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WO2008136045A1 - 共有メモリ型スカラ並列計算機向け、実対称行列の三重対角化の並列処理方法 - Google Patents

共有メモリ型スカラ並列計算機向け、実対称行列の三重対角化の並列処理方法 Download PDF

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Publication number
WO2008136045A1
WO2008136045A1 PCT/JP2007/000424 JP2007000424W WO2008136045A1 WO 2008136045 A1 WO2008136045 A1 WO 2008136045A1 JP 2007000424 W JP2007000424 W JP 2007000424W WO 2008136045 A1 WO2008136045 A1 WO 2008136045A1
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WIPO (PCT)
Prior art keywords
matrix
diagonalization
shared memory
tri
lower triangular
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Ceased
Application number
PCT/JP2007/000424
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English (en)
French (fr)
Inventor
Makoto Nakanishi
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Fujitsu Ltd
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Fujitsu Ltd
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Application filed by Fujitsu Ltd filed Critical Fujitsu Ltd
Priority to PCT/JP2007/000424 priority Critical patent/WO2008136045A1/ja
Priority to JP2009512784A priority patent/JP5110081B2/ja
Publication of WO2008136045A1 publication Critical patent/WO2008136045A1/ja
Priority to US12/550,040 priority patent/US8527569B2/en
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Computational Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Computing Systems (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Complex Calculations (AREA)
  • Devices For Executing Special Programs (AREA)

Abstract

　実対称行列の三重対角化を共有メモリ型スカラ並列計算機で行う場合、行列の更新を各スレッドに分割して行う。このとき、行列が対称行列であるので、下三角行列部分のデータを使って計算する。下三角行列部分は、縦に分割し、各ＣＰＵに割り当てるが、その際、各ＣＰＵに割り当てる要素数が同じになるように割り当てる。そして、１回のデータのロードで、縦方向の演算と横方向の演算を同時に行い、メモリロードの回数を減らす。対角ブロック行列部分の下三角行列部分は、１つの小さな正方行列と２つの小さな下三角行列に分割することを再帰的に行いながら更新をする。
PCT/JP2007/000424 2007-04-19 2007-04-19 共有メモリ型スカラ並列計算機向け、実対称行列の三重対角化の並列処理方法 Ceased WO2008136045A1 (ja)

Priority Applications (3)

Application Number Priority Date Filing Date Title
PCT/JP2007/000424 WO2008136045A1 (ja) 2007-04-19 2007-04-19 共有メモリ型スカラ並列計算機向け、実対称行列の三重対角化の並列処理方法
JP2009512784A JP5110081B2 (ja) 2007-04-19 2007-04-19 共有メモリ型スカラ並列計算機向け、実対称行列の三重対角化の並列処理方法
US12/550,040 US8527569B2 (en) 2007-04-19 2009-08-28 Parallel processing method of tridiagonalization of real symmetric matrix for shared memory scalar parallel computer

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
PCT/JP2007/000424 WO2008136045A1 (ja) 2007-04-19 2007-04-19 共有メモリ型スカラ並列計算機向け、実対称行列の三重対角化の並列処理方法

Related Child Applications (1)

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US12/550,040 Continuation US8527569B2 (en) 2007-04-19 2009-08-28 Parallel processing method of tridiagonalization of real symmetric matrix for shared memory scalar parallel computer

Publications (1)

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WO2008136045A1 true WO2008136045A1 (ja) 2008-11-13

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ID=39943170

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PCT/JP2007/000424 Ceased WO2008136045A1 (ja) 2007-04-19 2007-04-19 共有メモリ型スカラ並列計算機向け、実対称行列の三重対角化の並列処理方法

Country Status (3)

Country Link
US (1) US8527569B2 (ja)
JP (1) JP5110081B2 (ja)
WO (1) WO2008136045A1 (ja)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US10013393B2 (en) 2015-06-02 2018-07-03 Fujitsu Limited Parallel computer system, parallel computing method, and program storage medium
CN113704691A (zh) * 2021-08-26 2021-11-26 中国科学院软件研究所 一种申威众核处理器的小规模对称矩阵并行三对角化方法
WO2024122067A1 (ja) * 2022-12-09 2024-06-13 日本電信電話株式会社 ハッシュ値計算装置、ハッシュ値計算方法及びプログラム

