A mixed precision LOBPCG algorithm

The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A . In this work, we propose a mixed precision variant of LOBPCG that uses a...

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Vydáno v:	Numerical algorithms Ročník 94; číslo 4; s. 1653 - 1671
Hlavní autoři:	Kressner, Daniel, Ma, Yuxin, Shao, Meiyue
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.12.2023 Springer Nature B.V
Témata:	Algebra Algorithms Approximation Cholesky factorization Computer Science Convergence Eigenvalues Eigenvectors Error analysis Impact analysis Mathematical analysis Matrices (mathematics) Numeric Computing Numerical Analysis Numerical prediction Original Paper Theory of Computation Symmetric eigenvalue problem 65F50 65F15 LOBPCG algorithm 65F08 Mixed precision algorithm
ISSN:	1017-1398, 1572-9265
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Abstract	The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A . In this work, we propose a mixed precision variant of LOBPCG that uses a (sparse) Cholesky factorization of A computed in lower precision as the preconditioner. To further enhance performance, a mixed precision orthogonalization strategy is proposed. To analyze the impact of reducing precision in the preconditioner on performance, we carry out a rounding error and convergence analysis of PINVIT, a simplified variant of LOBPCG. Our theoretical results predict and our numerical experiments confirm that the impact on convergence remains marginal. In practice, our mixed precision LOBPCG algorithm typically reduces the computation time by a factor of 1.4 – 2.0 on both CPUs and GPUs.
AbstractList	The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A. In this work, we propose a mixed precision variant of LOBPCG that uses a (sparse) Cholesky factorization of A computed in lower precision as the preconditioner. To further enhance performance, a mixed precision orthogonalization strategy is proposed. To analyze the impact of reducing precision in the preconditioner on performance, we carry out a rounding error and convergence analysis of PINVIT, a simplified variant of LOBPCG. Our theoretical results predict and our numerical experiments confirm that the impact on convergence remains marginal. In practice, our mixed precision LOBPCG algorithm typically reduces the computation time by a factor of 1.4–2.0 on both CPUs and GPUs. The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A . In this work, we propose a mixed precision variant of LOBPCG that uses a (sparse) Cholesky factorization of A computed in lower precision as the preconditioner. To further enhance performance, a mixed precision orthogonalization strategy is proposed. To analyze the impact of reducing precision in the preconditioner on performance, we carry out a rounding error and convergence analysis of PINVIT, a simplified variant of LOBPCG. Our theoretical results predict and our numerical experiments confirm that the impact on convergence remains marginal. In practice, our mixed precision LOBPCG algorithm typically reduces the computation time by a factor of 1.4 – 2.0 on both CPUs and GPUs.
Author	Ma, Yuxin Shao, Meiyue Kressner, Daniel
Author_xml	– sequence: 1 givenname: Daniel surname: Kressner fullname: Kressner, Daniel organization: Institute of Mathematics, EPFL – sequence: 2 givenname: Yuxin surname: Ma fullname: Ma, Yuxin email: yxma18@fudan.edu.cn organization: School of Mathematical Sciences, Fudan University – sequence: 3 givenname: Meiyue surname: Shao fullname: Shao, Meiyue organization: School of Data Science, Fudan University, MOE Key Laboratory for Computational Physical Sciences, Fudan University
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Cites_doi	10.1016/j.jocs.2010.07.002 10.1137/17M1129830 10.1007/s11075-022-01327-6 10.1145/1391989.1391995 10.1017/S0962492922000022 10.1007/s13160-019-00348-4 10.1177/10943420211003313 10.1090/S0025-5718-01-01357-6 10.1137/S1064827500366124 10.1137/17M1140819 10.1137/1.9781611970739 10.1007/s10208-015-9297-1 10.1016/j.cam.2019.112512 10.1016/j.jcp.2006.02.007 10.1137/14M0973773 10.1007/s10444-009-9141-8 10.1137/1.9780898718027 10.1007/s13160-018-0310-3 10.1145/356012.356016 10.56021/9781421407944 10.1145/2832080.2832082 10.1145/3578178.3578240 10.14569/IJACSA.2016.070160
