Gaussian_elimination

%the goal of this matlab program is to creat an upper triangular matrix
%from a square matrix. It uses Gaussian_elimination
%matrix A --> U(A).
%First it makes sure that A(1,1) contains the highest value for that
%column.
%Then does the pivot for the 2nd line and down the first colum.
%It then checks for the highest abs value of the 2nd column and permutes if
%needed.
%The program then continues for the 2nd column.

disp("This program is going to create an upper triangular matrix")
s = input('Press enter to continue','s') ;
disp("There must be a Matrix stored in memory (A)")
exist A; %test if a matrix is present
    if ans ~= 0
        B=A;
        i=1; %initialse variable
        [maxB,indice]=max(abs(B(:,1))); %indexes first column with highest value
        P=B(i,:);
        B(i,:)=B(indice,:);
        B(indice,:)=P; %rearenges matrix
        sB=size(B); %creates variable to check linear independecy of matrix
        n=sB(1,1); %creats variable used to count how many lines the matrix has
        
        
            if rank(B) == sB(:,1) %if rank of matrix is different to the number of lines, the matrix can't compute a solution for a linear equation
                j=2; %initialse variable
                for j=2:n
                    i=j-1;
                    B(j,i:n) = B(j,i:n) - B(i,i:n).*B(j,i:i)/B(i,i:i); %Gaussian_elimination on the 2nd line
                    k=j;
                    while k < n %Gaussian_elimination for the rest of the column
                        k=k+1;
                        B(k,i:n) = B(k,i:n) - B(i,i:n).*B(k,i:i)/B(i,i:i);
                        %s = input('Press enter to continue','s'); %prints process for debugging
                        %B %prints process for debugging
                    end 
                i=i+1;
                [maxB,indice]=max(abs(B(i:n,j))); %checks and permutes highest value for column
                indice = indice + (i - 1);
                P=B(i,:);
                B(i,:)=B(indice,:);
                B(indice,:)=P;
                %s = input('Press enter to continue','s'); %use for debugging
                end
            vars = {'ans','i','indice','j','k','maxB','n','p','sB'}; %free memory
            clear(vars{:})
            disp("The original matrix is")
            A
            disp("The U matrix is")
            B
            elseif rank(B) ~= sB(:,1)
                disp("Matrix can't be used because lines aren't independant")
                disp("check matrix")
                vars = {'sB','B','n'}; %free memory
                clear(vars{:})
                s = input('Press enter','s'); 
            end
     
    elseif ans == 0
      disp("No matrix")
      clear all %free memory
    end