Amul.m

function y = Amul(At,dense,x,transp)
% y = Amul(At,dense,x,transp)
%
% AMUL  Computes A*x (transp=0) or A'*x (transp=1), taking care of dense.A.
%
% **********  INTERNAL FUNCTION OF SEDUMI **********
%
% See also sedumi

% This file is part of SeDuMi 1.1 by Imre Polik and Oleksandr Romanko
% Copyright (C) 2005 McMaster University, Hamilton, CANADA  (since 1.1)
%
% Copyright (C) 2001 Jos F. Sturm (up to 1.05R5)
%   Dept. Econometrics & O.R., Tilburg University, the Netherlands.
%   Supported by the Netherlands Organization for Scientific Research (NWO).
%
% Affiliation SeDuMi 1.03 and 1.04Beta (2000):
%   Dept. Quantitative Economics, Maastricht University, the Netherlands.
%
% Affiliations up to SeDuMi 1.02 (AUG1998):
%   CRL, McMaster University, Canada.
%   Supported by the Netherlands Organization for Scientific Research (NWO).
%
% 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 2 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, write to the Free Software
% Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
% 02110-1301, USA
%

if nargin < 4
    transp = 0;
end
if transp == 0
    %Since At is sparse calculating At'*x takes a lot of time, while x'*At
    %is much faster!
    y = (x'*At)';                     %y(m) and x(N).
else
    y = full(At*x);        % y(N) and x(m)
end
if ~isempty(dense.cols)
    if transp == 0
        y = y + dense.A*x(dense.cols);
    else
        y(dense.cols) = dense.A'*x;
    end
end