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annotate toolboxes/FullBNT-1.0.7/graph/mk_2D_lattice_slow.m @ 0:e9a9cd732c1e tip

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first hg version after svn
author wolffd
date Tue, 10 Feb 2015 15:05:51 +0000
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wolffd@0 1 function G = mk_2D_lattice_slow(nrows, ncols, wrap_around)
wolffd@0 2 % MK_2D_LATTICE Return adjacency matrix for 4-nearest neighbor connected 2D lattice
wolffd@0 3 % G = mk_2D_lattice(nrows, ncols, wrap_around)
wolffd@0 4 % G(k1, k2) = 1 iff k1=(i1,j1) is connected to k2=(i2,j2)
wolffd@0 5 %
wolffd@0 6 % If wrap_around = 1, we use toroidal boundary conditions (default = 0)
wolffd@0 7 %
wolffd@0 8 % Nodes are assumed numbered as in the following 3x3 lattice
wolffd@0 9 % 1 4 7
wolffd@0 10 % 2 5 8
wolffd@0 11 % 3 6 9
wolffd@0 12 %
wolffd@0 13 % e.g., G = mk_2D_lattice(3, 3, 0) returns
wolffd@0 14 % 0 1 0 1 0 0 0 0 0
wolffd@0 15 % 1 0 1 0 1 0 0 0 0
wolffd@0 16 % 0 1 0 0 0 1 0 0 0
wolffd@0 17 % 1 0 0 0 1 0 1 0 0
wolffd@0 18 % 0 1 0 1 0 1 0 1 0
wolffd@0 19 % 0 0 1 0 1 0 0 0 1
wolffd@0 20 % 0 0 0 1 0 0 0 1 0
wolffd@0 21 % 0 0 0 0 1 0 1 0 1
wolffd@0 22 % 0 0 0 0 0 1 0 1 0
wolffd@0 23 % so find(G(5,:)) = [2 4 6 8]
wolffd@0 24 % but find(G(1,:)) = [2 4]
wolffd@0 25 %
wolffd@0 26 % Using wrap around, G = mk_2D_lattice(3, 3, 1), we get
wolffd@0 27 % 0 1 1 1 0 0 1 0 0
wolffd@0 28 % 1 0 1 0 1 0 0 1 0
wolffd@0 29 % 1 1 0 0 0 1 0 0 1
wolffd@0 30 % 1 0 0 0 1 1 1 0 0
wolffd@0 31 % 0 1 0 1 0 1 0 1 0
wolffd@0 32 % 0 0 1 1 1 0 0 0 1
wolffd@0 33 % 1 0 0 1 0 0 0 1 1
wolffd@0 34 % 0 1 0 0 1 0 1 0 1
wolffd@0 35 % 0 0 1 0 0 1 1 1 0
wolffd@0 36 % so find(G(5,:)) = [2 4 6 8]
wolffd@0 37 % and find(G(1,:)) = [2 3 4 7]
wolffd@0 38
wolffd@0 39 if nargin < 3, wrap_around = 0; end
wolffd@0 40
wolffd@0 41 % M contains the number of each cell e.g.
wolffd@0 42 % 1 4 7
wolffd@0 43 % 2 5 8
wolffd@0 44 % 3 6 9
wolffd@0 45 % North neighbors (assuming wrap around) are
wolffd@0 46 % 3 6 9
wolffd@0 47 % 1 4 7
wolffd@0 48 % 2 5 8
wolffd@0 49 % Without wrap around, they are
wolffd@0 50 % 1 4 7
wolffd@0 51 % 1 4 7
wolffd@0 52 % 2 5 8
wolffd@0 53 % The first row is arbitrary, since pixels at the top have no north neighbor.
