1% Sparse operator for staggering.
2%
3% S = sparse_stagger(sz1,m,cyclic)
4%
5% Create a sparse operator for staggering a field in dimension m.
6% The field is a "collapsed" matrix of the size sz1.
7%
8% Input:
9%   sz1: size of rhs
10%   m: dimension to stagger
11%   cyclic: true if domain is cyclic along dimension m. False is the
12%   default value
13
14function S = sparse_stagger(sz1,m,cyclic)
15
16
17if nargin == 2
18    cyclic = false;
19end
20
21n1 = prod(sz1);
22
23sz2 = sz1;
24
25if ~cyclic
26    sz2(m) = sz2(m)-1;
27end
28n2 = prod(sz2);
29
30n = length(sz1);
31
32for i=1:n
33  vi{i} = 1:sz2(i);
34end
35
36IJ = cell(n,1);
37
38[IJ{:}] = ndgrid(vi{:});
39
40for i=1:n
41  IJ{i} = IJ{i}(:);
42end
43
44L1 = [1:n2]';
45
46L2 = sub2ind(sz1,IJ{:});
47v = ones(size(L1))/2;
48
49IJ{m} = IJ{m} + 1;
50
51if cyclic
52    IJ{m} = mod(IJ{m}-1,sz1(m))+1;
53end
54
55L2o = sub2ind(sz1,IJ{:});
56
57S = sparse( ...
58       [L1;  L1;  ],  ...
59       [L2;  L2o; ],  ...
60       [v;   v    ], n2 , n1 );
61
62
63
64% Copyright (C) 2009 Alexander Barth <a.barth@ulg.ac.be>
65%
66% This program is free software; you can redistribute it and/or modify
67% it under the terms of the GNU General Public License as published by
68% the Free Software Foundation; either version 2 of the License, or
69% (at your option) any later version.
70%
71% This program is distributed in the hope that it will be useful,
72% but WITHOUT ANY WARRANTY; without even the implied warranty of
73% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
74% GNU General Public License for more details.
75%
76% You should have received a copy of the GNU General Public License
77% along with this program; If not, see <http://www.gnu.org/licenses/>.
78
79