function [A,b,G,h,x,nu] = mkgp_sparse(n,szs,p,seed, sparsity)%% function [A,b,G,h,x,nu] = mkgp_sparse(n,szs,p,seed, sparsity)%% Input Arguments:%% n   : # of rows of A.% szs : size variable of each objective and inequality constraints.% p   : # of rows of G.% seed: seed of random number generation.% sparsity: sparsity of A and G matrix.%% Output Arguments:% % A,b,G,h : Problem data of a random GP in convex form.rand('state',seed);randn('state',seed);if size(szs,1) < size(szs,2),  szs = szs';  end;m = length(szs)-1;  N = sum(szs);% E is a matrix s.t. [1'*y0  1'*y1  ... 1'*ym ]' = E*yindsl = cumsum(szs);indsf = indsl-szs+1;lx    = zeros(N,1);lx(indsf) = 1;E = sparse(cumsum(lx),[1:N],ones(N,1));disp('pass')% random nu > 0nu = rand(N,1);% 1'*nu = 1nu(1:szs(1)) = nu(1:szs(1))/sum(nu(1:szs(1)));% random AA = sprandn(N,n,sparsity); % A = A - nu*(nu'*A)/(nu'*nu);% random xx = randn(n,1)/10;x(x> 3) =  3;x(x<-3) = -3;% b0 is randomb = zeros(N,1);b(1:szs(1)) = randn(szs(1),1);% other bi's are constructed so that f(Ai*x+bi) = zi with % random positive initial slacks zz = rand(m,1);b(szs(1)+1:N) = -A(szs(1)+1:N,:)*x - ...                E(2:m+1,szs(1)+1:N)'*(z + log(szs(2:m+1))); % rnadom Gfor i = 1:100    G = sprandn(p,n,sparsity);    if (condest(G*G') < 1e16) break; endend% G*x + h = 0h = -G*x;