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About Efficiency Sparse Dense Multiplication #550

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@khoinpd0411

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@khoinpd0411

Hi, thank you so much for a great project. May I ask a small question related to sparse and dense matrix operation? The case is that I want to conduct a multiplication between sparse and dense matrix. In detail, the sparsity of the 2 project is given as below:

X shape: (200000, 50000) C shape: (50000, 100)#nnz X: 99500704#nnz C: 3160328Sparsity of X:  0.0099500704Sparsity of C:  0.6320656

Where X is a sparse matrix and C is a dense one. In theory, C should be stored in dense format in order to make the operation to be efficient instead of sparse one. However, using bitmap/dense matrix provided by GraphBLAS is not as efficient as compared to MKL code for sparse * dense operation

##################### python-graphblas (Default Setting - 32 Threads - CSR Format * BitmapC Format) #####################Convert Scipy Sparse Format -> python-graphblas Format (s) 0.6137485504150391Sparse * Sparse computing time (s) 2.929335117340088Sparse * Sparse computing time (s) 2.9536073207855225Sparse * Sparse computing time (s) 2.9327011108398438Sparse * Sparse computing time (s) 2.946722984313965Sparse * Sparse computing time (s) 2.942711114883423Sparse * Sparse computing time (s) 2.959540843963623Sparse * Sparse computing time (s) 2.9557604789733887Sparse * Sparse computing time (s) 2.946617364883423Sparse * Sparse computing time (s) 2.9554543495178223Sparse * Sparse computing time (s) 2.9580225944519043Sparse * Sparse computing time (s) 2.9371848106384277Sparse * Sparse computing time (s) 2.9504570960998535Sparse * Sparse computing time (s) 2.956547498703003Sparse * Sparse computing time (s) 2.9532806873321533Sparse * Sparse computing time (s) 2.947199821472168Sparse * Sparse computing time (s) 2.952831745147705Sparse * Sparse computing time (s) 2.950216293334961Sparse * Sparse computing time (s) 2.950721025466919Sparse * Sparse computing time (s) 2.958610773086548Sparse * Sparse computing time (s) 2.952730894088745Mean Runtime:  2.9495126962661744Std Runtime:  0.008198427827772714##################### python-graphblas (Default Setting - 32 Threads - CSR Format * FullC Format) #####################Convert Scipy Sparse Format -> python-graphblas Format (s) 0.5988132953643799Sparse * Sparse computing time (s) 1.73736572265625Sparse * Sparse computing time (s) 1.744694709777832Sparse * Sparse computing time (s) 1.7468664646148682Sparse * Sparse computing time (s) 1.7360756397247314Sparse * Sparse computing time (s) 1.7450006008148193Sparse * Sparse computing time (s) 1.7598528861999512Sparse * Sparse computing time (s) 1.7438948154449463Sparse * Sparse computing time (s) 1.7407243251800537Sparse * Sparse computing time (s) 1.7503554821014404Sparse * Sparse computing time (s) 1.740696907043457Sparse * Sparse computing time (s) 1.757706642150879Sparse * Sparse computing time (s) 1.7401001453399658Sparse * Sparse computing time (s) 1.7460541725158691Sparse * Sparse computing time (s) 1.7468533515930176Sparse * Sparse computing time (s) 1.751969337463379Sparse * Sparse computing time (s) 1.7436254024505615Sparse * Sparse computing time (s) 1.7455754280090332Sparse * Sparse computing time (s) 1.7475886344909668Sparse * Sparse computing time (s) 1.7609961032867432Sparse * Sparse computing time (s) 1.7456836700439453Mean Runtime:  1.7465840220451354Std Runtime:  0.006642586857441714
##################### MKL (Default Settings - 16 Threads - Sparse CSR Format * Dense Numpy Format) #####################Sparse * Sparse computing time (s) 0.6445832252502441Sparse * Sparse computing time (s) 0.6223111152648926Sparse * Sparse computing time (s) 0.6190366744995117Sparse * Sparse computing time (s) 0.6191632747650146Sparse * Sparse computing time (s) 0.617084264755249Sparse * Sparse computing time (s) 0.6194536685943604Sparse * Sparse computing time (s) 0.6174299716949463Sparse * Sparse computing time (s) 0.6181790828704834Sparse * Sparse computing time (s) 0.6196620464324951Sparse * Sparse computing time (s) 0.6216928958892822Sparse * Sparse computing time (s) 0.6174044609069824Sparse * Sparse computing time (s) 0.6212775707244873Sparse * Sparse computing time (s) 0.6180646419525146Sparse * Sparse computing time (s) 0.6177294254302979Sparse * Sparse computing time (s) 0.6187028884887695Sparse * Sparse computing time (s) 0.6197123527526855Sparse * Sparse computing time (s) 0.6219933032989502Sparse * Sparse computing time (s) 0.6392252445220947Sparse * Sparse computing time (s) 0.6407394409179688Sparse * Sparse computing time (s) 0.6248526573181152Mean Runtime:  0.6229149103164673Std Runtime:  0.008091237575214866

Could you please kindly suggest any format from GraphBLAS to solve this problem? Thank you so much in advance!

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