function [w] = fdla(A)
% FDLA    Returns the fastest distributed linear averaging (FDLA) edge weights.
%
% [w] = FDLA(A) gives a vector of the fastest distributed linear averaging
% edge weights for a graph described by the incidence matrix A (n x m).
% Here n is the number of nodes and m is the number of edges in the graph;
% each column of A has exactly one +1 and one -1.
%
% The FDLA edge weights are given by the SDP:
%
%   minimize    s
%   subject to  -s*I <= I - L - (1/n)11' <= s*I
%
% where the variables are edge weights w in R^m and s in R.
% Here L is the weighted Laplacian defined by L = A*diag(w)*A'.

% For more details see the references:
% "Fast linear iterations for distributed averaging" by L. Xiao and S. Boyd
% "Convex Optimization of Graph Laplacian Eigenvalues" by S. Boyd
%
% Written for CVX by Almir Mutapcic 08/29/06
[n,m] = size(A);

cvx_begin
  variable w(m,1)   % edge weights
  variable s        % epigraph variable

  minimize( s )
  subject to
    eye(n) - A*diag(w)*A' - ones(n)/n +s*eye(n) == semidefinite(n);
    eye(n) - A*diag(w)*A' - ones(n)/n -s*eye(n) == -semidefinite(n);
cvx_end