Mercurial > hg > octave-lyh
annotate scripts/linear-algebra/subspace.m @ 14383:07c55bceca23 stable
Fix guarded_eval() subfunction in fminunc (bug #35534).
* fminunc.m: Fix guarded_eval() subfunction in fminunc (bug #35534).
| author | Olaf Till <olaf.till@uni-jena.de> |
|---|---|
| date | Wed, 15 Feb 2012 14:44:37 +0100 |
| parents | 72c96de7a403 |
| children | 1c89599167a6 |
| rev | line source |
|---|---|
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maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
parents:
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1 ## Copyright (C) 2008-2012 VZLU Prague, a.s., Czech Republic |
| 7611 | 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 | |
| 7 ## the Free Software Foundation; either version 3 of the License, or (at | |
| 8 ## your option) any later version. | |
| 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 | |
| 16 ## along with Octave; see the file COPYING. If not, see | |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 18 | |
| 19 ## -*- texinfo -*- | |
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Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
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20 ## @deftypefn {Function File} {@var{angle} =} subspace (@var{A}, @var{B}) |
| 7611 | 21 ## Determine the largest principal angle between two subspaces |
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Rik <octave@nomad.inbox5.com>
parents:
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22 ## spanned by the columns of matrices @var{A} and @var{B}. |
| 7611 | 23 ## @end deftypefn |
| 24 | |
| 25 ## Author: Jaroslav Hajek <highegg@gmail.com> | |
| 26 | |
| 27 ## reference: | |
| 28 ## [1] Andrew V. Knyazev, Merico E. Argentati: | |
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all script files: untabify and strip trailing whitespace
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29 ## Principal Angles between Subspaces in an A-Based Scalar Product: |
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all script files: untabify and strip trailing whitespace
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parents:
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30 ## Algorithms and Perturbation Estimates. |
| 7611 | 31 ## SIAM Journal on Scientific Computing, Vol. 23 no. 6, pp. 2008-2040 |
| 32 ## | |
| 33 ## other texts are also around... | |
| 34 | |
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Rik <octave@nomad.inbox5.com>
parents:
8920
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35 function ang = subspace (A, B) |
| 7611 | 36 |
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error check for subspace.m
Jaroslav Hajek <highegg@gmail.com>
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37 if (nargin != 2) |
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error check for subspace.m
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38 print_usage (); |
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Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
8920
diff
changeset
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39 elseif (ndims (A) != 2 || ndims (B) != 2) |
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error check for subspace.m
Jaroslav Hajek <highegg@gmail.com>
parents:
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40 error ("subspace: expecting A and B to be 2-dimensional arrays"); |
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11469
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
8920
diff
changeset
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41 elseif (rows (A) != rows (B)) |
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c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
8920
diff
changeset
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42 error ("subspace: column dimensions of A and B must match"); |
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error check for subspace.m
Jaroslav Hajek <highegg@gmail.com>
parents:
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changeset
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43 endif |
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c1702f963a5e
error check for subspace.m
Jaroslav Hajek <highegg@gmail.com>
parents:
7611
diff
changeset
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44 |
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11469
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
8920
diff
changeset
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45 A = orth (A); |
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c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
8920
diff
changeset
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46 B = orth (B); |
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Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
8920
diff
changeset
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47 c = A'*B; |
| 7611 | 48 scos = min (svd (c)); |
| 49 if (scos^2 > 1/2) | |
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Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
8920
diff
changeset
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50 if (columns (A) >= columns (B)) |
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c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
8920
diff
changeset
|
51 c = B - A*c; |
| 7611 | 52 else |
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11469
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
8920
diff
changeset
|
53 c = A - B*c'; |
| 7611 | 54 endif |
| 55 ssin = max (svd (c)); | |
| 56 ang = asin (min (ssin, 1)); | |
| 57 else | |
| 58 ang = acos (scos); | |
| 59 endif | |
| 60 | |
| 61 endfunction |