Block Sparse Matrix

[00shiv]

I would like to deal with very large sparse matrices with dense sub-blocks; for example, block arrow-head matrices, or a block periodic tridiagonal matrices.

I know about the BlockArrays package. That supports blocking of sparse matrices. I found a package called “BlockSparseArrays” but it seems to be abandoned.

It is not convenient for me to first create a sparse matrix and then block it using BlockArrays. The converse of starting with an uninitialized BlockArray is also not scalable for me as I have a large number of partitions, and I am assuming BlockArray will allocate O(N^2) pointers at least.

Before I start writing my own BlockSparseMatrix code I was wondering if someone had a way to use SparseArrays and BlockArrays to achieve what I want?

Thanks.
–shiv–

[Palli]

It took me a while to find this, I recalled the first package that I put at the top of the list (maybe none applies to you, but posting just in case, what I found while searching):

[ANN] Fast SpMv with CompressedSparseBlocks.jl

If you have a computation with an iteration where the time is dominated by a large sparse matrix multiplication, julia> using LinearAlgebra, SparseArrays, BenchmarkTools julia> n = 2^22; d = 10; A = sprand(n,n,d/n); x = rand(n); julia> y = @btime $A*$x; 909.738 ms (2 allocations: 32.00 MiB) julia> yt = @btime $(transpose(A))*$x; 640.637 ms (2 allocations: 32.00 MiB) you may want to consider the CompressedSparseBlocks package, a Julia wrapper to the CSB Library. julia> using Compressed…

[ANN] Announcing ThreadedSparseCSR.jl

ThreadedSparseCSR.jl provides a multithreaded version of CSR matrix - vector multiplication in Julia. The CSR matrix format is implemented in the Julia package SparseMatricesCSR.jl, which must be installed for this package to work. The package exports the functions: tmul!(y, A, x, [alpha], [beta]), 5 argument (y = alpha*A*x +beta*y ) and 3 argument (y = A*x) in-place multithreaded versions of mul!, using Base.Threads threading (using @spawn) tmul(A, x), multithreaded version of A*x, using Ba…

[ANN] Announcing ThreadedSparseCSR.jl

ThreadedSparseCSR.jl provides a multithreaded version of CSR matrix - vector multiplication in Julia. The CSR matrix format is implemented in the Julia package SparseMatricesCSR.jl, which must be installed for this package to work. The package exports the functions: tmul!(y, A, x, [alpha], [beta]), 5 argument (y = alpha*A*x +beta*y ) and 3 argument (y = A*x) in-place multithreaded versions of mul!, using Base.Threads threading (using @spawn) tmul(A, x), multithreaded version of A*x, using Ba…

Best way to use CuSparseMatrixBSR

I’ve been writing a set of kernels in which I calculate many small (mostly on the order of ~10x10) square matrices column by column, like in this toy example using CUDA # each slice L[:, :, j] is a matrix of interest Ls = CUDA.rand(3, 3, 100) f(x) = 3 * x - 2 function matrix_kernel(f, Ls) ind = (blockIdx().x - 1) * blockDim().x + threadIdx().x stride = gridDim().x * blockDim().x sz = size(Ls) len = sz[2] * sz[3] for i in ind : stride : len m, n = Tuple(CartesianInd…

[pitsianis]

If a) your block sparse matrix does not change and b) your dense sublocks are not full, and c) you iterate with your matrices (not just a single multiplication), consider the CompressedSparseBlocks package.

If the sub-blocks have to be dense, it is a trivial exercise to define a CSC matrix datatype where the elements are dense matrices. Give it a try and we can help you out.