Debian Science Mathematics-dev packages

Armadillo is a streamlined C++ linear algebra library (matrix maths) aiming towards a good balance between speed and ease of use. Integer, floating point and complex numbers are supported, as well as a subset of trigonometric and statistics functions. Optional integration with LAPACK and ATLAS libraries is also provided.

This package has the development libraries and headers for Armadillo.

ARPACK software is capable of solving large scale symmetric, nonsymmetric, and generalized eigenproblems from significant application areas. The software is designed to compute a few (k) eigenvalues with user specified features such as those of largest real part or largest magnitude. Storage requirements are on the order of n*k locations. No auxiliary storage is required. A set of Schur basis vectors for the desired k-dimensional eigen-space is computed which is numerically orthogonal to working precision. Numerically accurate eigenvectors are available on request.

This package contains the static libraries and the documentation for development with libarpack and libparpack (including examples).

ATLAS is an approach for the automatic generation and optimization of numerical software. Currently ATLAS supplies optimized versions for the complete set of linear algebra kernels known as the Basic Linear Algebra Subroutines (BLAS), and a subset of the linear algebra routines in the LAPACK library.

This package includes the static libraries and symbolic links needed for program development.

This package is a binary incompatible upgrade to the blas-dev package. Several minor changes to the C interface have been incorporated.

BLAS (Basic Linear Algebra Subroutines) is a set of efficient routines for most of the basic vector and matrix operations. They are widely used as the basis for other high quality linear algebra software, for example lapack and linpack. This implementation is the Fortran 77 reference implementation found at netlib.

This package contains a static version of the library.

Blitz++ offers a high level of abstraction, but performance which rivals Fortran. The current version supports arrays and vectors.

This package contains the static library and header files for compiling programs with blitz++.

GLPK (GNU Linear Programming Kit) is intended for solving large-scale linear programming (LP), mixed integer programming (MIP), and other related problems. It is a set of routines written in ANSI C and organized in the form of a callable library.

This package contains static library, headers, and the development manpage for libvc.

The GNU Scientific Library (GSL) is a collection of routines for numerical analysis. The routines are written from scratch by the GSL team in C, and present a modern API for C programmers, while allowing wrappers to be written for very high level languages.

This package contains the header files, static libraries and symbolic links that developers using GNU GSL will need.

JAMA/C++ was adapted for The Template Numerical Toolkit (TNT) from JAMA, a Java Matrix Library, developed jointly by the Mathworks and NIST. See http://math.nist.gov/javanumerics/jama for more information.

TNT is a collection of interfaces and reference implementations of numerical objects useful for scientific computing in C++. The toolkit defines interfaces for basic data structures, such as multidimensional arrays and sparse matrices, commonly used in numerical applications. The goal of this package is to provide reusable software components that address many of the portability and maintenance problems with C++ codes.

TNT provides a distinction between interfaces and implementations of TNT components. For example, there is a TNT interface for two-dimensional arrays which describes how individual elements are accessed and how certain information, such as the array dimensions, can be used in algorithms; however, there can be several implementations of such an interface: one that uses expression templates, or one that uses BLAS kernels, or another that is instrumented to provide debugging information. By specifying only the interface, applications codes may utilize such algorithms, while giving library developers the greatest flexibility in employing optimization or portability strategies.

 Homepage: [http://math.nist.gov/tnt/](http://math.nist.gov/tnt/)

This package is a binary incompatible upgrade to the lapack-dev package. The (minor) incompatibilities are entirely due to changes in the blas library, against which this library is linked. Please see the documentation for the refblas3 package for details.

LAPACK version 3.X is a comprehensive FORTRAN library that does linear algebra operations including matrix inversions, least squared solutions to linear sets of equations, eigenvector analysis, singular value decomposition, etc. It is a very comprehensive and reputable package that has found extensive use in the scientific community.

Lip interpolates scattered multivariate data with a Lipschitz function.

Methods of interpolation of multivariate scattered data are scarce. The programming library Lip implements a new method by G. Beliakov, which relies on building reliable lower and upper approximations of Lipschitz functions. If we assume that the function that we want to interpolate is Lipschitz-continuous, we can provide tight bounds on its values at any point, in the worse case scenario. Thus we obtain the interpolant, which approximates the unknown Lipschitz function f best in the worst case scenario. This translates into reliable learning of f, something that other methods cannot do (the error of approximation of most other methods can be infinitely large, depending on what f generated the data).

Lipschitz condition implies that the rate of change of the function is bounded:

|f(x)-f(y)|<M||x-y||.

It is easily interpreted as the largest slope of the function f. f needs not be differentiable.

