Debian Science Mathematics-dev packages

The basic capabilities of Code_Saturne enable the handling of either incompressible or expandable flows with or without heat transfer and turbulence. Dedicated modules are available for specific physics such as radiative heat transfer, combustion (gas, coal, heavy fuel oil, ...), magneto-hydrodynamics, compressible flows, two-phase flows (Euler-Lagrange approach with two-way coupling), extensions to specific applications (e.g. Mercure_Saturne for atmospheric environment).

It runs in parallel with MPI on distributed memory machines. Developed since 1997 at EDF R&D, it is based on a co-located Finite Volume approach that accepts meshes with any type of cell (tetrahedral, hexahedral, prismatic, pyramidal, polyhedral...) and any type of grid structure (unstructured, block structured, hybrid, conforming or with hanging nodes, ...).

This package contains the binary files.

The basic capabilities of Code_Saturne enable the handling of either incompressible or expandable flows with or without heat transfer and turbulence. Dedicated modules are available for specific physics such as radiative heat transfer, combustion (gas, coal, heavy fuel oil, ...), magneto-hydrodynamics, compressible flows, two-phase flows (Euler-Lagrange approach with two-way coupling), extensions to specific applications (e.g. Mercure_Saturne for atmospheric environment).

It runs in parallel with MPI on distributed memory machines. Developed since 1997 at EDF R&D, it is based on a co-located Finite Volume approach that accepts meshes with any type of cell (tetrahedral, hexahedral, prismatic, pyramidal, polyhedral...) and any type of grid structure (unstructured, block structured, hybrid, conforming or with hanging nodes, ...).

This package contains the include files.

The Coin-MP optimizer is an open source solver, it is part of the COIN-OR project which is an initiative to spur the development of open-source software for the operations research community.

CoinMP is a C-API library that supports most of the functionality of CLP (Coin LP), CBC (Coin Branch-and-Cut), and CGL (Cut Generation Library) projects.

This package contains the files needed to build applications using libCoinMP.

CppAD is a package for automatic differentiation (AD) of algorithms written in C++. Given appropriately written C++ code that computes a function, CppAD augments it to also compute derivative values. The system uses templates, supports forward and reverse accumulation modes, and allows nested derivatives.

This transition package helps with the move to libcppad-dev.

FEniCS is a collection of free software for automated, efficient solution of differential equations.

FEniCS has an extensive list of features, including automated solution of variational problems, automated error control and adaptivity, a comprehensive library of finite elements, high performance linear algebra and many more.

FEniCS is organized as a collection of interoperable components, including the problem-solving environment DOLFIN, the form compiler FFC, the finite element tabulator FIAT, the just-in-time compiler Instant, the code generation interface UFC, the form language UFL and a range of additional components.

This is a metapackage which depends on all FEniCS components.

This is the legacy version of FEniCS. You may want to consider installing the next-generation FEniCS-X (fenicx package).

FFLAS-FFPACK consists in the creation of a set of routines, giving the same tools as a set of classical Basic Linear Algebra Subroutines, but working over finite fields. In the same way, some other routines of higher level (such as the one in LAPACK) are also produced.

This library computes FFTs in one or more dimensions. It is extremely fast. This package contains the statically linked library and the header files.

GAP is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects. GAP is used in research and teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more.

This package contains the GAP compiler and the headers files and objects files necessary to build GAP packages.

The GAP compiler (GAC) creates C code from GAP code and then calls the system's C compiler to produce machine code from it. This can result in a speedup.

The JEL library enables users to enter algebraic expressions into their program. Since JEL converts expressions directly into Java bytecode, it significantly speeds up their evaluation time. If the user's Java virtual machine has a JIT compiler, expressions are transparently compiled into native machine code.

JEL may be a very useful tool for a variety of applications in science involving user-defined functions, e.g. to create plots, to apply fits to a data set and to solve integrals or differential equations. Another relevant use case for JEL is given by algebraic operations between two or more columns of a database table.

