Umeå University's logo

umu.sePublikasjoner
Endre søk
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
PDHGEQZ user guide
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
SB–MATHICSE–ANCHP, EPF Lausanne.
2015 (engelsk)Rapport (Annet vitenskapelig)
Abstract [en]

Given a general matrix pair (A,B) with real entries, we provide software routines for computing a generalized Schur decomposition (S, T). The real and complex conjugate pairs of eigenvalues appear as 1×1 and 2×2 blocks, respectively, along the diagonals of (S, T) and can be reordered in any order. Typically, this functionality is used to compute orthogonal bases for a pair of deflating subspaces corresponding to a selected set of eigenvalues. The routines are written in Fortran 90 and targets distributed memory machines.

sted, utgiver, år, opplag, sider
Umeå: Department of Computing Science, Umeå University , 2015. , s. 16
Serie
Report / UMINF, ISSN 0348-0542 ; 15.12
Emneord [en]
software, userguide, generalized eigenvalue problem, nonsymmetric QZ algorithm, multishift, bulge chasing, infinite eigenvalues, parallel algorithms, level 3 performance, aggressive early deflation
HSV kategori
Identifikatorer
URN: urn:nbn:se:umu:diva-120008OAI: oai:DiVA.org:umu-120008DiVA, id: diva2:926165
Tilgjengelig fra: 2016-05-04 Laget: 2016-05-04 Sist oppdatert: 2018-06-07bibliografisk kontrollert
Inngår i avhandling
1. Parallel Algorithms and Library Software for the Generalized Eigenvalue Problem on Distributed Memory Computer Systems
Åpne denne publikasjonen i ny fane eller vindu >>Parallel Algorithms and Library Software for the Generalized Eigenvalue Problem on Distributed Memory Computer Systems
2016 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
Alternativ tittel[sv]
Parallella algoritmer och biblioteksprogramvara för det generaliserade egenvärdesproblemet på datorsystem med distribuerat minne
Abstract [en]

We present and discuss algorithms and library software for solving the generalized non-symmetric eigenvalue problem (GNEP) on high performance computing (HPC) platforms with distributed memory. Such problems occur frequently in computational science and engineering, and our contributions make it possible to solve GNEPs fast and accurate in parallel using state-of-the-art HPC systems. A generalized eigenvalue problem corresponds to finding scalars y and vectors x such that Ax = yBx, where A and B are real square matrices. A nonzero x that satisfies the GNEP equation is called an eigenvector of the ordered pair (A,B), and the scalar y is the associated eigenvalue. Our contributions include parallel algorithms for transforming a matrix pair (A,B) to a generalized Schur form (S,T), where S is quasi upper triangular and T is upper triangular. The eigenvalues are revealed from the diagonals of S and T. Moreover, for a specified set of eigenvalues an associated pair of deflating subspaces can be computed, which typically is requested in various applications. In the first stage the matrix pair (A,B) is reduced to a Hessenberg-triangular form (H,T), where H is upper triangular with one nonzero subdiagonal and T is upper triangular, in a finite number of steps. The second stage reduces the matrix pair further to generalized Schur form (S,T) using an iterative QZ-based method. Outgoing from a one-stage method for the reduction from (A,B) to (H,T), a novel parallel algorithm is developed. In brief, a delayed update technique is applied to several partial steps, involving low level operations, before associated accumulated transformations are applied in a blocked fashion which together with a wave-front task scheduler makes the algorithm scale when running in a parallel setting. The potential presence of infinite eigenvalues makes a generalized eigenvalue problem ill-conditioned. Therefore the parallel algorithm for the second stage, reduction to (S,T) form, continuously scan for and robustly deflate infinite eigenvalues. This will reduce the impact so that they do not interfere with other real eigenvalues or are misinterpreted as real eigenvalues. In addition, our parallel iterative QZ-based algorithm makes use of multiple implicit shifts and an aggressive early deflation (AED) technique, which radically speeds up the convergence. The multi-shift strategy is based on independent chains of so called coupled bulges and computational windows which is an important source of making the algorithm scalable. The parallel algorithms have been implemented in state-of-the-art library software. The performance is demonstrated and evaluated using up to 1600 CPU cores for problems with matrices as large as 100000 x 100000. Our library software is described in a User Guide. The software is, optionally, tunable via a set of parameters for various thresholds and buffer sizes etc. These parameters are discussed, and recommended values are specified which should result in reasonable performance on HPC systems similar to the ones we have been running on.

sted, utgiver, år, opplag, sider
Umeå: Umeå universitet, 2016. s. 18
Serie
Report / UMINF, ISSN 0348-0542 ; 16.11
HSV kategori
Forskningsprogram
data- och systemvetenskap
Identifikatorer
urn:nbn:se:umu:diva-119439 (URN)978-91-7601-491-2 (ISBN)
Presentation
2016-05-27, MC313, Umeå universitet, Umeå, 10:00 (engelsk)
Veileder
Tilgjengelig fra: 2016-04-19 Laget: 2016-04-19 Sist oppdatert: 2018-06-07bibliografisk kontrollert

Open Access i DiVA

fulltext(553 kB)245 nedlastinger
Filinformasjon
Fil FULLTEXT01.pdfFilstørrelse 553 kBChecksum SHA-512
220ae487e96abe06c917eb2349e25544e58581ec48f1e685082ca68404c6d3583e7e50de94c5527c1b5efe16edce827bf8bce8c5707c7c9d6196e8e114ce28a3
Type fulltextMimetype application/pdf

Andre lenker

URL

Person

Adlerborn, BjörnKågström, Bo

Søk i DiVA

Av forfatter/redaktør
Adlerborn, BjörnKågström, Bo
Av organisasjonen

Søk utenfor DiVA

GoogleGoogle Scholar
Totalt: 245 nedlastinger
Antall nedlastinger er summen av alle nedlastinger av alle fulltekster. Det kan for eksempel være tidligere versjoner som er ikke lenger tilgjengelige

urn-nbn

Altmetric

urn-nbn
Totalt: 7316 treff
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf