compute_mesh_weight(vertex,face,type,options)

function L = compute_mesh_weight(vertex,face,type,options)

% compute_mesh_laplacian - compute a laplacian matrix
%
%   L = compute_mesh_laplacian(vertex,face,type,options);
%
%   If options.symmetrize=1 and options.normalize=0 then 
%       L = D-W
%   If options.symmetrize=1 and options.normalize=1 then 
%       L = eye(n)-D^{-1/2}*W*D^{-1/2}
%   If options.symmetrize=0 and options.normalize=1 then 
%       L = eye(n)-D^{-1}*W.
%   where D=diag(sum(W,2)) and W is the unormalized weight matrix 
%   (see compute_mesh_weight).
%
%   type can 'combinatorial', 'distance', 'conformal'.
%
%   See also compute_mesh_weight.
%
%   Copyright (c) 2007 Gabriel Peyre

options.null = 0;
if isfield(options, 'normalize')
    normalize = options.normalize;
else
    normalize = 1;
end
if isfield(options, 'symmetrize')
    symmetrize = options.symmetrize;
else
    symmetrize = 1;
end

options.normalize = 0;
W = compute_mesh_weight(vertex,face,type,options);
n = size(W,1);
if symmetrize==1 && normalize==0
    L = diag(sum(W,2)) - W;
elseif symmetrize==1 && normalize==1
    L = speye(n) - diag(sum(W,2).^(-1/2)) * W * diag(sum(W,2).^(-1/2));
elseif symmetrize==0 && normalize==1
    L = speye(n) - diag(sum(W,2).^(-1)) * W;
else
    error('Does not work with symmetrize=0 and normalize=0');    
end