SLEPc
Encyclopedia
SLEPc is a software library for the parallel computation of eigenvalues and eigenvectors of large, sparse matrices. It can be seen as a module of PETSc
that provides solvers for different types of eigenproblems, including linear (standard and generalized) and quadratic, as well as the SVD
. It uses the MPI
standard for parallelization. Both real and complex arithmetic are supported, with single and double precision.
When using SLEPc, the application programmer can use any of the PETSc's data structures and solvers. Other PETSc features are incorporated into SLEPc as well, such as command-line option setting, automatic profiling, error checking, portability to virtually all computing platforms, etc.
ST encapsulates spectral transformations and other preconditioners for eigenvalue problems.
SVD contains solvers for the singular value decomposition
.
QEP is intended for the quadratic eigenvalue problem.
Portable, Extensible Toolkit for Scientific Computation
The Portable, Extensible Toolkit for Scientific Computation , is a suite of data structures and routines for the scalable solution of scientific applications modeled by partial differential equations. It employs the Message Passing Interface standard for all message-passing communication...
that provides solvers for different types of eigenproblems, including linear (standard and generalized) and quadratic, as well as the SVD
Singular value decomposition
In linear algebra, the singular value decomposition is a factorization of a real or complex matrix, with many useful applications in signal processing and statistics....
. It uses the MPI
Message Passing Interface
Message Passing Interface is a standardized and portable message-passing system designed by a group of researchers from academia and industry to function on a wide variety of parallel computers...
standard for parallelization. Both real and complex arithmetic are supported, with single and double precision.
When using SLEPc, the application programmer can use any of the PETSc's data structures and solvers. Other PETSc features are incorporated into SLEPc as well, such as command-line option setting, automatic profiling, error checking, portability to virtually all computing platforms, etc.
Components
EPS provides iterative algorithms for linear eigenvalue problems.- Krylov methods such as Krylov-Schur, ArnoldiArnoldi iterationIn numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of iterative methods. Arnoldi finds the eigenvalues of general matrices; an analogous method for Hermitian matrices is the Lanczos iteration. The Arnoldi iteration was invented by W. E...
and LanczosLanczos algorithmThe Lanczos algorithm is an iterative algorithm invented by Cornelius Lanczos that is an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix or the singular value decomposition of a rectangular matrix. It is particularly useful for finding decompositions of very...
. - Davidson methods such as Generalized Davidson and Jacobi-Davidson.
- Interface to some external eigensolvers, such as ARPACKARPACKARPACK, the ARnoldi PACKage, is a numericalsoftware library written in FORTRAN 77 for solving large scale eigenvalue problems.The package is designed to compute a few eigenvalues and corresponding...
and BLOPEXBLOPEXThe Block Locally Optimal Preconditioned Eigenvalue Xolvers is a suite of routines for the scalable solution of eigenvalue problems. Its object-oriented design allows easy portability. Currently available built-in interfaces are Hypre, PETSc, MATLAB, GNU Octave, and a serial stand-alone version...
. - Customization options include: number of wanted eigenvalues, tolerance, size of the employed subspaces, part of the spectrum of interest.
ST encapsulates spectral transformations and other preconditioners for eigenvalue problems.
- Shift-and-invert, Cayley, and folding spectral transformations.
- Support for preconditioned eigensolvers (such as Jacobi-Davidson) by using the preconditioners provided by PETSc.
SVD contains solvers for the singular value decomposition
Singular value decomposition
In linear algebra, the singular value decomposition is a factorization of a real or complex matrix, with many useful applications in signal processing and statistics....
.
- Solvers based on the cross-product matrix or the cyclic matrix, that rely on EPS solvers.
- Specific solvers based on bidiagonalizationBidiagonalizationBidiagonalization is one of unitary matrix decompositions such that U* A V = B, where U and V are unitary matrices; * denotes Hermitian transpose; and B is upper bidiagonal...
such as Golub-Kahan-Lanczos and a thick-restarted variant.
QEP is intended for the quadratic eigenvalue problem.
- Solvers based on linearization, that rely on EPS solvers.
- Specific solvers such Q-Arnoldi.
See also
- Portable, Extensible Toolkit for Scientific ComputationPortable, Extensible Toolkit for Scientific ComputationThe Portable, Extensible Toolkit for Scientific Computation , is a suite of data structures and routines for the scalable solution of scientific applications modeled by partial differential equations. It employs the Message Passing Interface standard for all message-passing communication...
(PETSc) - List of numerical libraries