ALGLIB is a cross-platform numerical analysis and data processing library. This package support C++. ALGLIB features include:

• Linear algebra (direct algorithms, EVD/SVD)
• Solvers (linear and nonlinear)
• Interpolation
• Optimization
• Fast Fourier transforms
• Numerical integration
• Linear and nonlinear least-squares fitting
• Ordinary differential equations
• Special functions
• Statistics (descriptive statistics, hypothesis testing)
• Data analysis (classification/regression, including neural networks)

This package contains the development files (headers and documentation) for ALGLIB.

ANN is a library written in C++, which supports data structures and algorithms for both exact and approximate nearest neighbor searching in arbitrarily high dimensions. ANN assumes that distances are measured using any class of distance functions called Minkowski metrics. These include the well known Euclidean distance, Manhattan distance, and max distance. ANN performs quite efficiently for point sets ranging in size from thousands to hundreds of thousands, and in dimensions as high as 20.

This package contains the header files for developing applications with the ANN library.

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++ is an object-oriented version of the ARPACK package. It consists a collection of classes that offers c++ programmers an interface to ARPACK. It preserves the full capability, performance, accuracy and low memory requirements of the FORTRAN package, but takes advantage of the c++ object-oriented programming environment.

ARPACK stands for ARnoldi PACKage and provides standard and generalized eigenvalue solvers for sparse matrices that arises typically from finite element codes. See the corresponding Debian package.

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 (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 headers, the static libraries and symbolic links needed for program development.

Computes FE basis functions and derivatives for the following elements:

• Lagrange (interval, triangle, tetrahedron, prism, pyramid, quadrilateral, hexahedron)
• Nédélec (triangle, tetrahedron)
• Nédélec Second Kind (triangle, tetrahedron)
• Raviart-Thomas (triangle, tetrahedron)
• Regge (triangle, tetrahedron)
• Crouzeix-Raviart (triangle, tetrahedron)

Computes quadrature rules on different cell types

Provides reference topology and geometry for reference cells of each type.

Python wrapper provided with pybind11.

This package installs the development files for the shared library.

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.

BLIS is a portable software framework for instantiating high-performance BLAS-like dense linear algebra libraries. The framework was designed to isolate essential kernels of computation that, when optimized, immediately enable optimized implementations of most of its commonly used and computationally intensive operations. BLIS is written in ISO C99 and available under a new/modified/3-clause BSD license. While BLIS exports a new BLAS-like API, it also includes a BLAS compatibility layer which gives application developers access to BLIS implementations via traditional BLAS routine calls. An object-based API is also available for more experienced users.

The package pulls development files for one of the 32-bit BlasInt variants.

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++.

libbraiding is a library to compute several properties of braids, including centralizer and conjugacy check.

It is based on CBraid by Jae Choon Cha and Braiding by Juan Gonzalez-Meneses.

This package contains the development files for the library.

The core of BRiAl is a C++ library, which provides high-level data types for Boolean polynomials and monomials, exponent vectors, as well as for the underlying polynomial rings and subsets of the powerset of the Boolean variables. As a unique approach, binary decision diagrams are used as internal storage type for polynomial structures. On top of this C++-library a Python interface is provided. This allows parsing of complex polynomial systems, as well as sophisticated and extendable strategies for Groebner base computation. BRiAl features a powerful reference implementation for Groebner basis computation.

This package contains the BRiAl core development files.

The cddlib library is a C library for manipulating general convex polyhedra. It supports converting between the system of linear inequalities representation and a vertices and extreme rays representation of a polyhedron, and also supports solving linear programming problems.

This package contains the cddlib development files.

Minpack includes software for solving nonlinear equations and nonlinear least squares problems. Five algorithmic paths each include a core subroutine and an easy-to-use driver. The algorithms proceed either from an analytic specification of the Jacobian matrix or directly from the problem functions. The paths include facilities for systems of equations with a banded Jacobian matrix, for least squares problems with a large amount of data, and for checking the consistency of the Jacobian matrix with the functions.

