PRIMME: PReconditioned Iterative MultiMethod Eigensolver

PRIMME, pronounced as prime, is a high-performance library for computing a few eigenvalues/eigenvectors, and singular values/vectors. PRIMME is especially optimized for large, difficult problems. Real symmetric and complex Hermitian problems, standard A x = \lambda x and generalized A x = \lambda B x, are supported. Besides, standard eigenvalue problems with a normal matrix are supported. It can find largest, smallest, or interior singular/eigenvalues, and can use preconditioning to accelerate convergence. PRIMME is written in C99, but complete interfaces are provided for Fortran, MATLAB, Python, and R.

Making and Linking

To generate the static and the shared library type:

make lib     #  builds lib/libprimme.a
make solib   #  builds lib/libprimme.so (or lib/libprimme.dylib)

The shared library is generated with the action solib instead. Usual flags are supported

CC, compiler program such as gcc, clang or icc
CFLAGS, compiler options such as -g or -O3
CUDADIR, directory of CUDA installation (optional)
MAGMADIR, directory of MAGMA installation (optional)
PRIMME_WITH_HALF, activates support for half precision if it set to yes; compiler supporting __fp16 is required, e.g., clang.

The flags can be indicated by customizing Make_flags or directly introduced at the command line:

make lib CC=clang CFLAGS='-O3'

For building the external interfaces just do:

make matlab       # Set MATLAB=/path/Matlab/bin/matlab MEX=/path/Matlab/bin/mex if needed
make matlab-cuda  # Requires to set CUDADIR and MAGMADIR
make octave
make python
make R_install

We provide packages of the released version for R (see R PRIMME):

install.packages('PRIMME')

and Python (see Python primme):

pip install numpy   # if numpy is not installed yet
pip install scipy   # if scipy is not installed yet
pip install future  # if using python 2
conda install mkl-devel # if using Anaconda Python distribution
pip install primme

C Library Interface

To compute few eigenvalues and eigenvectors from a real symmetric matrix call:

int dprimme(double *evals, double *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.

To compute few singular values and vectors from a matrix call:

int dprimme_svds(double *svals, double *svecs, double *resNorms,
            primme_svds_params *primme_svds);

The call arguments are:

svals, array to return the found singular values;
svecs, array to return the found vectors;
resNorms, array to return the residual norms of the triplets; and
primme_svds, structure that specify the matrix problem, which values are wanted and several method options.

There are available versions for half and float and complex variants. See documentation in readme.txt file and in doc directory; also it is online at doc. The examples directory has several self-contained examples in C, C++ and F77, some of them using PETSc and MAGMA.

Citing this code

Please cite (bibtex):

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.
L. Wu, E. Romero and A. Stathopoulos, PRIMME_SVDS: A High-Performance Preconditioned SVD Solver for Accurate Large-Scale Computations, SIAM J. Sci. Comput., Vol. 39, No. 5, (2017), S248--S271.

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.
L. Wu and A. Stathopoulos, A Preconditioned Hybrid SVD Method for Computing Accurately Singular Triplets of Large Matrices, SIAM J. Sci. Comput. 37-5(2015), pp. S365-S388.

National Science Foundation through grants CCF 1218349, ACI SI2-SSE 1440700, and NSCI 1835821
Department of Energy through grant Exascale Computing Project 17-SC-20-SC