Storing parameters from a for loop in arrays

Hi,

I am trying to apply the Gauss-Newton method with a set of data and then use the theta parameters found and plot these over my number of iterations. The values should converge but at the moment my data and plot are not working with my code and I think it has to do with my set up of the array storage. Could someone please help debug my code.

Thank you!!

% Gauss Newton 1
clear
clc
close all

% --- Task 3 ---%
% h = importdata('LLS_Data1.mat');
% t = h(:, 1);
% y = h(:, 2);
t = [0:0.2:3].';
y = [3.43101641262231;-0.527550212558249;3.43697613505530;0.186721377613475;5.11301585254667;
    6.78626419728379;9.69387139109200;7.94303873884149;14.8277080957188;19.2249360936885;20.4921937831721;
    14.2323004458775;21.8155194641984;21.1095884066726;37.9339164089595;41.1133734753079];

% Set iterations and initial guess
n = length(t);
iter = 10;
initialguess = [0; 0];
theta = initialguess;

% Initialise Arrays to Store Parameter Values and Iteration Number
theta1 = zeros(iter,1);
theta2 = zeros(iter,1);
theta1(:,1) = initialguess(1);
theta2(:,2) = initialguess(2);

for i = 1: iter
    % Model Equation
    yM = theta(1)*exp(t) - theta(2);
    
    %Compute Error (data - model equation)
    E = y - yM;
    
    % Compute Jacobian (grad E)
    J = [-exp(t), -ones(n,1)];
    
    delta_theta = theta - inv((J')*(J)) * (J')*(E);
    
    % Update Theta Value
    theta = delta_theta + theta;
    
    
    theta1(i, :) = theta(1);
    theta2(i, :) = theta(1);
end

theta = [theta1(1);theta2(1)];

%--- Task 4 ---%
% Plot Identified Parameters
figure(1);
plot(1:iter, theta1(1))
hold on
plot(1:iter, theta2(2))
xlabel('Iteration');
ylabel('Parameter Value');
legend('Theta 1', 'Theta 2');
title("Identified Parameters vs Iterations");
grid on;

Answer 1

[Walter Roberson]

You have

    theta1(i, :) = theta(1);
    theta2(i, :) = theta(1);

Notice you are storing theta(1) in both cases. You should be storing theta(2) for one of the two.

[Matt Boyles]

Correct thanks for spotting that!

The code however is still not iterating properly and getting the convergence I am after...

[Walter Roberson]

% --- Task 3 ---%
% h = importdata('LLS_Data1.mat');
% t = h(:, 1);
% y = h(:, 2);
t = [0:0.2:3].';
y = [3.43101641262231;-0.527550212558249;3.43697613505530;0.186721377613475;5.11301585254667;
    6.78626419728379;9.69387139109200;7.94303873884149;14.8277080957188;19.2249360936885;20.4921937831721;
    14.2323004458775;21.8155194641984;21.1095884066726;37.9339164089595;41.1133734753079];

% Set iterations and initial guess
n = length(t);
iter = 10;
initialguess = [0; 0];
theta = initialguess;

% Initialise Arrays to Store Parameter Values and Iteration Number
theta1 = zeros(iter,1);
theta2 = zeros(iter,1);
theta1(:,1) = initialguess(1);
theta2(:,2) = initialguess(2);

for i = 1: iter
    % Model Equation
    yM = theta(1)*exp(t) - theta(2);
    
    %Compute Error (data - model equation)
    E = y - yM;
    
    % Compute Jacobian (grad E)
    J = [-exp(t), -ones(n,1)];
    
    delta_theta = theta - inv((J')*(J)) * (J')*(E);
    
    % Update Theta Value
    theta = delta_theta + theta;
    
    
    theta1(i, :) = theta(1);
    theta2(i, :) = theta(2);
end

theta = [theta1(i);theta2(i)];

%--- Task 4 ---%
% Plot Identified Parameters
figure(1);
subplot(2,1,1);

plot(1:iter, theta1, 'k')
xlabel('Iteration');
ylabel('Parameter Value');
title('Theta 1')
grid on

subplot(2,1,2)
plot(1:iter, theta2, 'b')
xlabel('Iteration');
ylabel('Parameter Value');
title("Theta 2");
grid on;

Answer 2

[Torsten]

t = [0:0.2:3].';
y = [3.43101641262231;-0.527550212558249;3.43697613505530;0.186721377613475;5.11301585254667;
    6.78626419728379;9.69387139109200;7.94303873884149;14.8277080957188;19.2249360936885;20.4921937831721;
    14.2323004458775;21.8155194641984;21.1095884066726;37.9339164089595;41.1133734753079];

% Set iterations and initial guess
n = length(t);
iter = 10;
initialguess = [0; 0];

% Initialise Arrays to Store Parameter Values and Iteration Number
theta = zeros(2,iter+1);
theta(:,1) = initialguess;

for i = 1:iter
    % Model Equation
    yM = theta(1,i)*exp(t) - theta(2,i);
    
    %Compute Error (data - model equation)
    E = y - yM;
    
    % Compute Jacobian (grad E)
    J = [-exp(t), ones(n,1)];
    
    delta_theta = - inv((J')*(J)) * (J')*(E);
    
    % Update Theta Value
    theta(:,i+1) = theta(:,i) + delta_theta;
    
end


%--- Task 4 ---%
% Plot Identified Parameters
figure(1);
plot(1:iter+1, [theta(1,:);theta(2,:)])
xlabel('Iteration');
ylabel('Parameter Value');
legend('Theta 1', 'Theta 2');
title("Identified Parameters vs Iterations");
grid on;

figure(2)
hold on
plot(t,y,'o')
plot(t,theta(1,end)*exp(t) - theta(2,end))
hold off
grid on