This is the C re-write of the original fortran minpack implementation.

This package contains development files needed to build cminpack applications.

Neartree is an API and a library for finding nearest neighbors among points in spaces of arbitrary dimensions. This package provides a C++ template, TNear.h, and C library and header files for compiling programs using Neartree.

The library uses the Nearest Neighbor algorithm after Kalantari and McDonald, (IEEE Transactions on Software Engineering, v. SE-9, pp. 631-634,1983) modified to use recursion instead of a double-linked tree and simplified so that it does less checking for things like is the distance to the right less than the distance to the left; it was found that these checks make little to no difference.

The Combinatorial BLAS (CombBLAS) is an extensible distributed-memory parallel graph library offering a small but powerful set of linear algebra primitives specifically targeting graph analytics.

• The Combinatorial BLAS development influences the Graph BLAS standardization process.
• It achieves scalability via its two dimensional distribution and coarse-grained parallelism.
• CombBLAS powers HipMCL, a highly-scalable parallel implementation of the Markov Cluster Algorithm (MCL).
• Operations among sparse matrices and vectors use arbitrary user defined semirings.

This package provides development files for building client applications against combblas.

Quaternions are four-dimensional numbers which form an associative normed division algebra over the real numbers. Unit quaternions are a convenient and efficient way to represent orientations and rotations in three dimensions.

CQRlib is an ANSI C implementation of a utility library for quaternion arithmetic and quaternion rotation math.

This package contains files needed for compiling programs using CQRlib.

CVector is an ANSI C library which implements dynamic arrays approximating the functionality of the C++ vector class. It provides functions to create and manipulate an abstract vector container. Vector elements can be of any datatype.

This package contains files needed for compiling programs using CVector.

deal.II is a C++ program library targeted at the computational solution of partial differential equations using adaptive finite elements. It uses state-of-the-art programming techniques to offer you a modern interface to the complex data structures and algorithms required.

This package contains the development files.

Solves unconstrained nonlinear least squares problems using Powell's dog-leg method. The user specifies a callback C function that returns the value and gradients of the model function at a particular operating point. This library takes a series of dog-leg steps to find a local minimum of the residual surface.

This library works with sparse matrices, which makes it suitable for efficiently solving very large problems.

Development files

DOLFIN is the Python and C++ interface of the FEniCS project for the automated solution of differential equations, providing a consistent PSE (Problem Solving Environment) for solving ordinary and partial differential equations. Key features include a simple, consistent and intuitive object-oriented API; automatic and efficient evaluation of variational forms; automatic and efficient assembly of linear systems; and support for general families of finite elements.

This package contains the common development files and depends on the real or complex development package.

This is the next-generation version of libdolfinx-dev (DOLFIN-X). The legacy version of DOLFIN is provided by libdolfin-dev.

This library provides routines to convert IEEE single and double floats to and from string representations. It offers at lot of flexibility with respect to the conversion format: shortest, fixed, precision or exponential representation; decimal, octal or hexadecimal basis; control over number of digits, leading/trailing zeros and spaces.

The library consists of efficient conversion routines that have been extracted from the V8 JavaScript engine. The code has been refactored and improved so that it can be used more easily in other projects.

This package contains a static version of the library and development headers.

DUNE, the Distributed and Unified Numerics Environment is a modular toolbox for solving partial differential equations (PDEs) with grid-based methods. It supports the easy implementation of methods like Finite Elements (FE), Finite Volumes (FV), and also Finite Differences (FD).

This package contains the development files for the grid interface.

This library implements 2-descent on elliptic curves over Q and computations with modular symbols.

This package contains the development files for the library.

This is a dummy package.

Eigen 3 is a lightweight C++ template library for vector and matrix math, a.k.a. linear algebra.

