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approved for public release and unlimited distribution. This Talk Background: How and why to use matrix algebra for graphs? What are the important data structures and concepts? Prior work in the GraphBLAS approved for public release and unlimited distribution. This Talk Background: How and why to use matrix algebra for graphs? What are the important data structures and concepts? Prior work in the GraphBLAS approved for public release and unlimited distribution. This Talk Background: How and why to use matrix algebra for graphs? What are the important data structures and concepts? Prior work in the GraphBLAS

Algebra Coming to Standard C++ Mark Hoemmen, NVIDIA | CppCon 20233 Agenda • Motivating example: Matrix multiply • Where std::linalg fits in linear algebra’s layers • std::linalg builds on the C++ Standard std::linalg builds on the long history of the BLAS • Detailed example: Cholesky matrix factorization4 Motivating example: Updating matrix multiply 𝐶 := 𝛽𝐶 + 𝛼𝐴𝐵𝑇 𝛼 and 𝛽 are scalars; 𝐴, 𝐵, and 𝐶 data_handle(), &LDA, &beta, C.data_handle(), &LDC); // AFTER: Use std::linalg #include matrix_product(par_unseq, scaled(alpha, A), transposed(B), scaled(beta, C), C);5 Does a “linear algebra

. . . . . . . . . . . . . . . . 435 34.18 Consider StaticArrays.jl for small fixed-size vector/matrix operations . . . . . . . . . 436 34.19 Avoid string interpolation for I/O . . . . . . . . . . . Special matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1230 77.2 Matrix factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1232 77.3 Orthogonal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1234 77.5 Low-level matrix operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1329 77.6 BLAS functions

. . . . . . . . . . . . . . . . 435 34.18 Consider StaticArrays.jl for small fixed-size vector/matrix operations . . . . . . . . . 436 34.19 Avoid string interpolation for I/O . . . . . . . . . . . Special matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1230 77.2 Matrix factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1232 77.3 Orthogonal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1234 77.5 Low-level matrix operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1329 77.6 BLAS functions

. . . . . . . . . . . . . . . . 465 35.20 Consider StaticArrays.jl for small fixed-size vector/matrix operations . . . . . . . . . 466 35.21 Avoid string interpolation for I/O . . . . . . . . . . . Special matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1436 79.2 Matrix factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1438 79.3 Orthogonal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1442 79.6 Low-level matrix operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1553 79.7 BLAS functions

. . . . . . . . . . . . . . . . 465 35.20 Consider StaticArrays.jl for small fixed-size vector/matrix operations . . . . . . . . . 466 35.21 Avoid string interpolation for I/O . . . . . . . . . . . Special matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1436 79.2 Matrix factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1438 79.3 Orthogonal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1442 79.6 Low-level matrix operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1553 79.7 BLAS functions

. . . . . . . . . . . . . . . . 465 35.20 Consider StaticArrays.jl for small fixed-size vector/matrix operations . . . . . . . . . 466 35.21 Avoid string interpolation for I/O . . . . . . . . . . . Special matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1436 79.2 Matrix factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1438 79.3 Orthogonal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1442 79.6 Low-level matrix operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1553 79.7 BLAS functions

. . . . . . . . . . . . . . . . . 388 34.17Consider StaticArrays.jl for small fixed-size vector/matrix operations . . . . . . . . . . . . . . . 389 34.18Avoid string interpolation for I/O . . . . . Elementary operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1031 Matrix factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1032 scaling operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1032 75.2 Matrix factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034

. . . . . . . . . . . . . . . . . 388 34.17Consider StaticArrays.jl for small fixed-size vector/matrix operations . . . . . . . . . . . . . . . 389 34.18Avoid string interpolation for I/O . . . . . Elementary operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1019 Matrix factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1020 scaling operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1020 73.2 Matrix factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1022