function [luz,p]=optzerlegung(A)
    epsilon=10^-6
    for i=1:size(A,1)-1
        //disp(A)
        //disp(b)
        p(i,1)=i
        if abs(A(i,i)) < epsilon
           for j=i+1:size(A,1)
               if abs(A(j,i)) > epsilon
                   p(i,1)=j
                   merke=A(j,1:size(A,1))
                   A(j,1:size(A,1)) = A(i,1:size(A,1))
                   A(i,1:size(A,1)) = merke
                   break
               end
           end
        end
        faktor=(A(i+1:size(A,1),i)./A(i,i))
        A(i+1:size(A,1),i+1:size(A,1))=A(i+1:size(A,1),i+1:size(A,1))-faktor*A(i,i+1:size(A,1))
        A(i+1:size(A,1),i)=faktor
    end
    luz=A
endfunction