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annotate toolbox/eigsens.m @ 2:c124219d7bfa draft

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Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author Antonio Pino Robles <data.script93@gmail.com>
date Thu, 07 May 2015 18:36:24 +0200
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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1 function [X, D, s] = eigsens(A)
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2 %EIGSENS Eigenvalue condition numbers.
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3 % EIGSENS(A) is a vector of condition numbers for the eigenvalues
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4 % of A (reciprocals of the Wilkinson s(lambda) numbers).
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5 % These condition numbers are the reciprocals of the cosines of the
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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6 % angles between the left and right eigenvectors.
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7 % [V, D, s] = EIGSENS(A) is equivalent to
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8 % [V, D] = EIG(A); s = EIGSENS(A);
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9
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10 % Reference:
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11 % G.H. Golub and C.F. Van Loan, Matrix Computations, Second
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12 % Edition, Johns Hopkins University Press, Baltimore, Maryland,
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13 % 1989, sec. 7.2.2.
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14
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15 n = max(size(A));
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16 s = zeros(n,1);
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17
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18 [X, D] = eig(A);
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19 Y = inv(X);
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20
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21 for i=1:n
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22 s(i) = norm(Y(i,:)) * norm(X(:,i)) / abs( Y(i,:)*X(:,i) );
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23 end
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24
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25 if nargout <= 1, X = s; end