Construct Power of Matrix without for loop

Hi, everyone:

Suppose I have a 2 by 2 matrix A, if I want construct a larger matrix B that is defined as:

B=[A, A^2, A^3, A^4, ... A^N];

is it possible to do it without for loop?

Thanks

Answer 1

[Azzi Abdelmalek]

Example

A=magic(2);
N=3;
B=cell2mat(arrayfun(@(x) A^x,1:N,'un',0))

Answer 2

[Jan]

Azzi's suggestion is fine for N=3. If you are talking about larger N, neither the repeated power operator nor arrayfun nor cell2mat are efficient:

N = 10000
A = rand(2, 2);
tic;
B = cell2mat(arrayfun(@(x) A^x,1:N,'un',0));
toc

tic;
B = zeros(2, 2, N);
P = 1;
for k = 1:N
  P=P*A;
  B(:,:,k) = P;
end
B = reshape(B, 2, N * 2);
toc

 Elapsed time is 0.199776 seconds.
 Elapsed time is 0.039983 seconds.

So I'd prefer the more efficient FOR loop.

[Andrei Bobrov]

+1

[Azzi Abdelmalek]

Good idea to avoid repeating power operation.

Answer 3

[Ming]

Thanks very much!

Do you know if A is a 2 by 2 by N matrix, can I use "arrayfun" or any other way to do:

B=[A(:,:,1), A(:,:,1)*A(:,:,2), A(:,:,1)*A(:,:,2)*A(:,:,3), ... , A(:,:,1)*A(:,:,2)*A(:,:,3)* ... *A(:,:,N)]

without for loop?

[Walter Roberson]

Note: arrayfun() just hides the "for" loop. If you are willing to use it, then Azzi's example does what you ask.