# multi array vectorization problem (reformulated)

2 views (last 30 days)
Michal on 18 May 2022
Edited: Michal on 19 May 2022
How to vectorize (for-loop elimination) the following code?
% init
A = [ -0.8013 -0.4981; -0.2278 -0.9009];
t = 0:0.01:1e2;
% eigen space
[V,D]=eig(A,'vector');
D = reshape(D,1,[]);
% computing
expmAt = zeros([size(A),length(t)]);
for i = 1:length(t)
expmAt(:,:,i) = V.*(exp(D*t(i)))/V;
end
Michal on 19 May 2022
Edited: Michal on 19 May 2022
@Jan I just completely reformulated my question ...

Matt J on 19 May 2022
Edited: Matt J on 19 May 2022
runtest(1e2)
Elapsed time is 0.002075 seconds. Elapsed time is 0.000805 seconds.
function runtest(N)
A = [ -0.8013 -0.4981; -0.2278 -0.9009];
t = 0:0.01:N;
b = [2;3];
[V,d]=eig(A,'vector');
tic;
E=exp(d*t);
expmAtb=repmat(eye(size(V)),1,1,numel(t));
expmAtb(logical(expmAtb))=E(:);
expmAtb3=squeeze(pagemtimes( pagemtimes(V,expmAtb), V\b));
toc
tic;
expmAtb4=V*(exp(d*t).*(V\b));
toc
end
Michal on 19 May 2022
Edited: Michal on 19 May 2022
expmAtb4=V*(exp(d*t).*(V\b));
Simple, nice and fast!

Bruno Luong on 19 May 2022
A = [ -0.8013 -0.4981; -0.2278 -0.9009];
t = 0:3;
% eigen space
[V,D]=eig(A,'vector');
D = reshape(D,1,[]);
% computing
expmAt = zeros([size(A),length(t)]);
for i = 1:length(t)
expmAt(:,:,i) = V.*(exp(D*t(i)))/V;
end
expmAt
expmAt =
expmAt(:,:,1) = 1 0 0 1 expmAt(:,:,2) = 0.4736 -0.2168 -0.0991 0.4303 expmAt(:,:,3) = 0.2458 -0.1960 -0.0896 0.2066 expmAt(:,:,4) = 0.1358 -0.1376 -0.0629 0.1083
expmAt2 = pagemrdivide(V.*exp(D.*reshape(t,1,1,[])),V)
expmAt2 =
expmAt2(:,:,1) = 1 0 0 1 expmAt2(:,:,2) = 0.4736 -0.2168 -0.0991 0.4303 expmAt2(:,:,3) = 0.2458 -0.1960 -0.0896 0.2066 expmAt2(:,:,4) = 0.1358 -0.1376 -0.0629 0.1083
Michal on 19 May 2022
Edited: Michal on 19 May 2022
@Bruno Luong I am sorry, you are obviously right. Thanks for help. Your final solution is good!

Catalytic on 19 May 2022
Edited: Catalytic on 19 May 2022
% init
A = [ -0.8013 -0.4981; -0.2278 -0.9009];
t = 0:0.01:1e2;
tic;
% eigen space
[V,D]=eig(A,'vector');
D = reshape(D,1,[]);
% computing
expmAt = zeros([size(A),length(t)]);
for i = 1:length(t)
expmAt(:,:,i) = V.*(exp(D*t(i)))/V;
end
toc
Elapsed time is 0.057550 seconds.
tic
toc
Elapsed time is 0.007411 seconds.
[lb,ub]=bounds(expmAt-out,'all')
lb = -1.3878e-16
ub = 1.1102e-16
[V,d]=eig(A,'vector');
E=exp(d*t);
expmAt=repmat(eye(size(A)),1,1,numel(t));
expmAt(logical(expmAt))=E(:);
expmAt=pagemtimes( pagemtimes(V,expmAt), inv(V));
end
Matt J on 19 May 2022
I wouldn't expect the addition of squeeze() to impact timing significantly.
Also, I find it strange that pagemrdivide(A,B) is not optimized for the case where B has only one page.

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