spnull(S, varargin)

function Z = spnull(S, varargin)
% Z = SPNULL(S)
% returns a sparse orthonormal basis for the null space of S, that is,
% S*Z has negligible elements, and Z'*Z = I
%
% If S is sparse, Z is obtained from the QR decomposition.
% Otherwise, Z is obtained from the SVD decomposition
%
% Bruno Luong <[e-mail]>
% History
%   10-May-2010: original version
%
% See also SPORTH, NULL, QR, SVD, ORTH, RANK

if issparse(S)
    [m n] = size(S);
    try
        [Q R E] = qr(S.'); %#ok %full QR
        if m > 1
            s = diag(R);
        elseif m == 1
            s = R(1);
        else
            s = 0;
        end
        s = abs(s);
        tol = norm(S,'fro') * eps(class(S));
        r = sum(s > tol);
        Z = Q(:,r+1:n);
    catch %#ok
        % sparse QR is not available on old Matlab versions
        err = lasterror(); %#ok
        if strcmp(err.identifier, 'MATLAB:maxlhs')
            Z = null(full(S), varargin{:});
        else
            rethrow(err);
        end
    end
else % Full matrix
    Z = null(S, varargin{:});
end

end