199 lines
6.3 KiB
Mathematica
199 lines
6.3 KiB
Mathematica
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%%*****************************************************************
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%% Examples of SQLP.
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%%
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%% this is an illustration on how to use our SQLP solvers
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%% coded in sqlp.m
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%%
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%% feas = 1 if want feasible initial iterate
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%% = 0 otherwise
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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 sqlpdemo;
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randn('seed',0); rand('seed',0);
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feas = input('using feasible starting point? [yes = 1, no = 0] ');
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if (feas)
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fprintf('\n using feasible starting point\n\n');
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else
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fprintf('\n using infeasible starting point\n\n');
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end
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pause(1);
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ntrials = 1;
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iterm = zeros(2,6); infom = zeros(2,6); timem = zeros(2,6);
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sqlparameters;
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for trials = [1:ntrials];
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for eg = [1:6]
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if (eg == 1);
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disp('******** random sdp **********')
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n = 10; m = 10;
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[blk,At,C,b,X0,y0,Z0] = randsdp(n,[],[],m,feas);
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text = 'random SDP';
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elseif (eg == 2);
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disp('******** Norm minimization problem. **********')
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n = 10; m = 5; B = [];
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for k = 1:m+1; B{k} = randn(n); end;
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[blk,At,C,b,X0,y0,Z0] = norm_min(B,feas);
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text = 'Norm min. pbm';
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elseif (eg == 3);
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disp('******** Max-cut *********');
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N = 10;
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B = graph2(N);
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[blk,At,C,b,X0,y0,Z0] = maxcut(B,feas);
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text = 'Maxcut';
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elseif (eg == 4);
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disp('********* ETP ***********')
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N = 10;
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B = randn(N); B = B*B';
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[blk,At,C,b,X0,y0,Z0] = etp(B,feas);
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text = 'ETP';
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elseif (eg == 5);
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disp('**** Lovasz theta function ****')
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N = 10;
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B = graph2(N);
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[blk,At,C,b,X0,y0,Z0] = thetaproblem(B,feas);
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text = 'Lovasz theta fn.';
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elseif (eg == 6);
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disp('**** Logarithmic Chebyshev approx. pbm. ****')
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N = 20; m = 5;
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B = rand(N,m); f = rand(N,1);
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[blk,At,C,b,X0,y0,Z0] = logcheby(B,f,feas);
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text = 'Log. Chebyshev approx. pbm';
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end;
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%%
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m = length(b);
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nn = 0;
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for p = 1:size(blk,1),
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nn = nn + sum(blk{p,2});
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end
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%%
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Gap = []; Feas = []; legendtext = [];
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for vers = [1 2];
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OPTIONS.vers = vers;
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[obj,X,y,Z,infoall,runhist] = ...
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sqlp(blk,At,C,b,OPTIONS,X0,y0,Z0);
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gaphist = runhist.gap;
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infeashist = max([runhist.pinfeas; runhist.dinfeas]);
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eval(['Gap(',num2str(vers),',1:length(gaphist)) = gaphist;']);
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eval(['Feas(',num2str(vers),',1:length(infeashist))=infeashist;']);
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if (vers==1); legendtext = [legendtext, ' ,''HKM'' '];
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elseif (vers==2); legendtext = [legendtext, ' ,''NT'' '];
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end;
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end;
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h = plotgap(Gap,Feas);
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xlabel(text);
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eval(['legend(h(h>0)' ,legendtext, ')']);
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fprintf('\n**** press enter to continue ****\n'); pause
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end
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end
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%%
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%%======================================================================
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%% plotgap: plot the convergence curve of
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%% duality gap and infeasibility measure.
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%%
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%% h = plotgap(Gap,Feas);
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%%
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%% Input: Gap = each row of Gap corresponds to a convergence curve
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%% of the duality gap for an SDP.
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%% Feas = each row of Feas corresponds to a convergence curve
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%% of the infeasibility measure for an SDP.
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%%
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%% Output: h = figure handle.
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%%
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%% SDPT3: version 3.0
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%% Copyright (c) 1997 by
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%% K.C. Toh, M.J. Todd, R.H. Tutuncu
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%% Last modified: 7 Jul 99
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%%********************************************************************
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function h = plotgap(Gap,Feas)
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clf;
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set(0,'defaultaxesfontsize',12);
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set(0,'defaultlinemarkersize',2);
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set(0,'defaulttextfontsize',12);
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%%
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%% get axis scale for plotting duality gap
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%%
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tmp = [];
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for k = 1:size(Gap,1);
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gg = Gap(k,:);
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if ~isempty(gg);
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idx = find(gg > 5*eps); gg = gg(idx);
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tmp = [tmp abs(gg)];
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iter(k) = length(gg);
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else
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iter(k) = 0;
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end;
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end;
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ymax = exp(log(10)*(round(log10(max(tmp)))+0.5));
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ymin = exp(log(10)*min(floor(log10(tmp)))-0.5);
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xmax = 5*ceil(max(iter)/5);
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%%
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%% plot duality gap
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%%
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color = '-r --b--m-c ';
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if nargin == 2; subplot('position',[0.05 0.3 0.45 0.45]); end;
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for k = 1:size(Gap,1);
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gg = Gap(k,:);
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if ~isempty(gg);
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idx = find(gg > 5*eps);
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if ~isempty(idx); gg = gg(idx); len = length(gg);
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semilogy(len-1,gg(len),'.b','markersize',12); hold on;
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h(k) = semilogy(idx-1,gg,color([3*(k-1)+1:3*k]),'linewidth',2);
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end;
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end;
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end;
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title('duality gap'); axis('square');
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if nargin == 1; axis([0 xmax ymin ymax]); end;
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hold off;
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%%
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%% get axis scale for plotting infeasibility
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%%
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if nargin == 2;
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tmp = [];
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for k = 1:size(Feas,1);
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ff = Feas(k,:);
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if ~isempty(ff);
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idx = find(ff > 0); ff = ff(idx);
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tmp = [tmp abs(ff)];
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iter(k) = length(ff);
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else
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iter(k) = 0;
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end;
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end;
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fymax = exp(log(10)*(round(log10(max(tmp)))+0.5));
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fymin = exp(log(10)*(min(floor(log10(tmp)))-0.5));
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ymax = max(ymax,fymax); ymin = min(ymin,fymin);
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xmax = 5*ceil(max(iter)/5);
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axis([0 xmax ymin ymax]);
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%%
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%% plot infeasibility
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%%
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subplot('position',[0.5 0.3 0.45 0.45]);
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for k = 1:size(Feas,1);
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ff = Feas(k,:);
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ff(1) = max(ff(1),eps);
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if ~isempty(ff);
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idx = find(ff > 1e-20);
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if ~isempty(idx); ff = ff(idx); len = length(ff);
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semilogy(len-1,ff(len),'.b','markersize',12); hold on;
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h(k) = semilogy(idx-1,ff,color([3*(k-1)+1:3*k]),'linewidth',2);
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end;
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end;
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end;
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title('infeasibility measure');
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axis('square'); axis([0 xmax ymin max(1,ymax)]);
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hold off;
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end;
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%%====================================================================
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