Construct Power of Matrix without for loop

1 次查看（过去 30 天）
Ming
Ming 2013-8-11
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

请先登录，再回答此问题。

采纳的回答

Azzi Abdelmalek
Azzi Abdelmalek 2013-8-11
编辑：Azzi Abdelmalek 2013-8-11
Example
A=magic(2);
N=3;
B=cell2mat(arrayfun(@(x) A^x,1:N,'un',0))

更多回答（2 个）

Jan
Jan 2013-8-12
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.
Ming
Ming 2013-8-11
编辑：Ming 2013-8-11
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?
  1 个评论
Walter Roberson
Walter Roberson 2013-8-11
Note: arrayfun() just hides the "for" loop. If you are willing to use it, then Azzi's example does what you ask.

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Matrix Indexing 的更多信息

标签

产品

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by