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39 lines
992 B
Mathematica
39 lines
992 B
Mathematica
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% [USES] Eigenvalues/PowerMethod, Eigenvalues/InversePowerMethod
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function [L, V] = Deflation(A, max_iter, tol)
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[n n] = size(A);
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% initialize the eigenvalues' vector
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L = zeros(1, n);
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% initialize the eigenvectors' matrix
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V = zeros(n);
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% save a backup for A
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C = A;
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for k = 1 : n - 1
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% get the current eigenvalue
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[lam y] = PowerMethod(A, tol, max_iter);
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L(k) = lam;
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V(:, k) = y;
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% compute Wielandt deflation vector
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x = A(k, :)' / (lam * y(k));
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% remove the dominant eigenvalue and its
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% eigenvector from the current matrix
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B = A - lam * y * x';
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A = B;
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endfor
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% get the last eigenvalue
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[lam y] = PowerMethod(A, tol, max_iter);
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L(n) = lam;
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V(:, n) = y;
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% the eigenvectors are not very precise, so
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% we use Inverse Power Method to find a better set of eigenvectors
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% because we know the eigenvalues
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for k = 1 : n
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[lam y] = InversePowerMethod(C, tol, max_iter, L(k));
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V(:, n) = y;
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endfor
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endfunction
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