DOCSLIB.ORG

WP 8 Project Presentations - 28 September 2020

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
WP 8 Project Presentations - 28 September 2020 Linear Algebra, Krylov-subspace methods, and multigrid solvers for the discovery of New Physics (LyNcs): WP 8 Project Presentations - 28 September 2020 Jacob Finkenrath CaSToRC, The Cyprus Institute 1 PRACE 6IP – WP8 – LyNcs – CaSToRC www.prace-ri.eu PRACE 6IP WP8 LyNcs: People ▶ Constantia Alexandrou, CaSToRC – PI ▶ Emmanuel Agullo, Inria ▶ Simone Bacchio, CaSToRC ▶ Olivier Coulaud, Inria ▶ Jacob Finkenrath, CaSToRC ▶ Luc Giraud, Inria ▶ Kyriakos Hadjiyiannakou, CaSToRC ▶ Giannis Koutsou, CaSToRC ▶ Stéphane Lanteri, Inria ▶ Gilles Marait, Inria ▶ Michele Martone, LRZ ▶ Shuhei Yamamoto, CaSToRC 2 PRACE 6IP – WP8 – LyNcs – CaSToRC www.prace-ri.eu Project Objectives LyNcs: Linear Algebra, Krylov-subspace methods, and multigrid solvers for the discovery of New Physics Address the Exascale challenge for sparse linear systems & iterative solvers ▶ Targeting all level of software stack ● on lowest level: sparse Matrix vector kernels: librsb ● on intermediate level: iterative linear solver libraries: fabulous, DDalphaAMG, QUDA ● on highest level : community codes: LyNcs API, tmLQCD, openQCD Applications in: ▶ Fundamental Physics - lattice QCD ▶ Electrodynamics ▶ Computational Chemistry 3 PRACE 6IP – WP8 – LyNcs – CaSToRC www.prace-ri.eu Talk Outline ▶ Motivation ▶ LyNcs within 6IP Prace WP8 ● Project structure ● Tasks and Deliverables ▶ Overview on software developments ● Lyncs API - New community-driven software ● Fabulous - Iterative Block Krylov Solvers library ● librsb - a Sparse BLAS format library ● DDalphaAMG - Multigrid library for lattice QCD ▶ Outlook 4 PRACE 6IP – WP8 – LyNcs – CaSToRC www.prace-ri.eu LyNcs vision: Towards Exascale Computing ▶ Objective 1: Performance and Efficiency ● focusing on efficient node level performance by using state of the art implementations and algorithms like Block Krylov solvers and multigrid approaches ▶ Objective 2: Scaling ● extend scalability and speeding up the time to solution beyond DD+strong scaling with alternative parallelization strategies ▶ Objective 3: Diversity ● Hardware and software: Software stack of community software is rich and optimized for various hardware systems, optimizations and algorithm developments are on going in various tasks like given by DOEs Exascale initiative Focus of LyNcs is to be complementary/in a synergy to those efforts ▶ on user-friendly API to enable the rich software stack of solver and application codes ▶ on specific software optimization and developments used in the European Community 5 PRACE 6IP – WP8 – LyNcs – CaSToRC www.prace-ri.eu Tasks & Targets: Project identifies 4 tasks: Task 1: Sparse linear solvers suitable for Exascale Task 2: Prototyping new methods for Exascale Task 3: Portable APIs Task 4: Community code enabling We target software implementation, matching the objectives of the tasks: Target 1: LyNcs API (Task 3,4,2) - New community-driven software - portable, flexible, modular and user-friendly Target 2: Fabulous (Task 1,2) - Iterative Block Krylov Solvers library - study and implementation of new algorithms Target 3: librsb (Task 1) - Recursive Sparse Blocks format library - improved portability, benchmarking and code quality Target 4: DDalphaAMG (Task 1,2) - Multigrid library for lattice QCD - extension to block solver and linkage to Fabulous 6 PRACE 6IP – WP8 – LyNcs – CaSToRC www.prace-ri.eu Deliverables & contributions PRACE WP 8 – Deliverables Contribution by LyNcs ▶ D8.2 (MS 6) Interim progress report: ▶ Finalized set of tasks and milestones, PM distribution, and staff and established project structure team, including any new staff. ▶ D8.3 (MS 12) Interim progress report: ▶ First version of APIs from Task 3. Progress of library Public Prototype software release and optimization (Task 1) and evaluation of prototypes new development infrastructure algorithms (Task 2) ▶ D8.4 (MS 24) Interim progress report: ▶ First release of software, including documentation, Public Software release (docs, testing, benchmark results and issue tracking statistics (Tasks 1, issue tracker) and integration in external and 3). Report on evaluation of new methods of Task 2, and codes candidates selected for implementation within Task 1. Progress of integration