 if (nr == 0 || nc == 0) | |
| 55 retval = 0.0; | |
| 56 elseif (any (any (isinf (a) | isnan (a)))) | |
| 57 error ("cond: argument must not contain Inf or NaN values"); | |
| 58 else | |
| 59 sigma = svd (a); | |
| 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 |
| 7484 | 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 |