Sparse Matrix Julia Multiplication

24 Jul, 2021

Sparse matrix multiplication in julia. In the case of OpenBLAS this is already multithreaded.

How To Multiply Matrices Geeksforgeeks

The naıve matrix multiplication algorithm on the other hand can be used to.

Sparse matrix julia multiplication. 00 00 10 20. The following sparse matrix multiplication takes about 8124084 seconds 299 M allocations. 7 4 1 8 5 2 9 6 3 0.

23445 KiB julia N 30000. Julia asprand1000 1000 01 1000x1000 sparse matrix with 99749 Float64 entries. Julia btime A x.

1 1 0 2 2 1 julia B 1 Inf. Index Termssparse matrix multiplication sparse formats spatial hardware I. A sprandN N 1000N.

1 10 3 10. Julia x 4-element VectorFloat64-11 00 40-72 Vectorequality. Julia y copyx.

More concretely SpGEMM is a building block. Julia d 7 8 9 0. 23445 KiB julia N 30000.

00 NaN 10 20 julia ArrayA B 22 ArrayFloat642. 5 1 0725824 17 1 0420022 19 1 0404282 21 1 00307138 52 1 0453376 55 1 030054 69 1 0360203 74 1 0346881 94 1 0312849 932 1000 0978966 933 1000 0149551 954 1000 0417852 959 1000 0722707 964 1000 0519931 967 1000. The result should consist of three sparse matrices one obtained by adding the two input matrices one by multiplying the two matrices and one obtained by transpose of the first matrix.

23445 KiB julia btime B x. Columns ofAare accumu- lated as speciﬁed by the nonzero entriesin a column ofBusing a sparse accumulator or SPA. Julia ssparse ones 10001000 1000x1000 sparse matrix with 1000000 nonzeros.

A Julia library for parallel sparse matrix multiplication using shared memory star_rate. Another way to create a sparse array is to convert a dense array into a sparse array using the sparse function. Julia Tridiagonaldl d du 44 Tridiagonal Int64 Vector Int64.

A sprandN N 100N. It uses the CSC format and the datatype Tv for the non-zeros and all indices Ti can optionally be specified SparseMatrixCSC TvTi. Matrix multiplication algorithms mentioned above cannot utilize the sparsity of the matricesmultipliedThecomplexityofthealgorithmofCoppersmithandWinograd 1990 for example remains On238evenifthe multiplied matrices are extremely sparse.

For arrays with size 2000x2000 the simple matrixmultiplication. The contents of the SPA are stored intoa column ofConce all required columns are accumulated. To install just open a Julia prompt and call.

As a comparison the equivalent code takes 0119242 seco. No method SparseMatrixCSC Float64Int64SparseMatrixCSC Float64Int64 in method_missing at basejl60. Note that other entries of matrices will be zero as matrices are sparse.

Julia y 4-element VectorFloat64-11 00 36-72 julia y1 20. Here I am using julia 050. Julia supports sparse matrices in the SparseMatrixCSC type.

Julia dl 1 2 3. Julia x3 40. This library implements SharedSparseMatrixCSC and SharedBilinearOperator types to make it easy to multiply by sparse matrices in parallel on shared memory systems.

Julia sparseMatrix10I 5 5 55 SparseMatrixCSCFloat64 Int64 with 5 stored entries. Julia N 30000. Make available to Julia the sparse functionality in MKL star_rate.

Julia btime A x. Semicolons separate rows I sizeA returns the size of A as a pair ie A_rows A_cols sizeA or A_rows is sizeA1 A_cols is sizeA2 I row vectors are 1 nmatrices eg 4 87 -9 2. 1 1 10 2 1 10 3 1 10 4 1 10.

INTRODUCTION Sparse-sparse matrix-matrix multiplication SpGEMM is a key computational primitive in many important application do-mains such as graph analytics machine learning and scientiﬁc computation. 00 NaN 10 NaN julia dropzerosA B 22 ArrayFloat642. 10 Inf 10 20 julia A B 22 ArrayFloat642.

1 2 22 ArrayFloat642. Julia du 4 5 6. 10 10 10 10 10 julia sparse10 00 10 3-element SparseVectorFloat64 Int64 with 2 stored entries.

Julia using SparseArrays julia using LinearAlgebra julia A spdiagm0 0 1 22 SparseMatrixCSCInt64Int64 with 2 stored entries. Julia x -11 00 36 -72. Time c sa sb.

Includepathtosparse_diffjl S sparse_diff100010001. Tridiagonal A Construct a tridiagonal matrix from the first sub-diagonal diagonal and first super-diagonal of the matrix A. 77542 ms 2 allocations.

A Julia library for parallel sparse matrix multiplication using shared memory. Time A SS. Fortwovectorsarraysa andbtheJuliaexpressionab evaluatestotrue if.

Results in 03 seconds multithreaded and 07 seconds singlethreaded. A sprandN N 250N. I omitted the rest of the output.

312158 MB 159 gc time. Multiplication of sparse matrices stored bycolumns. 23445 KiB julia btime B x.

Sparse Matrices in Julia. 7787 ms 2 allocations. I matrices in Julia are repersented by 2D arrays I 2 -4 82.

A Julia library for parallel sparse matrix multiplication using shared memory star_rate. Instantly share code notes and snippets. -55 35 63 creates the 2 3 matrix A 2 4 82 55 35 63 I spaces separate entries in a row.

65791 ms 2 allocations. Splitting of a single dimension in multiplication the times get even worse and reach around 17 seconds in singlethreaded mode. 8688 ms 2 allocations.

Juliaintro