ILNumerics is a mathematical

class 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 ...

for

Common Language Infrastructure The Common Language Infrastructure (CLI) is an open specification and technical standard originally developed by Microsoft and standardized by International Organization for Standardization, ISO/International Electrotechnical Commission, IEC (ISO/ ...

(CLI) developers and a domain specific language (DSL) for the

implementation Implementation is the realization of an application, execution of a plan, idea, scientific modelling, model, design, specification, Standardization, standard, algorithm, policy, or the Management, administration or management of a process or Goal ...

of numerical

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

s on the .NET platform. While algebra systems with

graphical user interface A graphical user interface, or GUI, is a form of user interface that allows user (computing), users to human–computer interaction, interact with electronic devices through Graphics, graphical icon (computing), icons and visual indicators such ...

s focus on

prototyping A prototype is an early sample, model, or release of a product built to test a concept or process. It is a term used in a variety of contexts, including semantics, design, electronics, and software programming. A prototype is generally used to ...

of algorithms, implementation of such algorithms into distribution-ready

applications Application may refer to: Mathematics and computing * Application software, computer software designed to help the user to perform specific tasks ** Application layer, an abstraction layer that specifies protocols and interface methods used in a ...

is done using development environments and general purpose programming languages (GPL). ILNumerics is an extension to

Visual Studio Visual Studio is an integrated development environment (IDE) developed by Microsoft. It is used to develop computer programs including web site, websites, web apps, web services and mobile apps. Visual Studio uses Microsoft software development ...

and aims at supporting the creation of technical applications based on .NET.

History

ILNumerics started in 2006 as an open source project, originating from

Technische Universität Berlin (TU Berlin; also known as Berlin Institute of Technology and Technical University of Berlin, although officially the name should not be translated) is a public university, public research university located in Berlin, Germany. It was the first ...

. In 2007 ILNumerics won the BASTA! Innovation Awards 2007 as most innovative .NET project in

Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...

Switzerland Switzerland, officially the Swiss Confederation, is a landlocked country located in west-central Europe. It is bordered by Italy to the south, France to the west, Germany to the north, and Austria and Liechtenstein to the east. Switzerland ...

and

Austria Austria, formally the Republic of Austria, is a landlocked country in Central Europe, lying in the Eastern Alps. It is a federation of nine Federal states of Austria, states, of which the capital Vienna is the List of largest cities in Aust ...

. After 6 years of open source development, the project added a closed source, proprietary license in 2011, aiming business and academic developers at the same time. The project quickly gained popularity (download numbers and engagement at stackoverflow.com, download counts from website not available). The .NET framework was selected as a managed foundation, since earlier attempts on the

Java platform Java is a set of computer software and specifications that provides a software platform for developing application software and deploying it in a cross-platform computing environment. Java is used in a wide variety of computing platforms fr ...

had been abandoned due to technical limitations. Similarly, the .NET framework has not been designed with the focus on requirements of technical application development. ILNumerics added interfaces to popular codes (

LAPACK LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It als ...

FFTW The Fastest Fourier Transform in the West (FFTW) is a software library for computing discrete Fourier transforms (DFTs) developed by Matteo Frigo and Steven G. Johnson at the Massachusetts Institute of Technology. FFTW is one of the fastest fre ...

complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...

s and generic mult-dimensional array classes. In 2010 graphical capabilities have been added. Efforts to increase the performance of the technology were introduced in 2011. At the same time, a company was founded to continue the development. The technological goal is to establish the .NET framework as a feasible alternative to unmanaged

languages Language is a structured system of communication that consists of grammar and vocabulary. It is the primary means by which humans convey meaning, both in spoken and signed forms, and may also be conveyed through writing. Human language is ch ...

for numeric computing.

Syntax

ILNumerics implements base functionality frequently needed for application development in technical areas: N-dimensional

arrays An array is a systematic arrangement of similar objects, usually in rows and columns. Things called an array include: {{TOC right Music * In twelve-tone and serial composition, the presentation of simultaneous twelve-tone sets such that the ...

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...

, FFT and plotting controls (2D and 3D). The array classes are fully compatible with the array features of

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 ...

and

numpy NumPy (pronounced ) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. The predeces ...

, including internal storage order, subarray creation, expansion, and advanced indexing. Higher level functionality is provided by toolboxes for

interpolation In the mathematics, mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one ...

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfiel ...

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

HDF5 Hierarchical Data Format (HDF) is a set of file formats (HDF4, HDF5) designed to store and organize large amounts of data. Originally developed at the U.S. National Center for Supercomputing Applications, it is supported by The HDF Group, a non- ...

and

machine learning Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task ( ...

