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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
Preconditioning and finding largest, smallest or interior
eigenvalues is supported.
PRIMME is a multimethod eigensolver.
Based on the Davidson/Jacobi-Davidson main iteration, it can transform to most
known preconditioned eigensolvers by the appropriate choice of parameters.
Preset methods are also provided, including the nearly optimal eigensolvers
GD+k and JDQMR (see [1, 2]).
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
PRIMME has many features such as blocking, locking,
locally optimal restarting, and a host of others that make it
extremely robust and efficient.
Full interface to MATLAB and Fortran77 is provided.
The software has been tested extensively on a variety of architectures,
systems, and applications.
Changes in Version 1.2.1
MATLAB interface to full PRIMME functionality.
Support for BLAS/LAPACK with 64bits integers (-DPRIMME_BLASINT_SIZE=64).
Simplified configuration of Make_flags and Make_links (removed TOP variable
and replaced defines NUM_SUM and NUM_IBM by F77UNDERSCORE).
Replaced directories DTEST and ZTEST by TEST that has:
(a) driver.c: read matrices in MatrixMarket format and PETSc binary and call PRIMME with the parameters specified in a file;
support complex arithmetic and MPI and can use PETSc preconditioners.
(b) ex*.c and ex*.f: small, didactic examples of usage in C and Fortran and in parallel (with PETSc).
Fixed a few minor bugs and improved documentation (especially the F77 interface).
Using Sphinx to manage documentation.
Changes in Version 1.2
Version 1.2 implements performance improvements and bug fixes that have been
reported over the years by PRIMME's users, who the authors are indebted to.
A Fortran compiler is no longer required for building the PRIMME library.
Fortran programs can still be linked to PRIMME's F77 interface.
Fixed some uncommon issues with the F77 interface
PRIMME can be called now multiple times from the same program.
Performance improvements in the QMR inner solver, especially for
Fixed a couple of bugs with the locking functionality.
In certain extreme cases where all eigenvalues of a matrix were needed.
The order of selecting interior eigenvalues.
The above fixes have improved robustness and performance.
PRIMME now assigns unique random seeds per parallel process
for up to 4096^3 (140 trillion processes)
For the DYNAMIC method, fixed issues with initialization and
synchronization decisions across multiple processes.
Fixed uncommon library interface bugs, coordinated better the
set_method() and the user setting of parameters, and improved
the interface in the sample programs and makefiles
Version 1.2 (Dec 24, 2014)
Version 1.1 (October 2006)
Besides comments left on GitHub, consider contacting the developers with questions, bug reports, or requests.
Contact: 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 .
The work has been supported by a number of grants from the National Science Foundation.
Versions 1.2 and 1.2.1 were supported by NSF CCF 1218349 and ACI SI2-SSE 1440700.
James R. McCombs, Eloy Romero, Andreas Stathopoulos, Lingfei Wu