Block Toeplitz Matrix

[Ahmad]

Hi,

Is there any method in Matlab to generate a BLOCK Toeplitz matrix whose structure is

[a b c 0 0
0 a b c 0
0 0 a b c ]

where a,b, c, and all 0's are COLUMN vectors of the same length r x 1.

[Bruno Luong]

Post by Ahmad
Hi,
Is there any method in Matlab to generate a BLOCK Toeplitz matrix whose structure is
[a b c 0 0
0 a b c 0
0 0 a b c ]
where a,b, c, and all 0's are COLUMN vectors of the same length r x 1.

One way:

a=rand(3,2); b=rand(3,2); c=rand(3,2);

abc = {a b c};
% use z = zeros(size(a)) instead to build full matrix
z = sparse([], [], [], size(a,1), size(a,2));
% z = zeros(size(a));
abc = [{z} abc];
n = length(abc);

s = spdiags(repmat(1:n-1,n+1,1),0:n-2,n+1,n+1);
M = cell2mat(abc(s+1))

I would recommend to go back to the basic: use the SPARSE command to build the matrix from scratch.

Bruno

[Matt J]

Post by Ahmad
Hi,
Is there any method in Matlab to generate a BLOCK Toeplitz matrix whose structure is
[a b c 0 0
0 a b c 0
0 0 a b c ]
where a,b, c, and all 0's are COLUMN vectors of the same length r x 1.

Here's another one. It's efficient in syntax, but not in execution:

A=kron( speye(N), [a,b,c]); %N is number of recurrences of the blocks

[Bruno Luong]

Post by Matt J
A=kron( speye(N), [a,b,c]); %N is number of recurrences of the blocks

The structure of the blocks generated like the above are disjoint like SPDIAGS, not like TOEPLITZ.

Bruno

[Bruno Luong]

Sorry for the typo

The structure of the blocks generated like the above are disjoint like BLKDIAG, not like TOEPLITZ.
Bruno

[Matt J]

Post by Bruno Luong

Post by Matt J
A=kron( speye(N), [a,b,c]); %N is number of recurrences of the blocks

The structure of the blocks generated like the above are disjoint like SPDIAGS, not like TOEPLITZ.

Yeah. Oh well, just for the hell of it, here's a brute force way, using kron()

e=ones(N,1);
A=kron(spdiags(e,0,N,N+2),a)+...
kron(spdiags(e,1,N,N+2),b)+...
kron(spdiags(e,2,N,N+2),c)

[Jos (10584)]

Post by Ahmad
Hi,
Is there any method in Matlab to generate a BLOCK Toeplitz matrix whose structure is
[a b c 0 0
0 a b c 0
0 0 a b c ]
where a,b, c, and all 0's are COLUMN vectors of the same length r x 1.

Here is a aproach

% original arrays
r = 4 ;
a = rand(r,1) ; b = 10*rand(size(a)) ; c = 10*rand(size(a)) ;

% create block toeplitz matrix
X = {zeros(size(a)) a b c} ;
idx = toeplitz([1:3 0 0],[0 0 0]).' + 1 % indices
X = X(idx)
X = cell2mat(X)
% or in 1 step: X = cell2mat(X (toeplitz(..)+1))

hth
Jos