Unlike most other linear algebra libraries, Eigen 3 focuses on the simple mathematical needs of applications: games and other OpenGL apps, spreadsheets and other office apps, etc. Eigen 3 is dedicated to providing optimal speed with GCC. A lot of improvements since 2-nd version of Eigen.

The FFTW library computes Fast Fourier Transforms (FFT) in one or more dimensions. It is extremely fast. This package contains the statically linked library, header files and test programs.

This package contains the header files and static libraries. For documentation, see libfftw3-doc.

libflame is a portable library for dense matrix computations, providing much of the functionality present in LAPACK, developed by current and former members of the Science of High-Performance Computing (SHPC) group in the Institute for Computational Engineering and Sciences at The University of Texas at Austin. libflame includes a compatibility layer, lapack2flame, which includes a complete LAPACK implementation.

This package contains the static library and the development files.

FLANN is a library for performing fast approximate nearest neighbor searches in high dimensional spaces. It contains a collection of algorithms found to work best for nearest neighbor search and a system for automatically choosing the best algorithm and optimum parameters depending on the dataset.

This package contains development files needed to build FLANN applications.

The Fast Library for Integer Number Theory is a C library which supports polynomial arithmetic over the integers, fast integer arithmetic and factoring (including a highly optimized quadratic sieve).

FLINT has functionality similar to that of the Number Theory Library (NTL). However, unlike NTL, which is designed primarily for asymptotic performance, FLINT is designed for good performance in small cases as well.

This package contains the FLINT development files.

fpLLL is a library for computing reduced (nearly orthogonal) bases for Euclidean lattices using the floating-point LLL algorithm.

fpLLL contains multiple different implementations of the floating-point LLL reduction algorithm, offering multiple different speed/guarantees ratios.

It contains a 'wrapper' that chooses the estimated best sequence of variants in order to provide a guaranteed output as fast as possible. In the case of the wrapper, the succession of variants is oblivious to the user.

This package contains development files for libfplll.

FreeFem++ is an implementation of a language dedicated to the finite element method. It enables you to solve Partial Differential Equations (PDE) easily.

Problems involving PDE from several branches of physics such as fluid-structure interactions require interpolations of data on several meshes and their manipulation within one program. FreeFem++ includes a fast quadtree-based interpolation algorithm and a language for the manipulation of these data on multiple meshes. It contains also a powerful mesh generation and adaption tool integrated seamlessly in FreeFem++ called bamg.

FreeFem++ is written in C++ and the FreeFem++ language is a C++ idiom allowing for a smooth learning curve.

This package contains the development files of FreeFem++.

FreeFEM is a language adapted to Partial Differential equation. The underlying method used is the Finite Element Method. This tool has been successfully used as a teaching tool and even as a research tool.

Frobby is a software system and project for computations with monomial ideals. Frobby is free software and it is intended as a vehicle for computational and mathematical research on monomial ideals.

The current functionality includes Euler characteristic, Hilbert series, maximal standard monomials, combinatorial optimization on monomial ideals, primary decomposition, irreducible decomposition, Alexander dual, associated primes, minimization and intersection of monomial ideals as well as the computation of Frobenius problems (using 4ti2) with very large numbers. Frobby is also able to translate between formats that can be used with several different computer systems, such as Macaulay 2, Monos, 4ti2, CoCoA4 and Singular. Thus Frobby can be used with any of those systems.

This package contains the development tools.

This is not a full linear algebra library, only a GEMM library: it only does general matrix multiplication ("GEMM").

Its performance goals differ from typical GEMM performance goals in the following ways: 1. It cares not only about speed, but also about minimizing power usage.

   It specifically cares about charge usage in mobile/embedded devices.
2. Most GEMMs are optimized primarily for large dense matrix sizes (>= 1000).
   It does care about large sizes, but it also cares specifically about the
   typically smaller matrix sizes encountered in various mobile applications.

Keep in mind (previous section) that gemmlowp itself is a pure-headers-only library.

GF2X is a C/C++ software package containing routines for fast arithmetic in GF(2)[x] (multiplication, squaring, GCD) and searching for irreducible/primitive trinomials.

