Writing matrix for 2D plane of atoms

Hello all

I have a row of 100 atoms and i am considering nearest neighbour interaction. What that means is that each atom has an interaction with itself (self interaction) of magnitude 2; and each atom interacts with its two nearest neighbour atoms from each side of magnitude 1. This 1D problem is represented in matrix as

 2  1  0 0 0 0 ...
-1  2  1 0 0 0 ...
 0 -1  2 1 0 0 ...
 0  0 -1 2 1 0 ...
 .............
 .............

Now, my problem is that i dont know how to write this matrix when instead of a 1D problem, i have a 2D plane of atoms with the same nearest neighbour interaction condition. Can someone please help me ???

Thanks in advance.

Sazzad

Answer 1

[Andrei Bobrov]

a = [-1 2 1];
n = 100;
m = numel(a)-1;

out = full(spdiags(ones(n,1)*[-1 2 1],-m:m,n,n));