# Generate a 100000x100000 matrix that takes less time and memory

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Jay Vaidya on 19 Oct 2020
Commented: Jay Vaidya on 20 Oct 2020
I have written a random matrix generator code that generates an adjacency matrix of any size. I am targetting larger size like 100kx100k but the problem that I face is the time to generate that (which is related to the RAM memory). It needs ~ 60 GB to do this.
I presume that there has to be a smarter way to do this, like by using a small int instead of a double word or something similar to the datatype. Any help would be appreciated. Thanks
function [a,ed] = Random_graph_genar_function(nodes, connectivity)
for it=1:3
ni = nodes;
ac= connectivity;
mi=(ni*(ni-1))/2;
no=round(mi*ac);
a=zeros(ni,ni);
in=randperm(mi,no); p=1;
for i=1:ni
for j=i+1:ni
if (any(in(:)==p))
a(i,j)=1;
a(j,i)=1;
end
p=p+1;
end
end
p=0;
for i=1:ni
for j=i+1:ni
if (a(i,j)==1)
p=p+1;
ed(1,p)=i;
ed(2,p)=j;
end
end
end
s=sum(a);
mx=max(s)
for i=1:ni
bc(i)=mx-s(i);
end
tbc=sum(bc);
end
end

Show 1 older comment
Jay Vaidya on 19 Oct 2020
The percentage of the matrix that is non-zero is random and changes with different simulations.
But, I only need to store binary values (0 or 1) in the adjacency matrix. That means it is a non-weighted graph.
I get the following error when I try running the code below
Random_graph_genar_function(1e6,0.8)
Error using zeros
Requested 1000000x1000000 (7450.6GB) array exceeds maximum array size preference. Creation of arrays
greater than this limit may take a long time and cause MATLAB to become unresponsive. See array size limit
Walter Roberson on 20 Oct 2020
The percentage of the matrix that is non-zero is random
Is it going to be 0.000378% in one run, but 82.19% in another run? You have no idea what the percentage will be, other than more than 0% and less than 100% ?
Jay Vaidya on 20 Oct 2020
No, I meant that I would like to control the connectivity of the graph (percentage of non-zero elements) using the connectivity parameter in the above function.

Matt J on 20 Oct 2020
Edited: Matt J on 20 Oct 2020
Seems to me the whole code can be replaced by,
function [a,ed] = Random_graph_genar_function(nodes, connectivity)
a=logical(sprandsym(nodes,connectivity));
a=a-a.*speye(nodes);
G=graph(a);
ed=table2array(G.Edges).';
end
although instead of having the function return a and ed, I suspect that everything you are trying to do is more easily accomplished with the graph object G instead.

Matt J on 20 Oct 2020
I don't think your current implementation ensures that does it?
Walter Roberson on 20 Oct 2020
If you have a fixed number of iterations to work with, then you will need to proceed by either
1. growing the graph step by step so that at no point are there disconnected points; or
2. imposing a maximum distance away from other existing points upon new points, and "reserving" a number of iterations to do nothing but "fix-up" the disconnected subtrees by connecting them to other sub-trees; or
3. after the initial iterations, find all disconnected subtrees and move them to be attached to the main tree. If you have a constrained geometry, it might take some searching to find attachment points that satisfy the constraints
I suspect that the first option, growing step by step, is the easiest.
Jay Vaidya on 20 Oct 2020
Thanks, Walter and Matt. I agree that growing step by step would be easier. I have made another question about this. It would be great if you have some time to see that. It is here. Thanks in advance.

Ameer Hamza on 19 Oct 2020
If most of the elements equal to zero, then use sparse array: https://www.mathworks.com/help/matlab/ref/sparse.html. You can also try to create uint8 array which will only use 1/8 memory
a=zeros(ni,ni,'uint8');

Steven Lord on 20 Oct 2020
Do you need the adjacency matrix as a full matrix, or can you work on it as a sparse matrix?
Jay Vaidya on 20 Oct 2020
That gives the matrix that is quite sparse. I needed a matrix that can have the connectivity that I would like to have. Can we control the connectivity/density in this?
Jay Vaidya on 20 Oct 2020
My entire code used to use double datatype. I don't know using sparse can change other things. At the end of the day, I need an adjacency matrix that has 0.1 (connectivity) and 100k nodes (100k rows and 100k columns).
I changed the
a=zeros(ni,ni);
to
a=zeros(ni,ni,'uint8');
But, it is not making a big difference in the above code for n = 1e3 (1000 nodes).

Walter Roberson on 19 Oct 2020
a=zeros(ni,ni,'uint8');
You are already using only one byte per entry.
If you were to create logic that packed 8 adjacent entries into one byte, you could potentially get 8:1 compression... and would still need 116.4 gigabytes of memory.
Your only hope would be if you could use a sparse() array. See https://www.mathworks.com/matlabcentral/answers/100287-how-much-memory-a-sparse-matrix-created-using-sprand-with-given-number-of-rows-columns-and-density for a guideline to the amount of memory a sparse array uses. I suspect the 16 is 8 bytes for an offset, plus 8 bytes for storage -- so using a sparse logical array possibly only takes 8+1 = 9 bytes per entry (this could be tested.)
Which is to say that if your occupancy is more than about 1/20 then sparse would be less efficient. If you had a target of (say) 16 gigabytes then you would need to be about only 1/1000 occupied.

R2020b

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