Construct Power of Matrix without for loop
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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
采纳的回答
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
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.
2 个评论
Andrei Bobrov
2013-8-12
+1
Azzi Abdelmalek
2013-8-12
Good idea to avoid repeating power operation.
1 个评论
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.
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