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175 lines
7.2 KiB
175 lines
7.2 KiB
% This file's purpose is to compare quadtree, gauss-green, and szego-green...
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% quadrature methods using a small suite of test cases defined by two
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% domains and various integrands:
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% Domains:
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% close all;
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% clear all;
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shape=3;
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testIntegrands=0;
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timings=0;
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strgctr=1;
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counter=1;
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for i=0:5
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for j=0:i
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a=i-j; b=j;
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monfuncts(counter) = {@(x,y) x.^a.*y.^(b)};
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bla(counter,:)=[a,b];
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counter=counter+1;
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end
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end
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% 2. Three polynomials of degree 2 (bilinear), 4 (biquadratic), and 6
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% (bicubic)
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polyfuncts={@(x,y) (2*x.^2 +x.*y - y +2);
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@(x,y) (2*x.^2.*y.^2 +.3*x.^2.*y - y.^4 + 3*x +2);
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@(x,y) (x.^5 - 5*y.^3.*x.^3 + .2*x.^2 + 2*y.*x.^2 +3);};
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% 3. A rational function of degree 4 and an exponential function.
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otherfuncts={@(x,y) (y.^3 - (x.^3.*y.^2) - (x.*y) -3)./((x.^2).*(y.^2) +10);
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@(x,y) 10*(exp( - x.^2 ) + 2*y);
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@(x,y) sqrt((x+10).^2+(x+10).*(y+10).^2 +x)};
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% addpath("../Rational_Quadrature/Matlab/Src",...
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% "../Rational_Quadrature/Matlab/Tests",...
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% "../Rational_Quadrature/Matlab/ThirdPartySupportingCode")
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d=2;
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% figNum ==1 yields a square plate with a circular hole
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% figNum ==2 yields an L-bracket with 3 holes
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% figNum ==3 yields a wrench figure
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% figNum ==4 yields a guitar-shaped object
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% figNum ==5 yields a treble clef
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filenames={'circle'};
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f{1}=figure('PaperPositionMode','auto','Units','inches','Position',[-0.010416666666667 -0.010416666666667 5.5 3.25],'Color','w');
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f{2}=figure('PaperPositionMode','auto','Units','inches','Position',[-0.010416666666667 -0.010416666666667 5.5 3.25],'Color','w');
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for jjj=1:1
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for mondegs=1:6%length(integrands)
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functs=monfuncts(((mondegs-1)*(mondegs)/2 +1):((mondegs)*(mondegs+1)/2));
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kg=mondegs-1;
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orientations=[1 -1 -1 -1 -1];
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[avgDAT,DAT]=convergenceAnalysis(filenames{jjj},...
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orientations,...
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functs,...
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kg,...
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timings);
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figure(f{1})
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subplot(4,2,mondegs+2)
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loglog(avgDAT{1}(1,:),abs(avgDAT{1}(2,:)),'mo-','MarkerSize',3);
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hold on
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loglog(avgDAT{2}(1,:),abs(avgDAT{2}(2,:)),'co-','MarkerSize',3);
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loglog(avgDAT{3}(1,:),abs(avgDAT{3}(2,:)),'ko-','MarkerSize',3);
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loglog(avgDAT{4}(1,:),abs(avgDAT{4}(2,:)),'bx-.','MarkerSize',3);
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loglog(avgDAT{5}(1,:),abs(avgDAT{5}(2,:)),'gx-.','MarkerSize',3);
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loglog(avgDAT{6}(1,:),abs(avgDAT{6}(2,:)),'rx-.','MarkerSize',3);
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loglog(avgDAT{7}(1,:),abs(avgDAT{7}(2,:)),'x-.','Color',[.5 .5 0],'MarkerSize',3);
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% eqn=func2str(funct); eqn=replace(eqn,'.',''); eqn=replace(eqn,'*','');
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% eqn=eqn(7:end);
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xlabel('Number of Quadrature Points')
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pl=get(gcf);
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pl.FontName='times';
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pl.FontSize=12;
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set(gca,'yscale','log')
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set(gca,'xscale','log')
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yyaxis('right')
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set(gca,'yscale','log')
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xlim([1e1 1e5])
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xticks([ 1e2 1e4 1e6])
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ylim([1e-17 1])
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yticks([1e-15 1e-10 1e-5 1])
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set(gca,'YColor','black','FontName','times');
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if mondegs==4
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ylabel('Integration Error','FontSize',12,'FontName','times','Interpreter','Latex')
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end
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if mondegs==6
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xlabel('# of Quad Points','FontSize',12,'FontName','times','Interpreter','Latex')
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end
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yyaxis('left')
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ylim([1e-17 1])
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set(gca,'YTickLabel',[]);
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if jjj==1