The interpolant based on the Lipschitz properties of the function is piecewise linear, it possesses many useful properties, and it is shown that it is the best possible approximation to f in the worst case scenario. The value of the interpolant depends on the data points in the immediate neigbourhood of the point in question, and in this sense, the method is similar to the natural neighbour interpolation.

There are two methods of construction and evaluation of the interpolant. The explicit method processes all data points to find the neighbours of the point in question. It does not require any preprocessing, but the evaluation of the interpolant has linear complexity O(K) in terms of the number of data.

"Fast" method requires substantial preprocessing in the case of more than 3-4 variables, but then it provides O(log K) evaluation time, and thus is suitable for very large data sets (K of order of 500000) and modest dimension (n=1-4). For larger dimension, explicit method becomes practically more efficient. The class library Lip implements both fast and explicit methods.

GNU libmatheval is library comprising several procedures that makes possible to create in-memory tree representation of mathematical functions over single or multiple variables and later use this representation to evaluate function for specified variable values, to create corresponding tree for function derivative over specified variable or to print textual representation of in-memory tree to specified string. The library supports arbitrary variable names in expressions, decimal constants, basic unary and binary operators and elementary mathematical functions. This package contains the header files and development libraries.

matio is an ISO C library (with a limited Fortran 90 interface) for reading and writing Matlab MAT files.

This package contains the development files needed to compile software to use the libmatio API.

MEI stands for Mathematical Expression Interpreter. It is intended to provide interpretation of mathematical formula in a string. It is destined to be used by scientific codes (Computational Fluid Dynamics).

This package contains the development files needed to compile software to use the libmei API.

The libMesh library is a C++ framework for the numerical simulation of partial differential equations on serial and parallel platforms. Development began in March 2002 with the intent of providing a friendly interface to a number of high-quality software packages that are publicly available. Currently the library supports 1D, 2D, and 3D steady and transient finite element and finite volume simulations. PETSc is currently used for the solution of linear systems on both serial and parallel platforms.

This package contains the C++ header files and shared library links (only needed for developing programs with libmesh).

NETGEN is an automatic 3d tetrahedral mesh generator. It accepts input from constructive solid geometry (CSG) or boundary representation (BRep) from STL file format. The connection to a geometry kernel allows the handling of IGES and STEP files. NETGEN contains modules for mesh optimization and hierarchical mesh refinement.

This package contains the static libraries and header files.

Newmat library is intended for scientists and engineers who need to manipulate a variety of types of matrices using standard matrix operations. Emphasis is on the kind of operations needed in statistical calculations such as least squares, linear equation solve and eigenvalues.

Newmat supports matrix types: Matrix (rectangular matrix); UpperTriangularMatrix; LowerTriangularMatrix; DiagonalMatrix; SymmetricMatrix; BandMatrix; UpperBandMatrix; LowerBandMatrix; SymmetricBandMatrix; IdentityMatrix; RowVector; ColumnVector.

Only one element type (float or double) is supported (default is double).

The library includes the operations , +, -, =, +=, -=, Kronecker product, Schur product, concatenation, inverse, transpose, conversion between types, submatrix, determinant, Cholesky decomposition, QR triangularisation, singular value decomposition, eigenvalues of a symmetric matrix, sorting, fast Fourier and trig. transforms and printing.

libnewmat-dev contains static libraries, headers, and some documentation.

RanLip generates random variates with an arbitrary multivariate Lipschitz density.

While generation of random numbers from a variety of distributions is implemented in many packages (like GSL library http://www.gnu.org/software/gsl/ and UNURAN library http://statistik.wu-wien.ac.at/unuran/), generation of random variate with an arbitrary distribution, especially in the multivariate case, is a very challenging task. RanLip is a method of generation of random variates with arbitrary Lipschitz-continuous densities, which works in the univariate and multivariate cases, if the dimension is not very large (say 3-10 variables).

Lipschitz condition implies that the rate of change of the function (in this case, probability density p(x)) is bounded:

|p(x)-p(y)|<M||x-y||.

From this condition, we can build an overestimate of the density, so called hat function h(x)>=p(x), using a number of values of p(x) at some points. The more values we use, the better is the hat function. The method of acceptance/rejection then works as follows: generatea random variate X with density h(x); generate an independent uniform on (0,1) random number Z; if p(X)<=Z h(X), then return X, otherwise repeat all the above steps.

RanLip constructs a piecewise constant hat function of the required density p(x) by subdividing the domain of p (an n-dimensional rectangle) into many smaller rectangles, and computes the upper bound on p(x) within each of these rectangles, and uses this upper bound as the value of the hat function.

STXXL provides an STL replacement using an abstraction layer to storage devices to allow for the optimal layout of data structures. This allows for multi-terabyte datasets to be held and manipulated in standard C++ data structures, whilst abstracting the complexity of managing this behaviour efficiently. STXXL utilises multi-disk I/O to speed up I/O bound calculations. STXXL has been developed at the University of Karlsruhe.