This package contains the development files for the library.

Givaro is a C++ library for arithmetic and algebraic computations. Its main features are implementations of the basic arithmetic of many mathematical entities: Primes fields, Extensions Fields, Finite Fields, Finite Rings, Polynomials, Algebraic numbers, and Arbitrary precision integers and rationals (C++ wrappers over gmp).

Givaro also provides data-structures and templated classes for the manipulation of basic algebraic objects, such as vectors, matrices (dense, sparse, structured), univariate polynomials (and therefore recursive multivariate).

It contains different program modules and is fully compatible with the LinBox linear algebra library and the Athapascan environment, which permits parallel programming.

This package contains development files for Givaro.

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.

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.

GLPK supports the GNU MathProg language, which is a subset of the AMPL language. GLPK also supports the standard MPS and LP formats.

This package contains the Java binding to GLPK.

This interface allows gnuplot to be controlled from C++ and is designed to be the lowest hanging fruit. In other words, if you know how gnuplot works it should only take 30 seconds to learn this library. Basically it is just an iostream pipe to gnuplot with some extra functions for pushing data arrays and getting mouse clicks. Data sources include STL containers (eg. vector or map) and one or two dimensional Blitz++ arrays (of scalars or TinyVectors). Support for other data sources should be easy to add.

Basically there are two functions defined: send() sends arrays of data values (it is overloaded to do the right thing based upon what type of variable you pass) and getMouse() gets the position of a mouse click. Everything else is accomplished by sending commands manually to gnuplot via the iostream interface.

libhomfly is a library to compute the homfly polynomial of knots and links.

It is based on a program written by Robert J Jenkins Jr.

This package contains the development files for the library.

Hypre is a set of matrix preconditioning libraries to aid in the solution of large systems of linear equations.

This package contains the headers and symlinks necessary to develop programs which use hypre.

igraph is a library for creating and manipulating graphs. It is intended to be as powerful (ie. fast) as possible to enable the analysis of large graphs.

This package contains the include files and static library for the igraph C library.

IML is a library for exact, dense linear algebra over the integers. IML contains algorithms for nonsingular rational system solving, computing the right nullspace of an integer matrix, and certified linear system solving.

In addition, IML provides some low level routines for a variety of mod p matrix operations: computing the row-echelon form, determinant, rank profile, and inverse of a mod p matrix. These mod p routines are not general purpose; they require that p satisfy some preconditions based on the dimension of the input matrix (usually p should be prime and should be no more than about 20 bits long).

This package contains development files for IML.

ITSOL is a library of iterative solvers for general sparse linear systems of equations. ITSOL can be viewed as an extension of the itsol module in SPARSKIT. It is written in C and offers a selection of recently developed preconditioners. The preconditioner suite includes:

• ILUK (ILU preconditioner with level of fill)
• ILUT (ILU preconditioner with threshold)
• ILUC (Crout version of ILUT)
• VBILUK (variable block preconditioner with level of fill - with automatic block detection)
• VBILUT (variable block preconditioner with threshold - with automatic block detection)
• ARMS (Algebraic Recursive Multilevel Solvers -- includes actually several methods - In particular the standard ARMS and the ddPQ version which uses nonsymmetric permutations)

Note that ITSOL is a scalar package. You may find parallel implementations of some of the preconditioners listed above in pARMS.

This package provides the itsol header files required to compile C/C++ programs that use ITSOL.

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.

