% SolveThis.m
% this uses three programs that you must write. 
% You must write 
%    (1)  myLUfact(A) which returns L and U. 
%    (2)  Lsol(L,b) solves Lx = b for x given L lower triangular
%    (3)  Usol(U,b) solves Ux = b for x given U upper triangular
% only have the output specified below print to the command window. 
% Once it runs successfully. Clear the command window run this program
% then print the command window and turn it in to me. 

% We seek to solve Ax = b where 

A = [6 -2 2 4; 
    12 -8 4 10; 
    3 -13 3 3; 
    -6 4 2 -18];

b = [0 -10 -39 -16]';

% by the LU factorization method. 


% This factors the matrix. You must write myLUfact.m
[myL,myU] = myLUfact(A);

% Now solve Ly = b. You must write Lsol.m 
myY = Lsol(myL,b);

% Now solve Ux = y. You must write Usol.m 
myX = Usol(myU,myY);

 % Now have MATLAB do it. 
matX = A\b;


% This is the 2-norm of the difference between your method and MATLAB's.
difference = norm(myX - matX);

% These are the 2-norms of the residuals 
myresid = norm(A*myX - b);
Matresid = norm(A*matX - b);


% Output to the screen
% These should be the only things printed to the command window !!!!

disp('Solving Ax = b.')
disp('A = ')
disp(A)

disp('b = ')
disp(b)

disp('In the LU factorization of A, L = ')
disp(myL)

disp('In the LU factorization of A, U = ')
disp(myU)

disp('My solution to Uy = b is y = ')
disp(myY)

disp('My solution to Lx = y is x = ')
disp(myX)

disp('The 2-norm of the difference between my solution and Matlabs is')
disp(difference)


if myresid < Matresid
    disp('My residual is smaller.')
elseif Matresid < myresid
    disp('Matlabs residual is smaller.')
else
    disp('The residuals are the same.')
end