Development libraries for STXXL, required for building programs that utilise the STXXL library

SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations on high performance machines. The library is written in C and is callable from either C or Fortran. The library routines will perform an LU decomposition with partial pivoting and triangular system solves through forward and back substitution. The LU factorization routines can handle non-square matrices but the triangular solves are performed only for square matrices. The matrix columns may be preordered (before factorization) either through library or user supplied routines. This preordering for sparsity is completely separate from the factorization. Working precision iterative refinement subroutines are provided for improved backward stability. Routines are also provided to equilibrate the system, estimate the condition number, calculate the relative backward error, and estimate error bounds for the refined solutions.

The Template Numerical Toolkit (TNT) is a collection of interfaces and reference implementations of numerical objects useful for scientific computing in C++. The toolkit defines interfaces for basic data structures, such as multidimensional arrays and sparse matrices, commonly used in numerical applications. The goal of this package is to provide reusable software components that address many of the portability and maintenance problems with C++ codes.

TNT provides a distinction between interfaces and implementations of TNT components. For example, there is a TNT interface for two-dimensional arrays which describes how individual elements are accessed and how certain information, such as the array dimensions, can be used in algorithms; however, there can be several implementations of such an interface: one that uses expression templates, or one that uses BLAS kernels, or another that is instrumented to provide debugging information. By specifying only the interface, applications codes may utilize such algorithms, while giving library developers the greatest flexibility in employing optimization or portability strategies.

 Homepage: [http://math.nist.gov/tnt/](http://math.nist.gov/tnt/)

Numpy contains a powerful N-dimensional array object, sophisticated (broadcasting) functions, tools for integrating C/C++ and Fortran code, and useful linear algebra, Fourier transform, and random number capabilities.

Numpy replaces the python-numeric and python-numarray modules which are now deprecated and shouldn't be used except to support older software.

Numerical optimization framework developed in Python which provides connections to lots of solvers with easy and unified OpenOpt syntax. Problems which can be tackled with OpenOpt

• Linear Problem (LP)
• Mixed-Integer Linear Problem (MILP)
• Quadratic Problem (QP)
• Non-Linear Problem (NLP)
• Non-Smooth Problem (NSP)
• Non-Linear Solve Problem (NLSP)
• Least Squares Problem (LSP)
• Linear Least Squares Problem (LLSP)
• Mini-Max Problem (MMP)
• Global Problem (GLP)

A variety of solvers is available (e.g. IPOPT, ALGENCAN).

IT++ is a C++ library of mathematical, signal processing and communication classes and functions. Its main use is in simulation of communication systems and for performing research in the area of communications. The kernel of the library consists of generic vector and matrix classes, and a set of accompanying routines. Such a kernel makes IT++ similar to MATLAB or GNU Octave .

This package has the development libraries and headers for IT++.

A convex polyhedron is the set of points satisfying a finite family of linear inequalities. The study of the vertices and extreme rays of such systems is important and useful in e.g. mathematics and optimization. In a dual interpretation, finding the vertices of a (bounded) polyhedron is equivalent to finding the convex hull (bounding inequalities) of an (arbitrary dimensional) set of points. Lrs (lexicographic reverse search) has two important features that can be very important for certain applications: it works in exact arithmetic, and it consumes memory proportional to the input, no matter how large the output is.

This package contains the optional static libraries and headers, useful for developers.

CGAL (Computational Geometry Algorithms Library) makes the most important of the solutions and methods developed in computational geometry available to users in industry and academia in a C++ library. The goal is to provide easy access to useful, reliable geometric algorithms.

This package contains the header files and static libraries.

nauty (no automorphisms, yes?) is a set of procedures for determining the automorphism group of a vertex-coloured graph. It provides this information in the form of a set of generators, the size of the group, and the orbits of the group. It is also able to produce a canonically-labelled isomorph of the graph, to assist in isomorphism testing. This package provides a C API.

SLEPc is a software library for the solution of large scale sparse eigenvalue problems on parallel computers. It is an extension of PETSc and can be used for either standard or generalized eigenproblems, with real or complex arithmetic. It can also be used for computing a partial SVD of a large, sparse, rectangular matrix.

Install this package if you need to compile or link against SLEPc.

 Homepage: [http://www.grycap.upv.es/slepc](http://www.grycap.upv.es/slepc)

TetGen generates the Delaunay tetrahedralization, Voronoi diagram, and convex hull for three-dimensional point sets, generates the constrained Delaunay tetrahedralizations and quality tetrahedral meshes for three-dimensional domains with piecewise linear boundary.

This package provides header file and static library.