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22 lines
832 B
Mathematica
22 lines
832 B
Mathematica
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function [lambda, y, step] = PowerMethod(A, tol, max_iter)
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% This function returns the largest eigenvalue of the matrix and the characteristic vector
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[n n] = size(A);
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% We randomly choose the vector y with values in the interval (0, 1)
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y = rand(n, 1);
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lambda = inf;
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% iterate to the maximum number of iterations
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for step = 1 : max_iter
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z = A * y;
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% update the eigenvector
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y = z / norm(z);
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% backup the last eigenvalue approximation
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lambda_old = lambda;
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% update the lambda value
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lambda = y' * A * y;
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% when the new values get close enough to the last values
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% regarding the imposed tolerance "tol", we reached the solution
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if abs((lambda - lambda_old) / lambda) < tol
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break;
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endif
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endfor
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endfunction
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