into community codes (Task 4). ▶ D8.5 (MS 30) Final report: including ▶ Performance results on community software linked to APIs performance results on (pre)Exascale (Tasks 1, 2, 3, and 4). Report on results presented in systems conferences. Publication of results of Task 2 (as peer-review publication or PRACE white paper) 7 PRACE 6IP – WP8 – LyNcs – CaSToRC www.prace-ri.eu Deliverables & contributions PRACE WP 8 – Deliverables Contribution by LyNcs ▶ D8.2 (MS 6) Interim progress report: ▶ Finalized set of tasks and milestones, PM distribution, and staff and established project structure team, including any new staff. ▶ D8.3 (MS 12) Interim progress report: ▶ First version of APIs from Task 3. Progress of library Public Prototype software release and optimization (Task 1) and evaluation of prototypes new development infrastructure algorithms (Task 2) ▶ D8.4 (MS 24) Interim progress report: ▶ First release of software, including documentation, Public Software release (docs, testing, benchmark results and issue tracking statistics (Tasks 1, issue tracker) and integration in external and 3). Report on evaluation of new methods of Task 2, and codes candidates selected for implementation within Task 1. Progress of integration into community codes (Task 4). ▶ D8.5 (MS 30) Final report: including ▶ Performance results on community software linked to APIs performance results on (pre)Exascale (Tasks 1, 2, 3, and 4). Report on results presented in systems conferences. Publication of results of Task 2 (as peer-review publication or PRACE white paper) 8 PRACE 6IP – WP8 – LyNcs – CaSToRC www.prace-ri.eu Project Synergy DDalphaAMG Integration of major software for Lattice QCD simulations Advance Krylov block solvers for multigrid methods Lyncs API Implementation of high-quality community-software standards Fabulous librsb Performance improvements of low level kernels 9 PRACE 6IP – WP8 – LyNcs – CaSToRC www.prace-ri.eu Lyncs API - Overview Lyncs-API A Python API for LQCD applications Flexible, portable, extendible Task and data parallelism ▶ Lyncs-API covers the entire stack, from low-level dask.distributed, mpi4py libraries to fully-fledged community codes Distributed data Python bindings dask.Array cppyy Main features: LQCD libraries Data management DDalphaAMG, QUDA, numpy, cupy, h5py tmLQCD, OpenQCD... ➔ Flexible framework for easy-integration of external libraries C/C++ libraries Python modules ➔ Parallel tasking and modular computing Developed / wrapped / contributed to ➔ Automatic benchmarking and cross Contribution to Objectives checking of different implementations ▶ O2: alternative parallelization methods will speed-up real ➔ High-level user-friendly Python API time to solution of Markov-Chains beyond strong scaling regime ➔ Low-level integration of C/C++ libraries ▶ O3: flexible to diversity in hardware by utilization of community software stack, e.g. QUDA for GPU systems 10 PRACE 6IP – WP8 – LyNcs – CaSToRC www.prace-ri.eu Lyncs API - Targeted libraries ▶ Lyncs-API provides standalone Python In the Lyncs-API we aim to target as many LQCD interfaces to several LQCD libraries: libraries as possible, such that we can DDalphaAMG, clime, tmLQCD, QUDA, openQCD, QphiX and others to come... ▶ Optimally support various architecture with ▶ Source-codes are downloaded, patched and architecture-specific libraries compiled using git & CMake ▶ Crosscheck and benchmark various ▶ Python bindings are automatically generated implementations via cppyy ▶ Involve all the community and be open to contributions ▶ Cover most of the research interests cppyy ▶ Give a second life to legacy codes Automatic C/C++ bindings >>> cppyy.include(‘header.h’) >>> cppyy.load_library(‘lib.so’) For doing this we have created several low- and ➢ Direct access to library functions high-level interfacing tools... ➢ Automatic casting of Python types ➢ Support of templates and overloading 11 PRACE 6IP – WP8 – LyNcs – CaSToRC www.prace-ri.eu Lyncs API - Python interface ▶ Top level: Lyncs, an API that offers a high-level common framework for LQCD Natively scales Python ▶ Task scheduling, parallelism and data distribution is managed by Dask with ➢ Management of distributed data and tasks improved support for MPI applications ➢ Task scheduling and parallelism via futures via Lyncs-mpi ➢ Distributed numpy arrays ▶ Available implementations of the