Mercurial > octave-nkf
annotate scripts/special-matrix/pascal.m @ 12747:901d466ee55a stable release-3-4-1
Version 3.4.1 released.
* configure.ac (AC_INIT): Version is now 3.4.1.
(OCTAVE_API_VERSION_NUMBER): Now 45.
(OCTAVE_RELEASE_DATE): Now 2011-06-15.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 15 Jun 2011 10:35:37 -0400 |
parents | 4d777e05d47c |
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11523 | 1 ## Copyright (C) 1999-2011 Peter Ekberg |
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2 ## Copyright (C) 2009 VZLU Prague |
5827 | 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. | |
5827 | 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/>. | |
5827 | 19 |
20 ## -*- texinfo -*- | |
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21 ## @deftypefn {Function File} {} pascal (@var{n}) |
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22 ## @deftypefnx {Function File} {} pascal (@var{n}, @var{t}) |
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23 ## Return the Pascal matrix of order @var{n} if @code{@var{t} = 0}. @var{t} |
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24 ## defaults to 0. Return the pseudo-lower triangular Cholesky@tie{}factor of |
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25 ## the Pascal matrix if @code{@var{t} = 1} (The sign of some columns may be |
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26 ## negative). This matrix is its own inverse, that is @code{pascal (@var{n}, |
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27 ## 1) ^ 2 == eye (@var{n})}. If @code{@var{t} = -1}, return the true |
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28 ## Cholesky@tie{}factor with strictly positive values on the diagonal. If |
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29 ## @code{@var{t} = 2}, return a transposed and permuted version of @code{pascal |
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30 ## (@var{n}, 1)}, which is the cube root of the identity matrix. That is, |
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31 ## @code{pascal (@var{n}, 2) ^ 3 == eye (@var{n})}. |
5827 | 32 ## |
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33 ## @seealso{chol} |
5827 | 34 ## @end deftypefn |
35 | |
36 ## Author: Peter Ekberg | |
37 ## (peda) | |
38 | |
39 function retval = pascal (n, t) | |
40 | |
41 if (nargin > 2) || (nargin == 0) | |
42 print_usage (); | |
43 endif | |
44 | |
45 if (nargin == 1) | |
46 t = 0; | |
47 endif | |
48 | |
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49 if (! isscalar (n) || ! isscalar (t)) |
5827 | 50 error ("pascal: expecting scalar arguments, found something else"); |
51 endif | |
52 | |
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53 if (t < -1 || t > 2) |
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54 error ("pascal: expecting T to be -1, 0, 1, or 2, found %d", t); |
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55 endif |
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56 |
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57 retval = zeros (n); |
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58 retval(:,1) = 1; |
5827 | 59 |
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60 if (t == -1) |
9096 | 61 for j = 2:n |
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62 retval(j:n,j) = cumsum (retval (j-1:n-1,j-1)); |
5827 | 63 endfor |
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64 else |
9096 | 65 for j = 2:n |
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66 retval(j:n,j) = -cumsum (retval (j-1:n-1,j-1)); |
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67 endfor |
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68 endif |
5827 | 69 |
70 if (t == 0) | |
71 retval = retval*retval'; | |
72 elseif (t == 2) | |
73 retval = retval'; | |
74 retval = retval(n:-1:1,:); | |
75 retval(:,n) = -retval(:,n); | |
76 retval(n,:) = -retval(n,:); | |
77 if (rem(n,2) != 1) | |
78 retval = -retval; | |
79 endif | |
80 endif | |
81 | |
82 endfunction | |
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83 |
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84 %!assert (pascal(3,-1), [1,0,0;1,1,0;1,2,1]) |
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85 %!assert (pascal(3,0), [1,1,1;1,2,3;1,3,6]) |
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86 %!assert (pascal(3,0), pascal(3)) |
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87 %!assert (pascal(3,1), [1,0,0;1,-1,0;1,-2,1]) |
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88 %!assert (pascal(3,2), [0,0,-1;0,-1,2;-1,-1,1]) |
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89 %!error (pascal(3,4)) |
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90 %!error (pascal(3,-2)) |
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91 %!error (pascal()) |
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92 %!error (pascal(1,2,3)) |