A list of useful numerical libraries

A comprehensive list of Numerical libraries ......... for daily use

A library used is a hundred bugs eliminated

Multi-language

• ALGLIB is an open source numerical analysis library which may be used from C++, C#, FreePascal, Delphi, VBA.
• IMSL Numerical Libraries are libraries of numerical analysis functionality implemented in standard programming languages like C, Java, C# .NET, Fortran, and Python.
• The NAG Library is a collection of mathematical and statistical routines for multiple programming languages (C, C++, Fortran, Visual Basic, Java and C#) and packages (MATLAB, Excel, R, LabVIEW).

C

• BLOPEX (Block Locally Optimal Preconditioned Eigenvalue Xolvers) is an open-source library for the scalable (parallel) solution of eigenvalue problems. Its object-oriented design allows easy portability.
• FFTW (Fastest Fourier Transform in the West) is a software library for computing Fourier and related transforms.
• GNU Scientific Library, a popular, free numerical analysis library implemented in C.
• GNU Multi-Precision Library is a library for doing arbitrary precision arithmetic.
• hypre (High Performance Preconditioners) is an open-source library of routines for scalable (parallel) solution of linear systems and preconditioning.
• IMSL Numerical Libraries are cross-platform libraries containing a comprehensive set of mathematical and statistical functions that can be embedded in a users application.
• LabWindows/CVI is an ANSI C IDE that includes built-in libraries for analysis of raw measurement data, signal generation, windowing, filter functions, signal processing, linear algebra, array and complex operations, curve fitting and statistics.
• Lis is a scalable parallel library for solving systems of linear equations and standard eigenvalue problems with real sparse matrices using iterative methods.
• Portable, Extensible Toolkit for Scientific Computation (PETSc), is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations.
• SLEPc Scalable Library for Eigenvalue Problem Computations is a PETSc-based open-source library for the scalable (parallel) solution of eigenvalue problems.
• Trilinos, an effort to develop scalable (parallel) solver algorithms and libraries within an object-oriented software framework for the solution of large-scale, complex multi-physics engineering and scientific applications. A unique design feature of Trilinos is its focus on packages.

C++

• Armadillo is a C++ linear algebra library (matrix and vector maths), aiming towards a good balance between speed and ease of use. It employs template classes, and has optional links to BLAS and LAPACK.
• Blitz++ is a high-performance vector mathematics library written in C++.
• Eigen is a a vector mathematics library wth performance comparable with Intel's Math Kernel Library
• Hermes Project: C++/Python library for rapid prototyping of space- and space-time adaptive hp-FEM solvers.
• IML++ is a C++ library for solving linear systems of equations, capable of dealing with dense, sparse, and distributed matrices.
• IT++ is a C++ library for linear algebra (matrices and vectors), signal processing and communications. Functionality similar to MATLAB and Octave.
• LAPACK++, a C++ wrapper library for LAPACK and BLAS
• LinBox is a C++ template library for doing exact computational linear algebra.
• MTL4 is a generic C++ template library providing sparse and dense BLAS functionality. MTL4 establishes an intuitive interface (similar to MATLAB) and broad applicability thanks to Generic programming.
• NTL is a C++ library for number theory.
• GNU Scientific Library (GSL) is a numerical library for C and C++ programmers. It is free software under the GNU General Public License. The library provides a wide range of mathematical routines such as random number generators, etc. There are over 1000 functions in total with an extensive test suite.

.NET Framework languages C#, F# and VB.NET

• ILNumerics.Net high performance, typesafe numerical array classes and functions for general math, FFT and linear algebra, aims .NET/mono, 32&64 bit, script-like syntax in C#, 2D & 3D plot controls, efficient memory management
• IMSL Numerical Libraries for .NET is a set of mathematical, statistical, data mining, financial and charting classes written in C#.
• Measurement Studio is an integrated suite UI controls and class libraries for use in developing test and measurement applications. The analysis class libraries provide various digital signal processing, signal filtering, signal generation, peak detection, and other general mathematical functionality.
• NMath by CenterSpace Software: numerical component libraries for the .NET platform, including signal processing (FFT) classes, a linear algebra (LAPACK & BLAS) framework, and a statistics package.
• suanshu.net by Numerical Method Inc.: is a large collection of numerical algorithms including linear algebra, (advanced) optimization, interpolation, Markov model, principal component analysis, time series analysis, hypothesis testing, regressions, statistics, ordinary and partial differential equation solvers, and suanshu.
• NLinear is a generic linear algebra toolkit in C# compatible with Silverlight.

Fortran

• BLAS (Basic Linear Algebra Subprograms) is a de facto application programming interface standard for publishing libraries to perform basic linear algebra operations such as vector and matrix multiplication.
• CERNLIB is a collection of FORTRAN 77 libraries and modules.
• EISPACK is a software library for numerical computation of eigenvalues and eigenvectors of matrices, written in FORTRAN. It contains subroutines for calculating the eigenvalues of nine classes of matrices: complex general, complex Hermitian, real general, real symmetric, real symmetric banded, real symmetric tridiagonal, special real tridiagonal, generalized real, and generalized real symmetric matices.
• IMSL Numerical Libraries are cross-platform libraries containing a comprehensive set of mathematical and statistical functions that can be embedded in a users application.
• Harwell Subroutine Library is a collection of Fortran 77 and 95 codes that address core problems in numerical analysis.
• LAPACK, the Linear Algebra PACKage, is a software library for numerical computing originally written in FORTRAN 77 and now written in Fortran 90.
• LINPACK is a software library for performing numerical linear algebra on digital computers. It was written in Fortran by Jack Dongarra, Jim Bunch, Cleve Moler, and Pete Stewart, and was intended for use onsupercomputers in the 1970s and early 1980s. It has been largely superseded by LAPACK, which will run more efficiently on modern architectures.
• Lis is a scalable parallel library for solving systems of linear equations and standard eigenvalue problems with real sparse matrices using iterative methods.
• MINPACK is a library of FORTRAN subroutines for the solving of systems of nonlinear equations, or the least squares minimization of the residual of a set of linear or nonlinear equations.
• NOVAS is a software library for astrometry-related numerical computations. Both Fortran and C versions are available.
• Netlib is a repository of scientific computing software which contains a large number of separate programs and libraries including BLAS, EISPACK, LAPACK and others.
• Portable, Extensible Toolkit for Scientific Computation (PETSc), is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations.
• QUADPACK is a FORTRAN 77 library for numerical integration of one-dimensional functions
• SLATEC is a FORTRAN 77 library of over 1400 general purpose mathematical and statistical routines.
• SOFA is a collection of subroutines that implement official IAU algorithms for astronomical computations. Both Fortran and C versions are available.
• SPARSKIT is a tool package for working with sparse matrices.
• ARPACK is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems.
• SHTOOLS is an archive of fortran 95 based software that can be used to perform (among others) spherical harmonic transforms and reconstructions, rotations of spherical harmonic coefficients, and multitaper spectral analyses on the sphere.

Source ::
http://en.wikipedia.org/wiki/List_of_numerical_libraries