same function are benchmarked, cross-checked and selected via tuneit. tuneit ▶ All the low-level interfaces to external Tune, benchmark and crosscheck libraries can be used independently of Lyncs and the Lyncs-API is independent from them ➢ Generic-purpose package developed relying on alternative implementations beside Lyncs as a necessity ➢ Function implementations/parameters >> pip install lyncs_DDalphaAMG are used for tuning to best performance >> pip install lyncs[DDalphaAMG] ➢ Benchmarking and testing tools provided 12 PRACE 6IP – WP8 – LyNcs – CaSToRC www.prace-ri.eu Lyncs API - Development status Available on github.com/Lyncs-API ▶ Currently in alpha-state ▶ Open-source, BSD-3-Clause license ▶ Modular structure of many packages: ○ divided purpose-wise, e.g. interfaces, common tools, target architecture, etc.. ○ with independent testing, version control and installation Contribution to Task 2, 3 and 4 ▶ High-quality community-software standards ▶ D8.4: First release of software, including
Load more

Recommended publications
  • Easybuild Documentation Release 20210907.0
    EasyBuild Documentation Release 20210907.0 Ghent University Tue, 07 Sep 2021 08:55:41 Contents 1 What is EasyBuild? 3 2 Concepts and terminology 5 2.1 EasyBuild framework..........................................5 2.2 Easyblocks................................................6 2.3 Toolchains................................................7 2.3.1 system toolchain.......................................7 2.3.2 dummy toolchain (DEPRECATED) ..............................7 2.3.3 Common toolchains.......................................7 2.4 Easyconfig files..............................................7 2.5 Extensions................................................8 3 Typical workflow example: building and installing WRF9 3.1 Searching for available easyconfigs files.................................9 3.2 Getting an overview of planned installations.............................. 10 3.3 Installing a software stack........................................ 11 4 Getting started 13 4.1 Installing EasyBuild........................................... 13 4.1.1 Requirements.......................................... 14 4.1.2 Using pip to Install EasyBuild................................. 14 4.1.3 Installing EasyBuild with EasyBuild.............................. 17 4.1.4 Dependencies.......................................... 19 4.1.5 Sources............................................. 21 4.1.6 In case of installation issues. .................................. 22 4.2 Configuring EasyBuild.......................................... 22 4.2.1 Supported configuration
    [Show full text]
  • Interfacing Epetra to the RSB Sparse Matrix Format for Shared-Memory Performance
    Interfacing Epetra to the RSB sparse matrix format for shared-memory performance Michele Martone High Level Support Team Max Planck Institute for Plasma Physics Garching bei M¨unchen,Germany 5th European Trilinos User Group Meeting Garching bei M¨unchen, Germany April 19, 2016 1 / 18 Background: sparse kernels can be performance critical Sparse kernel Operation definition1 SpMV: Matrix-Vector Multiply \y β y + α A x" SpMV-T: (Transposed) \y β y + α AT x" SpSV : Triangular Solve \x α L−1 x" SpSV-T : (Transposed) \x α L−T x" Epetra_... Epetra_CrsMatrix I CRS (Compressed Row Storage) versatile and straightforward I class Epetra CrsMatrix can rely on Intel MKL 1A is a sparse matrix, L sparse triangular, x; y vectors or multi-vectors, α; β scalars. 2 / 18 Background: optimized sparse matrix classes Epetra_... Epetra_CrsMatrix Epetra_OskiMatrix I OSKI (Optimized Sparse Kernels Interface) library, by R.Vuduc I kernels for iterative methods, e.g. SpMV, SpSV I autotuning framework I OSKI + Epetra = class Epetra OskiMatrix, by I.Karlin 3 / 18 Background: librsb I a stable \Sparse BLAS"-like kernels library: I Sparse BLAS API (blas sparse.h) I own API (rsb.h) I LGPLv3 licensed I librsb-1.2 at http://librsb.sourceforge.net/ I OpenMP threaded 2 I C/C++/FORTRAN interface 2ISO-C-BINDING for own and F90 for Sparse BLAS 4 / 18 What can librsb do 3 I can be multiple times faster than Intel MKL's CRS in I symmetric/transposed sparse matrix multiply (SpMV) I multi-RHS (SpMM) I large matrices I threaded SpSV/SpSM (sparse triangular solve) I iterative methods ops: scaling, extraction, update, ..
