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32 lines
1.0 KiB
Mathematica
32 lines
1.0 KiB
Mathematica
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function [eigenvalues, allIterations] = eigenvaluesWithShifts(A, tol, maxIterations)
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height = size(A,1);
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eigenvalues = diag(zeros(height));
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initialSubmatrix = A;
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allIterations = 0;
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for k = height:-1:2
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DK = initialSubmatrix;
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iteration = 0;
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while iteration<=maxIterations && max(abs(DK(k,1:k-1))) > tol
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DD = DK(k-1:k,k-1:k);
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EV = eigenvalues2x2Matrix(DD);
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shift = EV(2);
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if abs(EV(1) - DD(2,2)) < abs(EV(2) - DD(2,2))
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shift = EV(1);
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end
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DK = DK - eye(k) * shift;
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[Q, R] = qrGramSchmidt(DK);
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DK = R * Q + eye(k) * shift;
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iteration = iteration + 1;
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allIterations = allIterations + 1;
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end
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if iteration > maxIterations
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error('More iterations needed');
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end
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eigenvalues(k) = DK(k,k);
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if k > 2
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initialSubmatrix = DK(1:k-1,1:k-1);
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else
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eigenvalues(1) = DK(1,1);
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end
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end
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end
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