Mercurial > matrix-functions
diff 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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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/toolbox/eigsens.m Wed May 06 14:56:53 2015 +0200 @@ -0,0 +1,25 @@ +function [X, D, s] = eigsens(A) +%EIGSENS Eigenvalue condition numbers. +% EIGSENS(A) is a vector of condition numbers for the eigenvalues +% of A (reciprocals of the Wilkinson s(lambda) numbers). +% These condition numbers are the reciprocals of the cosines of the +% angles between the left and right eigenvectors. +% [V, D, s] = EIGSENS(A) is equivalent to +% [V, D] = EIG(A); s = EIGSENS(A); + +% Reference: +% G.H. Golub and C.F. Van Loan, Matrix Computations, Second +% Edition, Johns Hopkins University Press, Baltimore, Maryland, +% 1989, sec. 7.2.2. + +n = max(size(A)); +s = zeros(n,1); + +[X, D] = eig(A); +Y = inv(X); + +for i=1:n + s(i) = norm(Y(i,:)) * norm(X(:,i)) / abs( Y(i,:)*X(:,i) ); +end + +if nargout <= 1, X = s; end