    [Show full text]
  • Using Machine Learning to Improve Dense and Sparse Matrix Multiplication Kernels
    Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2019 Using machine learning to improve dense and sparse matrix multiplication kernels Brandon Groth Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Part of the Applied Mathematics Commons, and the Computer Sciences Commons Recommended Citation Groth, Brandon, "Using machine learning to improve dense and sparse matrix multiplication kernels" (2019). Graduate Theses and Dissertations. 17688. https://lib.dr.iastate.edu/etd/17688 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Using machine learning to improve dense and sparse matrix multiplication kernels by Brandon Micheal Groth A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Applied Mathematics Program of Study Committee: Glenn R. Luecke, Major Professor James Rossmanith Zhijun Wu Jin Tian Kris De Brabanter The student author, whose presentation of the scholarship herein was approved by the program of study committee, is solely responsible for the content of this dissertation. The Graduate College will ensure this dissertation is globally accessible and will not permit alterations after a degree is conferred. Iowa State University Ames, Iowa 2019 Copyright c Brandon Micheal Groth, 2019. All rights reserved. ii DEDICATION I would like to dedicate this thesis to my wife Maria and our puppy Tiger.
    [Show full text]
  • Best Practice Guide
    Best Practice Guide - Application porting and code-optimization activities for European HPC systems Sebastian Lührs, JSC, Forschungszentrum Jülich GmbH, Germany Björn Dick, HLRS, Germany Chris Johnson, EPCC, United Kingdom Luca Marsella, CSCS, Switzerland Gerald Mathias, LRZ, Germany Cristian Morales, BSC, Spain Lilit Axner, KTH, Sweden Anastasiia Shamakina, HLRS, Germany Hayk Shoukourian, LRZ, Germany 30-04-2020 1 Best Practice Guide - Application porting and code-optimization ac- tivities for European HPC systems Table of Contents 1. Introduction .............................................................................................................................. 3 2. EuroHPC Joint Undertaking ........................................................................................................ 3 3. Application porting and optimization activities in PRACE ................................................................ 4 3.1. Preparatory Access .......................................................................................................... 4 3.1.1. Overview ............................................................................................................ 4 3.1.2. Application and review processes ............................................................................ 4 3.1.3. Project white papers .............................................................................................. 4 3.2. SHAPE ........................................................................................................................
    [Show full text]
  • Efficient Multithreaded Untransposed, Transposed Or Symmetric Sparse
    Efficient Multithreaded Untransposed, Transposed or Symmetric Sparse Matrix-Vector Multiplication with the Recursive Sparse Blocks Format Michele Martonea,1,∗ aMax Planck Society Institute for Plasma Physics, Boltzmannstrasse 2, D-85748 Garching bei M¨unchen,Germany Abstract In earlier work we have introduced the \Recursive Sparse Blocks" (RSB) sparse matrix storage scheme oriented towards cache efficient matrix-vector multiplication (SpMV ) and triangular solution (SpSV ) on cache based shared memory parallel computers. Both the transposed (SpMV T ) and symmetric (SymSpMV ) matrix-vector multiply variants are supported. RSB stands for a meta-format: it recursively partitions a rectangular sparse matrix in quadrants; leaf submatrices are stored in an appropriate traditional format | either Compressed Sparse Rows (CSR) or Coordinate (COO). In this work, we compare the performance of our RSB implementation of SpMV, SpMV T, SymSpMV to that of the state-of-the-art Intel Math Kernel Library (MKL) CSR implementation on the recent Intel's Sandy Bridge processor. Our results with a few dozens of real world large matrices suggest the efficiency of the approach: in all of the cases, RSB's SymSpMV (and in most cases, SpMV T as well) took less than half of MKL CSR's time; SpMV 's advantage was smaller. Furthermore, RSB's SpMV T is more scalable than MKL's CSR, in that it performs almost as well as SpMV. Additionally, we include comparisons to the state-of-the art format Compressed Sparse Blocks (CSB) implementation. We observed RSB to be slightly superior to CSB in SpMV T, slightly inferior in SpMV, and better (in most cases by a factor of two or more) in SymSpMV.
