function G = gsp_estimate_lmax(G)
%GSP_ESTIMATE_LMAX estimates the maximum laplacian eigenvalue
%   Usage: G = gsp_estimate_lmax(G);
%
%   Inputs parameters:
%       G   : Graph structure (or cell array of graph structure)
%   Outputs parameters:
%       G   : Graph structure (or cell array of graph structure)
%
%   This function will compute an approximation of the maximum laplacian
%   eigenvalue and fill it in the field G.lmax*
%
%   Runs Arnoldi algorithm with a large tolerance, then increases
%   calculated maximum eigenvalue by 1 percent. For much of the gspbox
%   machinery, we need to approximate the wavelet kernels on an
%   interval that contains the spectrum of L. The only cost of using
%   a larger interval is that the polynomial approximation over the
%   larger interval may be a slightly worse approxmation on the
%   actual spectrum. As this is a very mild effect, it is not likely
%   necessary to obtain very tight bonds on the spectrum of L
%
%   This function is inspired by the sgwt_toolbox
%
%   Url: http://lts2research.epfl.ch/gsp/doc/utils/gsp_estimate_lmax.php

% Copyright (C) 2013-2016 Nathanael Perraudin, Johan Paratte, David I Shuman.
% This file is part of GSPbox version 0.7.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program.  If not, see <http://www.gnu.org/licenses/>.

% If you use this toolbox please kindly cite
%     N. Perraudin, J. Paratte, D. Shuman, V. Kalofolias, P. Vandergheynst,
%     and D. K. Hammond. GSPBOX: A toolbox for signal processing on graphs.
%     ArXiv e-prints, Aug. 2014.
% http://arxiv.org/abs/1408.5781

% Author: David K. Hammond, Nathanael Perraudin
% Date:   15 March 2014


if numel(G)>1
    Ng = numel(G);
    for ii = 1:Ng
       G{ii} = gsp_estimate_lmax(G{ii});
    end     
    return;
end


try
    opts=struct('tol',5e-3,'p',min(G.N,10),'disp',0);
    lmax=eigs(G.L,1,'lm',opts);

    G.lmax=abs(lmax)*1.01; % just increase by 1 percent to be robust to error
    
catch
    warning('GSP_ESTIMATE_LMAX: Cannot use the default method')
    G.lmax = 2*max(G.d);
end

if isfield(G,'Gm')
    G = gsp_estimate_oose_lmax(G);
end

end