Construct Power of Matrix without for loop

Question

Ming 2013-8-11

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/84493-construct-power-of-matrix-without-for-loop

采纳的回答： Azzi Abdelmalek

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

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Answer 1

Azzi Abdelmalek 2013-8-11

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https://ww2.mathworks.cn/matlabcentral/answers/84493-construct-power-of-matrix-without-for-loop#answer_94056

编辑：Azzi Abdelmalek 2013-8-11

在 MATLAB Online 中打开

Example

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

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Answer 2

Jan 2013-8-12

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https://ww2.mathworks.cn/matlabcentral/answers/84493-construct-power-of-matrix-without-for-loop#answer_94090

在 MATLAB Online 中打开

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.