Memory cost of multiplying sparse matrices
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What is the memory cost for multiplying sparse matrices? It seems to be much larger than the memory used by either of the matrices being multiplied:
>> A = sprand(5e9,2, 1e-7); B = sparse(eye(2));
whos
Name Size Bytes Class Attributes
A 5000000000x2 16024 double sparse
B 2x2 56 double sparse
>> A*B;
Error using *
Out of memory. Type HELP MEMORY for your options.
As you can see in the example above, the sparse matrices A and B are not taking up much memory, but computing A*B still results in an out of memory error. Why does this happen, and is there a way to avoid it?
8 个评论
Bruno Luong
2020-9-18
编辑:Bruno Luong
2020-9-18
Agress that task manager could miss it. I don't see any spike on my 32 Gb PC while
AB = A*B
is being carried out sous MATLAB
采纳的回答
Matt J
2020-9-15
编辑:Matt J
2020-9-15
I believe it is simply because Matlab sparse matrix routines don't handle very tall & thin matrix dimensions very well. It becomes much faster and less memory-consuming if you reshape A to have a few orders of magnitude fewer rows, and do the following equivalent computation:
A = sprand(5e9,2, 1e-7); B = speye(2);
%%Begin workaround
Ar=reshape(A,[],1000);
Br=kron(B, speye(500));
result= reshape(Ar*Br,size(A));
9 个评论
Matt J
2020-9-16
Never mind. I assume your sparse 3D tensors never actually exist in 3D form anyway, right? Internally, you would have to carry them around as reshaped 2D sparse arrays, because that is the only sparse form that Matlab supports.
更多回答(2 个)
Bruno Luong
2020-9-15
编辑:Bruno Luong
2020-9-15
I guess MATLAB creates a temporary buffer of length equals to the number of rows of A when A*B is invoked. The exact detail only TMW employees who can acces to the source code can answer.
Here is what I suggest to multiply A*B for very long tall A
[iA, jA, a] = find(A);
m = size(A,1);
n = size(B,2);
p = numel(jA)*n; % Guess of size of I, J, S
% Preallocate
I = zeros(p,1,'uint32');
J = zeros(p,1,'uint32');
S = zeros(p,1);
p = 0;
for k=1:n
[jB, ~, b] = find(B(:,k));
[i, l] = ismember(jA,jB);
q = nnz(i);
idx = p+(1:q);
I(idx) = iA(i);
J(idx) = k;
S(idx) = a(i).*b(l(i));
p = p+q;
end
idx = 1:p;
AB = sparse(I(idx), J(idx), S(idx), m, n);
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Bruno Luong
2020-9-15
编辑:Bruno Luong
2020-9-15
A variant
[iA, jA, a] = find(A);
m = size(A,1);
n = size(B,2);
p = numel(jA)*n; % Guess of size of I, J, S
% Preallocate
I = zeros(p,1,'uint32');
J = zeros(p,1,'uint32');
S = zeros(p,1);
p = 0;
for k=1:n
Bk = B(:,k);
jB = find(Bk);
i = ismembc(jA,jB); % undocumented stock function, too bad it's doesn't return second argument of ISMEMBER
q = nnz(i);
idx = p+(1:q);
I(idx) = iA(i);
J(idx) = k;
S(idx) = a(i).*Bk(jA(i));
p = p+q;
end
idx = 1:p;
AB = sparse(I(idx), J(idx), S(idx), m, n);
It doesn't seem to be faster than the first method when I test with tic/toc, but the tests I conducted are far from cover all the cases.
Matt J
2020-9-16
编辑:Matt J
2020-9-16
Here's another customized multiplication routine for tall A. I do not know how it compares to Bruno's in terms of speed, but it is loop-free.
A = sprand(5e9,2, 1e-7); B = speye(2);
tic
m=size(A,1);
n=size(B,2);
Ia=find(any(A,2));
Jb=find(any(B,1));
C=A(Ia,:)*B(:,Jb);
[Ic,Jc,S]=find(C);
AB=sparse( Ia(Ic) , Jb(Jc) , S , m,n); %equal to A*B
toc%Elapsed time is 0.001254 seconds.
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