Mercurial > hg > octave-lyh
annotate scripts/special-matrix/pascal.m @ 17181:3a23cbde59d5
interpft.m: Fix interpolation to preserve spectral symmetry (bug #39566)
* interpft.m: Fix interpolation to preserve spectral symmetry, be compatible
with Matlab. Add test cases.
author | Mike Miller <mtmiller@ieee.org> |
---|---|
date | Sun, 04 Aug 2013 17:27:40 -0400 |
parents | 72c96de7a403 |
children |
rev | line source |
---|---|
14138
72c96de7a403
maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
parents:
13907
diff
changeset
|
1 ## Copyright (C) 1999-2012 Peter Ekberg |
9094
2e35cfcf6a6a
fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents:
9051
diff
changeset
|
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 -*- | |
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 | 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 | 34 ## @end deftypefn |
35 | |
36 ## Author: Peter Ekberg | |
37 ## (peda) | |
38 | |
13902
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
39 function retval = pascal (n, t = 0) |
5827 | 40 |
13902
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
41 if (nargin < 1 || nargin > 2) |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
42 print_usage (); |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
43 elseif (! (isscalar (n) && isscalar (t))) |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
44 error ("pascal: N and T must be scalars"); |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
45 elseif (! any (t == [-1, 0, 1, 2])) |
12480
139f993936af
Uppercase variables in script error strings.
Rik <octave@nomad.inbox5.com>
parents:
12448
diff
changeset
|
46 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
|
47 endif |
dcde7c5a1d29
new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents:
10791
diff
changeset
|
48 |
9094
2e35cfcf6a6a
fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents:
9051
diff
changeset
|
49 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
|
50 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
|
51 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
|
52 endif |
5827 | 53 |
9094
2e35cfcf6a6a
fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents:
9051
diff
changeset
|
54 if (t == -1) |
9096 | 55 for j = 2:n |
13904 | 56 retval(j:n,j) = cumsum (retval(j-1:n-1,j-1)); |
5827 | 57 endfor |
9094
2e35cfcf6a6a
fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents:
9051
diff
changeset
|
58 else |
9096 | 59 for j = 2:n |
13904 | 60 retval(j:n,j) = -cumsum (retval(j-1:n-1,j-1)); |
9094
2e35cfcf6a6a
fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents:
9051
diff
changeset
|
61 endfor |
2e35cfcf6a6a
fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents:
9051
diff
changeset
|
62 endif |
5827 | 63 |
64 if (t == 0) | |
65 retval = retval*retval'; | |
66 elseif (t == 2) | |
13902
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
67 retval = rot90 (retval, 3); |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
68 if (rem (n,2) != 1) |
13907
755f6b340453
pascal.m: Use in-place assignment operator for faster negation
Rik <octave@nomad.inbox5.com>
parents:
13904
diff
changeset
|
69 retval *= -1; |
5827 | 70 endif |
71 endif | |
72 | |
73 endfunction | |
11098
dcde7c5a1d29
new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents:
10791
diff
changeset
|
74 |
13902
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
75 |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
76 %!assert (pascal (3,-1), [1,0,0;1,1,0;1,2,1]) |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
77 %!assert (pascal (3,0), [1,1,1;1,2,3;1,3,6]) |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
78 %!assert (pascal (3,0), pascal (3)) |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
79 %!assert (pascal (3,1), [1,0,0;1,-1,0;1,-2,1]) |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
80 %!assert (pascal (3,2), [1,1,1;-2,-1,0;1,0,0]) |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
81 %!assert (pascal (0,2), []) |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
82 |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
83 %% Test input validation |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
84 %!error pascal () |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
85 %!error pascal (1,2,3) |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
86 %!error <N and T must be scalars> pascal ([1 2]) |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
87 %!error <N and T must be scalars> pascal (1, [1 2]) |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
88 %!error <expecting T to be> pascal (3,-2) |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
89 %!error <expecting T to be> pascal (3,4) |
3af19cfc2e0f
pascal.m: Update coding style. Use in-place operations where possible.
Rik <octave@nomad.inbox5.com>
parents:
13894
diff
changeset
|
90 |