PReconditioned Iterative MultiMethod Eigensolver

PRIMME

PReconditioned Iterative MultiMethod Eigensolver

Version 1.1 (Oct 18, 2006)

Available under the Lesser GPL license

Download the tar file: primme_v1.1.tar.gz

Optional: send your e-mail to andreas to be included in the distribution list for future releases/updates.

New documentation in pdf or in HTML

Use the filestyle: primmestyle.css for local html installation.

Symmetric and Hermitian eigenvalue problems enjoy a remarkable theoretical structure that allows for efficient and stable algorithms for obtaining a few required eigenpairs. This is probably one of the reasons that enabled applications requiring the solution of symmetric eigenproblems to push their accuracy and thus computational demands to unprecedented levels. Materials science, structural engineering, and some QCD applications routinely compute eigenvalues of matrices of dimension more than a million; and often much more than that! Typically, with increasing dimension comes increased ill conditioning, and thus the use of preconditioning becomes essential.

PRIMME is a C library to find a number of eigenvalues and their corresponding eigenvectors of a
Real Symmetric, or Complex Hermitian matrix A.
Preconditioning and finding largest, smallest or interior eigenvalues is supported.
PRIMME is a multimethod eigensolver. Based on Davidson/Jacobi-Davidson main iteration, it can transform to most known preconditioned eigensolvers, by the appropriate choice of parameters. Two of the choices, GD+1 and JDQMR, have proved nearly optimal eigensolvers (see [1,2]). For user friendliness it provides the following predefined choices of methods:
DYNAMIC,
DEFAULT_MIN_TIME,
DEFAULT_MIN_MATVECS,
Arnoldi,
GD,
GD_plusK,
GD_Olsen_plusK,
JD_Olsen_plusK,
RQI,
JDQR,
JDQMR,
JDQMR_ETol,
SUBSPACE_ITERATION,
LOBPCG_OrthoBasis,
LOBPCG_OrthoBasis_Window
Under DYNAMIC method, the software alternates between DEFAULT_MIN_TIME and DEFAULT_MIN_MATVECS to estimate the parameters of a cost model, and identify the method that minimizes execution time for the given problem.
A multi-layer user interface allows efficient use by non-expert end-users, and a powerful experimentation testbed for eigenvalue research experts.
PRIMME is both parallel and sequential, based on an SMPD type of parallelization.
PRIMME has many features such as blocking, locking, locally optimal restarting, and a host of others that make it extremely robust and efficient.
A full Fortran77 interface is provided.
The software has been tested extensively on a variety of architectures, systems, and applications.

One known bug --discovered October 2009--. In line 303 of ZSRC/inner_solve_z.c the following line:
{ztmp.r = -gamma; ztmp.i = 0.0L;}
should be
{ztmp.r = gamma; ztmp.i = 0.0L;}
This was impairing the performance of the Complex JDQMR method. It will be fixed in a soon upcoming version.

Known omissions in the sample test programs that will be fixed in the next version:
In the parallel test program driver_par.c the variable (int procID) must be passed as a parameter into broadCast().
In the Makefile_par the linking line should include $(INCLUDE).

For any questions/reports/bugs send a message to "andreas" at cs dot wm dot edu

The following papers describe the research that has led to this software. To cite PRIMME, please cite paper [1]. More information can be found in the rest of the papers. The work has been supported by a number of grants from the National Science Foundation.

Andreas Stathopoulos and James R. McCombs

PRIMME: PReconditioned Iterative MultiMethod Eigensolver: Methods and software description ACM Transaction on Mathematical Software Vol. 37, No. 2, (2010), 21:1--21:30.
A. Stathopoulos, "Nearly optimal preconditioned methods for Hermitian eigenproblems under limited memory. Part I: Seeking one eigenvalue", SIAM J. Sci. Comput., Vol. 29, No. 2, (2007), 481--514. [ pdf ]
A. Stathopoulos and J. R. McCombs, "Nearly optimal preconditioned methods for Hermitian eigenproblems under limited memory. Part II: Seeking many eigenvalues", SIAM J. Sci. Comput., Vol. 29, No. 5, (2007), 2162-2188. [ pdf ]
J. R. McCombs and A. Stathopoulos, "Iterative Validation of Eigensolvers: A Scheme for Improving the Reliability of Hermitian Eigenvalue Solvers", SIAM J. Sci. Comput., Vol. 28, No. 6, (2006), 2337--2358. [ pdf ]
A. Stathopoulos, "Locking issues for finding a large number of eigenvectors of Hermitian matrices", Tech Report: WM-CS-2005-09, July, 2005, submitted. [ pdf ]
A. Stathopoulos and K. Wu, "A block orthogonalization procedure with constant synchronization requirements", SIAM Journal on Scientific Computing, Volume 23, Number 6, (2002), 2165--2182. [ pdf ]
A. Stathopoulos "Some insights on restarting symmetric eigenvalue methods with Ritz and harmonic Ritz vectors", in Iterative Methods in Scientific Computation IV, D. R. Kincaid & Anne C. Elster (eds.), pp. 297--311, Series in Computational and Applied Mathematics, IMACS, NJ (1999). [ pdf ]
A. Stathopoulos and Y. Saad, "Restarting techniques for (Jacobi-)Davidson symmetric eigenvalue methods", special issue on eigenvalue methods, Electronic Transactions on Numerical Analysis, Vol. 7, (1998), 163-181.
K. Wu, Y. Saad and A. Stathopoulos, "Inexact Newton Preconditioning Techniques for Eigenvalue Problems", special issue on eigenvalue methods, Electronic Transactions on Numerical Analysis, Vol. 7, (1998), 202-214.
A. Stathopoulos, Y. Saad, and K. Wu, "Dynamic Thick Restarting of the Davidson, and the Implicitly Restarted Arnoldi Methods", SIAM J. Scientific Computing, 19, 1, (1998) 227-45. Copyright © 1998 Society for Industrial and Applied Mathematics. [ pdf ]
A. Stathopoulos, Y. Saad, and C. F. Fischer, "Robust Preconditioning of Large, Sparse, Symmetric Eigenvalue Problems," the Journal of Computational and Applied Mathematics, 64 (1995) 197-215. [ pdf ]
A. Stathopoulos and C. F. Fischer, "A Davidson Program for Finding a Few Selected Extreme Eigenpairs of a Large, Sparse, Real, Symmetric Matrix," Computer Physics Communications, 79 (1994) 268-290. [ pdf ]

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