ARPACK, the ARnoldi PACKage, is a
numerical
software library
In computing, a library is a collection of resources that can be leveraged during software development to implement a computer program. Commonly, a library consists of executable code such as compiled functions and classes, or a library can ...
written in
FORTRAN 77 for solving large scale
eigenvalue
In linear algebra, an eigenvector ( ) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a ...
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 (: matrices or matrixes) or MATRIX may refer to:
Science and mathematics
* Matrix (mathematics), a rectangular array of numbers, symbols or expressions
* Matrix (logic), part of a formula in prenex normal form
* Matrix (biology), the ...
, 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, fast Fourier ...
,
Mathematica
Wolfram (previously known as Mathematica and Wolfram Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network ...
,
Julia_(programming_language)
Julia is a high-level programming language, high-level, general-purpose programming language, general-purpose dynamic programming language, dynamic programming language, designed to be fast and productive, for e.g. data science, artificial intel ...
,
GNU Octave
GNU Octave is a scientific programming language for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly ...
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, implementat ...
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, a different matrix-free method for symmetric or Hermitian matrices only, implemented in C in BLOPEX, ported to hypre and SLEPc, in C++ in Anasazi ( Trilinos), in Python 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, fast Fourier ...
, in Julia language, 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, implementat ...
, GNU Octave
GNU Octave is a scientific programming language for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly ...
, as well as in Matrix Algebra on GPU and Multicore Architectures (MAGMA) and NVIDIA
Nvidia Corporation ( ) is an American multinational corporation and technology company headquartered in Santa Clara, California, and incorporated in Delaware. Founded in 1993 by Jensen Huang (president and CEO), Chris Malachowsky, and Curti ...
CUDA
In computing, CUDA (Compute Unified Device Architecture) is a proprietary parallel computing platform and application programming interface (API) that allows software to use certain types of graphics processing units (GPUs) for accelerated gene ...
.
* LAPACK, 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 simul ...
, GNU Octave
GNU Octave is a scientific programming language for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly ...
, Debian
Debian () is a free and open-source software, free and open source Linux distribution, developed by the Debian Project, which was established by Ian Murdock in August 1993. Debian is one of the oldest operating systems based on the Linux kerne ...
, and others.
{{DEFAULTSORT:Arpack
Fortran libraries
Free software programmed in Fortran
Numerical software
Software using the BSD license