?? pare_marq_step.m
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function [x, lambda] = pare_marq_step(X, x, lambda);%PARE_MARQ_STEP Gauss-Newton step with Marquardt%% [x, lambda] = pare_marq_step(X, x, lambda);% makes basic step for this x with marquardt correction. %% X: given points <X(i,1), X(i,2)>% x: given parameters% lambda: lambda(i) i-th previous marquardt correction factor%% x: updated parameters% lambda: updated marquardt factors [phi, alpha, a, b, z] = pare_get (x); mu = 1e-3; omega = 0.5; W = ones(size(x,1), 1); m = size(X,1); Y = pare_residual (X, x);%% form Jacobian S = sin(phi); C = cos(phi); s = sin(alpha); c = cos(alpha); A = [-b*S C zeros(size(phi)) c*ones(size(phi)) s*ones(size(phi))]; B = [ a*C zeros(size(phi)) S -s*ones(size(phi)) c*ones(size(phi))]; [cg, sg] = rot_cossin (-a*S, b*C); G = sparse([diag(cg), -diag(sg); diag(sg), diag(cg)]); Y = G*Y; D = - a*S.*cg - b*C.*sg; AB = G*[A; B];%% do marquart step istep = 0; while (1), [cg, sg] = rot_cossin (D, lambda(1)*ones(m,1)); DD = D.*cg - lambda(1)*sg; AA = sparse(diag(cg))*AB(1:m,:); YY = [sparse(diag(cg))*Y(1:m,:); Y(m+1:2*m,:); ... sparse(diag(sg))*Y(1:m,:)]; BB = [AB(m+1:2*m,:); sparse(diag(sg))*AB(1:m,:); ... lambda(1)*eye(5,5)]; [qq, RR] = qr(BB); YY = [YY(1:m,:); qq(1:2*m,1:5)'*YY(m+1:3*m,:)]; JJ = [diag(DD), AA; zeros(5,m), RR(1:5,:)]; s = JJ\YY; h = norm(Y) - norm(pare_residual (X, x + s)); if (h >= 0), break; end; lambda(1) = lambda(1)/omega; istep = istep + 1; end % while if (istep == 0), lambda(1) = lambda(1)*omega; end x = x + s;end % pare_marq_step?? 快捷鍵說明
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