265 lines
8.3 KiB
Mathematica
265 lines
8.3 KiB
Mathematica
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%%*******************************************************************
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%% randinfsdp.m : creates random infeasible SDP problems with various block
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%% diagonal structures.
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%%
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%% [blk,Avec,C,b,X0,y0,Z0] =
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%% randinfsdp(dense_blk,sparse_blk,diag_blk,m,infeas,solve);
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%%
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%% E.g.
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%% randinfsdp([32 20],[10 5],100,10,infeas,solve);
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%%
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%% dense_blk : for generating dense blocks, where
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%% dense_blk(i) is the dimension of the ith block
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%% sparse_blk: for generating a sparse block of small subblocks, where
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%% sparse_blk(i) is the size of the ith subblock.
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%% diag_blk: for generating a column vector of length specified by
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%% diag_blk (this corresponds to a diagonal block).
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%% infeas = 1 if want primal infeasible pair of problems
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%% = 2 if want dual infeasible pair of problems
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%% solve = 0 just to initialize
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%% = 1 if want to solve the problem.
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%%*****************************************************************
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%% SDPT3: version 4.0
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%% Copyright (c) 1997 by
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%% Kim-Chuan Toh, Michael J. Todd, Reha H. Tutuncu
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%% Last Modified: 16 Sep 2004
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%%*****************************************************************
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function [blk,Avec,C,b,X0,y0,Z0] = ...
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randinfsdp(dense_blk,sparse_blk,diag_blk,m,infeas,solve);
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if nargin < 6; solve = 0; end;
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if nargin < 5; error(' insufficient number of inputs '); end;
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if all(infeas-[1 2]);
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error(' infeas must be 1 or 2 ');
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end
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blk = [];
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if ~isempty(dense_blk);
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for k = 1:length(dense_blk);
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blk{k,1} = 's'; blk{k,2} = dense_blk(k);
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end;
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end;
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if ~isempty(sparse_blk);
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if size(sparse_blk,1) > size(sparse_blk,2); sparse_blk = sparse_blk'; end;
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tmp = size(blk,1);
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blk{tmp+1,1} = 's';
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blk{tmp+1,2} = sparse_blk;
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end;
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if ~isempty(diag_blk);
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tmp = size(blk,1);
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blk{tmp+1,1} = 'l';
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blk{tmp+1,2} = diag_blk;
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end;
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N = size(blk,1);
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if (infeas == 1),
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%%
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%% primal infeasible
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%%
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%% generate infeasibility certificate Zi and Z0
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%%
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tmp_sp = sparse(sum(sparse_blk));
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for L = 1:2,
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T = [];
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if ~isempty(dense_blk);
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for k = 1:length(dense_blk);
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n = dense_blk(k);
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tmp = randn(n);
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tmp = tmp*tmp';
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tmp = 0.5*(tmp + tmp');
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%mineig = min(real(eig(tmp)));
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%if (mineig < 0); tmp = tmp - 1.1*mineig*eye(n); end;
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T{k,1} = tmp;
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end;
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end;
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if ~isempty(sparse_blk);
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for k = 1:length(sparse_blk);
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n = sparse_blk(k);
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pos = [sum(sparse_blk(1:k-1))+1 : sum(sparse_blk(1:k))];
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tmp = randn(n);
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tmp = tmp*tmp';
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tmp = 0.5*(tmp + tmp');
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%mineig = min(real(eig(tmp)));
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%if (mineig < 0); tmp = tmp - 1.1*mineig*eye(n); end;
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tmp_sp(pos,pos) = sparse(tmp);
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end;
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T{size(T,1)+1,1} = tmp_sp;
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end;
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if ~isempty(diag_blk);
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tmp = randn(diag_blk,1);
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tmp = tmp.*tmp;
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%mineig = min(tmp);
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%if (mineig < 0); tmp = tmp - 1.1*mineig*ones(diag_blk,1); end;
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T{size(T,1)+1,1} = tmp;
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end;
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if (L == 1); Zi = T; else; Z0 = T; end;
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end;
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%%
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%% set up the matrices Ak and b
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%%
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A = cell(N,m);
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Ak_sp = sparse(sum(sparse_blk),sum(sparse_blk));
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for k = 1:m;
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Ak = [];
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if ~isempty(dense_blk);
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for j = 1:length(dense_blk);
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tmp = randn(dense_blk(j)); tmp = 0.5*(tmp+tmp');
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Ak{j,1} = tmp;
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end;
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end;
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if ~isempty(sparse_blk);
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for j = 1:length(sparse_blk);
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n = sparse_blk(j);
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tmp = randn(n); tmp = 0.5*(tmp+tmp');
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pos = [sum(sparse_blk(1:j-1))+1 : sum(sparse_blk(1:j))];
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Ak_sp(pos,pos) = tmp;
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end;
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Ak{size(Ak,1)+1,1} = Ak_sp;
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end;
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if ~isempty(diag_blk);
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Ak{size(Ak,1)+1,1} = randn(diag_blk,1);
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end;
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A(:,k) = Ak;
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end;
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y = ones(m,1);
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SAZm = ops(ops(Zi,'+',Asum(blk,A,y)),'/',m);
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SAZm = ops(ops(SAZm,'+',ops(SAZm,'transpose')),'*',0.5);
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yi = randn(m,1);
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for k = 1:m,
