Create Block Toeplitz Matrix

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Marco Lago
Marco Lago on 3 May 2021
Edited: Stephen23 on 20 May 2021
How can I create a block toeplitz matrix with all zero elements apart from the main diagonal band?
If A and B are scalars the example below works
rng(123)
A = rand(3);
B = rand(3);
T=100;
Omega = toeplitz([A,B,zeros(T,3)]);
  2 Comments
Jan
Jan on 4 May 2021
Edited: Jan on 4 May 2021
A and B are not scalars in your example and if they are some, the last line fails also.
Please show us, which output you want to get.
Marco Lago
Marco Lago on 20 May 2021
Sorry, my bad. With the scalar example I meant something like the example below. Which gives a squared toeplitz matrix like the folloqing but where A and B are, say, 3x3 matrices.
A B 0 ...0
B A B ...0
0 B A ...0
0 0 B ...0
: : : ....B
0 0 0 ...A
A =1;
B = 2;
T=100;
Omega = toeplitz([A;B;zeros(T,1)])

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Answers (2)

Stephen23
Stephen23 on 20 May 2021
Edited: Stephen23 on 20 May 2021
C = {zeros(3),randi(9,3),randi(9,3)}; % {0,B,A}
N = 5;
X = toeplitz([3,2,ones(1,N-2)]);
M = cell2mat(C(X))
M = 15×15
5 5 9 4 9 7 0 0 0 0 0 0 0 0 0 8 2 3 4 9 7 0 0 0 0 0 0 0 0 0 9 2 3 2 1 9 0 0 0 0 0 0 0 0 0 4 9 7 5 5 9 4 9 7 0 0 0 0 0 0 4 9 7 8 2 3 4 9 7 0 0 0 0 0 0 2 1 9 9 2 3 2 1 9 0 0 0 0 0 0 0 0 0 4 9 7 5 5 9 4 9 7 0 0 0 0 0 0 4 9 7 8 2 3 4 9 7 0 0 0 0 0 0 2 1 9 9 2 3 2 1 9 0 0 0 0 0 0 0 0 0 4 9 7 5 5 9 4 9 7

Stephan
Stephan on 4 May 2021
Try:
rng(123)
A = eye(3);
B = randi(10,3);
Omega = kron(A,B)
gives:
Omega =
7 6 10 0 0 0 0 0 0
3 8 7 0 0 0 0 0 0
3 5 5 0 0 0 0 0 0
0 0 0 7 6 10 0 0 0
0 0 0 3 8 7 0 0 0
0 0 0 3 5 5 0 0 0
0 0 0 0 0 0 7 6 10
0 0 0 0 0 0 3 8 7
0 0 0 0 0 0 3 5 5
  2 Comments
Marco Lago
Marco Lago on 4 May 2021
but that will be a block diagonal matrix, not toeplitz
Stephan
Stephan on 4 May 2021
Edited: Stephan on 4 May 2021
What is your desired output? Do you mean:
rng(123)
A = randi(10,1,4)
T=3;
Omega = toeplitz([A,zeros(1,T)]
Omega =
7 3 3 6 0 0 0
3 7 3 3 6 0 0
3 3 7 3 3 6 0
6 3 3 7 3 3 6
0 6 3 3 7 3 3
0 0 6 3 3 7 3
0 0 0 6 3 3 7

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