JGraphT is a free Java graph library that provides mathematical graph theory objects and algorithms. JGraphT supports various types of graphs including:

• directed and undirected graphs
• graphs with weighted, unweighted, labeled or user-defined edges
• various edge multiplicity options, including simple graphs, multigraphs and pseudographs
• unmodifiable graphs: allow modules to provide "read-only" access to internal graphs
• listenable graphs: allow external listeners to track modification events
• subgraphs: graphs that are auto-updating subgraph views on other graphs

JGraphT is a free Java graph library that provides mathematical graph theory objects and algorithms. JGraphT supports various types of graphs including:

• directed and undirected graphs;
• graphs with weighted, unweighted, labeled or user-defined edges;
• various edge multiplicity options, including simple graphs, multigraphs and pseudographs;
• unmodifiable graphs: allow modules to provide "read-only" access to internal graphs;
• listenable graphs: allow external listeners to track modification events;
• subgraphs: graphs that are auto-updating subgraph views on other graphs;
• all compositions of above graphs.

JGraphT is designed to be simple and type-safe (via Java generics): graph vertices can be of any objects: Strings, URLs, XML documents, even graphs themselves.

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.

This package contains a static version of the library.

Solves nonlinear optimization problems using the limited-memory BFGS method. The user specifies a callback C function that returns the value and gradients of the cost function at a particular operating point. This library estimates the Hessians from user input, and applies Newton's method iteratively to find a local minimum of the cost function. This is a small library, written in C with minimal dependencies.

This package contains development files

liblfunction is a library for computing zeros and values of L-functions. Supported L-functions include the Riemann zeta function, the L-function of the Ramanujan delta function, and L-functions of elliptic curves defined over the rationals.

This package contains the development files for the library.

This package implements the Leiden algorithm in C++. It relies on igraph for it to function. Besides the relative flexibility of the implementation, it also scales well, and can be run on graphs of millions of nodes (as long as they can fit in memory). The core class is Optimiser which finds the optimal partition using the Leiden algorithm, which is an extension of the Louvain algorithm for a number of different methods. The methods currently implemented are (1) modularity, (2) Reichardt and Bornholdt's model using the configuration null model and the Erdös-Rényi null model, (3) the Constant Potts model (CPM), (4) Significance, and finally (5) Surprise. In addition, it supports multiplex partition optimisation allowing community detection on for example negative links or multiple time slices. There is the possibility of only partially optimising a partition, so that some community assignments remain fixed. It also provides some support for community detection on bipartite graphs.

This package contains the C++ development files. Most people will find it easier to work with the Python interface provided by python3-leidenalg.

LinBox is a C++ template library for exact, high-performance linear algebra computation with dense, sparse, and structured matrices over the integers and over finite fields.

This package contains the LinBox development files.

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.

The "Littlewood-Richardson Calculator" is a package of C programs for computing Littlewood-Richardson coefficients, providing fast calculation of single LR coefficients, products of Schur functions, and skew Schur functions. Its interface uses the same notation as the SF package of John Stembridge, to make it easier to use both packages at the same time.

This package contains the development files for the library.

M4RI is a library for fast arithmetic with dense matrices over F2. The name M4RI comes from the first implemented algorithm: The "Method of the Four Russians" inversion algorithm. This algorithm in turn is named after the "Method of the Four Russians" multiplication algorithm which is probably better referred to as Kronrod's method.

This package contains development files for libm4ri.

M4RIE is a library for fast arithmetic with dense matrices over small finite fields of even characteristic. It uses the M4RI library, implementing the same operations over the finite field F2.

The name M4RI comes from the first implemented algorithm: The "Method of the Four Russians" inversion algorithm. This algorithm in turn is named after the "Method of the Four Russians" multiplication algorithm which is probably better referred to as Kronrod's method.

This package contains development files for the M4RIE library.

This package contains the development files (headers, so and static libraries) for MAdLib.

MAdLib is a library that performs global node repositioning and mesh adaptation by local mesh modifications on tetrahedral or triangular meshes. It is designed to frequently adapt the mesh in transient computations. MAdLib is written in C++.

The adaptation procedure is driven by two objectives:

• make the edge lengths as close as possible to a (non-homogenous)

  prescribed length,

• maintain a satisfying element quality everywhere.

MAdLib can be used in transient computations in order to maintain a satisfying element quality (moving boundaries, multiphase flows with interface tracking, ...) or/and to apply selective refinements and coarsenings (error estimators based, interface capturing: shocks, free surfaces, ...).

