// Author: Felipe Rodrigues
// Course: Algebra Linear Computacional
// Algorithm: Upper Triangular


function [r] = back_substitution (A)
    [row, col] = size(A)
    r(1:row) = 0
    if  ( (row ~= 1) & (col ~= 2) ) then
        for i = row:-1:1
           sum_ = 0
           for j=col-1:-1:1
               sum_=sum_+A(i,j)*r(j,1)
           end
           r(i,1)=(A(i, row+1)-sum_)/A(i,i)
        end

    end


endfunction


function [r] = gaussian_elimination(A)
    //Get a tuple representing matrix dimension
    [row, col] = size(A)

    if  ( (row ~= 1) & (col ~= 2) ) then

        for k = 1:row
            disp(A)
            if A(k, k) ~= 0 then

                for i = k+1:row
                    m = real(A(i, k)/A(k, k))

                    for j = 1:col
                        a = A(k, j)

                        new_element = A(i, j) - m*a

                        printf("Novo Elemento A(%d, %d) = %f - %f*%f = %f\n", i, j, A(i,j), m, a, new_element)

                        A(i,j) = 0
                        A(i,j) = new_element

                        disp(A(i,j))

                    end
                end
            else
                A = "Sistema Inconsistente"
                break
            end
        end
    else
        A = A(1,1)
    end
    r = A


endfunction


function main()

   opt = input("Digite (1)-A1, (2)-A2 ou (3)-Nova Matriz:")
   A = null

   if (opt == 1) then
       A = [-1,2,0.3,-119 ; 3,-5,7,120 ; -0.1,13,0,-139] //Expandida A1 | b
   else
       if (opt == 2) then
           A = [3.03,-12.1,14,-119 ; -3.03,12.1,-7,120 ; 6.11,-14.2,21,-139] //Expandida A2 | b
       else
           opt_2 = input("Digite (1) para n=5 ou (2) para n=15:")
           n = null

           if (opt_2 == 1) then
               n = 5
           else
               n = 15
           end

           A = zeros(n,n+1)

           for i=1:n
               for j=1:n
                   A(i,j) = 1/(i+j-1)
               end
           end
           A(1:n,n+1) = 1
           disp(A)

       end

   end


   disp(A)

   [row, col] = size(A)
   b = A(1:row,col)


   [row, col] = size(A)


   if  ( (row ~= 1) & (col ~= 1) ) then
       ut = gaussian_elimination(A)
       solution = back_substitution (ut)
       disp(ut)
       //disp(solution)

       return
   else
       disp(matrixx)
   end

   return

   disp(f)


endfunction

opt = 1
while (opt == 1) then
    main()
    in = input("Digite (1) para continuar ou qualquer numero para encerrar:")
    if in ~= 1 then
        opt = 0
    end
end