    [Show full text]
  • Auto-Tuning Shared Memory Parallel Sparse BLAS Operations In
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE Auto-tuning shared memory parallel Sparse BLAS provided by MPG.PuRe operations in librsb-1.2 Michele MARTONE ([email protected]) Max Planck Institute for Plasma Physics, Garching bei Munchen,¨ Germany Intro 2/9 HCSR 1.5e+04 Sparse BLAS (Basic Linear Algebra Subroutines) [2] speci- • 1/9 HCOO 2.0e+03 fies main kernels for iterative methods: – sparseMultiply byMatrix:“MM” 3/9 HCSR 1.3e+04 4/9 HCOO 2.0e+03 – sparse triangularSolve byMatrix:“SM” Untuned. Tuned for NRHS=1. Tuned for NRHS=3. Tuning example on symmetric matrix audikw 1. • Focus on MM:C C+αop(A) B , with Here only lower triangle, ca.1M 1M, 39M nonzeroes. • ← × • × 5/9 HCOO 9.8e+02 6/9 HCSR 1.0e+04 –A has dimensionsm k and is sparse(nnz nonzeroes) On a machine with 256 KB sized L2 cache. × • T H Left one (625 blocks, avg 491 KB) is before tuning. – op(A) can be either of A, A ,A (parameter transA) 9/9 HCOO 5.0e+03 • { } Middle one (271 blocks, avg 1133 KB) after tuning (1.057x – left hand side(LHS)B isk n, • × speedup, 6436.6 ops to amortize) forMV(MM with NRHS=1). right hand side(RHS)C isn m( n=NRHS), × 7/9 HCSR 8.5e+03 8/9 HCSR 7.0e+03 Right one (1319 blocks, avg 233 KB) after tuning (1.050x both dense (eventually with strided access incB, incC, ...) • speedup, 3996.2 ops to amortize) forMM with NRHS=3.
    [Show full text]
  • GRILLIX: a 3D Turbulence Code for Magnetic Fusion Devices Based on a Field Line
    GRILLIX: A 3D turbulence code for magnetic fusion devices based on a field line map Andreas Korbinian Stegmeir TECHNISCHE UNIVERSITAT¨ MUNCHEN¨ Max-Planck-Institut f¨urPlasmaphysik GRILLIX: A 3D turbulence code for magnetic fusion devices based on a field line map Andreas Korbinian Stegmeir Vollst¨andigerAbdruck der von der Fakult¨atf¨urPhysik der Technischen Universit¨atM¨unchen zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzender: Univ.-Prof. Dr. Stephan Paul Pr¨uferder Dissertation: 1. Hon.-Prof. Dr. Sibylle G¨unter 2. Univ.-Prof. Dr. Katharina Krischer 3. Univ.-Prof. Dr. Karl-Heinz Spatschek (i.R.) Heinrich-Heine-Universit¨atD¨usseldorf Die Dissertation wurde am 13.10.2014 bei der Technischen Universit¨atM¨unchen eingereicht und durch die Fakult¨atf¨urPhysik am 13.01.2015 angenommen. Abstract The main contribution to the (anomalous) cross field transport in tokamaks is known to be due to turbulence and numerical codes are essential tools in order to predict transport levels and understand physical mechanisms. Whereas for the interior closed field line region sophisticated turbulence codes are already quite advanced, the outer region of a tokamak, i.e. the edge and scrape-off layer (SOL), still lacks such tools to a large extent. The presence of many spatio- temporal scales and the complex geometry in diverted machines pose a huge challenge for the modelling of the edge/SOL. In this work the newly developed code GRILLIX is presented, which is aimed to set a first milestone in the development of a 3D turbulence code for the edge/SOL.
