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199 lines
7.3 KiB
199 lines
7.3 KiB
2 years ago
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% 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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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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gaussOrders=[2:25];
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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={'plate_with_hole','l_bracket','guitar','treble_clef','two_rotors'};
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f{1}=figure('Position',[0 0 900 700],'Color','w');
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f{2}=figure('Position',[0 0 900 700],'Color','w');
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for jjj=1:5
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for mondegs=1:3%length(integrands)
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functs=monfuncts(((mondegs-1)*(mondegs)/2 +1):((mondegs)*(mondegs+1)/2));
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kg=invTri(mondegs-1)+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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figure(f{1})
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subplot(5,4,(jjj-1)*4+mondegs+1)
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loglog(avgDAT{1}(1,:),abs(avgDAT{1}(2,:)),'mo-','MarkerSize',5);
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hold on
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loglog(avgDAT{2}(1,:),abs(avgDAT{2}(2,:)),'co-','MarkerSize',5);
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loglog(avgDAT{3}(1,:),abs(avgDAT{3}(2,:)),'ko-','MarkerSize',5);
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loglog(avgDAT{4}(1,:),abs(avgDAT{4}(2,:)),'bx-.','MarkerSize',5);
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loglog(avgDAT{5}(1,:),abs(avgDAT{5}(2,:)),'gx-.','MarkerSize',5);
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loglog(avgDAT{6}(1,:),abs(avgDAT{6}(2,:)),'rx-.','MarkerSize',5);
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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([1e1 1e7])
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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 jjj==3 && mondegs==3
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ylabel('Integration Error','FontSize',14,'Interpreter','Latex')
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end
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if jjj==5 && mondegs==2
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xlabel('# of Quad points','FontSize',14)
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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 order',mondegs-1),'Interpreter','Latex','FontSize',12);
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end
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figure(f{2})
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subplot(5,4,(jjj-1)*4+mondegs+1)
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loglog(avgDAT{1}(3,:),abs(avgDAT{1}(2,:)),'mo-','MarkerSize',5);
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hold on
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loglog(avgDAT{2}(3,:),abs(avgDAT{2}(2,:)),'co-','MarkerSize',5);
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loglog(avgDAT{3}(3,:),abs(avgDAT{3}(2,:)),'ko-','MarkerSize',5);
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loglog(avgDAT{4}(3,:),abs(avgDAT{4}(2,:)),'bx-.','MarkerSize',5);
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loglog(avgDAT{5}(3,:),abs(avgDAT{5}(2,:)),'gx-.','MarkerSize',5);
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loglog(avgDAT{6}(3,:),abs(avgDAT{6}(2,:)),'rx-.','MarkerSize',5);
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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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xticks([10^-2 10^-1 1 10 100]);
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xlim([10^-3 10^2])
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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 jjj==3 && mondegs==3
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ylabel('Integration Error','FontSize',14,'Interpreter','Latex')
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end
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if jjj==5 && mondegs==2
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xlabel('Timing (s)','FontSize',14,'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 order',mondegs-1),'Interpreter','Latex','FontSize',12);
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end
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end
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end
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for iii=1:2
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figure(iii)
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for jjj=1:5
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subplot(5,4,(jjj-1)*4 +1)
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delete(gca)
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subplot(5,4,(jjj-1)*4 +1)
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ss=generateTestFigures(jjj);
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vals = plot_rat_bern_poly(ss,2,.01,{},[1 0 0 0])
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ll=get(gca,'Children')
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% for i=1:length(ll)
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% set(ll(i),'SizeData',5)
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% end
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if jjj==5 || jjj==2
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axis equal
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if jjj==2
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ylim([-2.1,2.1]);
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end
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if jjj==5
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ylim([0,2.25]);
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xlim([-.1,4.2]);
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end
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elseif jjj==4
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axis ij
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xlim([-1 2]);
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ylim([1.1,4.3]);
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else
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axis ij
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axis square
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end
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if jjj==1
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title("Region",'Interpreter','Latex','FontSize',12)
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xlim([-.1,2.1])
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ylim([-.1,2.1])
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end
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msize = @(bla) size(bla,1);
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xlabel(sprintf("$M=%d,n_c=%d,p=%d$",length(ss),sum(cellfun(msize,ss))/3,size(ss{1},2)-1),'Interpreter','Latex','FontSize',10)
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axis on
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h=get(gca,'xlabel');
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set(gca, 'Xcolor', 'w', 'Ycolor', 'w')
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set(h, 'Color', 'k')
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set(gca, 'XTick', []);
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set(gca, 'YTick', []);
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end
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% subplot(5,4,2+4)
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% legend('Exact mesh','Linear mesh',...
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% 'Quadtree','Cubic spline',...
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% 'Present method','Mod. method','Interpreter','Latex')
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% ax = get(gcf,'children');
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% ind = find(isgraphics(ax,'Legend'));
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% set(gcf,'children',ax([ind:end,1:ind-1]))
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end
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%
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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_monomial_comparisons
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