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Ak = A(:,k);
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Ak = ops(ops(Ak,'-',SAZm),'/',yi(k));
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Ak = ops(ops(Ak,'+',ops(Ak,'transpose')),'*',0.5);
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A(:,k) = Ak;
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end;
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b = randn(m,1);
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if (b'*yi < 0), b = -b; end;
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y0 = randn(m,1);
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C = ops(Z0,'+',Asum(blk,A,y0));
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C = ops(ops(C,'+',ops(C,'transpose')),'*',0.5);
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%%
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%% (yi,Zi) is a primal infeasibility certificate
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%%
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elseif (infeas == 2),
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%%
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%% dual infeasible
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%%
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%% generate infeasibility certificate Xi, positive definite X0, and C
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%%
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tmp_sp_Xi = sparse(sum(sparse_blk));
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tmp_sp_X0 = sparse(sum(sparse_blk));
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tmp_sp_C = sparse(sum(sparse_blk));
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Xi = [];
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X0 = [];
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C = [];
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if ~isempty(dense_blk);
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for k = 1:length(dense_blk);
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n = dense_blk(k);
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tmp = randn(n);
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tmp = tmp*tmp';
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tmp = 0.5*(tmp + tmp');
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%mineig = min(real(eig(tmp)));
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%if (mineig < 0); tmp = tmp - 1.1*mineig*eye(n); end;
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Xi{k,1} = tmp;
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tmp = randn(n);
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tmp = tmp*tmp';
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tmp = 0.5*(tmp + tmp');
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%mineig = min(real(eig(tmp)));
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%if (mineig < 0); tmp = tmp - 1.1*mineig*eye(n); end;
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X0{k,1} = tmp;
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tmp = randn(n); tmp = 0.5*(tmp + tmp');
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C{k,1} = tmp;
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end;
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end;
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if ~isempty(sparse_blk);
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for k = 1:length(sparse_blk);
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n = sparse_blk(k);
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pos = [sum(sparse_blk(1:k-1))+1 : sum(sparse_blk(1:k))];
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tmp = randn(n);
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tmp = tmp*tmp';
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tmp = 0.5*(tmp + tmp');
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%mineig = min(real(eig(tmp)));
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%if (mineig < 0); tmp = tmp - 1.1*mineig*eye(n); end;
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tmp_sp_Xi(pos,pos) = sparse(tmp);
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tmp = randn(n);
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tmp = tmp*tmp';
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tmp = 0.5*(tmp + tmp');
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%mineig = min(real(eig(tmp)));
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%if (mineig < 0); tmp = tmp - 1.1*mineig*eye(n); end;
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tmp_sp_X0(pos,pos) = sparse(tmp);
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tmp = randn(n); tmp = 0.5*(tmp + tmp');
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tmp_sp_C(pos,pos) = sparse(tmp);
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end;
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Xi{size(Xi,1)+1,1} = tmp_sp_Xi;
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X0{size(X0,1)+1,1} = tmp_sp_X0;
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C{size(C,1)+1,1} = tmp_sp_C;
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end;
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if ~isempty(diag_blk);
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n = diag_blk;
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tmp = randn(n,1);
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tmp = tmp.*tmp;
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%mineig = min(tmp);
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%if (mineig < 0); tmp = tmp - 1.1*mineig*ones(n,1); end;
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Xi{size(X0,1)+1,1} = tmp;
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tmp = randn(n,1);
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tmp = tmp.*tmp;
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%mineig = min(tmp);
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%if (mineig < 0); tmp = tmp - 1.1*mineig*ones(n,1); end;
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X0{size(X0,1)+1,1} = tmp;
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tmp = randn(n,1);
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C{size(C,1)+1,1} = tmp;
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end;
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%%
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%% set up the matrices Ak and b
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%%
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trXX = blktrace(blk,Xi,Xi);
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A = cell(N,m);
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Ak_sp = sparse(sum(sparse_blk),sum(sparse_blk));
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b = ones(m,1);
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for k = 1:m;
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Ak = [];
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if ~isempty(dense_blk);
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for j = 1:length(dense_blk);
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n = dense_blk(j);
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Aj = randn(n);
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Ak{j,1} = (Aj + Aj')/2;
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end;
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end;
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if ~isempty(sparse_blk);
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for j = 1:length(sparse_blk);
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pos = [sum(sparse_blk(1:j-1))+1 : sum(sparse_blk(1:j))];
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n = sparse_blk(j);
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Aj = randn(n);
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Ak_sp(pos,pos) = (Aj + Aj')/2;
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end;
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Ak{size(Ak,1)+1,1} = Ak_sp;
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end;
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if ~isempty(diag_blk);
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n = diag_blk;
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Ak{size(Ak,1)+1,1} = randn(n,1);
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end;
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trAX = blktrace(blk,Ak,Xi);
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Ak = ops(Ak,'-',ops(Xi,'*',(trAX/trXX)));
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Ak = ops(ops(Ak,'+',ops(Ak,'transpose')),'*',0.5);
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A(:,k) = Ak;
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b(k) = blktrace(blk,Ak,X0);
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end;
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if (blktrace(blk,C,Xi) > 0), C = ops(C,'*',-1); end;
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%%
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%% Xi is a dual infeasibility certificate
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%%
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end;
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%%
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%% infeasible initial iterate
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%%
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Avec = svec(blk,A,ones(size(blk,1),1));
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[X0,y0,Z0] = infeaspt(blk,Avec,C,b);
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%%
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if solve;
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[obj,X,y,Z] = sqlp(blk,Avec,C,b,[],X0,y0,Z0);
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end;
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%%=================================================
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