Diffusion ISFC clustering (master) Browse

distance_wei_floyd.m
3209cc2b0b1dmaster

distance_wei_floyd.m
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			function [SPL,hops,Pmat] = distance_wei_floyd(D,transform)
			% DISTANCE_WEI_FLOYD Distance matrix (Floyd-Warshall algorithm)
			%
			% [SPL,hops,Pmat] = distance_wei_floyd(D,transform)
			%
			% Computes the topological length of the shortest possible path
			% connecting every pair of nodes in the network.
			%
			% Inputs:
			%
			% D,
			% Weighted/unweighted directed/undirected
			% connection weight OR length matrix.
			%
			% transform,
			% If the input matrix is a connection weight matrix, specify a
			% transform that map input connection weights to connection
			% lengths. Two transforms are available.
			% 'log' -> l_ij = -log(w_ij)
			% 'inv' -> l_ij = 1/w_ij
			%
			% If the input matrix is a connection length matrix, do not
			% specify a transform (or specify an empty transform argument).
			%
			%
			% Outputs:
			%
			% SPL,
			% Unweighted/Weighted shortest path-length matrix.
			% If W is directed matrix, then SPL is not symmetric.
			%
			% hops,
			% Number of edges in the shortest path matrix. If W is
			% unweighted, SPL and hops are identical.
			%
			% Pmat,
			% Elements {i,j} of this matrix indicate the next node in the
			% shortest path between i and j. This matrix is used as an input
			% argument for function 'retrieve_shortest_path.m', which returns
			% as output the sequence of nodes comprising the shortest path
			% between a given pair of nodes.
			%
			%
			% Notes:
			%
			% There may be more than one shortest path between any pair of nodes
			% in the network. Non-unique shortest paths are termed shortest path
			% degeneracies, and are most likely to occur in unweighted networks.
			% When the shortest-path is degenerate, The elements of matrix Pmat
			% correspond to the first shortest path discovered by the algorithm.
			%
			% The input matrix may be either a connection weight matrix, or a
			% connection length matrix. The connection length matrix is typically
			% obtained with a mapping from weight to length, such that higher
			% weights are mapped to shorter lengths (see above).
			%
			%
			% Algorithm: Floyd–Warshall Algorithm
			%
			%
			% Andrea Avena-Koenigsberger, IU, 2012

			% Modification history
			% 2016 - included transform variable that maps weights to lengths

			if exist('transform','var') && ~isempty(transform)

			switch transform

			case 'log'

			if any((D<0) & D>1)
			error('connection-strengths must be in the interval [0,1) to use the transform -log(w_ij) \n')
			else
			SPL = -log(D);
			end

			case 'inv'

			SPL = 1./D;

			otherwise

			error('Unexpected transform type. Only "log" and "inv" are accepted \n')
			end

			else % the input is a connection lengths matrix.
			SPL = D;
			SPL(SPL == 0) = inf;
			end

			n=size(D,2);

			if nargout > 1
			flag_find_paths = true;
			hops = double(D ~= 0);
			Pmat = 1:n;
			Pmat = Pmat(ones(n,1),:);
			else
			flag_find_paths = false;
			end

			for k=1:n
			i2k_k2j = bsxfun(@plus, SPL(:,k), SPL(k,:));

			if flag_find_paths
			path = bsxfun(@gt, SPL, i2k_k2j);
			[i,j] = find(path);
			hops(path) = hops(i,k) + hops(k,j)';
			Pmat(path) = Pmat(i,k);
			end

			SPL = min(SPL, i2k_k2j);
			end

			SPL(eye(n)>0)=0;

			if flag_find_paths
			hops(eye(n)>0)=0;
			Pmat(eye(n)>0)=0;
			end

ISFCClustering/2019_03_03_BCT/distance_wei_floyd.m3209cc2b0b1dmaster

distance_wei_floyd.mView Options

ISFCClustering/2019_03_03_BCT/distance_wei_floyd.m
3209cc2b0b1dmaster

distance_wei_floyd.m
View Options