. The ILNumerics DSL is embedded into .NET. Computational algorithms are formulated using any CLI language. However, only C# and

Visual Basic Visual Basic is a name for a family of programming languages from Microsoft. It may refer to: * Visual Basic (.NET), the current version of Visual Basic launched in 2002 which runs on .NET * Visual Basic (classic), the original Visual Basic suppo ...

are officially supported. Due to the strong type system of the .NET framework algorithms created with ILNumerics are strongly typed. This deviates from the syntax of

alternatives Founded in 1994, Alternatives, Action and Communication Network for International Development, is a non-governmental, international solidarity movement, international solidarity organization based in Montreal, Quebec, Canada. Alternatives works ...

, which are often weakly typed and therefore easier to adopt.

Graphics

scene graph A scene graph is a general data structure commonly used by vector-based graphics editing applications and modern computer games, which arranges the logical and often spatial representation of a graphical scene. It is a collection of nodes in a g ...

is used in ILNumerics to realize graphical output. Interactive 2D and 3D plots are used in Windows Forms applications. Hardware accelerated drawing is available via

OpenGL OpenGL (Open Graphics Library) is a Language-independent specification, cross-language, cross-platform application programming interface (API) for rendering 2D computer graphics, 2D and 3D computer graphics, 3D vector graphics. The API is typic ...

. A software renderer is provided for legacy hardware, based on GDI+ and SVG.

IDE integration

ILNumerics is distributed as an extension to

. It adds a tool window to the IDE for the graphical inspection of mathematical objects while stepping through user code.

Performance

Since ILNumerics comes as a CLI assembly, it targets

(CLI) applications. Just like

Java Java is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea (a part of Pacific Ocean) to the north. With a population of 156.9 million people (including Madura) in mid 2024, proje ...

- those frameworks are often criticized for not being suitable for numerical computations. Reasons are the

memory Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembe ...

management by a

garbage collector A waste collector, also known as a garbage man, garbage collector, trashman (in the U.S), binman or dustman (in the UK), is a person employed by a public or private enterprise to collect and dispose of municipal solid waste (refuse) and recycla ...

, the

intermediate language An intermediate representation (IR) is the data structure or code used internally by a compiler or virtual machine to represent source code. An IR is designed to be conducive to further processing, such as optimization and translation. A "good" ...

execution and deficient optimizations by the

compilers In computing, a compiler is a computer program that translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs tha ...

involved. ILNumerics approaches these limitations by performing

loop unrolling Loop unrolling, also known as loop unwinding, is a loop transformation technique that attempts to optimize a program's execution speed at the expense of its binary size, which is an approach known as space–time tradeoff. The transformation c ...

, removal of bound checks on array accesses and cache optimizations. Further speed-up is gained by the auto-management of the memory of large array objects. Numerical operations are parallelized on

multicore A multi-core processor (MCP) is a microprocessor on a single integrated circuit (IC) with two or more separate central processing units (CPUs), called ''cores'' to emphasize their multiplicity (for example, ''dual-core'' or ''quad-core''). Ea ...

systems. Linear algebra routines rely on processor specific optimized versions of

and

BLAS Blas is mainly a Spanish given name and surname, related to Blaise. It may refer to Places *Piz Blas, mountain in Switzerland * San Blas (disambiguation) People * Ricardo Blas Jr. (born 1986) Judo athlete from Guam * Blas Antonio Sáenz (fl. 18 ...

. ILNumerics arrays utilize the unmanaged heap for storing data. This way, the

size Size in general is the Magnitude (mathematics), magnitude or dimensions of a thing. More specifically, ''geometrical size'' (or ''spatial size'') can refer to three geometrical measures: length, area, or volume. Length can be generalized ...

of ILNumerics arrays is no
limited by the CLR
and

interoperability Interoperability is a characteristic of a product or system to work with other products or systems. While the term was initially defined for information technology or systems engineering services to allow for information exchange, a broader de ...

with 3rd party libraries is improved.

References

External links

*
Article about Math Libraries for .NET at MSDN
{{DEFAULTSORT:Ilnumerics.Net 3D graphics software 3D scenegraph APIs Array programming languages C Sharp libraries Computer vision software Data analysis software Data and information visualization software Mathematical software Numerical analysis software for Linux Numerical analysis software for macOS Numerical analysis software for Windows Numerical linear algebra Numerical programming languages Object-oriented programming languages OpenGL Parallel computing Science software Unix programming tools