wolffd@0 54
wolffd@0 55 if nrows==1
wolffd@0 56 G = zeros(1, ncols);
wolffd@0 57 for i=1:ncols-1
wolffd@0 58 G(i,i+1) = 1;
wolffd@0 59 G(i+1,i) = 1;
wolffd@0 60 end
wolffd@0 61 if wrap_around
wolffd@0 62 G(1,ncols) = 1;
wolffd@0 63 G(ncols,1) = 1;
wolffd@0 64 end
wolffd@0 65 return;
wolffd@0 66 end
wolffd@0 67
wolffd@0 68
wolffd@0 69 npixels = nrows*ncols;
wolffd@0 70
wolffd@0 71 N = 1; E = 2; S = 3; W = 4;
wolffd@0 72 if wrap_around
wolffd@0 73 rows{N} = [nrows 1:nrows-1]; cols{N} = 1:ncols;
wolffd@0 74 rows{E} = 1:nrows; cols{E} = [2:ncols 1];
wolffd@0 75 rows{S} = [2:nrows 1]; cols{S} = 1:ncols;
wolffd@0 76 rows{W} = 1:nrows; cols{W} = [ncols 1:ncols-1];
wolffd@0 77 else
wolffd@0 78 rows{N} = [1 1:nrows-1]; cols{N} = 1:ncols;
wolffd@0 79 rows{E} = 1:nrows; cols{E} = [1 1:ncols-1];
wolffd@0 80 rows{S} = [2:nrows nrows]; cols{S} = 1:ncols;
wolffd@0 81 rows{W} = 1:nrows; cols{W} = [2:ncols ncols];
wolffd@0 82 end
wolffd@0 83
wolffd@0 84 M = reshape(1:npixels, [nrows ncols]);
wolffd@0 85 nbrs = cell(1, 4);
wolffd@0 86 for i=1:4
wolffd@0 87 nbrs{i} = M(rows{i}, cols{i});
wolffd@0 88 end
wolffd@0 89
wolffd@0 90
wolffd@0 91 G = zeros(npixels, npixels);
wolffd@0 92 if wrap_around
wolffd@0 93 for i=1:4
wolffd@0 94 if 0
wolffd@0 95 % naive
wolffd@0 96 for p=1:npixels
wolffd@0 97 G(p, nbrs{i}(p)) = 1;
wolffd@0 98 end
wolffd@0 99 else
wolffd@0 100 % vectorized
wolffd@0 101 ndx2 = sub2ind([npixels npixels], 1:npixels, nbrs{i}(:)');
wolffd@0 102 G(ndx2) = 1;
wolffd@0 103 end
wolffd@0 104 end
wolffd@0 105 else
wolffd@0 106 i = N;
wolffd@0 107 mask = ones(nrows, ncols);
wolffd@0 108 mask(1,:) = 0; % pixels in row 1 have no nbr to the north
wolffd@0 109 ndx = find(mask);
wolffd@0 110 ndx2 = sub2ind([npixels npixels], ndx, nbrs{i}(ndx));
wolffd@0 111 G(ndx2) = 1;
wolffd@0 112
wolffd@0 113 i = E;
wolffd@0 114 mask = ones(nrows, ncols);
wolffd@0 115 mask(:,ncols) = 0;
wolffd@0 116 ndx = find(mask);
wolffd@0 117 ndx2 = sub2ind([npixels npixels], ndx, nbrs{i}(ndx));
wolffd@0 118 G(ndx2) = 1;
wolffd@0 119
wolffd@0 120 i = S;
wolffd@0 121 mask = ones(nrows, ncols);
wolffd@0 122 mask(nrows,:)=0;
wolffd@0 123 ndx = find(mask);
wolffd@0 124 ndx2 = sub2ind([npixels npixels], ndx, nbrs{i}(ndx));
wolffd@0 125 G(ndx2) = 1;
wolffd@0 126
wolffd@0 127 i = W;
wolffd@0 128 mask = ones(nrows, ncols);
wolffd@0 129 mask(:,1)=0;
wolffd@0 130 ndx = find(mask);
wolffd@0 131 ndx2 = sub2ind([npixels npixels], ndx, nbrs{i}(ndx));
wolffd@0 132 G(ndx2) = 1;
wolffd@0 133 end
wolffd@0 134
wolffd@0 135 G = setdiag(G, 0);