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Graph algorithms can be expressed in terms of linear algebra. GraphBLAS is a library of low-level building blocks for such algorithms that targets algorithm developers. LAGraph builds on top of the GraphBLAS to target users of graph algorithms with high-level algorithms common in network analysis. In this paper, we describe the first release of the LAGraph library, the design decisions behind the library, and performance using the GAP benchmark suite. LAGraph, however, is much more than a library. It is also a project to document and analyze the full range of algorithms enabled by the GraphBLAS. To that end, we have developed a compact and intuitive notation for describing these algorithms. In this paper, we present that notation with examples from the GAP benchmark suite.
The level of abstraction at which application experts reason about linear algebra computations and the level of abstraction used by developers of high-performance numerical linear algebra libraries do not match. The former is conveniently captured by
We present high performance implementations of the QR and the singular value decomposition of a batch of small matrices hosted on the GPU with applications in the compression of hierarchical matrices. The one-sided Jacobi algorithm is used for its si
SciPy is an open source scientific computing library for the Python programming language. SciPy 1.0 was released in late 2017, about 16 years after the original version 0.1 release. SciPy has become a de facto standard for leveraging scientific algor
BLASFEO is a dense linear algebra library providing high-performance implementations of BLAS- and LAPACK-like routines for use in embedded optimization. A key difference with respect to existing high-performance implementations of BLAS is that the co
Numerical software in computational science and engineering often relies on highly-optimized building blocks from libraries such as BLAS and LAPACK, and while such libraries provide portable performance for a wide range of computing architectures, th