Explaining a matlab code
Hello, and thank you for taking your time to read this message. I just want to understand how does this code work line by line.
R = input(‘Enter radii [R1, R2, R3]: ‘);
theta = input(‘Enter angles [theta1, theta2, theta3] in degrees: ‘);
stopping_criterion = input(‘Enter stopping criterion for Newton-Raphson iterations: ‘);
% Choose solution method
disp(‘Choose a solution method:’);
disp(‘1. Gauss-Elimination with partial pivoting’);
disp(‘2. Cramer Rule’);
disp(‘3. Naïve Gauss-Jordan’);
method = input(‘Enter the method number: ‘);
if method < 1 || method > 3
error(‘Invalid method number’);
end
f = @(params) [params(1)/(1 + params(2) * sind(theta(1) + params(3))) – R(1);
params(1)/(1 + params(2) * sind(theta(2) + params(3))) – R(2);
params(1)/(1 + params(2) * sind(theta(3) + params(3))) – R(3)];
C = 1000;
e = 0.5;
alpha = 30;
relative_errors_C = zeros(100, 1);
relative_errors_e = zeros(100, 1);
relative_errors_alpha = zeros(100, 1);
for iteration = 1:100
J = numerical_jacobian(f, [C, e, alpha]);
if det(J) == 0
error(‘The Jacobian matrix is not invertible. The Newton-Raphson method cannot be used.’);
end
switch method
case 1
update = gauss_elimination_pivoting(J, f([C, e, alpha]));
case 2
update = cramers_rule_solver(J, f([C, e, alpha]));
case 3
update = naive_gauss_jordan(J, f([C, e, alpha]));
end
% Check for convergence
if norm(update) < stopping_criterion
% Update constants
C = C – update(1);
e = e – update(2);
alpha = alpha – update(3);
relative_errors_C(iteration) = abs(update(1) / C);
relative_errors_e(iteration) = abs(update(2) / e);
relative_errors_alpha(iteration) = abs(update(3) / alpha);
fprintf(‘Iteration %d: Relative Error in C = %f, e = %f, alpha = %fn’, iteration, relative_errors_C(iteration), relative_errors_e(iteration), relative_errors_alpha(iteration));
break;
end
end
figure;
subplot(3, 1, 1);
plot(1:iteration, relative_errors_C(1:iteration), ‘o-‘);
xlabel(‘Iteration’);
ylabel(‘Relative Error in C’);
title(‘Convergence’);
subplot(3, 1, 2);
plot(1:iteration, relative_errors_e(1:iteration), ‘o-‘);
xlabel(‘Iteration’);
ylabel(‘Relative Error in e’);
subplot(3, 1, 3);
plot(1:iteration, relative_errors_alpha(1:iteration), ‘o-‘);
xlabel(‘Iteration’);
ylabel(‘Relative Error in alpha’);
fprintf(‘Final values:nC = %fn e = %fn alpha = %fn’, C, e, alpha);
theta_values = linspace(0, 360, 1000);
R_values = C./(1 + e * sind(theta_values + alpha));
figure;
polarplot(deg2rad(theta_values), R_values);
hold on;
polarplot(deg2rad(theta), R, ‘ro’);
title(‘Satellite Orbit’);
legend(‘Orbit’, ‘Data Points’);
hold off;
function J = numerical_jacobian(f, params)
n = length(params);
m = length(f(params));
J = zeros(m, n);
delta = 1e-8;
for i = 1:n
params_plus = params;
params_minus = params;
params_plus(i) = params_plus(i) + delta;
params_minus(i) = params_minus(i) – delta;
J(:, i) = (f(params_plus) – f(params_minus)) / (2 * delta);
end
endHello, and thank you for taking your time to read this message. I just want to understand how does this code work line by line.
R = input(‘Enter radii [R1, R2, R3]: ‘);
theta = input(‘Enter angles [theta1, theta2, theta3] in degrees: ‘);
stopping_criterion = input(‘Enter stopping criterion for Newton-Raphson iterations: ‘);
% Choose solution method
disp(‘Choose a solution method:’);
disp(‘1. Gauss-Elimination with partial pivoting’);
disp(‘2. Cramer Rule’);
disp(‘3. Naïve Gauss-Jordan’);
method = input(‘Enter the method number: ‘);
if method < 1 || method > 3
error(‘Invalid method number’);
end
f = @(params) [params(1)/(1 + params(2) * sind(theta(1) + params(3))) – R(1);
params(1)/(1 + params(2) * sind(theta(2) + params(3))) – R(2);
params(1)/(1 + params(2) * sind(theta(3) + params(3))) – R(3)];
C = 1000;
e = 0.5;
alpha = 30;
relative_errors_C = zeros(100, 1);
relative_errors_e = zeros(100, 1);
relative_errors_alpha = zeros(100, 1);
for iteration = 1:100
J = numerical_jacobian(f, [C, e, alpha]);
if det(J) == 0
error(‘The Jacobian matrix is not invertible. The Newton-Raphson method cannot be used.’);
end
switch method
case 1
update = gauss_elimination_pivoting(J, f([C, e, alpha]));
case 2
update = cramers_rule_solver(J, f([C, e, alpha]));
case 3
update = naive_gauss_jordan(J, f([C, e, alpha]));
end
% Check for convergence
if norm(update) < stopping_criterion
% Update constants
C = C – update(1);
e = e – update(2);
alpha = alpha – update(3);
