%% MatrixMarket matrix coordinate double symmetric
% This example is 0-based without (optional) nnz
%
% This is a 1D diffusive 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.
%
%                i     j
%              | d_ii  d_ij | i
%  diffusion = |            |
%              | d_ji  d_jj | j
%
%  d_ii = int_[i,j](phi_i.grad(phi_i)) = int_[i,j]((1-x)*(-1.)) = -d*0.5  = -0.5
%  d_ij = int_[i,j](phi_i.grad(phi_j)) = int_[i,j]((1-x)*( 1.)) =  d*0.5  =  0.5
%  d_ji = int_[i,j](phi_j.grad(phi_i)) = int_[i,j](   x *(-1.)) = -d*0.5  = -0.5
%  d_jj = int_[i,j](phi_j.grad(phi_j)) = int_[i,j](   x *( 1.)) =  d*0.5  =  0.5
%
% A <=> assembly of {kappa*laplacian + rho*diffusion}
%       where kappa = 100 and rho = 2
%
% 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  101.

1  0     0.
2  1  -101.
3  2  -101.
4  3  -101.
5  4  -101.
6  5  -101.
7  6  -101.

0  1    0.
1  2  -99.
2  3  -99.
3  4  -99.
4  5  -99.
5  6  -99.
6  7  -99.