PReconditioned Iterative MultiMethod Eigensolver for solving symmetric/Hermitian eigenvalue problems and singular value problems
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README.rst

PRIMME: PReconditioned Iterative MultiMethod Eigensolver

PRIMME, pronounced as prime, computes a few eigenvalues and their corresponding eigenvectors of a real symmetric or complex Hermitian matrix. It can also compute singular values and vectors of a square or rectangular matrix. It can find largest, smallest, or interior singular/eigenvalues and can use preconditioning to accelerate convergence. It is especially optimized for large, difficult problems, and can be a useful tool for both non-experts and experts. PRIMME is written in C99, but complete interfaces are provided for Fortran 77, MATLAB, Python, and R.

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'

Optionally for building some of the external interfaces just do:

make matlab
make octave
make python
make R_install

Alternatively to install the development version of PRIMME on R:

library(devtools)
install_github("primme/primme", subdir="R")

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 complex double, float and float double. See documentation in readme.txt file and in doc directory; also it is online at doc. The examples directory is plenty of self-contained examples in C, C++ and F77, and some of them using PETSc.

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, 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.

License Information

PRIMME is licensed under the 3-clause license BSD. Python and Matlab interfaces have BSD-compatible licenses. Source code under tests is compatible with LGPLv3. Details can be taken from COPYING.txt.

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.