Invalid expression. Check for missing or extra characters

L = 3;
eta_0 = 1 % Initial value of eta
tol = 1e-5;
rho = 1;
max_iter = 100; % Maximum number of iterations

% Define the function Psi as a separate MATLAB function
function y = Psi(eta);
    y = rho/2; % Implementation of the contraction mapping with coefficient rho = 1
end

% Step 2: Implement the iteration loop
iter = 1;

Function definitions in a script must appear at the end of the file.
Move all statements after the "Psi" function definition to before the first local function definition.

eta_n = eta_0;
delta_eta = [];

while iter <= max_iter
    omega_n = 1 / (iter * (iter + 1));
    zeta_n = 1 / (iter + 1);
    vartheta_n = 1 / (iter + 1);

    eta_n_plus_1 = vartheta_n * Psi((eta_n + eta_n_plus_1) / 2) + zeta_n * (eye(size(A)) - omega_n * A * J) * ((eta_n + eta_n_plus_1) / 2);

    if norm(eta_n_plus_1 - eta_n) < tol
        break;
    end

    delta_eta = [delta_eta, norm(eta_n_plus_1 - eta_n)];
    eta_n = eta_n_plus_1;
    iter = iter + 1;
end

% Step 4: Plot the convergence rate
figure;
plot(1:length(delta_eta), delta_eta);
xlabel('Iteration number');
ylabel('||eta_{n+1} - eta_n||');

% Step 5: Generate the table of number of iterations
iter_vec = 1:iter;
eta_vec = [eta_0, eta_n];
table_data = [iter_vec' eta_vec'];

% Step 6: Display the table and plot
disp('Table of number of iterations:');
disp(table_data);

% Plot the convergence rate graph

[Stephen23]

One obvious bug is the a function in the middle of a script rather than at the end:

https://www.mathworks.com/help/matlab/matlab_prog/local-functions-in-scripts.html

What value do you expect eta_n_plus_1 to have on the first loop iteration? You refer to it before it has been defined.

[Pooja Kumari]

rho is not passed as an input to the function psi()

[Pooja Kumari]

Variable A and Variable J are not defined

[Walter Roberson]

rho = 1;
max_iter = 100; % Maximum number of iterations
% Define the function Psi as a separate MATLAB function
function y = Psi(eta);
y = rho/2; % Implementation of the contraction mapping with coefficient rho = 1
end

Your function takes a parameter named eta but ignores it and uses the value of rho which is not defined inside the function and is not passed as a parameter.

There are some cases in which a function can refer to variables that have been defined in another function -- but this only happens when a function is defined inside another function . You are defining a function inside a script rather than inside a function, and this kind of sharing is not permitted between scripts and functions.

You need to either pass rho to Psi, or else you need to use nested functions.

[John]

This is what i always encounter

Error: File: untitled5.m Line: 19 Column: 1

Function definitions in a script must appear at the end of the file.

Move all statements after the "Psi" function definition to before the first local function definition.

[Torsten]

@Stephen23 already told you what to do:

Move

% Define the function Psi as a separate MATLAB function
function y = Psi(eta);
    y = rho/2; % Implementation of the contraction mapping with coefficient rho = 1
end

to the end of your script and define the unknown variable "rho" therein. Why don't you use "eta" if you supply it as input to the function ?

Answer 1

[Walter Roberson]

Doing what the error message says to do fixes that error... exposing other errors.

L = 3;
eta_0 = 1 % Initial value of eta

eta_0 = 1

tol = 1e-5;
rho = 1;
max_iter = 100; % Maximum number of iterations


% Step 2: Implement the iteration loop
iter = 1;
eta_n = eta_0;
delta_eta = [];

while iter <= max_iter
    omega_n = 1 / (iter * (iter + 1));
    zeta_n = 1 / (iter + 1);
    vartheta_n = 1 / (iter + 1);

    eta_n_plus_1 = vartheta_n * Psi((eta_n + eta_n_plus_1) / 2) + zeta_n * (eye(size(A)) - omega_n * A * J) * ((eta_n + eta_n_plus_1) / 2);

    if norm(eta_n_plus_1 - eta_n) < tol
        break;
    end

    delta_eta = [delta_eta, norm(eta_n_plus_1 - eta_n)];
    eta_n = eta_n_plus_1;
    iter = iter + 1;
end

Unrecognized function or variable 'eta_n_plus_1'.

