How to avoid repeated computation when the result is a symmetric matrix?
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Hi all,
When obtaining a symmetric matrix, we know that we only need to compute and store the elements of upper triangular part. Is there a way to only perform these computations related to the upper triangular part, such that the total number of computation can be reduced by almost half?
Check this example:
clear; clc;
a = rand(5, 1);
b = rand(5, 1);
c = rand(5, 1);
x = {a b c};
xtx = zeros(3, 3);
for i = 1:3
for j = 1:3
pass = x{i}' * x{j};
xtx(i, j) = xtx(i, j) + pass;
end
end
'xtx' is symmetric, but the for loop here computed all elements. Total number of vector products is 9, while we know only 6 products are really needed. If the number of computations is large, then the saving can be dramatic. So how can we solve this?
Many thanks!
4 个评论
When using a for loop it should simply be a case of the inner loop running as
for j = (i+1):3
and then updating both xtx( i, j ) and xtx( j, i ).
For a more general solution where a vectorised approach is used it is less simple though and I'll leave that to someone else!
Xh Du
2017-3-30
Xh Du
2017-3-30
Adam
2017-3-30
I started out with that and changed it. You can just calculate the diagonal separately, but I guess j = i:3 is fine after all.
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