%% 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.