% Step 4: Plot the convergence rate
figure;
plot(1:length(delta_eta), delta_eta);
xlabel('Iteration number');
ylabel('||eta_{n+1} - eta_n||');

% Step 5: Generate the table of number of iterations
iter_vec = 1:iter;
eta_vec = [eta_0, eta_n];
table_data = [iter_vec' eta_vec'];

% Step 6: Display the table and plot
disp('Table of number of iterations:');
disp(table_data);

% Plot the convergence rate graph

% Define the function Psi as a separate MATLAB function
function y = Psi(eta);
    y = rho/2; % Implementation of the contraction mapping with coefficient rho = 1
end

[John]

Can you also check. I try all kind of means and this is what am facing

L = 3;
eta_0 = 1 % Initial value of eta
tol = 1e-5;
rho = 1;
max_iter = 100; % Maximum number of iterations
iter = 1:max_iter;
eta_n = eta_0;
delta_eta = [];


% Define the function Psi as a separate MATLAB function
function y = Psi(eta);
    y = rho/2; % Implementation of the contraction mapping with coefficient rho = 1
end

% Step 2: Implement the iteration loop

while iter <= max_iter

Function definitions in a script must appear at the end of the file.
Move all statements after the "Psi" function definition to before the first local function definition.

    omega_n = 1 / (iter * (iter + 1));
    zeta_n = 1 / (iter + 1);
    vartheta_n = 1 / (iter + 1);

    eta_(n+1) = vartheta_n * Psi((eta_n + eta_(n+1)) / 2) + zeta_n * (eye(size(A)) - omega_n * A * J) * ((eta_n + eta_(n+1)) / 2);

    if norm(eta_(n+1) - eta_n) < tol
        break;
    end

    delta_eta = [delta_eta, norm(eta_(n+1) - eta_n)];
    eta_n = eta_(n+1);
    iter = iter + 1;
end

% Step 4: Plot the convergence rate
figure;
plot(1:length(delta_eta), delta_eta);
xlabel('Iteration number');
ylabel('||eta_{n+1} - eta_n||');

% Step 5: Generate the table of number of iterations
iter_vec = 1:iter;
eta_vec = [eta_0, eta_n];
table_data = [iter_vec' eta_vec'];

% Step 6: Display the table and plot
disp('Table of number of iterations:');
disp(table_data);

% Plot the convergence rate graph

[Walter Roberson]

If you have a specific reason for not moving the function definition like I showed, then you must use nested functions.

I also had to convert a number of * to .* and a number of / into ./ in order to be able to handle the fact that you are defining iter as a vector 1:max_iter . (I recommend firmly that you re-consider whether iter should be a vector or a scalar.)

draw_my_plots();

eta_0 = 1

Unrecognized function or variable 'eta_'.

Error in solution>draw_my_plots (line 31)
eta_(n+1) = vartheta_n * Psi((eta_n + eta_(n+1)) / 2) + zeta_n * (eye(size(A)) - omega_n * A * J) * ((eta_n + eta_(n+1)) / 2);

%an outer function is needed in order to be permitted to define a nested
%function. A nested function is needed in order to be able to access the
%rho variable inside Psi

function draw_my_plots

L = 3;
eta_0 = 1 % Initial value of eta
tol = 1e-5;
rho = 1;
max_iter = 100; % Maximum number of iterations
iter = 1:max_iter;
eta_n = eta_0;
delta_eta = [];


% Define the function Psi as a separate MATLAB function
function y = Psi(eta);
    y = rho/2; % Implementation of the contraction mapping with coefficient rho = 1
end

% Step 2: Implement the iteration loop

while iter <= max_iter
    omega_n = 1 ./ (iter .* (iter + 1));
    zeta_n = 1 ./ (iter + 1);
    vartheta_n = 1 ./ (iter + 1);

    eta_(n+1) = vartheta_n * Psi((eta_n + eta_(n+1)) / 2) + zeta_n * (eye(size(A)) - omega_n * A * J) * ((eta_n + eta_(n+1)) / 2);

    if norm(eta_(n+1) - eta_n) < tol
        break;
    end

    delta_eta = [delta_eta, norm(eta_(n+1) - eta_n)];
    eta_n = eta_(n+1);
    iter = iter + 1;
end

% Step 4: Plot the convergence rate
figure;
plot(1:length(delta_eta), delta_eta);
xlabel('Iteration number');
ylabel('||eta_{n+1} - eta_n||');

% Step 5: Generate the table of number of iterations
iter_vec = 1:iter;
eta_vec = [eta_0, eta_n];
table_data = [iter_vec' eta_vec'];

% Step 6: Display the table and plot
disp('Table of number of iterations:');
disp(table_data);

% Plot the convergence rate graph

end