Mercurial > hg > octave-lyh
annotate scripts/linear-algebra/rref.m @ 13485:59d266f7ed89
Removed plotter tab.
| author | Jacob Dawid <jacob.dawid@googlemail.com> |
|---|---|
| date | Wed, 27 Apr 2011 14:21:28 +0200 |
| parents | 7ef7e20057fa |
| children | c5c94b63931f |
| rev | line source |
|---|---|
| 11523 | 1 ## Copyright (C) 2000-2011 Paul Kienzle |
| 5827 | 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. | |
| 5827 | 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/>. | |
| 5827 | 18 |
| 19 ## -*- texinfo -*- | |
|
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20 ## @deftypefn {Function File} {} rref (@var{A}) |
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parents:
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21 ## @deftypefnx {Function File} {} rref (@var{A}, @var{tol}) |
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22 ## @deftypefnx {Function File} {[@var{r}, @var{k}] =} rref (@dots{}) |
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23 ## Return the reduced row echelon form of @var{A}. @var{tol} defaults |
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24 ## to @code{eps * max (size (@var{A})) * norm (@var{A}, inf)}. |
| 5827 | 25 ## |
| 26 ## Called with two return arguments, @var{k} returns the vector of | |
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27 ## "bound variables", which are those columns on which elimination |
| 5827 | 28 ## has been performed. |
| 29 ## | |
| 30 ## @end deftypefn | |
| 31 | |
| 32 ## Author: Paul Kienzle <pkienzle@users.sf.net> | |
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33 ## (based on an anonymous source from the public domain) |
| 5827 | 34 |
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35 function [A, k] = rref (A, tol) |
| 5827 | 36 |
| 37 if (nargin < 1 || nargin > 2) | |
| 38 print_usage (); | |
| 39 endif | |
| 40 | |
| 41 if (ndims (A) > 2) | |
| 42 error ("rref: expecting matrix argument"); | |
| 43 endif | |
| 44 | |
| 45 [rows, cols] = size (A); | |
| 46 | |
| 47 if (nargin < 2) | |
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48 if (isa (A, "single")) |
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49 tol = eps ("single") * max (rows, cols) * norm (A, inf ("single")); |
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50 else |
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51 tol = eps * max (rows, cols) * norm (A, inf); |
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parents:
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52 endif |
| 5827 | 53 endif |
| 54 | |
| 55 used = zeros (1, cols); | |
| 56 r = 1; | |
| 57 for c = 1:cols | |
| 58 ## Find the pivot row | |
| 59 [m, pivot] = max (abs (A(r:rows,c))); | |
| 60 pivot = r + pivot - 1; | |
| 61 | |
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62 if (m <= tol) |
| 5827 | 63 ## Skip column c, making sure the approximately zero terms are |
| 64 ## actually zero. | |
| 65 A (r:rows, c) = zeros (rows-r+1, 1); | |
| 66 else | |
| 67 ## keep track of bound variables | |
| 68 used (1, c) = 1; | |
| 69 | |
| 70 ## Swap current row and pivot row | |
| 71 A ([pivot, r], c:cols) = A ([r, pivot], c:cols); | |
| 72 | |
| 73 ## Normalize pivot row | |
| 74 A (r, c:cols) = A (r, c:cols) / A (r, c); | |
| 75 | |
| 76 ## Eliminate the current column | |
| 77 ridx = [1:r-1, r+1:rows]; | |
| 78 A (ridx, c:cols) = A (ridx, c:cols) - A (ridx, c) * A(r, c:cols); | |
| 79 | |
| 80 ## Check if done | |
| 81 if (r++ == rows) | |
| 10549 | 82 break; |
| 5827 | 83 endif |
| 84 endif | |
| 85 endfor | |
| 86 k = find (used); | |
| 87 | |
| 88 endfunction |