How to calculate reveral summations

I need to calculate sigma=sum(u(t)*u(t+a)), from a to 600(t=a to 600), and a is from 1 to 600. So I should get 600 different sigma.

How to do it?

[Rik]

What is your actual data and what exactly do you want to calculate? Can you give an example for the calculation of one value?

[Walter Roberson]

Is it correct that u is least length 600+h, so that u(t+h) can be in range for indexing when t becomes 600 ?

[Xuefei Sun]

Sorry, the "h" should be a.

The data is u. For example u1 to u1500. And when a=1, I will get sigma(1)=u1*u(1+1)+u(2)*u(2+1)+...u(600)*u(600+1), and then a=2, I will get sigma(2)=u2*u(2+2)+u(3)*u(3+2)+...u(600)*u(600+2). ... a=600, sigma(600)=u600*u(600+600)

Answer 1

[Matt J]

Use conv() or xcorr().

[Xuefei Sun]

Could you please wtite that down? Since I don't know how to use that function. Thank you!

[Walter Roberson]

conv(u,u) would be for sum(u(t)*u(h-t)) rather than for sum(u(t)*u(t+h)) . You could deal with the - by using conv(u, fliplr(u)) to effectively get sum(u(t)*u(t-h)) but at the moment I do not see how to use conv for t+h

[Xuefei Sun]

Sorry, the "h" actually should be "a", and it has a range from 1 to 600

[Xuefei Sun]

You are right, actually the problem is find the autocorrelated value, and I can use conv function to get that. I will have a try. Thank you!

[Walter Roberson]

https://www.mathworks.com/help/matlab/ref/xcorr.html?s_tid=srchtitle

[Xuefei Sun]

I write this code, but I got 1199 sigma. But I need to get 600 sigma, since I have 600 numbers "a". Do you know what's wrong with it?

a=1:600;
y=circshift(u,a);
sigma=xcorr(u,y);

[Walter Roberson]

Y = circshift(A,K) circularly shifts the elements in array A by K positions. If K is an integer, then circshift shifts along the first dimension of A whose size does not equal 1. If K is a vector of integers, then each element of K indicates the shift amount in the corresponding dimension of A.

I don't think you have 600 dimensions to your u .

If you did not get an error when you did the xcorr() then that implies that u and y must both have been vectors.

The example in doc xcorr for Cross-Correlation of Two Vectors shows a vector of length 16 correlated with a modified version of itself. The output is length 31, reflecting a lag up to (16-1) before, and a lag up to (16-1) after, for a total of (16-1) + 1 + (16-1) = 2*16-1 .

Therefore for a vector of length 600, you should expect a length of 2*600-1 = 1199 for the output.

[Xuefei Sun]

Yes, I think that is my problem, since my u data is 600x1, my y data is also 600x1. Both of them are Vrctors.

So how to fix it?

Answer 2

[Matt J]

T=triu(ones(600));
I=(1:600).' + (1:600);
ur=u(:).';

sigma= (T.*ur(I))*ur(1:600).';

[Xuefei Sun]

It won't use xcorr() anymore? But when I type this code, it said: "Index exceeds the number of array elements (600)"

[Matt J]

Works fine when I run it.

u=rand(1,1500); %Example data

T=triu(ones(600));
I=(1:600).' + (1:600);
ur=u(:).';

sigma= (T.*ur(I))*ur(1:600).';

whos sigma

  Name         Size            Bytes  Class     Attributes

  sigma      600x1              4800  double