quadruple summation using function

2 vues (au cours des 30 derniers jours)
CC SS le 24 Sep 2023
Modifié(e) : Matt J le 24 Sep 2023
If I use function to calculate the double summation for , the code is
n = 100;
a = @(p) sin(p);
sum(sum(a(0:n)' * a(0:n)))
However, if I want to calculate the quadruple summation , how to modify the code?
  4 commentaires
Matt J
Matt J le 24 Sep 2023
You should be exploiting the separability of the summation,
and likewise for the quadruple sum.
Dyuman Joshi
Dyuman Joshi le 24 Sep 2023
Good point, @Matt J

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Réponses (2)

Matt J
Matt J le 24 Sep 2023
Modifié(e) : Matt J le 24 Sep 2023
n = 100;
Elapsed time is 0.002355 seconds.

Steven Lord
Steven Lord le 24 Sep 2023
Déplacé(e) : Matt J le 24 Sep 2023
You could use implicit expansion to avoid having to create quite so many large arrays. It's not as fast as the case that exploits the separability, but it is significantly faster than the original general approach.
%Random value for N for example
N = 100;
kvec = 0:1:N; %1 as increment is not necessary
[p,q,r,s] = ndgrid(kvec);
arr = sin(p).*sin(q).*sin(r).*sin(s);
s1 = sum(arr,'all');
Elapsed time is 3.802691 seconds.
Elapsed time is 0.002488 seconds.
% Use implicit expansion
n = numel(kvec);
sinK = sin(kvec);
p = reshape(sinK, n, 1, 1, 1); % unnecessary in this case, but useful for generality
q = reshape(sinK, 1, n, 1, 1);
r = reshape(sinK, 1, 1, n, 1);
s = reshape(sinK, 1, 1, 1, n);
s3 = sum(p.*q.*r.*s, 'all');
Elapsed time is 0.332431 seconds.
The trailing 1's in the reshape calls aren't really necessary, but they do make the pattern of sizes quite easy to see.
format longg
results = [s1, s1-s2, s1-s3; s2-s1, s2, s2-s3; s3-s1, s3-s2, s3]
results = 3×3
1.0e+00 * 0.000261548679431158 -2.30172814402047e-13 0 2.30172814402047e-13 0.00026154867966133 2.30172814402047e-13 0 -2.30172814402047e-13 0.000261548679431158
Those diagonal elements are in pretty good agreement, and all the off-diagonal elements (the differences between the approaches) are all quite small in magnitude,
  1 commentaire
Matt J
Matt J le 24 Sep 2023
Modifié(e) : Matt J le 24 Sep 2023
You can simplify this by downloading ndgridVecs from the File Exchange,
[p,q,r,s] = ndgridVecs(sin(0:100));
result = sum( p.*q.*r.*s , 'all');
Elapsed time is 0.268219 seconds.

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