WUT_Computer_Science/ENUME/projectB/Code/task2MM1.asv

interval = [-5, 10];
rootBrackets = rootBracketing(@polynomial, interval(1), interval(2));

printGraph(@polynomial, 'MM1', @mm1, interval, rootBrackets, 'Approximate zeros of function for method of ');
     
printComplexGraph(@polynomial, 'MM1', @mm1, [-1 + i, 0], 'Aproximate complex roots of polynomial');

function y = polynomial(x)
    y = -2 * x^4 + 12 * x^3 + 4* x^2 + 1 * x + 3;
end

function [approximation, iterations] = mm1(polynomial, a, b, tolerance)

    [approximation, approximationValue, iterations] = initialize(a, b, polynomial);
    [approximation, iterations] = mm1Loop(approximation, tolerance, approximationValue, iterations, polynomial);
end

function [approximation, approximationValue, iterations] = initialize(a, b, polynomial)
    approximation = [a, b, (a + b) / 2];
    approximationValue = arrayfun(polynomial, approximation);
    iterations = [approximation(3); polynomial(approximation(3))];
end

function [approximation, iterations] = mm1Loop(approximation, tolerance, approximationValue, iterations, polynomial)
    while abs(polynomial(approximation(3))) > tolerance
        [approximation, approximationValue, iterations] = insideLoop(approximation, approximationValue, polynomial, iterations);
    end
end

function [approximation, approximationValue, iterations] = insideLoop(approximation, approximationValue, polynomial, iterations)
    eqsys = createEquationSystem(approximation, approximationValue);
    [zplus, zminus] = rootsOfQuadraticFormula(eqsys, approximationValue);
    [approximation, approximationValue, iterations] = updateApproximations(zplus, zminus, approximation, iterations, polynomial);
end

function eqsys = createEquationSystem(approximation, approximationValue)
    [z0, z1, diff0, diff1] = initializeEquationSystem(approximation, approximationValue);
    eqsys = solveEquationSystem(z0, diff0, z1, diff1);
end

function [zplus, zminus] = rootsOfQuadraticFormula(eqsys, approximationValue)
    [a, b, c] = createApproximatedQuadraticFormula(eqsys, approximationValue);
    [zplus, zminus] = findRootsOfQuadraticFormula(a, b, c);
end

function [approximation, approximationValue, iterations] = updateApproximations(zplus, zminus, approximation, iterations, polynomial)
    newapprx = chooseNewRoot(zplus, zminus, approximation);
    iterations = addZeroToIterationVector(newapprx, iterations, polynomial);
    worstapprxindex = getWorstApproximationIndex(approximation, newapprx);
    [approximation, approximationValue] = deleteWorstApproximation(worstapprxindex, approximation, polynomial, newapprx);
end

function [z0, z1, diff0, diff1] = initializeEquationSystem(approximation, approximationValue)
    z0 = approximation(1) - approximation(3);
    z1 = approximation(2) - approximation(3);
    diff0 = approximationValue(1) - approximationValue(3);
    diff1 = approximationValue(2) - approximationValue(3);
end

function eqsys = solveEquationSystem(z0, diff0, z1, diff1)
    eqsys = [z0 ^ 2, z0, diff0; z1 ^ 2, z1, diff1];
    reductor = eqsys(2, 1) / eqsys(1, 1);
    eqsys(2, :) = eqsys(2, :) - reductor * eqsys(1, :);
    eqsys(2, 1) = 0;
    eqsys(2, :) = eqsys(2, :) ./ eqsys(2, 2);
    eqsys(1, :) = eqsys(1, :) - eqsys(1, 2) * eqsys(2, :);
    eqsys(1, :) = eqsys(1, :) ./ eqsys(1, 1);
end

function [a, b, c] = createApproximatedQuadraticFormula(eqsys, approximationValue)
    a = eqsys(1, 3);
    b = eqsys(2, 3);
    c = approximationValue(3);
end

function [zplus, zminus] = findRootsOfQuadraticFormula(a, b, c)
    zplus = -2 * c / (b + sqrt(b ^ 2 - 4 * a * c));
    zminus = -2 * c / (b - sqrt(b ^ 2 - 4 * a * c));
end

function newapprx = chooseNewRoot(zplus, zminus, approximation)
    if abs(zplus) < abs(zminus)
        newapprx = approximation(3) + zplus;
    else
        newapprx = approximation(3) + zminus;
    end
end

function iterations = addZeroToIterationVector(newapprx, iterations, polynomial)
    zero = newapprx;
    iterations(:, size(iterations, 2) + 1) = [zero, polynomial(zero)];
end

function worstapprxindex = getWorstApproximationIndex(approximation, newapprx)
    worstapprxindex = -1;
    worstapprxdiff = 0;
    for i = 1:size(approximation, 2)
        diff = abs(approximation(i) - newapprx);
        if diff > worstapprxdiff
            worstapprxindex = i;
            worstapprxdiff = diff;
        end
    end
end

function [approximation, approximationValue] = deleteWorstApproximation(worstapprxindex, approximation, polynomial, newapprx)
    approximation(worstapprxindex) = [];
    approximation(3) = newapprx;
    approximationValue = arrayfun(polynomial, approximation);
end