Fine-grain task-parallel algorithms for matrix factorizations and inversion on many-threaded CPUs
[EN] We extend a two-level task partitioning previously applied to the inversion of dense matrices via Gauss-Jordan elimination to the more challenging QR factorization as well as the initial orthogonal reduction to band form found in the singular value decomposition. Our new task-parallel algorithm...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/212389 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/212389 |
| Access Level: | acceso abierto |
| Palabra clave: | CPUs High performance Matrix factorizations Matrix inversion OpenMP Task parallelism ARQUITECTURA Y TECNOLOGIA DE COMPUTADORES |
| Sumario: | [EN] We extend a two-level task partitioning previously applied to the inversion of dense matrices via Gauss-Jordan elimination to the more challenging QR factorization as well as the initial orthogonal reduction to band form found in the singular value decomposition. Our new task-parallel algorithms leverage the tasking mechanism currently available in OpenMP to exploit "nested" task parallelism, with a first outer level that operates on matrix panels and a second inner level that processes the matrix either by mu$$ \mu $$-panels or by tiles, in order to expose a large number of independent tasks. We present a detailed performance analysis, including execution traces, which shows that the two-level refinement into fine grain tasks allows for an improved load balancing and delivers high performance on current general-purpose many-core processors (CPUs) from Intel and AMD. |
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