Nan Mihai - Partial MN

%Factorizarea Givens aplicata unei matrice superior Hessenberg
function [Q R] = GivensHessenberg(H)
    %A - matrice superior Hessenberg
    [n, n] = size(H);
    c = zeros(n-1, 1);
    s = zeros(n-1, 1);
    for k=1:n-1
        [c(k), s(k)] = rotatieGivens(H(k, k), H(k+1,k));
        H = triunghiularizare(H, c(k), s(k), k, k+1, k, n);
    end
    R = H;
    Q = ortogonalizare(c, s, n);
end

function R = triunghiularizare(H, c, s, i, k, j1, j2)
    for j=j1:j2
        t1 = H(i, j);
        t2 = H(k, j);
        H(i, j) = c*t1-s*t2;
        H(k, j) = s*t1+c*t2;
    end
    R = H;
end

function Q = ortogonalizare(c, s, n)
    n1 = n-1;
    Q = eye(n);
    Q(n1, n1) = c(n1);
    Q(n, n) = c(n1);
    Q(n1, n) = s(n1);
    Q(n, n1) = -s(n1);
    for k=n-2:-1:1
        k1 = k+1;
        Q(k, k) = c(k);
        Q(k1, k) = -s(k);
        q = Q(k1, k1:n);
        Q(k, k1:n) = s(k)*q;
        Q(k1, k1:n) = c(k)*q
    end
end

function [c,s] = rotatieGivens(a,b)
    if b == 0
        c = 1;
        s = 0;
    else
        if abs(b) > abs(a)
            r = -a / b;
            s = 1 / sqrt(1 + r^2);
            c = s*r;
        else
            r = -b / a;
            c = 1 / sqrt(1 + r^2);
            s = c*r;
        end
    end
end