Mathieu Faverge, J. Langou, Y. Robert, J. Dongarra
{"title":"双对角化和r -双对角化:并行平铺算法、关键路径和分布式内存实现","authors":"Mathieu Faverge, J. Langou, Y. Robert, J. Dongarra","doi":"10.1109/IPDPS.2017.46","DOIUrl":null,"url":null,"abstract":"We study tiled algorithms for going from a \"full\" matrix to a condensed \"band bidiagonal\" form using orthog-onal transformations: (i) the tiled bidiagonalization algorithm BIDIAG, which is a tiled version of the standard scalar bidiago-nalization algorithm; and (ii) the R-bidiagonalization algorithm R-BIDIAG, which is a tiled version of the algorithm which consists in first performing the QR factorization of the initial matrix, then performing the band-bidiagonalization of the R- factor. For both BIDIAG and R-BIDIAG, we use four main types of reduction trees, namely FLATTS, FLATTT, GREEDY, and a newly introduced auto-adaptive tree, AUTO. We provide a study of critical path lengths for these tiled algorithms, which shows that (i) R-BIDIAG has a shorter critical path length than BIDIAG for tall and skinny matrices, and (ii) GREEDY based schemes are much better than earlier proposed algorithms with unbounded resources. We provide experiments on a single multicore node, and on a few multicore nodes of a parallel distributed shared- memory system, to show the superiority of the new algorithms on a variety of matrix sizes, matrix shapes and core counts.","PeriodicalId":209524,"journal":{"name":"2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2017-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Bidiagonalization and R-Bidiagonalization: Parallel Tiled Algorithms, Critical Paths and Distributed-Memory Implementation\",\"authors\":\"Mathieu Faverge, J. Langou, Y. Robert, J. Dongarra\",\"doi\":\"10.1109/IPDPS.2017.46\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study tiled algorithms for going from a \\\"full\\\" matrix to a condensed \\\"band bidiagonal\\\" form using orthog-onal transformations: (i) the tiled bidiagonalization algorithm BIDIAG, which is a tiled version of the standard scalar bidiago-nalization algorithm; and (ii) the R-bidiagonalization algorithm R-BIDIAG, which is a tiled version of the algorithm which consists in first performing the QR factorization of the initial matrix, then performing the band-bidiagonalization of the R- factor. For both BIDIAG and R-BIDIAG, we use four main types of reduction trees, namely FLATTS, FLATTT, GREEDY, and a newly introduced auto-adaptive tree, AUTO. We provide a study of critical path lengths for these tiled algorithms, which shows that (i) R-BIDIAG has a shorter critical path length than BIDIAG for tall and skinny matrices, and (ii) GREEDY based schemes are much better than earlier proposed algorithms with unbounded resources. We provide experiments on a single multicore node, and on a few multicore nodes of a parallel distributed shared- memory system, to show the superiority of the new algorithms on a variety of matrix sizes, matrix shapes and core counts.\",\"PeriodicalId\":209524,\"journal\":{\"name\":\"2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-05-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IPDPS.2017.46\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IPDPS.2017.46","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Bidiagonalization and R-Bidiagonalization: Parallel Tiled Algorithms, Critical Paths and Distributed-Memory Implementation
We study tiled algorithms for going from a "full" matrix to a condensed "band bidiagonal" form using orthog-onal transformations: (i) the tiled bidiagonalization algorithm BIDIAG, which is a tiled version of the standard scalar bidiago-nalization algorithm; and (ii) the R-bidiagonalization algorithm R-BIDIAG, which is a tiled version of the algorithm which consists in first performing the QR factorization of the initial matrix, then performing the band-bidiagonalization of the R- factor. For both BIDIAG and R-BIDIAG, we use four main types of reduction trees, namely FLATTS, FLATTT, GREEDY, and a newly introduced auto-adaptive tree, AUTO. We provide a study of critical path lengths for these tiled algorithms, which shows that (i) R-BIDIAG has a shorter critical path length than BIDIAG for tall and skinny matrices, and (ii) GREEDY based schemes are much better than earlier proposed algorithms with unbounded resources. We provide experiments on a single multicore node, and on a few multicore nodes of a parallel distributed shared- memory system, to show the superiority of the new algorithms on a variety of matrix sizes, matrix shapes and core counts.