Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Math Forum » Discussions » Software » comp.soft-sys.matlab

Topic: using matlab least squares functions
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  

Posts: 90
Registered: 8/28/10
using matlab least squares functions
Posted: Sep 27, 2013 12:24 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


I have my matlab code which solves a least squares problem and gives me the right answer. My code is below. I explicitly use my own analytically-derived Jacobian and so on. I just purchased the Optimization toolbox. Can anyone perhaps show me how my code can be used via the functions provided by the Optimization toolbox such as lsqnonlin and so on.

thank you.

%=========== MY least squares ==============%
clc;clear all;close all
beep off
X = [-0.734163292085050,-0.650030660496880;-0.734202821328435,-0.650069503240265;-0.738931528235336,-0.660060466119060;-0.737943703068185,-0.670101503002962;-0.736799998431314,-0.680143905314235;]
Y = [-0.736371316036657,-0.661615260180661;-0.736372829883012,-0.661616774027016;-0.736552116163647,-0.662004318693837;-0.736510559472223,-0.662391863360658;-0.736462980793180,-0.662779408027478;]
Z = X;
w2 =10
w1 = 1;
Zo = Z;
% Create kd-tree
kd = KDTreeSearcher(Y);
% Initialize linear system ||D^0.5(Av - b)||_2^2
% A is the Jacobian
% D is a weight matrix
dim = size(Z,1)*size(Z,2);
A = sparse(2*dim, dim+3);
A(1:dim,1:dim) = speye(dim,dim);
A((1+dim):end,1:dim) = speye(dim,dim);
A((1+dim):(dim+dim/2), end-1) = -ones(dim/2,1);
A((1+dim+dim/2):end, end) = -ones(dim/2,1);
b = zeros(2*dim,1)
D = sparse(2*dim, 2*dim);
D(1:dim,1:dim) = w1*speye(dim,dim);
for it=1:nit
% kd-tree look-up
idz = knnsearch(kd,Z);
P = Y(idz,:);
% Build linear system
b(1:dim) = reshape(P,dim,1);
b((1+dim):end) = reshape(X,dim,1);
Xr = X;
Xr(:,1) = -Xr(:,1);
Xr = fliplr(Xr);
A((1+dim):end,end-2) = reshape(Xr,dim,1);
D((dim+1):end,(dim+1):end) = w2*speye(dim,dim);
% Solve Least Squares
v = (A'*D*A)\(A'*D*b);
% Extract solution
Z = reshape(v(1:dim), size(X,1), size(X,2));
theta = v(end-2);
R = [cos(theta), -sin(theta); sin(theta) cos(theta)];
X = X*R' + repmat(v((end-1):end)', [size(X,1),1]);
% Stopping Criteria
if(norm(Z-Zo)/size(Z,1) < 1e-6)
Zo = Z;

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.