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US9262799B2 (en) * 2013-11-08 2016-02-16 Silicon Graphics International Corp. Shared memory eigensolver
JP6610350B2 (ja) * 2016-03-11 2019-11-27 富士通株式会社 計算機、行列分解方法、及び行列分解プログラム
JP6907700B2 (ja) * 2017-05-23 2021-07-21 富士通株式会社 情報処理装置、マルチスレッド行列演算方法、およびマルチスレッド行列演算プログラム
CN109766515B (zh) * 2018-12-26 2023-04-14 上海思朗科技有限公司 矩阵分解处理装置及方法
US11562239B2 (en) * 2019-05-23 2023-01-24 Google Llc Optimizing sparse graph neural networks for dense hardware
WO2023206074A1 (zh) * 2022-04-26 2023-11-02 浙江凌迪数字科技有公司 一种对称矩阵与向量相乘的并行计算方法及其系统
CN119358329B (zh) * 2024-10-17 2025-09-26 华南理工大学 基于分块对称特性的刚度矩阵压缩存储方法、系统及介质

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2002163246A (ja) * 2000-11-24 2002-06-07 Fujitsu Ltd 共有メモリ型スカラ並列計算機における並列行列処理方法、及び記録媒体
JP2004005488A (ja) * 2002-03-22 2004-01-08 Fujitsu Ltd 共有メモリ型スカラ並列計算機用逆行列の並列処理方法
JP2004005528A (ja) * 2002-03-29 2004-01-08 Fujitsu Ltd 共有メモリ型スカラ並列計算機用固有値問題の並列処理方法
JP2006259821A (ja) * 2005-03-15 2006-09-28 Hitachi Ltd 並列計算機の同期方法及びプログラム

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5790598A (en) * 1996-03-01 1998-08-04 Her Majesty The Queen In Right Of Canada Block decision feedback equalizer
US20030182518A1 (en) 2002-03-22 2003-09-25 Fujitsu Limited Parallel processing method for inverse matrix for shared memory type scalar parallel computer
US20030187898A1 (en) * 2002-03-29 2003-10-02 Fujitsu Limited Parallel processing method of an eigenvalue problem for a shared-memory type scalar parallel computer

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2002163246A (ja) * 2000-11-24 2002-06-07 Fujitsu Ltd 共有メモリ型スカラ並列計算機における並列行列処理方法、及び記録媒体
JP2004005488A (ja) * 2002-03-22 2004-01-08 Fujitsu Ltd 共有メモリ型スカラ並列計算機用逆行列の並列処理方法
JP2004005528A (ja) * 2002-03-29 2004-01-08 Fujitsu Ltd 共有メモリ型スカラ並列計算機用固有値問題の並列処理方法
JP2006259821A (ja) * 2005-03-15 2006-09-28 Hitachi Ltd 並列計算機の同期方法及びプログラム

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US10013393B2 (en) 2015-06-02 2018-07-03 Fujitsu Limited Parallel computer system, parallel computing method, and program storage medium
CN113704691A (zh) * 2021-08-26 2021-11-26 中国科学院软件研究所 一种申威众核处理器的小规模对称矩阵并行三对角化方法
CN113704691B (zh) * 2021-08-26 2023-04-25 中国科学院软件研究所 一种申威众核处理器的小规模对称矩阵并行三对角化方法
WO2024122067A1 (ja) * 2022-12-09 2024-06-13 日本電信電話株式会社 ハッシュ値計算装置、ハッシュ値計算方法及びプログラム

Also Published As

Publication number Publication date
JPWO2008136045A1 (ja) 2010-07-29
US8527569B2 (en) 2013-09-03
JP5110081B2 (ja) 2012-12-26
US20090319592A1 (en) 2009-12-24

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