Trying to form specific block matrix...

I want a matrix like the following:

for mxm matrix T: -20 in main diagonal, and 4 on diagonal 1 and -1. For example, m=3 gives

T=[-20 4 0; 
    4 -20 4; 
    0 4 -20]

and a mxm matrix S with 4 on main diagonal, and 1 on diagonal 1 and -1. For example, m=3 gives

S=[4 1 0; 
   1 4 1; 
   0 1 4]

I need a matrix like

A=[T S 0 0 0 ... 0;
   S T S 0 0 ... 0;
   ...............;
   0 ..... 0 S T S;
   0 ..... 0 0 S T]

I am trying to do this by modifying this code here.

% form matrix A:
I = speye(m);
e = ones(m,1);
T = spdiags([4*e -20*e 4*e],[-1 0 1],m,m);
S = spdiags([4*e e 4*e],[-1 0 1],m,m);
A = (kron(I,T) + kron(S,I))/ h^2;

[Ryles2014]

I found a solution here I believe http://m2matlabdb.ma.tum.de/poisson9.m?MP_ID=6

Answer 1

[Geoff Hayes]

Ryles2014 - you could use the diag function as follows

 t = 10;
 s = 4;
 n = 5;
 A = diag(repmat(t,n,1)) + diag(repmat(s,n-1,1),1) + diag(repmat(s,n-1,1),-1);

which will set A to be

 A =
    10     4     0     0     0
     4    10     4     0     0
     0     4    10     4     0
     0     0     4    10     4
     0     0     0     4    10

The first call to diag creates the diagonal matrix with t along the main diagonal. We add to this two other matrices which have the s set on the -1 and 1 diagonals.