% Modulis ir norm() vai abs()????
%% 1.uzd Gausa metode, rref(2. 6. variants
clear all
clc,format compact
A=[4,-4,4,7;4,8,-4,4;12,12,-4,15];
B=[7;3;13];
Ap=[A B];
% 1.1
Rangs=rank(Ap)
% 1.2
sol=sym(rref(Ap))
x4=1;
x3=1;

x1=sol(1,5)-sol(1,4)*x4-sol(1,3)*x3
x2=sol(2,5)-sol(2,4)*x4-sol(2,3)*x3

% Kas ir partikul?ra atrisin?juma modulis? norma?

%% 1.uzd 1.variants

clear all
clc,format compact
A=[4,-4,4,7;4,8,-4,4;12,12,-4,15];
B=[7;3;13];
Ap=[A B];
% 1.1
Rangs=rank(Ap)
% 1.2
sol=sym(rref(Ap))
x4=1;


x1=sol(1,5)-sol(1,4)*x4
x2=sol(2,5)-sol(2,4)*x4
x3=sol(3,5)-sol(3,4)*x4
%% 2.uzdevums jakobi metode 2. 6. variants

clear all, clc
A=[14,-7,4;-7,15,-3;4,-3,16];
B=[7;4;3];
n=length(B(:,1));
xtuv=[3;7;4];
N=1;
iter=0;
solnorm=1;
prnorm=zeros(1,2);
while solnorm>0.01
    N=N+1;
    iter=iter+1;
    for m=1:n
        promrez=0;
        for mm=1:n
            if mm~=m
               promrez=promrez+xtuv(mm,N-1)*A(m,mm);
            end
        end
        xtuv(m,N)=(B(m,1)-promrez)/A(m,m);
    end
    solnorm=norm(xtuv(:,N-1)-xtuv(:,N));

    prnorm(iter,:)=[iter,solnorm];
end
%2.1
N
%2.2
xtuv
x_tuvinajumi=xtuv(:,N)
%2.3
xsol=linsolve(A,B)
%2.4
kluda=xsol-x_tuvinajumi

prnorm

%% 2.uzdevums (1.variants)

clear all, clc
A=[1,8,4;8,1,6;4,6,1];
B=[3;5;1];
n=length(B(:,1));
xtuv=[1;3;5];
N=1;
iter=0;
solnorm=1;
prnorm=zeros(1,2);
while iter<10
    N=N+1;
    if iter==0
        xtuv
        nesaiste=abs(A*xtuv-B);
    end


    iter=iter+1;
    for m=1:n
        promrez=0;
        for mm=1:n
            if mm~=m
               promrez=promrez+xtuv(mm,N-1)*A(m,mm);
            end
        end
        xtuv(m,N)=(B(m,1)-promrez)/A(m,m);
    end

    solnorm=norm(xtuv(:,N-1)-xtuv(:,N));

    prnorm(iter,:)=[iter,solnorm];
end
%2.1
nesaiste
%2.2

x_tuvinajumi=xtuv(:,iter)
%2.3

nesaiste10=abs(A*x_tuvinajumi-B)
%2.4
xsol=linsolve(A,B)
kluda=xsol-x_tuvinajumi

%prnorm


%% 3.uzdevums (2. 6. variants)
clear all
A=[14,6,2,0;6,15,1,1,;1,1,16,8;0,1,8,17];
b=[7;4;3;7];
epsi=0.01;
itermax=1000;
n=length(b);

lambda=eig(A);
tau=2/(max(lambda)+min(lambda)) % optimala tau vertiba
k=0;
x=[3;4;7;3];
while norm(A*x-b) > epsi
x=x+tau*(b-A*x);
k=k+1;
end
% 3.1
N=k
%3.2
x
%3.3
linsolve_result= linsolve(A,b)
kl_modulis=abs(linsolve_result-x)
%3.4
konverge_ja_tau_ir_mazak_par=2/max(lambda)

%% 3.uzdevums (1.variants)
clear all
A=[3,-2,2,-4;-2,6,4,6;2,4,9,4;-4,6,4,12];
b=[3;5;1;3];
epsi=0.01;
itermax=1000;
n=length(b);

lambda=eig(A);
tau=5;
k=0;
x=[1;5;3;1];
while  k < 10
x=x+tau*(b-A*x);
k=k+1;

end
% 3.1
abs(x)
%3.2
Nesaistes_modulis=abs(A*x-b) % Norma vai modulis?
%3.3
mazakais_konvergences_tau=2/max(lambda)

%3.4
tau_optimal=2/(max(lambda)+min(lambda))