Memory efficient alternative to sprandsym?

Hello,

I try to create a sparse symmetric random matrix according to some pattern using the command sprandsym. It appears to me, however, that sprandsym consumes a lot of memory during the construction of the matrix even if the final matrix needs much less memory. Obviously, I like to avoid this.

Here is a minimal example where I use two lists (each has 150 elements) to create two matrices, which at the end, by cutting away elements above a certain threshold, determine the pattern of the random matrix:

listA = readmatrix('data/listA.csv');
listB = readmatrix('data/listB.csv');
A = listA(:) - listA(:)'; 
B = listB(:) - listB(:)'; 
Pattern_A = sparse(A >= -threshold & A <= threshold & A ~= 0);
Pattern_B = sparse(B >= -threshold & B <= threshold & B ~= 0);
Pattern = kron(Pattern_A,Pattern_B);

Now, everything works fine until here and the code consumes a bit less than 3 GB. But then, the next line of the code is

RM = sprandsym(Pattern);

During the computation of sprandsym the used memory grows up to 14 GB, but after execution of sprandsym the used memory is around 6.7 GB. This seems to indicate that only the execution of sprandsym seems to consume almost 10 GB extra memory, but I do not really understand why. Is there any explanation? And, ideally, is there any way to make it better?

If it helps, it turns out that the matrix Pattern is not extremely sparse (density of elements around 0.3). Maybe this explains it? I could reduce the density, say to 0.1, but I really like to avoid the extra use of memory during the execution of sprandsym.

Any help is greatly appreciated. Have a nice weekend!

Answer 1

[Jan]

It would be useful to create the input by some commands in the example, such that the readers can run the code without your files.

Does this simplification change the memory consumption:

A = sparse(listA(:) - listA(:)'); 
B = sparse(listB(:) - listB(:)'); 
Pattern_A = (A >= -threshold & A <= threshold & A);
Pattern_B = (B >= -threshold & B <= threshold & B);
Pattern   = kron(Pattern_A, Pattern_B);

[Philipp]

Hi Jan,

thanks for your reply. I am not sure what you mean by "create the input by some commands in the example", but you can think of the lists as 150 random numbers in [0,1] and take the threshold to be, say, 0.2. So the matrices A and B are certainly not sparse. Nevertheless, I tested your idea, but it had zero effect.

As I said, the code seems to work absolutely fine until the execution of sprandsym, which suddenly consumes a lot of memory, much more than what I would expect when running a for loop to create the sparse random matrix myself.

[Jan]

Creating the input by code means to replace

listA = readmatrix('data/listA.csv');

by code, which constructs meaningful testdata, e.g.:

listA = randi([0, 1], 1, 150)

It would be useful to answer questions for clarifications instead of ignoring them: Does this simplification change the memory consumption? Yes or no?

How do you measure the memory consumption?

[Philipp]

I see. Yes, one can put

listA=rand(150,1);

and set

threshold = 0.3;

The same problem appears.

And no, your initial solution didn't change anything. Also, A and B are not sparse at all.

Answer 2

[Philipp]

I have checked this further and it appears to me that part of the problem is that the matrix is not sparse enough. Indeed, I have just created a full random matrix (without any sparsity) of the same dimension and this consumed significantly less memory (around 7 GB) than sprandsym consumed for my not too sparse matrix.

If I increase the sparsity, say to a density of elements around 0.1, sprandsym becomes more efficient and uses only about 4 GB of memory. Still, storing the final sparse matrix in the memory consumes only around 2 GB of memory.

In this sense I am still puzzled how sprandsym works exactly and why it consumes significantly more memory than the final sparse matrix requires for storage?!...