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36 lines
1.7 KiB
36 lines
1.7 KiB
% Example 3: Numerical approximation of an integral on the interval [0,1]
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% where the integrand has one multiple complex conjugate pair
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% of singularities
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addpath("../Src","../Tests","../ThirdPartySupportingCode")
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clear;
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close;
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clc;
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disp('One multiple complex conjugate pair of poles \pm i*B ');
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disp('int_{0}^{1} sinh( 1/(x^2+B^2) ) dx');
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fun = @(x) ((1-sqrt(2))*x.^2 + (sqrt(2)-2)*x+1)./((2-sqrt(2))*x.^2+(sqrt(2)-2)*x+1);
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% B = [1:1:10]; % ten different cases
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% Exact = [0.87974890970966687009990261325026,0.23393310806757554569295582399079, ...
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% 0.10745651578818868161254072898437,0.061282997467641006451117098989414, ...
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% 0.03948937231856718098266526520331,0.027528255918594052999339126939024, ...
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% 0.020272396252557931274876024669302,0.015545000357541637593303195735998, ...
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% 0.012295556596944788759891908194807,0.0099670302697005460949357802401303];
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for jj=1:10000
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sgl=repmat(roots([(2-sqrt(2)),(sqrt(2)-2),1]),2,1);
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% disp(sprintf('\nPole is +/- %1.3fi',B(j)));
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% Whenever the complex conjugate counterpart of a complex pole is
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% missing in the sequence of poles, it will automatically be added
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% to the sequence by the program rfejer itself.
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% n = 16;
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% disp(sprintf('The maximal number of iterations is %1.3f',n+1));
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% sgl = 1i*B(j)*ones(1,n);
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% First we need to map the interval [0,1] onto the interval [-1,1]
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[fout,sglout ] = transf( @(x)fun(x) , sgl , [0,1] );
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x = rfejer(sglout);
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NumInt = fout(x(1,:))*x(2,:)';
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% disp(sprintf('Computed value: %1.16e',NumInt));
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% disp(sprintf('Estimated relative error : %1.16e',Err));
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ErrExact = abs(1-NumInt/0.6336517494806966);
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end
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% disp(sprintf('Exact relative error : %1.16e',ErrExact));
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