relative_errors_C(iteration) = abs(update(1) / C);
relative_errors_e(iteration) = abs(update(2) / e);
relative_errors_alpha(iteration) = abs(update(3) / alpha);
fprintf(‘Iteration %d: Relative Error in C = %f, e = %f, alpha = %fn’, iteration, relative_errors_C(iteration), relative_errors_e(iteration), relative_errors_alpha(iteration));
break;
end
end
figure;
subplot(3, 1, 1);
plot(1:iteration, relative_errors_C(1:iteration), ‘o-‘);
xlabel(‘Iteration’);
ylabel(‘Relative Error in C’);
title(‘Convergence’);
subplot(3, 1, 2);
plot(1:iteration, relative_errors_e(1:iteration), ‘o-‘);
xlabel(‘Iteration’);
ylabel(‘Relative Error in e’);
subplot(3, 1, 3);
plot(1:iteration, relative_errors_alpha(1:iteration), ‘o-‘);
xlabel(‘Iteration’);
ylabel(‘Relative Error in alpha’);
fprintf(‘Final values:nC = %fn e = %fn alpha = %fn’, C, e, alpha);
theta_values = linspace(0, 360, 1000);
R_values = C./(1 + e * sind(theta_values + alpha));
figure;
polarplot(deg2rad(theta_values), R_values);
hold on;
polarplot(deg2rad(theta), R, ‘ro’);
title(‘Satellite Orbit’);
legend(‘Orbit’, ‘Data Points’);
hold off;
function J = numerical_jacobian(f, params)
n = length(params);
m = length(f(params));
J = zeros(m, n);
delta = 1e-8;
for i = 1:n
params_plus = params;
params_minus = params;
params_plus(i) = params_plus(i) + delta;
params_minus(i) = params_minus(i) – delta;
J(:, i) = (f(params_plus) – f(params_minus)) / (2 * delta);
end
end Hello, and thank you for taking your time to read this message. I just want to understand how does this code work line by line.
R = input(‘Enter radii [R1, R2, R3]: ‘);
theta = input(‘Enter angles [theta1, theta2, theta3] in degrees: ‘);
stopping_criterion = input(‘Enter stopping criterion for Newton-Raphson iterations: ‘);
% Choose solution method
disp(‘Choose a solution method:’);
disp(‘1. Gauss-Elimination with partial pivoting’);
disp(‘2. Cramer Rule’);
disp(‘3. Naïve Gauss-Jordan’);
method = input(‘Enter the method number: ‘);
if method < 1 || method > 3
error(‘Invalid method number’);
end
f = @(params) [params(1)/(1 + params(2) * sind(theta(1) + params(3))) – R(1);
params(1)/(1 + params(2) * sind(theta(2) + params(3))) – R(2);
params(1)/(1 + params(2) * sind(theta(3) + params(3))) – R(3)];
C = 1000;
e = 0.5;
alpha = 30;
relative_errors_C = zeros(100, 1);
relative_errors_e = zeros(100, 1);
relative_errors_alpha = zeros(100, 1);
for iteration = 1:100
J = numerical_jacobian(f, [C, e, alpha]);
if det(J) == 0
error(‘The Jacobian matrix is not invertible. The Newton-Raphson method cannot be used.’);
end
switch method
case 1
update = gauss_elimination_pivoting(J, f([C, e, alpha]));
case 2
update = cramers_rule_solver(J, f([C, e, alpha]));
case 3
update = naive_gauss_jordan(J, f([C, e, alpha]));
end
% Check for convergence
if norm(update) < stopping_criterion
% Update constants
C = C – update(1);
e = e – update(2);
alpha = alpha – update(3);
relative_errors_C(iteration) = abs(update(1) / C);
relative_errors_e(iteration) = abs(update(2) / e);
relative_errors_alpha(iteration) = abs(update(3) / alpha);
fprintf(‘Iteration %d: Relative Error in C = %f, e = %f, alpha = %fn’, iteration, relative_errors_C(iteration), relative_errors_e(iteration), relative_errors_alpha(iteration));
break;
end
end
figure;
subplot(3, 1, 1);
plot(1:iteration, relative_errors_C(1:iteration), ‘o-‘);
xlabel(‘Iteration’);
ylabel(‘Relative Error in C’);
title(‘Convergence’);
subplot(3, 1, 2);
plot(1:iteration, relative_errors_e(1:iteration), ‘o-‘);
xlabel(‘Iteration’);
ylabel(‘Relative Error in e’);
subplot(3, 1, 3);
plot(1:iteration, relative_errors_alpha(1:iteration), ‘o-‘);
xlabel(‘Iteration’);
ylabel(‘Relative Error in alpha’);
fprintf(‘Final values:nC = %fn e = %fn alpha = %fn’, C, e, alpha);
theta_values = linspace(0, 360, 1000);
R_values = C./(1 + e * sind(theta_values + alpha));
figure;
polarplot(deg2rad(theta_values), R_values);
hold on;
polarplot(deg2rad(theta), R, ‘ro’);
title(‘Satellite Orbit’);
legend(‘Orbit’, ‘Data Points’);
hold off;
function J = numerical_jacobian(f, params)
n = length(params);
m = length(f(params));
J = zeros(m, n);
delta = 1e-8;
for i = 1:n
params_plus = params;
params_minus = params;
params_plus(i) = params_plus(i) + delta;
params_minus(i) = params_minus(i) – delta;
J(:, i) = (f(params_plus) – f(params_minus)) / (2 * delta);
end
end matlab ai chatbot, large language model, llm, matlab playground MATLAB Answers — New Questions
