% FEASCPX Generates a random sparse optimization problem with
%   linear, quadratic and semi-definite constraints. Output
%   can be used by SEDUMI. Includes complex-valued data.
%
%   The following two lines are typical:
% > [AT,B,C,K] = FEASCPX;
% > [X,Y,INFO] = SEDUMI(AT,B,C,K);
%
%   An extended version is:
% > [AT,B,C,K] = FEASCPX(m,lpN,lorL,rconeL,sdpL,denfac)
%
% SEE ALSO sedumi AND feasreal.

function [At,b,c,K] = feascpx(m,nLP,qL,rL,nL,denfac)

 %  
 %   This file is part of SeDuMi 1.02   (03AUG1998)
 %   Copyright (C) 1998 Jos F. Sturm
 %   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., 675 Mass Ave, Cambridge, MA 02139, USA.
 %

if nargin < 6
  denfac = 0.1;
  if nargin < 5
    nL = 1+ round(7*rand(1,5));
    fprintf('Choosing random SDP-product cone K.s.\n')
    if nargin < 4
      rL = 3 + round(4*rand(1,5));
      fprintf('Choosing random LORENTZ R-product cone K.r.\n')
      if nargin < 3
        qL = 3 + round(4*rand(1,5));
        fprintf('Choosing random LORENTZ-product cone K.q.\n')
        if(nargin < 2)
          nLP = 10;
          fprintf('Choosing default K.l=%3.0f.\n',nLP)
          if nargin < 1
            m=10;
            fprintf('Choosing default m=%3.0f.\n',m)
          end
        end
      end
    end
  end
end
if isempty(nLP)
  nLP = 0;
end
nblk = length(nL) + length(rL) + length(qL) + nLP;
denfac = min(1, max(denfac,2/nblk));
fprintf('Choosing block density denfac=%6.4f per row\n',denfac)
Apattern=sparse(m,nblk);
for j=1:m
  pati = sprandn(1,nblk,denfac);
  Apattern(j,:) = (pati~= 0);
end
sumnLsqr = sum(nL.^2);
x = zeros(nLP+sum(qL)+sum(rL)+sumnLsqr,1);
x(1:nLP) = rand(nLP,1); 
At = sparse(length(x),m);
At(1:nLP,:) = sprandn(Apattern(:,1:nLP)');
firstk = nLP+1;
[nA, mA] = size(At);
% LORENTZ:
for k=1:length(qL)
  nk = qL(k);  lastk = firstk + nk - 1;
  x(firstk) = rand;
  for j=1:m
    if Apattern(j,nLP+k)==1
      At(firstk:lastk,j) = sprand(nk,1,1/sqrt(nk)) + sqrt(-1) * ...
        sparse([0;sprand(nk-1,1,1/sqrt(nk))]);
    end
  end
  firstk = lastk + 1;
end
% RCONE (Rotated Lorentz):
for k=1:length(rL)
  nk = rL(k);  lastk = firstk + nk - 1;
  x(firstk) = rand; x(firstk+1) = rand;
  for j=1:m
    if Apattern(j,nLP+length(qL)+k)==1
      At(firstk:lastk,j) = sprand(nk,1,1/sqrt(nk)) + sqrt(-1) * ...
        sparse([0;0;sprand(nk-2,1,1/sqrt(nk-1))]);
    end
  end
  firstk = lastk + 1;
end
% SDP:
for k=1:length(nL)
  nk = nL(k);  lastk = firstk + nk*nk - 1;
  Xk = diag(rand(nk,1));            % diagonal, to keep sparsity structure
  x(firstk:lastk) = Xk;             %although symmetric, store nk^2 elts.
  for j=1:m
    if Apattern(j,nLP+length(qL)+length(rL)+k)==1
      rAik = sprandsym(nk,1/nk);       %on average 1 nonzero per row
      iAik = sprand(nk,nk,1/nk);       %on average 1 nonzero per row
      At(firstk:lastk,j) = vec(rAik + sqrt(-1)*(iAik-iAik'));
    end
  end
  firstk = lastk + 1;
end
b = real(full(At'*x));
y = rand(m,1)-0.5; 
c = sparse(At*y)+x;
K.l = nLP; K.q = qL; K.r = rL; K.s = nL;
