How to Sum the N newest data

Hi,

Say I have a code to simulate the time evolution of a very large 3D array E (the electric field), for instantce in finite-difference time-domina simulations. So, in each time step, E will be updated to a new value. Now I want to find the sum of the N (N=5 for example) newest E during each time of my simulation, what is the most efficient, that requires the least ammount of memory, to do this?

So, more intuitively,

at t=t1, E is updated to E1.

at t=t2, E is updated to E2.

at t=t3, E is updated to E3.

at t=t4, E is updated to E4.

at t=t5, E is updated to E5.

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.

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at t=tn, E is updated to En.

What I require is the following:

at t=t1, I require S=E1.

at t=t2, I require S=E1+E2.

at t=t3, I require S=E1+E2+E3.

at t=t4, I require S=E1+E2+E3+E4.

at t=t5, I require S=E1+E2+E3+E4+E5.

at t=t6, I require S=E2+E3+E4+E5+E6.

at t=t7, I require S=E3+E4+E5+E6+E7.

at t=t8, I require S=E4+E5+E6+E7+E8.

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at t=tn, I require S=E_{n-4}+E_{n-3}+E_{n-2}+E_{n-1}+E_{n}

I do not want to use a new vaiable to keep storing the 5 newest data since E is a very large 3D matrix. Is there any other way to do it?

Many thanks!!

Answer 1

[KALYAN ACHARJYA]

One way: % Assuming E1,E2,E3...are scalars

n=   %total_data t1,t2,t3........  
s=0;
E=zeros(1,);
for t=1:n     % t time represents in your case
E(t)=  ....% Updated 
S=sum(E(1:t))
end

Any issue let me know?

[Hao Zhang]

Thanks for your answer. But the whole point is to aviod storing the value of E at every time steps, because E is extremely large.

[KALYAN ACHARJYA]

You want to overwrite E?

As you mentioned

What I require is the following:
at t=t1, I require S=E1.
at t=t2, I require S=E1+E2.
at t=t3, I require S=E1+E2+E3.....

Then you have keep E1,E2..E3....to use compute later part..

If you want to avoid E1,E2,E3....then you can overwrite E, in that case E and s will be same.

[Hao Zhang]

E is overwritten to a new matrix at each time step, it is not possible to store the value at each time step because E could be of the size 2000X2000X200, but I do need the sum of the 5 latest value of E.

[KALYAN ACHARJYA]

If so??

%First calculate E(1) to E(5) then
for t=5:n
E(t)=sum(E(t-4:t))  ....% Updated
.....
end

E1,E2, are scalars or vectors?

[Hao Zhang]

E1 E2... are also very large 3D matrix. Even the 5 latest value of E I do not want to store them in memory. Because the 5 is just a number I use for this example. It can be much larger in the real calculation.

Any way to only store the result of summation without explicitly storing the 5 latest E?

[KALYAN ACHARJYA]

E1 E2... are also very large 3D matrix,, If you want to latest 5 also..

Then you have to use (save) E{1}, E{2} as cell array elements and call the respective to compute the required

Save the last 5 iterartion E in cell array and call the cell elemets to sum the data, after 6 iteration replace the first cell array elements ...so ..on....