    [Show full text]
  • HLST Core Team Report 2013
    EUROFUSION WPISA-REP(16) 16107 R Hatzky et al. HLST Core Team Report 2013 REPORT This work has been carried out within the framework of the EUROfusion Con- sortium and has received funding from the Euratom research and training pro- gramme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. This document is intended for publication in the open literature. It is made available on the clear under- standing that it may not be further circulated and extracts or references may not be published prior to publication of the original when applicable, or without the consent of the Publications Officer, EUROfu- sion Programme Management Unit, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK or e-mail Publications.Offi[email protected] Enquiries about Copyright and reproduction should be addressed to the Publications Officer, EUROfu- sion Programme Management Unit, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK or e-mail Publications.Offi[email protected] The contents of this preprint and all other EUROfusion Preprints, Reports and Conference Papers are available to view online free at http://www.euro-fusionscipub.org. This site has full search facilities and e-mail alert options. In the JET specific papers the diagrams contained within the PDFs on this site are hyperlinked HLST Core Team Report 2013 Contents 1. Executive Summary ..............................................................................................4 1.1. Progress made by each core team member on allocated projects ................ 4 1.2. Further tasks and activities of the core team .................................................9 1.2.1. Dissemination .........................................................................................9 1.3.
    [Show full text]
  • PRIMME SVDS: a High-Performance Preconditioned SVD Solver For
    PRIMME SVDS: A HIGH-PERFORMANCE PRECONDITIONED SVD SOLVER FOR ACCURATE LARGE-SCALE COMPUTATIONS LINGFEI WU,∗ ELOY ROMERO,∗ ANDREAS STATHOPOULOS∗ Abstract. The increasing number of applications requiring the solution of large scale singular value problems has rekindled an interest in iterative methods for the SVD. Some promising recent ad- vances in large scale iterative methods are still plagued by slow convergence and accuracy limitations for computing smallest singular triplets. Furthermore, their current implementations in MATLAB cannot address the required large problems. Recently, we presented a preconditioned, two-stage method to effectively and accurately compute a small number of extreme singular triplets. In this re- search, we present a high-performance library, PRIMME SVDS, that implements our hybrid method based on the state-of-the-art eigensolver package PRIMME for both largest and smallest singular values. PRIMME SVDS fills a gap in production level software for computing the partial SVD, especially with preconditioning. The numerical experiments demonstrate its superior performance compared to other state-of-the-art software and its good parallel performance under strong and weak scaling. 1. Introduction. We consider the problem of finding a small number, k n, of extreme singular values and corresponding left and right singular vectors of a≪ large m n sparse matrix A R × (m n). These singular values and vectors satisfy, ∈ ≥ (1.1) Avi = σiui, where the singular values are labeled in ascending order, σ1 σ2 ... σn. The m n ≤n n ≤ ≤ matrices U = [u ,...,un] R × and V = [v ,...,vn] R × have orthonormal 1 ∈ 1 ∈ columns. (σi,ui, vi) is called a singular triplet of A.
    [Show full text]
  • Matrix:“MM” 3/9 HCSR 1.3E+04 4/9 HCOO 2.0E+03 – Sparse Triangular Solve by Matrix:“SM” Untuned
    Auto-tuning shared memory parallel Sparse BLAS operations in librsb-1.2 Michele MARTONE ([email protected]) Max Planck Institute for Plasma Physics, Garching bei Munchen,¨ Germany Intro 2/9 HCSR 1.5e+04 Sparse BLAS (Basic Linear Algebra Subroutines) [2] speci- • 1/9 HCOO 2.0e+03 fies main kernels for iterative methods: – sparse Multiply by Matrix:“MM” 3/9 HCSR 1.3e+04 4/9 HCOO 2.0e+03 – sparse triangular Solve by Matrix:“SM” Untuned. Tuned for NRHS=1. Tuned for NRHS=3. Tuning example on symmetric matrix audikw 1. • Focus on MM: C C + αop(A) B , with Here only lower triangle, ca. 1M 1M, 39M nonzeroes. • ← × • × 5/9 HCOO 9.8e+02 6/9 HCSR 1.0e+04 – A has dimensions m k and is sparse (nnz nonzeroes) On a machine with 256 KB sized L2 cache. × • T H Left one (625 blocks, avg 491 KB) is before tuning. – op(A) can be either of A, A ,A (parameter transA) 9/9 HCOO 5.0e+03 • { } Middle one (271 blocks, avg 1133 KB) after tuning (1.057x – left hand side (LHS) B is k n, • × speedup, 6436.6 ops to amortize) for MV (MM with NRHS=1). right hand side (RHS) C is n m (n=NRHS), × 7/9 HCSR 8.5e+03 8/9 HCSR 7.0e+03 Right one (1319 blocks, avg 233 KB) after tuning (1.050x both dense (eventually with strided access incB, incC, ...) • speedup, 3996.2 ops to amortize) for MM with NRHS=3. – α is scalar Finer subdivision at NRHS=3 consequence of increased • – either single or double precision, either real or complex Instance of matrix bayer02 (ca.
