Mercurial > matrix-functions
comparison matrixcomp/gersh.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 [G, e] = gersh(A, noplot) | |
| 2 %GERSH Gershgorin disks. | |
| 3 % GERSH(A) draws the Gershgorin disks for the square 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(GALLERY('LESP',N)) and GERSH(GALLERY('SMOKE',N)). | |
| 9 | |
| 10 if diff(size(A)), error('Matrix must be square.'), end | |
| 11 | |
| 12 n = length(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 * linspace(0,2*pi,m)'); | |
| 21 | |
| 22 for j=1:n | |
| 23 G(:,j) = d(j)*ones(m,1) + 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)),'-') % Plot the disks. | |
| 31 hold on | |
| 32 end | |
| 33 plot(real(e), imag(e), 'x') % Plot the eigenvalues too. | |
| 34 axis(ax) | |
| 35 axis('square') | |
| 36 hold off | |
| 37 | |
| 38 end |