TRLan software package

By Kesheng Wu and Horst Simon

[Documentation (PS) (HTML)] [Software (gzipped tar file), last updated on Oct 10, 2010] [Software license]
By some estimates, more than 90% of the eigenvalue problems solved are real symmetric or complex Hermitian problems. For many of these problems, the discrete form of the operators (a.k.a the matrices) are simply too large to store in computer memory. Typically, a small fraction of the total eigenvalues and eigenvectors are wanted, and the wanted one are often the extreme eigenvalues. In these cases, it is fairly difficult to work with the matrices directly. However, through years of research, many fast schemes have been developed to multiply these matrices on vectors. The software package we developed is mainly targetted for this type of eigenvalue problems. By limiting the scope of its functionalities, we are able to provide a small, efficient and user-friendly software package.
Overview of the software
This software package implements the thick-restart Lanczos method. It can be used on either a single address space machine or a distributed parallel machine. The user can choose to implement or use a matrix-vector multiplication routine in any form convenient. Most of the arithmetic computations in the software are done through calls to BLAS and LAPACK.
The software is written in Fortran 90. Because Fortran 90 offers many utility functions such functions such as dynamic memory management, timing functions, random number generator and so on, the program is easily portable to different machines without modifying the source code. It can also be easily accessed from other language such as C or C++. Since the software is highly modularized, it relatively easy to adopt it for different type of situation. For example if the eigenvalue problem may have some symmetry and only a portion of the physical domain is discretized, then the dot-product routine needs to be modified. In this software, this modification is limited to one subroutine. It also can be instructed to write checkpoint files so that it can be restarted is a later time.
Selected publications
* I. Yamazaki, Z. Bai, H. Simon, L.-W. Wang, and K. Wu. Adaptive Projection Subspace Dimension for the Thick-Restart Lanczos Method. Tech report LBNL-1059E. 2008.ACM TOMS 37:3
* K. Wu and H. Simon, Thick-restart Lanczos method for large symmetric eigenvalue problems. SIAM Journal on Matrix Analysis and Applications Vol. 22, No. 2, pp. 602-616, 2001.
An early draft of this paper is available as LBNL tech report 41412.
* K. Wu and H. Simon, TRLAN user guide, Lawrence Berkeley National Laboratory tech report number LBNL-42953.
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Application known to use TRLan
Berkeley Segmentation Engine
Papers that cites TRLan
Papers that cite the TRLan algorithm
Papers that cite TRLan User Guide
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related work
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John Wu