%zad1

N = 10;
d = 0.85;	

Edges = [1, 1, 2, 2, 2, 2, 3, 3, 5, 6, 6, 7, 7, 8, 8, 8, 8, 9, 10, 10, 4, 4, 4, 4, 4, 4, 4, 4, 4;
		 2, 4, 3, 7, 8, 10, 1, 7, 7, 2, 4, 5, 8, 4, 5, 6, 7, 8, 5, 8, 1, 2, 3, 5, 6, 7, 8, 9, 10];

% Skonstruuj macierze A, B, I i wektor b dla po³¹czeñ wygenerowanych w Zadaniu A dla parametru d = 0.85.
% Wszystkie macierze powinny byæ przechowywane w formacie sparse, poniewa¿ s¹ to macierze rzadkie
I = eye(N);
B = full(sparse(Edges(2, :), Edges(1, :), 1));
A = diag(1./sum(B));
b = [];
b = ((1 - d) / N) * ones(N, 1);

M = I - d*B*A;
r = M\b;
r = r / norm(r);


%zad2
N = 10;
d = 0.85;	

Edges = [1, 1, 2, 2, 2, 2, 3, 3, 5, 6, 6, 7, 7, 8, 8, 8, 8, 9, 10, 10, 4, 4, 4, 4, 4, 4, 4, 4, 4;
		 2, 4, 3, 7, 8, 10, 1, 7, 7, 2, 4, 5, 8, 4, 5, 6, 7, 8, 5, 8, 1, 2, 3, 5, 6, 7, 8, 9, 10];

% Skonstruuj macierze A, B, I i wektor b dla po³¹czeñ wygenerowanych w Zadaniu A dla parametru d = 0.85.
% Wszystkie macierze powinny byæ przechowywane w formacie sparse, poniewa¿ s¹ to macierze rzadkie
I = eye(N);
B = full(sparse(Edges(2, :), Edges(1, :), 1));
A = diag(1./sum(B));
b = [];
b = ((1 - d) / N) * ones(N, 1);

M = I - d*B*A;

D = diag(diag(M));
L = tril(M) - D;
U = triu(M) - D;

% Jacobi %
LU = L + U;
D_inv = inv(D);
r = ones(N, 1)./N;

k = 0;
tic;
while norm(M*r - b) > 10^-14
	r = -D_inv * LU * r + D_inv * b;
	k = k + 1;
end
time = toc
k

% Gauss-Seidl %
DL = (D + L);
r = ones(N, 1)./N;

k = 0;
tic;
while norm(M*r - b) > 10^-14
	r = ((-DL) \ (U * r)) + (DL \ b);
	k = k + 1;
end
time = toc
k