%% MatrixMarket matrix coordinate double symmetric
% This example is 0-based without (optional) nnz
%
% This is a 1D laplacian matrix (fixed at first end <=> invertible)
%
%              1                              1          
%              .                             .--.        
%             / \                            |  |        
%            /   \ 0                       0 |  |        
%  phi_i  --o  o  o--o--  =>  grad(phi_i)  --o  o  o--o--
%              i  j                            i|  |j    
%                                               |  |     
%                                               .--.     
%                                                -1.     
%
%                 1                              1       
%                 .                             .--.     
%                / \                            |  |     
%               /   \ 0                        i|  |j    
%  phi_j  --o--o  o  o--  =>  grad(phi_j)  --o--o  o  o--
%              i  j                                |  | 0
%                                                  |  |  
%                                                  .--.  
%                                                   -1.  
%
%                  i     j
%              | l_ii  l_ij | i
%  laplacian = |            |
%              | l_ji  l_jj | j
%
%  distance(i, j) = d = 1.
%
%  l_ii = int_[i,j](grad(phi_i).grad(phi_i)) = d*(-1.)*(-1.) =  1.
%  l_ij = int_[i,j](grad(phi_i).grad(phi_j)) = d*(-1.)*( 1.) = -1.
%  l_ji = int_[i,j](grad(phi_j).grad(phi_i)) = d*( 1.)*(-1.) = -1.
%  l_jj = int_[i,j](grad(phi_j).grad(phi_j)) = d*( 1.)*( 1.) =  1.
%
% A <=> assembly of {kappa*laplacian}
%       where kappa = 100
%
% n m [nnz]
% i j Aij

8 8

0  0    1.
1  1  200.
2  2  200.
3  3  200.
4  4  200.
5  5  200.
6  6  200.
7  7  100.

1  0     0.00
2  1  -100.00
3  2  -100.00
4  3  -100.00
5  4  -100.00
6  5  -100.00
7  6  -100.00

0  1     0.00
1  2  -100.00
2  3  -100.00
3  4  -100.00
4  5  -100.00
5  6  -100.00
6  7  -100.00