Creating block tridiagonal matrix in matlab

Question

I am writing a Matlab code for a solution to a non-linear partial differential equations. I reached a point where I need an (M+1)^2 by (M+1)^2 block matrix containing say A as the main diagonal, B in position (i,i+1) while C in (i,i+2). i.e., B and C are above the main diagonal A. Is there a short way to build such block matrices?

nirvana-msu nirvana-msu · Accepted Answer · 2016-05-15T12:13:20

To begin with, you can build a single block using triu function like this:

M = 4;
A = 2; B = 3; C = 4;
onesMat = ones(M+1,M+1);
block = A*eye(M+1) + B*(triu(onesMat,1)-triu(onesMat,2)) + C*(triu(onesMat,2)-triu(onesMat,3));

block =
     2     3     4     0     0
     0     2     3     4     0
     0     0     2     3     4
     0     0     0     2     3
     0     0     0     0     2

If my understanding is correct and you want to create a block-diagonal matrix by repeating the same block M+1 times, you can use blkdiag for that:

blocks = repmat({block}, M+1, 1);
res = blkdiag(blocks{:});

Creating block tridiagonal matrix in matlab

1 Answers