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annotate scripts/special-matrix/wilkinson.m @ 11098:dcde7c5a1d29

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new tests for special-matrix functions
author John W. Eaton <jwe@octave.org>
date Thu, 14 Oct 2010 14:43:59 -0400
parents 3140cb7a05a1
children fd0a3ac60b0e
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1 ## Copyright (C) 1999, 2006, 2007 Peter Ekberg
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} wilkinson (@var{n})
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21 ## Return the Wilkinson matrix of order @var{n}. Wilkinson matrices are
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22 ## symmetric and tridiagonal with pairs of nearly, but not exactly, equal
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23 ## eigenvalues.
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24 ##
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25 ## @seealso{hankel, vander, sylvester_matrix, hilb, invhilb, toeplitz
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26 ## hadamard, rosser, compan, pascal}
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27 ## @end deftypefn
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28
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29 ## Author: Peter Ekberg
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30 ## (peda)
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31
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32 function retval = wilkinson (n)
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33
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34 if (nargin != 1)
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35 print_usage ();
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36 endif
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37
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38 if (! (isscalar (n) && (n == fix (n)) && n > 0))
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39 error ("wilkinson: N must be an integer greater than 0");
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40 endif
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41
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42 side = ones (n-1, 1);
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43 center = abs (-(n-1)/2:(n-1)/2);
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44 retval = diag (side, -1) + diag (center) + diag (side, 1);
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45
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46 endfunction
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47
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48 %!assert (wilkinson(1), [])
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49 %!assert (wilkinson(2), [0.5,1;1,0.5])
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50 %!assert (wilkinson(3), [1,1,0;1,0,1;0,1,1])
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51 %!assert (wilkinson(4), [1.5,1,0,0;1,0.5,1,0;0,1,0.5,1;0,0,1,1.5])
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52 %!error (wilkinson())
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53 %!error (wilkinson(1,2))