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title(sprintf('%dth degree',mondegs-1),'Interpreter','Latex','FontSize',12,'FontName','times');
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end
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%
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% figure(f{2})
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% subplot(4,2,mondegs+2)
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% loglog(avgDAT{1}(3,:),abs(avgDAT{1}(2,:)),'mo-','MarkerSize',3);
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% hold on
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% loglog(avgDAT{2}(3,:),abs(avgDAT{2}(2,:)),'co-','MarkerSize',3);
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% loglog(avgDAT{3}(3,:),abs(avgDAT{3}(2,:)),'ko-','MarkerSize',3);
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% loglog(avgDAT{4}(3,:),abs(avgDAT{4}(2,:)),'bx-.','MarkerSize',3);
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% loglog(avgDAT{5}(3,:),abs(avgDAT{5}(2,:)),'gx-.','MarkerSize',3);
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% loglog(avgDAT{6}(3,:),abs(avgDAT{6}(2,:)),'rx-.','MarkerSize',3);
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% % eqn=func2str(funct); eqn=replace(eqn,'.',''); eqn=replace(eqn,'*','');
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% % eqn=eqn(7:end);
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% % title({'Convergence Analysis of various quadrature schemes',['for the ', replace(filename,'_',' '),sprintf(' example and $f(x,y) = %s$',eqn)]},'Interpreter','Latex')
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% % xlabel('Number of Quadrature Points')
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% % legend({'Exact mesh + 3rd order Gauss',...
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% % 'Linear mesh + 1st order Gauss',...
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% % 'Quadtree + 3rd order Gauss',...
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% % 'Cubic Spline appr. + Gauss-Green',...
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% % 'Parametric Gauss-Green',...
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% % 'Exact Rational-Green'},'Location','southeast')
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% pl=get(gcf);
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% pl.FontName='times';
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% pl.FontSize=12;
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% set(gca,'yscale','log')
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% set(gca,'xscale','log')
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% yyaxis('right')
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% set(gca,'yscale','log')
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% xlim([1e-3 10])
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% xticks([10^-3 10^-2 10^-1 1 10 100]);
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% ylim([1e-17 1])
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% yticks([1e-15 1e-10 1e-5 1])
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% set(gca,'YColor','black','FontName','times');
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% if mondegs==4
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% ylabel('Integration Error','FontSize',12,'FontName','times','Interpreter','Latex')
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% end
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% if mondegs==6
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% xlabel('Time (s)','FontSize',12,'FontName','times','Interpreter','Latex')
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% end
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% yyaxis('left')
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% ylim([1e-17 1])
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% set(gca,'YTickLabel',[]);
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% if jjj==1
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% title(sprintf('%dth degree',mondegs-1),'Interpreter','Latex','FontSize',12,'FontName','times');
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% end
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% strg{strgctr}=avgDAT;
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% strgctr=strgctr+1;
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end
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end
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for i=1:2
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figure(f{i})
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ax = get(gca,'children');
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ind = find(isgraphics(ax,'Legend'));
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legend('DD-Rational mesh','DD-Linear mesh',...
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'DD-Quadtree','GT-Cubic spline',...
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"GT-SPECTRAL",'GT-SPECTRAL PE','GT-Linear',...
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'FontName','times','Interpreter','Latex',...
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'FontSize',12,'NumColumns',2)
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% set(gcf,'children',ax([ind:end,1:ind-1]));
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set(legend,'FontSize',12)
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end
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figure(f{i})
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subplot(4,2,2)
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hh1=loglog([.5*10^3 .5*10^5],[10^-1 10^-3],'k');
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hold on
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hh1t=text(.5*10^5,7*10^-3,'$\mathcal{O}(N^{-1})$','Interpreter','Latex','HorizontalAlignment','Left')
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hh3=loglog([.5*10^3 .5*10^5],[10^-2 10^-8],'k');
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hh3t=text(.5*10^5,5*10^-8,'$\mathcal{O}(N^{-3})$','Interpreter','Latex','HorizontalAlignment','Left')
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hh6=loglog([.5*10^3 .5*10^5],[10^-3 10^-15],'k');
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hh6t=text(.5*10^5,5*10^-15,'$\mathcal{O}(N^{-6})$','Interpreter','Latex','HorizontalAlignment','Left')
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xlim([1e1 1e5])
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ylim([1e-17 1])
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axis off
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for ii=3:8
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hh=subplot(4,2,ii);
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pos=get(hh,'Position');
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pos2=[pos(1)-.05 pos(2) pos(3) pos(4)];
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set(hh,'Position',pos2);
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end
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set(gcf, 'PaperUnits', 'normalized')
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set(gcf, 'PaperPosition', [0 0 1 1])
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print -dpdf paperFig_convergence_analysis_circle_comparisons
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