MATLAB: Compute mean and diff faster

Question

Hello everyone. I am working on a FD code and need to do a lot of averaging in very large 3D/2D matrices. I want to do the following task, take 1D as an example.

A vector is: A=[a,b,c,d,e,f], and I want to get the average value in between each two neighboring values, so I do A=(A(2:end)+A(1:end-1))/2. And I also do diff a lot, e.g. diff(A,1). And it is the same in 2D or 3D cases. But it becomes very slow when I am dealing with very large matrix, say 1000*1000*1000. Is there any faster way to do this?

Thank you very much.

Answer 1

Get more memory. Huge problems require more memory, or a cup of coffee. Sit down, relax, take out that old copy of War and Peace, and read away.

If your matrix is 1000x1000x1000, then it has 1e9 elements, each of which will require 8 bytes of RAM to store. So that matrix uses roughly 8 gigabytes of RAM to store.

Now, when you compute some operation on your array, like diff or the local average between consecutive elements, this creates a NEW array that is almost the same size. So a new array is formed that also requires 8 gigabytes of RAM.

Every copy of that array forces MATLAB to allocate 8 more gigabytes of RAM. How many gigs of RAM does your computer have? For example, mine is now just a bit old, so it has only 8 gigs in total.

What does MATLAB do when it runs out of RAM? It starts swapping things around, using virtual memory. That gets SLOW, real fast, even if it can find the disk space to do so.

So if you want your computations to be faster, you need more memory.

A poor alternative might be to use singles, instead of doubles. Create your matrix as a single array, and it will now require 4 gigabytes of RAM. It is still gonna be a memory hog, but a slightly leaner one. The cost of course is a loss of precision in your computations.