Mercurial > matrix-functions
comparison toolbox/eigsens.m @ 0:8f23314345f4 draft
Create local repository for matrix toolboxes. Step #0 done.
| author | Antonio Pino Robles <data.script93@gmail.com> |
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| date | Wed, 06 May 2015 14:56:53 +0200 |
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| -1:000000000000 | 0:8f23314345f4 |
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| 1 function [X, D, s] = eigsens(A) | |
| 2 %EIGSENS Eigenvalue condition numbers. | |
| 3 % EIGSENS(A) is a vector of condition numbers for the eigenvalues | |
| 4 % of A (reciprocals of the Wilkinson s(lambda) numbers). | |
| 5 % These condition numbers are the reciprocals of the cosines of the | |
| 6 % angles between the left and right eigenvectors. | |
| 7 % [V, D, s] = EIGSENS(A) is equivalent to | |
| 8 % [V, D] = EIG(A); s = EIGSENS(A); | |
| 9 | |
| 10 % Reference: | |
| 11 % G.H. Golub and C.F. Van Loan, Matrix Computations, Second | |
| 12 % Edition, Johns Hopkins University Press, Baltimore, Maryland, | |
| 13 % 1989, sec. 7.2.2. | |
| 14 | |
| 15 n = max(size(A)); | |
| 16 s = zeros(n,1); | |
| 17 | |
| 18 [X, D] = eig(A); | |
| 19 Y = inv(X); | |
| 20 | |
| 21 for i=1:n | |
| 22 s(i) = norm(Y(i,:)) * norm(X(:,i)) / abs( Y(i,:)*X(:,i) ); | |
| 23 end | |
| 24 | |
| 25 if nargout <= 1, X = s; end |