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1 function [T, bitv] = subsets(S, U, L, sorted, N)
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2 % SUBSETS Create a set of all the subsets of S which have cardinality <= U and >= L
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3 % T = subsets(S, U, L)
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4 % U defaults to length(S), L defaults to 0.
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5 % So subsets(S) generates the powerset of S.
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6 %
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7 % Example:
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8 % T = subsets(1:4, 2, 1)
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9 % T{:} = 1, 2, [1 2], 3, [1 3], [2 3], 4, [1 4], [2 4], [3 4]
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10 %
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11 % T = subsets(S, U, L, sorted)
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12 % If sorted=1, return the subsets in increasing size
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13 %
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14 % Example:
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15 % T = subsets(1:4, 2, 1, 1)
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16 % T{:} = 1, 2, 3, 4, [1 2], [1 3], [2 3], [1 4], [2 4], [3 4]
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17 %
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18 % [T, bitv] = subsets(S, U, L, sorted, N)
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19 % Row i of bitv is a bit vector representation of T{i},
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20 % where bitv has N columns (representing 1:N).
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21 % N defaults to max(S).
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22 %
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23 % Example:
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24 % [T,bitv] = subsets(2:4, 2^3, 0, 0, 5)
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25 % T{:} = [], 2, 3, [2 3], 4, [2 4], [3 4], [2 3 4]
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26 % bitv=
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27 % 0 0 0 0 0
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28 % 0 1 0 0 0
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29 % 0 0 1 0 0
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30 % 0 1 1 0 0
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31 % 0 0 0 1 0
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32 % 0 1 0 1 0
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33 % 0 0 1 1 0
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34 % 0 1 1 1 0
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35
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36 n = length(S);
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37
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38 if nargin < 2, U = n; end
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39 if nargin < 3, L = 0; end
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40 if nargin < 4, sorted = 0; end
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41 if nargin < 5, N = max(S); end
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42
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43 bits = ind2subv(2*ones(1,n), 1:2^n)-1;
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44 sm = sum(bits,2);
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45 masks = bits((sm <= U) & (sm >= L), :);
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46 m = size(masks, 1);
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47 T = cell(1, m);
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48 for i=1:m
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49 s = S(find(masks(i,:)));
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50 T{i} = s;
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51 end
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52
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53 if sorted
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54 T = sortcell(T);
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55 end
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56
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57 bitv = zeros(m, N);
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58 bitv(:, S) = masks;
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