Mercurial > matrix-functions
comparison toolbox/gersh.m @ 2:c124219d7bfa draft
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 |
| parents | 8f23314345f4 |
| children |
comparison
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| 1:e471a92d17be | 2:c124219d7bfa |
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| 1 function [G, e] = gersh(A, noplot) | |
| 2 %GERSH Gershgorin disks. | |
| 3 % GERSH(A) draws the Gershgorin disks for the matrix A. | |
| 4 % The eigenvalues are plotted as crosses `x'. | |
| 5 % Alternative usage: [G, E] = GERSH(A, 1) suppresses the plot | |
| 6 % and returns the data in G, with A's eigenvalues in E. | |
| 7 % | |
| 8 % Try GERSH(LESP(N)) and GERSH(SMOKE(N,1)). | |
| 9 | |
| 10 if diff(size(A)), error('Matrix must be square.'), end | |
| 11 | |
| 12 n = max(size(A)); | |
| 13 m = 40; | |
| 14 G = zeros(m,n); | |
| 15 | |
| 16 d = diag(A); | |
| 17 r = sum( abs( A.'-diag(d) ) )'; | |
| 18 e = eig(A); | |
| 19 | |
| 20 radvec = exp(i * seqa(0,2*pi,m)'); | |
| 21 | |
| 22 for j=1:n | |
| 23 G(:,j) = d(j)*ones(size(radvec)) + r(j)*radvec; | |
| 24 end | |
| 25 | |
| 26 if nargin < 2 | |
| 27 | |
| 28 ax = cpltaxes(G(:)); | |
| 29 for j=1:n | |
| 30 plot(real(G(:,j)), imag(G(:,j)),'-c5') % Plot the disks. | |
| 31 hold on | |
| 32 end | |
| 33 plot(real(e), imag(e), 'xg') % Plot the eigenvalues too. | |
| 34 axis(ax); | |
| 35 axis('square'); | |
| 36 hold off | |
| 37 | |
| 38 end |