NLAFET Website for the NLAFET project Thu, 13 Aug 2020 14:18:16 +0000 en-US hourly 1 StarNEig published in Special Issue of CCPE Thu, 13 Aug 2020 14:16:19 +0000 An extended paper describing the task-based StarNEig library for solving nonsymmetric standard and generalized eigenvalue problems has been published in a special issue of the international journal “Concurrency and Computation: Practice and Experience”. The publishers version can be found here. A post print can be found here.

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New release of the StarNEig library Thu, 26 Mar 2020 11:51:21 +0000 Read more »]]> StarNEig is a new task-based parallel library for solving nonsymmetric standard and generalized eigenvalue problems. A new version (StarNEig 0.1 Beta 4) is now freely available for download from the dedicated website

StarNEig is either comparable to LAPACK and ScaLAPACK or significantly faster depending on the computational step. Moreover, StarNEig realizes new parallel and blocked algorithms for computing eigenvectors without suffering from floating point overflow. In LAPACK the corresponding solvers are sequential scalar codes which compute eigenvectors one by one. In ScaLAPACK the corresponding solvers are vulnerable to overflow.

Eigenvalue problems can be found in every field of natural science. Clear examples are supplied by the analysis of systems of ordinary differential equations. The stability analysis of first order systems produces standard eigenvalue problems which are not necessarily symmetric and the analysis of second order systems produce quadratic eigenvalue problems which are equivalent to nonsymmetric generalized eigenvalue problems. Without the ability to solve eigenvalue problems rapidly and accurately, we would be unable to complete the calculations needed to maintain and advance our civilization. Therefore, it is important that we continue to develop new algorithms and software which maximizes both the performance and the accuracy using existing and emerging hardware

StarNEig is one of very few libraries to offer support for nonsymmetric eigenvalue problems. It is built on top of the runtime system StarPU which is used to schedule the tasks. Currently, StarNEig applies to real problems which have real or complex eigenvalues and eigenvectors. By design, StarNEig applies to both shared and distributed memory machines and it has experimental support for GPU accelerators.

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Three new papers published Thu, 26 Mar 2020 11:23:44 +0000 Read more »]]> Three papers based on research completed at Umeå University during the NLAFET project were presented at the conference PPAM-2019 (Parallel Processing and Applied Mathematics) in Bialystok, Poland in September 2019. They now appear as part of the peer-reviewed conference proceedings published by Springer as LNCS volume 12043. Free preprints are also available through arXiv.

1: Carl Christian Kjelgaard Mikkelsen and Mirko Myllykoski: Parallel Robust Computation of Generalized Eigenvectors of Matrix Pencils

In this paper, we consider the problem of computing generalized eigenvectors of a matrix pencil in real Schur form. In exact arithmetic, this problem can be solved using substitution. In practice, substitution is vulnerable to floating-point overflow. The robust solvers xtgevc in LAPACK prevent overflow by dynamically scaling the eigenvectors. These subroutines are scalar and sequential codes which compute the eigenvectors one by one. In this paper, we discuss how to derive robust algorithms which are blocked and parallel. The new StarNEig library contains a robust task-parallel solver Zazamoukh which runs on top of StarPU. Our numerical experiments show that Zazamoukh achieves a super-linear speedup compared with dtgevc for sufficiently large matrices.

2: Mirko Myllykoski and Carl Christian Kjelgaard Mikkelsen: Introduction to StarNEig – A Task-based Library for Solving Nonsymmetric Eigenvalue Problems.

In this paper, we present the StarNEig library for solving dense nonsymmetric (generalized) eigenvalue problems. The library is built on top of the StarPU runtime system and targets both shared and distributed memory machines. Some components of the library support GPUs. The library is currently in an early beta state and only real arithmetic is supported. Support for complex data types is planned for a future release. This paper is aimed at potential users of the library. We describe the design choices and capabilities of the library, and contrast them to existing software such as ScaLAPACK. StarNEig implements a ScaLAPACK compatibility layer that should make it easy for new users to transition to StarNEig. We demonstrate the performance of the library with a small set of computational experiments.

