octave-nkf: scripts/special-matrix/pascal.m annotate

annotate scripts/special-matrix/pascal.m @ 13894:d4404589498c

pascal.m: permutation compatibility with Matlab for n=2; fixed n=0 case (Bug #34365) * pascal.m: permutation compatibility with Matlab for n=2; fixed n=0 case (Bug #34365)

author	Vanya Sergeev <vsergeev@gmail.com>
date	Fri, 23 Sep 2011 05:13:01 -0400
parents	4d777e05d47c
children	3af19cfc2e0f

rev	line source
11523 fd0a3ac60b0e update copyright notices John W. Eaton <jwe@octave.org> parents: 11098 diff changeset	1 ## Copyright (C) 1999-2011 Peter Ekberg
9094 2e35cfcf6a6a fix, optimize & extend pascal Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	2 ## Copyright (C) 2009 VZLU Prague
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	3 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	4 ## This file is part of Octave.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	5 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	6 ## Octave is free software; you can redistribute it and/or modify it
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	7 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 5827 diff changeset	8 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 5827 diff changeset	9 ## your option) any later version.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	10 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	11 ## Octave is distributed in the hope that it will be useful, but
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	14 ## General Public License for more details.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	15 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	16 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 5827 diff changeset	17 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 5827 diff changeset	18 ## <http://www.gnu.org/licenses/>.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	19
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	20 ## -- texinfo --
10791 3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation Rik <octave@nomad.inbox5.com> parents: 9209 diff changeset	21 ## @deftypefn {Function File} {} pascal (@var{n})
3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation Rik <octave@nomad.inbox5.com> parents: 9209 diff changeset	22 ## @deftypefnx {Function File} {} pascal (@var{n}, @var{t})
12639 4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 12485 diff changeset	23 ## Return the Pascal matrix of order @var{n} if @code{@var{t} = 0}. @var{t}
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 12485 diff changeset	24 ## defaults to 0. Return the pseudo-lower triangular Cholesky@tie{}factor of
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 12485 diff changeset	25 ## the Pascal matrix if @code{@var{t} = 1} (The sign of some columns may be
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 12485 diff changeset	26 ## negative). This matrix is its own inverse, that is @code{pascal (@var{n},
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 12485 diff changeset	27 ## 1) ^ 2 == eye (@var{n})}. If @code{@var{t} = -1}, return the true
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 12485 diff changeset	28 ## Cholesky@tie{}factor with strictly positive values on the diagonal. If
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 12485 diff changeset	29 ## @code{@var{t} = 2}, return a transposed and permuted version of @code{pascal
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 12485 diff changeset	30 ## (@var{n}, 1)}, which is the cube root of the identity matrix. That is,
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 12485 diff changeset	31 ## @code{pascal (@var{n}, 2) ^ 3 == eye (@var{n})}.
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	32 ##
12639 4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter. Rik <octave@nomad.inbox5.com> parents: 12485 diff changeset	33 ## @seealso{chol}
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	34 ## @end deftypefn
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	35
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	36 ## Author: Peter Ekberg
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	37 ## (peda)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	38
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	39 function retval = pascal (n, t)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	40
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	41 if (nargin > 2) \|\| (nargin == 0)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	42 print_usage ();
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	43 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	44
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	45 if (nargin == 1)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	46 t = 0;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	47 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	48
9094 2e35cfcf6a6a fix, optimize & extend pascal Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	49 if (! isscalar (n) \|\| ! isscalar (t))
