www.pudn.com > LM_opti.rar > LM_opti.m

% Levenberg-Marquardt directions using BOX function 
clc 
clear 
% Starting point  
p0 = 5; q0 = 1; 
x=[0.1; 0.2; 0.3; 0.4; 0.5; 0.6; 0.7; 0.8; 0.9; 1.0]; 
% target values 
t = exp(-x) - exp(-10.0*x); 
 
point_n = 21; 
p = linspace(-1, 6, point_n); 
q = linspace(0, 11, point_n); 
[pp, qq] = meshgrid(p, q); 
E = zeros(point_n, point_n); 
 
for i = 1:point_n, 
	for j = 1:point_n, 
		y = exp(-pp(i,j)*x)-exp(-qq(i,j)*x); 
		E(i,j) = (t-y)'*(t-y);  
	end 
end 
% subplot(2,2,1); 
 
 
figure 
h = mesh(pp, qq, E); 
set(h, 'facecolor', 'none'); 
xlabel('p'); ylabel('q'); zlabel('E(p,q)'); 
axis([-inf inf -inf inf -inf inf]); 
set(gca, 'box', 'on'); 
y = exp(-x)-exp(-10*x); 
E_tmp = (t-y)'*(t-y) ; 
line(1, 10, E_tmp, 'linestyle', '*');  
hold on 
y = exp(-p0*x)-exp(-q0*x); 
E_tmp = (t-y)'*(t-y) ; 
line(p0, q0, E_tmp, 'linestyle', 'o');  
% plot(p0, q0, 'x');  
hold off 
view([-230 30]); 
 
 
figure 
% contour(pp, qq, E, 500); 
contour(pp, qq, E, 30); 
line(1, 10, 'linestyle', '*');  
hold on 
plot(p0, q0, 'o');  
hold on 
theta(:,1)=[p0;q0];thetaold=[0;0];k=1; 
point_n = 10;lambda=0.07; 
while sum(sqrt(abs(theta(:,k)-thetaold)))>0.01 
    thetaold=theta(:,k); 
    k=k+1; 
    J = zeros(point_n, 2);  
    lm_pos=zeros(10, 2);  
    J = [-(-x.*exp(-thetaold(1)*x))  -(x.*exp(-thetaold(2)*x)) ];  
    y = exp(-thetaold(1)*x)-exp(-thetaold(2)*x); 
    g = 2.0 * J' * ( t - y ); 
    JJ = J'*J; 
    lm_dir = -inv(JJ +lambda*eye(size(JJ)))*g; 
    if k==2 
        p_cur = [ p0; q0 ]; 
        % For displaying purpose, arrow length is set to 2.  
        lm_dirtmp = 2.0 * lm_dir / norm(lm_dir);  
        lm_pos = [p_cur p_cur+lm_dirtmp]; 
       % arrow(lm_pos(1, :), lm_pos(2, :), 0.2, 'r-'); 
        text(2.8, 2.9, 'LM','fontsize', 10); 
    end 
    theta(:,k)=thetaold+lm_dir; 
end 
% plot(theta(1,1:k),theta(2,1:k),'o'); 
% hold on 
plot(theta(1,1:k),theta(2,1:k)) 
xlabel('p'); ylabel('q'); 
axis image 
hold off