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CSR (Compressed Sparse Row) sparse format (current implementation of Math.NET) is efficient and can be parallelized for Ax but inefficient for A^Tx.
CSC (Compressed Sparse Column) sparse format is efficient and can be parallelized for A^Tx but inefficient for Ax.
CSB (Compressed Sparse Blocks) is a more recent format which is efficient and parallelizable for both, so it supersedes both CSR and CSC while consuming the same space.
I believe it would be a good idea to implement CSB instead of CSR.
CSB is presented extensively, including code snippets on "Parallel Sparse Matrix-Vector and Matrix-Transpose-Vector Multiplication Using Compressed Sparse Blocks".
It can be found (among other places), here: http://people.csail.mit.edu/jfineman/
This discussion was converted from issue #151 on July 24, 2021 08:07.
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From: https://mathnetnumerics.codeplex.com/workitem/5674
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