ARPACK, the ARnoldi PACKage, is a
numerical
software library
In computer science, a library is a collection of non-volatile resources used by computer programs, often for software development. These may include configuration data, documentation, help data, message templates, pre-written code and subr ...
written in
FORTRAN 77 for solving large scale
eigenvalue
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...
problems
in the
matrix-free fashion.
The package is designed to compute a few eigenvalues and corresponding
eigenvectors of large
sparse or structured
matrices
Matrix most commonly refers to:
* ''The Matrix'' (franchise), an American media franchise
** ''The Matrix'', a 1999 science-fiction action film
** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...
, using the
Implicitly Restarted Arnoldi Method (IRAM)
or, in the case of symmetric matrices, the corresponding variant of the
Lanczos algorithm
The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power iteration, power methods to find the m "most useful" (tending towards extreme highest/lowest) eigenvalues and eigenvectors of an n \times n ...
.
It is used by many popular numerical computing environments such as
SciPy
SciPy (pronounced "sigh pie") is a free and open-source Python library used for scientific computing and technical computing.
SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal ...
,
Mathematica
Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimizat ...
,
GNU Octave
GNU Octave is a high-level programming language primarily intended for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a langu ...
and
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation ...
to provide this functionality.
Reverse Communication Interface
A powerful
matrix-free feature of ARPACK is its ability to use any matrix storage format. This is possible because it doesn't operate on the matrices directly, but instead when a matrix operation is required it returns control to the calling program with a flag indicating what operation is required. The calling program must then perform the operation and call the ARPACK routine again to continue. The operations are typically matrix-vector products, and solving linear systems.
Fork
Due to stalled upstream development, ARPAŠ”K has been forked into ARPACK-NG,
ARPACK-NG
/ref> as a form of a collaborative effort of the various groups that rely on ARPACK.
See also
* LOBPCG Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free method for finding the largest (or smallest) eigenvalues and the corresponding eigenvectors of a symmetric generalized eigenvalue problem
:A x= \lambda B x,
for a g ...
, a different matrix-free method for symmetric or Hermitian matrices only, implemented in C in BLOPEX Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free method for finding the largest (or smallest) eigenvalues and the corresponding eigenvectors of a symmetric generalized eigenvalue problem
:A x= \lambda B x,
for a g ...
, ported to hypre and SLEPc
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 gen ...
, in C++
C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded significan ...
in Anasazi (Trilinos
Trilinos is a collection of open-source software libraries, called ''packages'', intended to be used as building blocks for the development of scientific applications. The word "Trilinos" is Greek and conveys the idea of "a string of pearls", sugg ...
), in Python
Python may refer to:
Snakes
* Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia
** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia
* Python (mythology), a mythical serpent
Computing
* Python (pro ...
in scipy
SciPy (pronounced "sigh pie") is a free and open-source Python library used for scientific computing and technical computing.
SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal ...
, in Julia language
Julia is a high-level, dynamic programming language. Its features are well suited for numerical analysis and computational science.
Distinctive aspects of Julia's design include a type system with parametric polymorphism in a dynamic programm ...
, MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation ...
, GNU Octave
GNU Octave is a high-level programming language primarily intended for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a langu ...
, as well as in Matrix Algebra on GPU and Multicore Architectures (MAGMA) and NVIDIA
Nvidia CorporationOfficially written as NVIDIA and stylized in its logo as VIDIA with the lowercase "n" the same height as the uppercase "VIDIA"; formerly stylized as VIDIA with a large italicized lowercase "n" on products from the mid 1990s to ...
CUDA
CUDA (or Compute Unified Device Architecture) is a parallel computing platform and application programming interface (API) that allows software to use certain types of graphics processing units (GPUs) for general purpose processing, an approach ca ...
.
* LAPACK
LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It also ...
, software library based on matrix transformations for dense matrices.
References
External links
* at Rice University
arpack-ng fork
joint effort between Scilab
Scilab is a free and open-source, cross-platform numerical computational package and a high-level, numerically oriented programming language. It can be used for signal processing, statistical analysis, image enhancement, fluid dynamics simulat ...
, GNU Octave
GNU Octave is a high-level programming language primarily intended for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a langu ...
, Debian
Debian (), also known as Debian GNU/Linux, is a Linux distribution composed of free and open-source software, developed by the community-supported Debian Project, which was established by Ian Murdock on August 16, 1993. The first version of D ...
, and others.
{{DEFAULTSORT:Arpack
Fortran libraries
Free software programmed in Fortran
Numerical software
Software using the BSD license