    [Show full text]
  • Fast Matrix-Vector Multiplications for Large-Scale Logistic Regression on Shared-Memory Systems
    Fast Matrix-vector Multiplications for Large-scale Logistic Regression on Shared-memory Systems Mu-Chu Lee Wei-Lin Chiang Chih-Jen Lin Department of Computer Science Department of Computer Science Department of Computer Science National Taiwan Univ., Taiwan National Taiwan Univ., Taiwan National Taiwan Univ., Taiwan Email: [email protected] Email: [email protected] Email: [email protected] Abstract—Shared-memory systems such as regular desktops modules. The core computational tasks of some popular now possess enough memory to store large data. However, the machine learning algorithms are sparse matrix operations. training process for data classification can still be slow if we do For example, if Newton methods are used to train logistic not fully utilize the power of multi-core CPUs. Many existing works proposed parallel machine learning algorithms by modi- regression for large-scale document data, the data matrix is fying serial ones, but convergence analysis may be complicated. sparse and sparse matrix-vector multiplications are the main Instead, we do not modify machine learning algorithms, but computational bottleneck [10], [11]. If we can apply fast consider those that can take the advantage of parallel matrix implementations of matrix operations, then machine learning operations. We particularly investigate the use of parallel sparse algorithms can be parallelized without any modification. Such matrix-vector multiplications in a Newton method for large- scale logistic regression. Various implementations from easy to an approach possesses the following advantages. sophisticated ones are analyzed and compared. Results indicate 1) Because the machine learning algorithm is not modified, the that under suitable settings excellent speedup can be achieved.
    [Show full text]
  • Librsb: a Shared Memory Parallel Sparse BLAS Implementation Using the Recursive Sparse Blocks Format
    librsb: A Shared Memory Parallel Sparse BLAS Implementation using the Recursive Sparse Blocks format Michele Martone High Level Support Team Max Planck Institute for Plasma Physics Garching bei Muenchen, Germany Sparse Days'13 Toulouse, France June 17{18, 2013 presentation outline Intro librsb: a Sparse BLAS implementation A recursive layout Performance measurements SpMV , SpMV-T SymSpMV performance COO to RSB conversion cost Auto-tuning RSB for SpMV /SpMV-T /SymSpMV Conclusions Summing up References Extra: RSB vs MKL plots Focus of the Sparse BLAS operations The numerical solution of linear systems of the form Ax = b (with A a sparse matrix, x; y dense vectors) using iterative methods requires repeated (and thus, fast) computation of (variants of) Sparse Matrix-Vector Multiplication and Sparse Matrix-Vector Triangular Solve: I SpMV :\y β y + α A x" T I SpMV-T :\y β y + α A x" T T I SymSpMV:\y βy + α A x; A = A " −1 I SpSV :\x α L x" −T I SpSV-T :\x α L x" librsb: a high performance Sparse BLAS implementation I uses the Recursive Sparse Blocks (RSB) matrix layout I provides (for true) a Sparse BLAS standard API I most of its numerical kernels are generated (from GNU M4 templates) I extensible to any integral C type I pseudo-randomly generated testing suite I get/set/extract/convert/... functions I 47 KLOC of C (C99), 20 KLOC of M4, 2 KLOC of GNU≈ Octave ≈ ≈ I bindings to C and Fortran (ISO C Binding), as OCT module for GNU Octave I LGPLv3 licensed design constraints of the Recursive Sparse Blocks (RSB) format I parallel, efficient SpMV /SpSV /COO RSB ! I in-place COO RSB COO conversion ! ! I no oversized COO arrays / no fillin (e.g.: in contrast to BCSR) 1 I no need to pad x; y vectors arrays I architecture independent (only C code, POSIX) I developed on/for shared memory cache based CPUs: I locality of memory references I coarse-grained workload partitioning 1e.g.
    [Show full text]