PRIMME: PReconditioned Iterative MultiMethod Eigensolver

PRIMME, pronounced as prime, finds a number of eigenvalues and their corresponding eigenvectors of a real symmetric, or complex hermitian matrix A. Largest, smallest and interior eigenvalues are supported. Preconditioning can be used to accelerate convergence. PRIMME is written in C, but complete interfaces are provided for Fortran 77 and MATLAB.

Making and Linking

Make_flags has the flags and compilers used to make libprimme.a:

• CC, compiler program such as gcc, clang or icc.
• CFLAGS, compiler options such as -g or -O3.

After customizing Make_flags, type this to generate libprimme.a:

make lib

Making can be also done at the command line:

make lib CC=clang CFLAGS='-O3'

C Library Interface

To solve real symmetric standard eigenproblems call:

int dprimme(double *evals, double *evecs, double *resNorms,
            primme_params *primme);

To solve Hermitian standard eigenproblems call:

int zprimme(double *evals, Complex_Z *evecs, double *resNorms,
            primme_params *primme);

The call arguments are:

• evals, array to return the found eigenvalues;
• evecs, array to return the found eigenvectors;
• resNorms, array to return the residual norms of the found eigenpairs; and
• primme, structure that specify the matrix problem, which eigenvalues are wanted and several method options.

See documentation in readme.txt file and in doc directory.

Citing this code

Please cite:

• A. Stathopoulos and J. 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.

More information on the algorithms and research that led to this software can be found in the rest of the papers. The work has been supported by a number of grants from the National Science Foundation.

• 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.
• 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.
• 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.
• A. Stathopoulos, Locking issues for finding a large number of eigenvectors of hermitian matrices, Tech Report: WM-CS-2005-03, July, 2005.

License Information

PRIMME is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version.

PRIMME is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA

Contact Information

For reporting bugs or questions about functionality contact Andreas Stathopoulos by email, andreas at cs.wm.edu. See further information in the webpage http://www.cs.wm.edu/~andreas/software .