%%%% Setup the matrix for 1D Laplacian in sparse format, with some perturbation 
%%%% to help you distinguish column and row indices.

clear all
% format long

N = 10;
%N = 100;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Setup the storage for non-zero entries
%%%% IA = the storage for index i
%%%% JA = the storage for index j
%%%% KA = the storage for entry values

IA = zeros(N-1+2*(N-2),1); % only three diagonals are nonzero;
                           % allocate a big vector to store i for those (i,j)
JA = IA ;                  % to store those j 
KA = IA ;                  % to store those A(i,j)

% Store the first nonzero entry: A(i,j) with i=1, j=1
k = 1 ; 
IA(k) = 1 ; JA(k) = IA(k)          ; KA(k) = -2 ;

% Store A(i,j) with i=1, j=2
k = k + 1 ; 
IA(k) = 1 ; JA(k) = IA(k) + 1      ; KA(k) =  1.01 ; 

%%%% Now, proceed to store the remaining nonzero entries.
for i = 2 : N-2
    k = k + 1 ;
    IA(k) = i ; JA(k) = IA(k)  -1      ; KA(k) =  1 ;
    k = k + 1 ;
    IA(k) = i ; JA(k) = IA(k)          ; KA(k) =  -2 ;
    k = k + 1 ;
    IA(k) = i ; JA(k) = IA(k) + 1      ; KA(k) =  1.01 ;
end

k = k + 1 ;
IA(k) = N-1 ; JA(k) = IA(k) -1        ; KA(k) = 1 ;
k = k + 1 ;
IA(k) = N-1 ; JA(k) = IA(k)           ; KA(k) = -2 ;

A = sparse(IA,JA,KA) 
% After you have actually seen the matrix A in matlab,
% you can switch last line to the one below
% A = sparse(IA,JA,KA);