GNU libmatheval is a library comprising of several procedures that make it possible to create an in-memory tree representation of mathematical functions over single or multiple variables and later use this representation to evaluate functions for specified variable values, to create corresponding trees for function derivatives over specified variables or to print textual representations of in-memory trees to a 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 static library.

Mathic is a C++ library of fast data structures designed for use in Groebner basis computation. This includes data structures for ordering S-pairs, performing divisor queries and ordering polynomial terms during polynomial reduction.

This package contains the developer tools.

Mathicgb is a program for computing Groebner basis and signature Groebner bases. Mathicgb is based on the fast data structures from mathic.

The paper "Practical Groebner Basis Computation" describes the algorithms in Mathicgb from a high level. It was presented at ISSAC 2012 and is available at http://arxiv.org/abs/1206.6940

This package contains the developer tools.

matio is a C library for reading and writing MATLAB MAT files.

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

These are files necessary for compiling programs with the meschach linear algebra library.

Implementation of the mesh normal filtering algorithm from the paper: Juyong Zhang, Bailin Deng, Yang Hong, Yue Peng, Wenjie Qin, Ligang Liu. Static/Dynamic Filtering for Mesh Geometry. arXiv:1712.03574.

This is a header-only library. This package contains the headers

This package provides a C library of functions for interval arithmetic computations with arbitrary precision.

The basic principle of interval arithmetic consists in enclosing every number by an interval containing it and being representable by machine numbers: for instance it can be stored as its lower and upper endpoints and these bounds are machine numbers, or as a centre and a radius which are machine numbers.

The arithmetic operations are extended for interval operands in such a way that the exact result of the operation belongs to the computed interval.

The purpose of an arbitrary precision interval arithmetic is on the one hand to get guaranteed results, thanks to interval computation, and on the other hand to obtain accurate results, thanks to multiple precision arithmetic. The MPFI library is built upon MPFR in order to benefit from the correct roundings provided by MPFR. Further advantages of using MPFR are its portability and compliance with the IEEE 754 standard for floating-point arithmetic.

This package provides the static library and symbolic links needed for development.

MPFR C++ introduces C++ arbitrary precision numeric types; based on GNU MPFR --- Multiple Precision Floating-Point Reliable Library.

MPFR C++ makes possible to use MPFR calculations in the same simple way as calculations with numbers of built-in types double or float: all arithmetic and boolean operators (+, -, *, /, >, !=, etc.) are implemented through operator overloading technique; elementary mathematical functions (sqrt, pow, sin, cos, etc.) are supported.

A polynomial rootfinder that can determine arbitrary precision approximations with guaranteed inclusion radii. It supports exploiting of polynomial structures such as sparsisty and allows for polynomial implicitly defined or in some non standard basis.

This package contains the development headers and the .so library of MPSolve.

muParser is a high performance mathematical parser library, written in pure C++. It is based on transforming an expression into a bytecode and precalculating constant parts of it.

This package contains the development 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.

NFFT3 is a software library written in C for computing nonequispaced fast Fourier and related transformations. In detail, NFFT3 implements:

1) The nonequispaced fast Fourier transform (NFFT)

• the forward transform (NFFT)
• the adjoint transform (adjoint NFFT)

2) Generalisations of the NFFT

• to arbitrary knots in time and frequency domain (NNFFT)
• to the sphere S^2 (NFSFT)
• to the hyperbolic cross (NSFFT)
• to real-valued data, i.e. (co)sine transforms, (NFCT, NFST)
• to the rotation group (NFSOFT)

3) Generalised inverses based on iterative methods, e.g. CGNR, CGNE

4) Applications in

• medical imaging (i) magnetic resonance imaging (ii) computerised tomography
• summation schemes (i) fast Gauss transform (FGT) (ii) singular kernels (iii) zonal kernels
• polar FFT, discrete Radon transform, ridgelet transform