MathGL is a library for making high-quality scientific graphics under Linux and Windows, fast data plotting and handling of large data arrays, working in window and console modes, and easily embedding into other programs. It has more than 40 general types of graphics for 1d, 2d, and 3d data arrays. It can export graphics to raster and vector (EPS or SVG) formats. It has an OpenGL interface and can be used from console programs. It has functions for data handling and MGL language scripting for simplification of data plotting. It has several types of transparency and smoothed lightning, vector fonts and TeX-like formula drawing, an arbitrary curvilinear coordinate system, and many other useful things.
The ATLAS (Automatically Tuned Linear Algebra Software) project is an ongoing research effort focusing on applying empirical techniques in order to provide portable performance. It provides C and Fortran77 interfaces to a portably efficient BLAS implementation, as well as a few routines from LAPACK.
FFTW is a fast C FFT library. It includes complex, real, symmetric, multidimensional, and parallel transforms, and can handle arbitrary array sizes efficiently.It is typically faster than other freely available FFT implementations, and is even competitive with vendor-tuned libraries (benchmarks are available at the homepage). To achieve this performance, it uses novel code generation and runtime self optimization techniques (along with many other tricks).
Calc is arbitrary precision arithmetic system that uses a C-like language. It's useful as a calculator, an algorithm prototype, and as a mathematical research tool. More importantly, calc provides a machine-independent means of computation. Calc comes with a rich set of builtin mathematical and programmatic functions.
SLEEF (SIMD Library for Evaluating Elementary Functions) is a library that facilitates programming with SIMD instructions. It implements the trigonometric functions, inverse trigonometric functions, exponential and logarithmic functions in double precision without table look-ups, scattering from, or gathering into SIMD registers, or conditional branches. This library also includes some functions for evaluation in single precision.
LAPACK is a linear algebra library, based on LINPACK and EISPACK, designed to provide routines for handling simultaneous equations and matrix algebra efficiently, particularly on shared memory vector processors, parallel processors, and clusters. The code is written in Fortran, and requires the BLAS (Basic Linear Algebra Subprograms) library.
alph implements and analyzes historical and traditional ciphers and codes, such as polyalphabetic, substitutional, and mixed employing human-reconstructable algorithms. It provides a pipe filter interface in order to encrypt and decrypt block text to achieve transparency. The program is meant to be used in conjunction with external programs that transfer data, resulting in transparent encryption or decryption of information. The program can thus be used as a mail filter, IRC filter, IM filter, and so on.
levmar is a robust and efficient C/C++ implementation of the Levenberg - Marquardt (LM) optimization algorithm. LM solves the non-linear least squares problem, i.e. fitting a set of m observations with a model that is non-linear in n unknown parameters (m>=n). levmar includes double and single precision LM variants, both with analytic and finite difference approximated Jacobians. It also has some support for constrained non-linear least squares, allowing linear equation and box constraints to be imposed. For problems with sparse Jacobians, the sparseLM project might be more efficient.