3: Angelika Beatrix Schwarz and Carl Christian Kjelgaard Mikkelsen: Robust Task-Parallel Solution of the Triangular Sylvester Equation.

The Bartels-Stewart algorithm is a standard approach to solving the dense Sylvester equation. It reduces the problem to the solution of the triangular Sylvester equation. The triangular Sylvester equation is solved with a variant of backward substitution. Backward substitution is prone to overflow. Overflow can be avoided by dynamic scaling of the solution matrix. An algorithm which prevents overflow is said to be robust. The standard library LAPACK contains the robust scalar sequential solver dtrsyl. This paper derives a robust, level-3 BLAS-based task-parallel solver. By adding overflow protection, our robust solver closes the gap between problems solvable by LAPACK and problems solvable by existing non-robust task-parallel solvers. We demonstrate that our robust solver achieves a performance similar to non-robust solvers.

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Public deliverables 2.7, 2.9, 5.3, 6.3, 6.5, 6.7, 7.7, and 7.8 uploaded. Thu, 02 May 2019 14:37:33 +0000 Public deliverables uploaded:

D2.7 Eigenvalue solvers for nonsymmetric problems
D2.9 Novel SVD Algorithms
D5.3 Validation and evaluation
D6.3 Evaluation of software prototypes
D6.5 Evaluation of auto-tuning techniques
D6.7 Prototypes for tiled one-sided factorizations with algorithm-based fault tolerance
D7.7 Dissemination report. Period M19-M42
D7.8 Release of the NLAFET library

For the full list of released public deliverables, see this page:

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Public deliverables (2.4, 3.7, 4.5) uploaded. Mon, 08 Apr 2019 15:53:17 +0000 Public deliverables uploaded:

For the full list of released public deliverables, see this page:

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CCPE – Paper Accepted for special issue Mon, 15 Oct 2018 11:38:19 +0000 Read more »]]> Paper accepted to a special issue of Concurrency and Computation: Practice and Experience (CCPE). This special issue will consist of extended versions of the best papers accepted by PPAM 2017. The title of the paper is “Parallel robust solution of triangular linear systems”

Robust algorithms do not suffer from overflow and always return a valid result. In LAPACK eigenvectors (standard and generalized) are computed using robust algorithms. The existing algorithms are scalar and sequential. This new work presents algorithms which are blocked and parallel. The analysis is supported by parallel software running on top of StarPU. Further improvements are possible, but the new software is already orders of magnitude faster than the existing software.

The authors are Carl Christian Kjelgaard Mikkelsen, Angelika Beatrix Schwarz and Lars Karlsson

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Working Note 20 have been uploaded Mon, 15 Oct 2018 11:33:55 +0000

Working Note 19 have been uploaded:

The full list of published Working Notes can be found on this page:

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Research poster award for Mawussi Zounon Thu, 28 Jun 2018 13:13:54 +0000 Research poster award for Mawussi Zounon on exploiting the low precision floating-point arithmetic available on NVIDIA V100 GPU in solving linear system of equations.

The title of the poster is “Using GPU’s FP16 Tensor Cores Arithmetic to Accelerate Mixed-Precision Iterative Refinement Solvers and Reduce Energy Consumption” with the authors Azzam Haidar, Stan Tomov, Ahmad Abdelfattah, Mawussi Zounon, Jack Dongarra

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A New Direction for HPC Math Libraries – NLAFET in the press Thu, 28 Jun 2018 13:10:40 +0000 NLAFET – A New Direction for HPC Math Libraries, talk by Jack Dongarra at ISC 2018

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Public Deliverables uploaded Wed, 18 Apr 2018 15:28:57 +0000

Several deliverables have been uploaded: D3.2, D3.6, D4.3, D6.2, and D6.6.

A full list, including links to all the public deliverables that have been posted until now can be found here:

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