matlab ultimul lab 29.05.2018

function x = Gausspivot(A,b)
n=size(A,1);
A(:,n+1)=b(:);
index=1:n
for k=1:n
    max=abs(A(k,k))
    for i=k:n
        for j=k:n
            if abs(A(i,j))>max
                max=abs(A(i,j))
                 p=i;
                 m=j;
            end
        end
    end
    if p~=k
        aux=A(k,:);
        A(k,:)=A(p,:);
        A(p,:)=aux;
    end
    if m~=k
        aux=A(:,m);
        A(:,m)=A(:,k);
        A(:,k)=aux
        aui=index(m);
        index(m)=index(k);
        index(k)=aui;
    end
    for l=k+1;n
        A(l,:)=A(l,:)-A(l,k)/A(k,k)*A(k,:);
    end
end
xmod=SubstDesc(A(:,1:n),A(:,n+1))
display('xmod=')
disp(xmod)
display('indice mod.')
disp(index)
for i=1:n
    x(i)=xmod(index(i));
end
end


function x = SubstDesc(A,b)
n=size(A,1);
x(n)=b(n)/A(n,n);
for k=n-1:-1:1
    s=0
    for j=k+1:n
        s=s+A(k,j)*x(j);
    end
    x(k)=(b(k)-s)/A(k,k);
end