How we can combine two different series and add them

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phoenix
phoenix 2017-8-4
编辑： Jan 2017-8-5
Suppose we have two different sets of arithmetic series ranging from 1 to n. how to combine or add them together so that the elements are not repeated.
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KSSV
KSSV 2017-8-4
That's what...it would be a number...adding numbers is not a deal...
Cong Ba
Cong Ba 2017-8-4
Could you provide an input&output pair so people understand what you expect?

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回答（2 个）

John BG
John BG 2017-8-4
1.
generating 2 sequences
p=randi([-10 10],1,12)
q=randi([-10 10],1,12)
p =
7 9 -8 9 3 -8 -5 1 10 10 -7 10
q =
10 0 6 -8 -2 9 6 10 3 -10 7 9
2.
calculating X
either by applying the first expression directly
p([1:2:end]).*q([2:2:end])
=
0 64 27 -50 -100 -63
X=sum(p([1:2:end]).*q([2:2:end]))
=
-122
or adding q(0)=0 just in case
q=[0 q]
X=sum(p([1:2:end]).*q([2:2:end]))
=
-122
same result
3.
calculating Y
Y=sum(p([2:2:end]).*q([1:2:end]))
=
266
if you find this answer useful would you please be so kind to consider marking my answer as Accepted Answer?
To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link
thanks in advance
John BG
<mailto:jgb2012@sky.com jgb2012@sky.com>
Jan
Jan 2017-8-5
编辑：Jan 2017-8-5
If you provide the input data and show what you have tried so far, posting an answer would require less guessing. I guess that p and q are vectors with n = length(p) / 2. Then what about:
X = 0;
for k = 2:2:n+1
X = X + p(k) * q(k-1);
end
Y = 0;
for c = 2:n
Y = p(2 * c) * q(2 * c - 1);
end
R = X + Y;
Note that I've shifted the indices by one, because they start at 1 in Matlab, not at 0, such that q(k-1) would fail for k=1. If this replies the wanted result, try:
R = sum(p(2:2:n+1) .* q(1:2:n)) + sum(p(2 * (2:n)) .* q(2 * (2:n) - 1))
or slightly faster:
R = sum(p(2:2:n+1) .* q(1:2:n)) + sum(p(4:2:2*n) .* q(4:2:2*n-1))

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