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139 lines
6.0 KiB
139 lines
6.0 KiB
% This file's purpose is to compare our gauss-green, and szego-green...
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% with various other quadrature methods using a small suite of test cases
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% defined by 5 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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% 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) +30);
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@(x,y) (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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timedfuncts={polyfuncts{3}; otherfuncts{3}};
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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 0 400 600],'Color','w');
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for iii=1:2
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functs=timedfuncts(iii);
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if iii==1
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kg=6;
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else
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kg=2.5;
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end
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orientations=[1 -1 -1 -1 -1];
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[avgDAT,DAT]=convergenceAnalysis(filenames{5},...
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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(3,2,iii+2)
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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^-1 1 10 100 1000]);
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xlim([10^-1 10^3])
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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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xlabel('Pre-processing (s)','FontSize',10)
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if iii==2
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ylabel('Integration Error','FontSize',12)
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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 iii==1
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title("$p_3(x,y)$",'Interpreter','Latex','FontSize',12);
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end
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if iii==2
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title("$f_3(x,y)$",'Interpreter','Latex','FontSize',12);
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end
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subplot(3,2,iii+4)
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loglog(avgDAT{1}(4,:),abs(avgDAT{1}(2,:)),'mo-','MarkerSize',5);
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hold on
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loglog(avgDAT{2}(4,:),abs(avgDAT{2}(2,:)),'co-','MarkerSize',5);
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loglog(avgDAT{3}(4,:),abs(avgDAT{3}(2,:)),'ko-','MarkerSize',5);
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loglog(avgDAT{4}(4,:),abs(avgDAT{4}(2,:)),'bx-.','MarkerSize',5);
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loglog(avgDAT{5}(4,:),abs(avgDAT{5}(2,:)),'gx-.','MarkerSize',5);
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loglog(avgDAT{6}(4,:),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^-5 10^-4 10^-3 10^-2 10^-1 1]);
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xlim([10^-5 10])
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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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xlabel('Evaluation (s)','FontSize',10)
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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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end
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subplot(3,2,4)
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legend('DD-Exact mesh','DD-Linear mesh',...
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'DD-Quadtree','GT-Cubic spline',...
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"GT-SPECTRAL",'GT-SPECTRAL PE',...
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'FontName','times','Interpreter','Latex','NumColumns',2)
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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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set(legend,'FontSize',10)
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for ii=3:6
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hh=subplot(3,2,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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