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References	Chen, Davis, Hager, Rajamanickam (CR23) 2008; 35 Abdelfattah, Anzt, Boman, Carson, Cojean, Dongarra, Fox, Gates, Higham, Li, Loe, Luszczek, Pranesh, Rajamanickam, Ribizel, Smith, Swirydowicz, Thomas, Tomov, Tsai, Yang (CR7) 2021; 35 Carson, Higham (CR9) 2018; 40 Ogita, Aishima (CR10) 2018; 35 Ogita, Aishima (CR11) 2019; 36 Bujanović, Kressner, Schröder (CR13) 2023; 92 Argentati, Knyazev, Neymeyr, Ovtchinnikov, Zhou (CR5) 2017; 17 Higham, Mary (CR8) 2022; 31 CR14 Higham (CR22) 2002 Rohwedder, Schneider, Zeiser (CR21) 2011; 34 Golub, Van Loan (CR16) 2013 Knyazev (CR6) 2001; 23 Saad (CR3) 2011 CR2 Neymeyr (CR4) 2002; 71 Balcan, Gonçalves, Hu, Ramasco, Colizza, Vespignani (CR1) 2010; 1 Hetmaniuk, Lehoucq (CR18) 2006; 218 CR25 CR24 Yamazaki, Tomov, Dongarra (CR19) 2015; 37 CR20 Dongarra (CR15) 1982; 8 Duersch, Shao, Yang, Gu (CR17) 2018; 40 Ogita, Aishima (CR12) 2020; 369 T Ogita (1550_CR10) 2018; 35 M Argentati (1550_CR5) 2017; 17 E Carson (1550_CR9) 2018; 40 1550_CR20 I Yamazaki (1550_CR19) 2015; 37 D Balcan (1550_CR1) 2010; 1 JJ Dongarra (1550_CR15) 1982; 8 Y Chen (1550_CR23) 2008; 35 K Neymeyr (1550_CR4) 2002; 71 T Ogita (1550_CR11) 2019; 36 T Ogita (1550_CR12) 2020; 369 AV Knyazev (1550_CR6) 2001; 23 1550_CR24 1550_CR25 GH Golub (1550_CR16) 2013 A Abdelfattah (1550_CR7) 2021; 35 NJ Higham (1550_CR8) 2022; 31 JA Duersch (1550_CR17) 2018; 40 NJ Higham (1550_CR22) 2002 1550_CR2 Y Saad (1550_CR3) 2011 Z Bujanović (1550_CR13) 2023; 92 U Hetmaniuk (1550_CR18) 2006; 218 1550_CR14 T Rohwedder (1550_CR21) 2011; 34
References_xml	– volume: 1 start-page: 132 issue: 3 year: 2010 end-page: 145 ident: CR1 article-title: Modeling the spatial spread of infectious diseases: the GLobal Epidemic and Mobility computational model publication-title: J. Comput. Sci. doi: 10.1016/j.jocs.2010.07.002 – volume: 40 start-page: 655 issue: 5 year: 2018 end-page: 676 ident: CR17 article-title: A robust and efficient implementation of LOBPCG publication-title: SIAM J. Sci. Comput. doi: 10.1137/17M1129830 – ident: CR14 – ident: CR2 – volume: 92 start-page: 247 issue: 1 year: 2023 end-page: 267 ident: CR13 article-title: Iterative refinement of Schur decompositions publication-title: Numer. Algorithms doi: 10.1007/s11075-022-01327-6 – volume: 35 start-page: 22 issue: 3 year: 2008 end-page: 12214 ident: CR23 article-title: Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate publication-title: ACM Trans. Math. Software doi: 10.1145/1391989.1391995 – volume: 31 start-page: 347 year: 2022 end-page: 414 ident: CR8 article-title: Mixed precision algorithms in numerical linear algebra publication-title: Acta Numer. doi: 10.1017/S0962492922000022 – volume: 36 start-page: 435 issue: 2 year: 2019 end-page: 459 ident: CR11 article-title: Iterative refinement for symmetric eigenvalue decomposition II: clustered eigenvalues publication-title: Japan J. Indust. Appl. Math. doi: 10.1007/s13160-019-00348-4 – volume: 35 start-page: 344 issue: 4 year: 2021 end-page: 369 ident: CR7 article-title: A survey of numerical linear algebra methods utilizing mixed-precision arithmetic publication-title: Int. J. High Perform. Comput. Appl. doi: 10.1177/10943420211003313 – volume: 71 start-page: 197 issue: 237 year: 2002 end-page: 216 ident: CR4 article-title: A geometric theory for preconditioned inverse iteration applied to a subspace publication-title: Math. Comp. doi: 10.1090/S0025-5718-01-01357-6 – volume: 23 start-page: 517 issue: 2 year: 2001 end-page: 541 ident: CR6 article-title: Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827500366124 – ident: CR25 – volume: 40 start-page: 817 issue: 2 year: 2018 end-page: 847 ident: CR9 article-title: Accelerating the solution of linear systems by iterative refinement in three precisions publication-title: SIAM J. Sci. Comput. doi: 10.1137/17M1140819 – year: 2011 ident: CR3 publication-title: Numerical Methods for Large Eigenvalue Problems doi: 10.1137/1.9781611970739 – volume: 17 start-page: 713 year: 2017 end-page: 727 ident: CR5 article-title: Convergence theory for preconditioned eigenvalue solvers in a nutshell publication-title: Found. Comput. Math. doi: 10.1007/s10208-015-9297-1 – volume: 369 year: 2020 ident: CR12 article-title: Iterative refinement for singular value decomposition based on matrix multiplication publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2019.112512 – volume: 218 start-page: 324 issue: 1 year: 2006 end-page: 332 ident: CR18 article-title: Basis selection in LOBPCG publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2006.02.007 – volume: 37 start-page: 307 issue: 3 year: 2015 end-page: 330 ident: CR19 article-title: Mixed-precision Cholesky QR factorization and its case studies on multicore CPU with multiple GPUs publication-title: SIAM J. Sci. Comput. doi: 10.1137/14M0973773 – volume: 34 start-page: 43 issue: 1 year: 2011 end-page: 66 ident: CR21 article-title: Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization publication-title: Adv. Comput. Math. doi: 10.1007/s10444-009-9141-8 – year: 2002 ident: CR22 publication-title: Accuracy and Stability of Numerical Algorithms doi: 10.1137/1.9780898718027 – volume: 35 start-page: 1007 issue: 3 year: 2018 end-page: 1035 ident: CR10 article-title: Iterative refinement for symmetric eigenvalue decomposition publication-title: Japan J. Indust. Appl. Math. doi: 10.1007/s13160-018-0310-3 – ident: CR24 – volume: 8 start-page: 371 issue: 4 year: 1982 end-page: 375 ident: CR15 article-title: Algorithm 589: SICEDR: A FORTRAN subroutine for improving the accuracy of computed matrix eigenvalues publication-title: ACM Trans. Math. Software doi: 10.1145/356012.356016 – year: 2013 ident: CR16 publication-title: Matrix Computations doi: 10.56021/9781421407944 – ident: CR20 – volume: 71 start-page: 197 issue: 237 year: 2002 ident: 1550_CR4 publication-title: Math. Comp. doi: 10.1090/S0025-5718-01-01357-6 – volume: 17 start-page: 713 year: 2017 ident: 1550_CR5 publication-title: Found. Comput. Math. doi: 10.1007/s10208-015-9297-1 – volume: 35 start-page: 1007 issue: 3 year: 2018 ident: 1550_CR10 publication-title: Japan J. Indust. Appl. Math. doi: 10.1007/s13160-018-0310-3 – volume-title: Numerical Methods for Large Eigenvalue Problems year: 2011 ident: 1550_CR3 doi: 10.1137/1.9781611970739 – ident: 1550_CR20 doi: 10.1145/2832080.2832082 – ident: 1550_CR24 doi: 10.1145/3578178.3578240 – volume: 369 year: 2020 ident: 1550_CR12 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2019.112512 – volume: 35 start-page: 22 issue: 3 year: 2008 ident: 1550_CR23 publication-title: ACM Trans. Math. Software doi: 10.1145/1391989.1391995 – ident: 1550_CR14 – volume: 40 start-page: 655 issue: 5 year: 2018 ident: 1550_CR17 publication-title: SIAM J. Sci. Comput. doi: 10.1137/17M1129830 – volume: 35 start-page: 344 issue: 4 year: 2021 ident: 1550_CR7 publication-title: Int. J. High Perform. Comput. Appl. doi: 10.1177/10943420211003313 – volume: 31 start-page: 347 year: 2022 ident: 1550_CR8 publication-title: Acta Numer. doi: 10.1017/S0962492922000022 – volume-title: Accuracy and Stability of Numerical Algorithms year: 2002 ident: 1550_CR22 doi: 10.1137/1.9780898718027 – volume: 1 start-page: 132 issue: 3 year: 2010 ident: 1550_CR1 publication-title: J. Comput. Sci. doi: 10.1016/j.jocs.2010.07.002 – volume: 40 start-page: 817 issue: 2 year: 2018 ident: 1550_CR9 publication-title: SIAM J. Sci. Comput. doi: 10.1137/17M1140819 – volume: 218 start-page: 324 issue: 1 year: 2006 ident: 1550_CR18 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2006.02.007 – volume: 34 start-page: 43 issue: 1 year: 2011 ident: 1550_CR21 publication-title: Adv. Comput. Math. doi: 10.1007/s10444-009-9141-8 – ident: 1550_CR2 – volume: 92 start-page: 247 issue: 1 year: 2023 ident: 1550_CR13 publication-title: Numer. Algorithms doi: 10.1007/s11075-022-01327-6 – volume: 36 start-page: 435 issue: 2 year: 2019 ident: 1550_CR11 publication-title: Japan J. Indust. Appl. Math. doi: 10.1007/s13160-019-00348-4 – ident: 1550_CR25 doi: 10.14569/IJACSA.2016.070160 – volume: 8 start-page: 371 issue: 4 year: 1982 ident: 1550_CR15 publication-title: ACM Trans. Math. Software doi: 10.1145/356012.356016 – volume: 37 start-page: 307 issue: 3 year: 2015 ident: 1550_CR19 publication-title: SIAM J. Sci. Comput. doi: 10.1137/14M0973773 – volume: 23 start-page: 517 issue: 2 year: 2001 ident: 1550_CR6 publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827500366124 – volume-title: Matrix Computations year: 2013 ident: 1550_CR16 doi: 10.56021/9781421407944
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SubjectTerms	Algebra Algorithms Approximation Cholesky factorization Computer Science Convergence Eigenvalues Eigenvectors Error analysis Impact analysis Mathematical analysis Matrices (mathematics) Numeric Computing Numerical Analysis Numerical prediction Original Paper Theory of Computation
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