% test_Gershorgin.m

%

% function iflag_main = test_Gershorgin(A);

%

% This MATLAB m-file tests Gershorgin's theorem

% for an input real square matrix A.

%

% K. Beers. MIT ChE. 6/27/2002

function iflag_main = test_Gershorgin(A);

iflag_main = 0;

if(size(A,1) ~= size(A,2))

    error('A is not square');

end

% First, make the figure for the complex

% domain, and add the points for the diagonal

% components.

figure;

hold on;

for k=1:size(A,1)

    plot(A(k,k),0,'o');

end

% Now, add the circles for the off-diagonal elements.

theta = linspace(0,2*pi,100);

theta_cos = cos(theta);

theta_sin = sin(theta);

for k=1:size(A,1)

    row_k_abs = abs(A(k,:));

    rk = sum(row_k_abs) - abs(A(k,k));

    x = A(k,k) + rk*theta_cos;

    y = rk*theta_sin;

    plot(x,y,'--');

end

axis equal;

xlabel('Re(\lambda)');

ylabel('Im(\lambda)');

title('Test of Gershorgin''s theorem');

% Now, calculate the eigenvalues.

iflag_main = 1;

eig_val = eig(A);

for k=1:length(eig_val)

    plot(real(eig_val(k)),imag(eig_val(k)),'d');

end

gtext('O are diagonal elements, diamonds are eigenvalues');

return;