WUT_Computer_Science/ENUME/projectA/jacobiMethod.m

function x = jacobiMethod(Matrix, Vector)
    [L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, flag] = initializeValues(Matrix);
    [x, whichIterationAreWeOn, demandedTolerance] = jacobiLoop(Matrix, L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, Vector, flag);
    dispFinalResults(x, demandedTolerance, whichIterationAreWeOn, Matrix, Vector);
end

function [L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, flag] = initializeValues(Matrix)
    [Rows, ~] = size(Matrix);
    [L, D, U] = decomposeMatrix(Matrix);
    initial_x = ones(Rows, 1);
    whichIterationAreWeOn = 0;
    demandedTolerance = 10e-10; % as per task description
    % Minimal values I got: 3.202372833989376e-15 for both system of
    % equations - original and task 2a)
    flag = 0;
end

function [L, D, U] = decomposeMatrix(Matrix)
    D = diag(diag(Matrix));
    U = triu(Matrix, 1); % Generates upper triangular part of matrix
    % where the second variable denotes on which diagonal of matrix should we
    % start
    L = tril(Matrix, -1); % Generates lower triangular part of matrix
    % where the second variable denotes on which diagonal of matrix should we
    % start
end

function [x, whichIterationAreWeOn, demandedTolerance]  = jacobiLoop(Matrix, L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, Vector, flag)
    while flag ~= 1 % flag denotes whether norm(Matrix*x-Vector) <= demandedTolerance
        [x, whichIterationAreWeOn, demandedTolerance, flag, initial_x] = jacobiInsideLoop(Matrix, L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, Vector);
    end
end

function [x, whichIterationAreWeOn, demandedTolerance, flag, initial_x] = jacobiInsideLoop(Matrix, L, D, U, initial_x, whichIterationAreWeOn, demandedTolerance, Vector)
    x = jacobiEquation(D, L, U, initial_x, Vector);
    [flag, demandedTolerance] = checkError(x, initial_x, demandedTolerance, Matrix, Vector);
    [initial_x, whichIterationAreWeOn] = endOfLoop(x, whichIterationAreWeOn);
end

function x = jacobiEquation(D, L, U, initial_x, Vector)
    x = - D \ ( L + U ) * initial_x + D \ Vector; % As per formula
    % We will be using D \ Vector and D \ ( ) instead of inverseD since
    % this is faster according to matlab
end

function [flag, demandedTolerance] = checkError(x, initial_x, demandedTolerance, Matrix, Vector)
    flag = 0;
    currentError = norm(x - initial_x);
    if currentError <= demandedTolerance
        currentError = norm(Matrix*x-Vector);

        if currentError <= demandedTolerance % if sequence as per textbook
            flag = 1;
        else 
            demandedTolerance = demandedTolerance * 1; % arbitrary value
        end
    end
end

function [initial_x, whichIterationAreWeOn, flag] = endOfLoop(x, whichIterationAreWeOn)
    initial_x = x;
    whichIterationAreWeOn = whichIterationAreWeOn + 1;
    flag = 0;
end
 
function dispFinalResults(x, demandedTolerance, whichIterationAreWeOn, Matrix, Vector)
    disp("Final demandedTolerance");
    disp(demandedTolerance);
    disp("Final Iteration: ");
    disp(whichIterationAreWeOn);
    disp("A\b matlab:");
    disp(Matrix \ Vector);
    disp("Error:");
    disp(norm(Matrix*x - Vector));
    disp("A\b error:");
    disp(norm(Matrix * (Matrix\Vector) - Vector));
end