function [W info]=lambertwmatrix(k,A)

% W=LAMBERTWMATRIX(k,A) computes the determination k of the Lambert W function of A
%   k: branch of the Lambert W function
%   A: matrix whose Lambert W is required
%
% The algorithm is based on the Newton iteration with a heuristic stategy for
% the initial value based depending on the branch.
% The initial value is obtained truncating some series expansion of the 
% Lambert W function around the branch points and infinity.
%
% Reference:
% M. Fasi, N. J. Higham and B. Iannazzo, An algorithm for the matrix 
% Lambert W function, MIMS Eprint 2014.58, November 2014