wolffd@0: function [T, bitv] = subsets(S, U, L, sorted, N)
wolffd@0: % SUBSETS Create a set of all the subsets of S which have cardinality <= U and >= L
wolffd@0: % T = subsets(S, U, L)
wolffd@0: % U defaults to length(S), L defaults to 0.
wolffd@0: % So subsets(S) generates the powerset of S.
wolffd@0: %
wolffd@0: % Example:
wolffd@0: % T = subsets(1:4, 2, 1) 
wolffd@0: % T{:} = 1, 2, [1 2], 3, [1 3], [2 3], 4, [1 4], [2 4], [3 4]
wolffd@0: %
wolffd@0: % T = subsets(S, U, L, sorted)
wolffd@0: % If sorted=1, return the subsets in increasing size
wolffd@0: %
wolffd@0: % Example:
wolffd@0: % T = subsets(1:4, 2, 1, 1) 
wolffd@0: % T{:} = 1, 2, 3, 4, [1 2], [1 3], [2 3], [1 4], [2 4], [3 4]
wolffd@0: %
wolffd@0: % [T, bitv] = subsets(S, U, L, sorted, N)
wolffd@0: % Row i of bitv is a bit vector representation of T{i},
wolffd@0: % where bitv has N columns (representing 1:N).
wolffd@0: % N defaults to max(S).
wolffd@0: %
wolffd@0: % Example:
wolffd@0: % [T,bitv] = subsets(2:4, 2^3, 0, 0, 5)
wolffd@0: % T{:} = [], 2, 3, [2 3], 4, [2 4], [3 4], [2 3 4]
wolffd@0: % bitv=
wolffd@0: %     0     0     0     0     0
wolffd@0: %     0     1     0     0     0
wolffd@0: %     0     0     1     0     0
wolffd@0: %     0     1     1     0     0
wolffd@0: %     0     0     0     1     0
wolffd@0: %     0     1     0     1     0
wolffd@0: %     0     0     1     1     0
wolffd@0: %     0     1     1     1     0
wolffd@0: 
wolffd@0: n = length(S);
wolffd@0: 
wolffd@0: if nargin < 2, U = n; end
wolffd@0: if nargin < 3, L = 0; end
wolffd@0: if nargin < 4, sorted = 0; end
wolffd@0: if nargin < 5, N = max(S); end
wolffd@0: 
wolffd@0: bits = ind2subv(2*ones(1,n), 1:2^n)-1;
wolffd@0: sm = sum(bits,2);
wolffd@0: masks = bits((sm <= U) & (sm >= L), :);
wolffd@0: m = size(masks, 1);
wolffd@0: T = cell(1, m);
wolffd@0: for i=1:m
wolffd@0:   s = S(find(masks(i,:)));
wolffd@0:   T{i} = s;
wolffd@0: end
wolffd@0: 
wolffd@0: if sorted 
wolffd@0:   T = sortcell(T);
wolffd@0: end
wolffd@0: 
wolffd@0: bitv = zeros(m, N);
wolffd@0: bitv(:, S) = masks;