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	50 error ("pascal: expecting scalar arguments, found something else");
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	51 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	52
11098 dcde7c5a1d29 new tests for special-matrix functions John W. Eaton <jwe@octave.org> parents: 10791 diff changeset	53 if (t < -1 \|\| t > 2)
12480 139f993936af Uppercase variables in script error strings. Rik <octave@nomad.inbox5.com> parents: 12448 diff changeset	54 error ("pascal: expecting T to be -1, 0, 1, or 2, found %d", t);
11098 dcde7c5a1d29 new tests for special-matrix functions John W. Eaton <jwe@octave.org> parents: 10791 diff changeset	55 endif
dcde7c5a1d29 new tests for special-matrix functions John W. Eaton <jwe@octave.org> parents: 10791 diff changeset	56
9094 2e35cfcf6a6a fix, optimize & extend pascal Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	57 retval = zeros (n);
13894 d4404589498c pascal.m: permutation compatibility with Matlab for n=2; fixed n=0 case (Bug #34365) Vanya Sergeev <vsergeev@gmail.com> parents: 12639 diff changeset	58 if (n > 0)
d4404589498c pascal.m: permutation compatibility with Matlab for n=2; fixed n=0 case (Bug #34365) Vanya Sergeev <vsergeev@gmail.com> parents: 12639 diff changeset	59 retval(:,1) = 1;
d4404589498c pascal.m: permutation compatibility with Matlab for n=2; fixed n=0 case (Bug #34365) Vanya Sergeev <vsergeev@gmail.com> parents: 12639 diff changeset	60 endif
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	61
9094 2e35cfcf6a6a fix, optimize & extend pascal Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	62 if (t == -1)
9096 5235caf89e12 fix typo in pascal Jaroslav Hajek <highegg@gmail.com> parents: 9094 diff changeset	63 for j = 2:n
9094 2e35cfcf6a6a fix, optimize & extend pascal Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	64 retval(j:n,j) = cumsum (retval (j-1:n-1,j-1));
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	65 endfor
9094 2e35cfcf6a6a fix, optimize & extend pascal Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	66 else
9096 5235caf89e12 fix typo in pascal Jaroslav Hajek <highegg@gmail.com> parents: 9094 diff changeset	67 for j = 2:n
9094 2e35cfcf6a6a fix, optimize & extend pascal Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	68 retval(j:n,j) = -cumsum (retval (j-1:n-1,j-1));
2e35cfcf6a6a fix, optimize & extend pascal Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	69 endfor
2e35cfcf6a6a fix, optimize & extend pascal Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	70 endif
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	71
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	72 if (t == 0)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	73 retval = retval*retval';
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	74 elseif (t == 2)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	75 retval = retval';
13894 d4404589498c pascal.m: permutation compatibility with Matlab for n=2; fixed n=0 case (Bug #34365) Vanya Sergeev <vsergeev@gmail.com> parents: 12639 diff changeset	76 retval = retval (:,n:-1:1);
5827 1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	77 if (rem(n,2) != 1)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	78 retval = -retval;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	79 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	80 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	81
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe] jwe parents: diff changeset	82 endfunction
11098 dcde7c5a1d29 new tests for special-matrix functions John W. Eaton <jwe@octave.org> parents: 10791 diff changeset	83
dcde7c5a1d29 new tests for special-matrix functions John W. Eaton <jwe@octave.org> parents: 10791 diff changeset	84 %!assert (pascal(3,-1), [1,0,0;1,1,0;1,2,1])
dcde7c5a1d29 new tests for special-matrix functions John W. Eaton <jwe@octave.org> parents: 10791 diff changeset	85 %!assert (pascal(3,0), [1,1,1;1,2,3;1,3,6])
dcde7c5a1d29 new tests for special-matrix functions John W. Eaton <jwe@octave.org> parents: 10791 diff changeset	86 %!assert (pascal(3,0), pascal(3))
dcde7c5a1d29 new tests for special-matrix functions John W. Eaton <jwe@octave.org> parents: 10791 diff changeset	87 %!assert (pascal(3,1), [1,0,0;1,-1,0;1,-2,1])
13894 d4404589498c pascal.m: permutation compatibility with Matlab for n=2; fixed n=0 case (Bug #34365) Vanya Sergeev <vsergeev@gmail.com> parents: 12639 diff changeset	88 %!assert (pascal(3,2), [1,1,1;-2,-1,0;1,0,0])
11098 dcde7c5a1d29 new tests for special-matrix functions John W. Eaton <jwe@octave.org> parents: 10791 diff changeset	89 %!error (pascal(3,4))
dcde7c5a1d29 new tests for special-matrix functions John W. Eaton <jwe@octave.org> parents: 10791 diff changeset	90 %!error (pascal(3,-2))
dcde7c5a1d29 new tests for special-matrix functions John W. Eaton <jwe@octave.org> parents: 10791 diff changeset	91 %!error (pascal())
dcde7c5a1d29 new tests for special-matrix functions John W. Eaton <jwe@octave.org> parents: 10791 diff changeset	92 %!error (pascal(1,2,3))

Mercurial > hg > octave-nkf

annotate scripts/special-matrix/pascal.m @ 13894:d4404589498c