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DnAnalytics
dnAnalytics was an open-source numerical library for .NET written in C# and F#. It featured functionality similar to BLAS and LAPACK. It was merged into Math.NET Numerics in 2009. Features The software library provides facilities for: * Linear algebra classes with support for sparse matrices and vectors (with an F# friendly interface). * Dense and sparse solvers. * Probability distributions. * Random number generation (including Mersenne Twister MT19937). * QR, LU, SVD, and Cholesky decomposition classes. * Matrix IO classes that read and write matrices from/to Matlab, Matrix Market, and delimited files. * Complex and “special” math routines. * Descriptive Statistics, Histogram, and Pearson Correlation Coefficient. * Overload mathematical operators to simplify complex expressions. * Visual Studio visual debuggers for matrices and vectors * Runs under Microsoft Windows and platforms that support Mono. * Optional support for Intel Math Kernel Library (Microsoft Windows an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C Sharp (programming Language)
C# ( pronounced: C-sharp) ( ) is a general-purpose high-level programming language supporting multiple paradigms. C# encompasses static typing, strong typing, lexically scoped, imperative, declarative, functional, generic, object-oriented (class-based), and component-oriented programming disciplines. The principal inventors of the C# programming language were Anders Hejlsberg, Scott Wiltamuth, and Peter Golde from Microsoft. It was first widely distributed in July 2000 and was later approved as an international standard by Ecma (ECMA-334) in 2002 and ISO/ IEC (ISO/IEC 23270 and 20619) in 2003. Microsoft introduced C# along with .NET Framework and Microsoft Visual Studio, both of which are technically speaking, closed-source. At the time, Microsoft had no open-source products. Four years later, in 2004, a free and open-source project called Microsoft Mono began, providing a cross-platform compiler and runtime environment for the C# programming language. A decad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Math
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Numerical Analysis Software
Listed here are notable end-user computer applications intended for use with numerical or data analysis: Numerical-software packages * Analytica is a widely used proprietary software tool for building and analyzing numerical models. It is a declarative and visual programming language based on influence diagrams. * FlexPro is a program to analyze and present measurement data. It has a rich Excel-like user interface and a built-in vector programming language FPScript has a syntax similar to MATLAB. * FreeMat, an open-source MATLAB-like environment with a GNU General Public License (GPL). * GNU Octave is a high-level programming language, intended for mainly numerical computing. It has a convenient command-line interface to solve linear and nonlinear problems numerically, and to perform other numerical experiments using a language that is compatible mostly with MATLAB. The 4.0 and newer releases of Octave include a GUI. Several independently developed Linux programs (Cantor, KA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Numerical Libraries
This is a list of numerical libraries, which are libraries used in software development for performing numerical calculations. It is not a complete listing but is instead a list of numerical libraries with articles on Wikipedia, with few exceptions. The choice of a typical library depends on a range of requirements such as: desired features (e.g. large dimensional linear algebra, parallel computation, partial differential equations), licensing, readability of API, portability or platform/compiler dependence (e.g. Linux, Windows, Visual C++, GCC), performance, ease-of-use, continued support from developers, standard compliance, specialized optimization in code for specific application scenarios or even the size of the code-base to be installed. Multi-language C C++ Delphi * ALGLIB - an open source numerical analysis library. .NET Framework languages C#, F#, VB.NET and PowerShell Fortran Java OCaml * OCaml programming language has support for array programming ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pearson Product-moment Correlation Coefficient
In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of children from a school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation). Naming and history It was developed by Karl Pearson from a related idea introduced by Francis Galton in the 1880s, and for which the mathematical formula was derived and published by Auguste Bravais in 1844. The naming ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cholesky Decomposition
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced ) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices, and posthumously published in 1924. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations. Statement The Cholesky decomposition of a Hermitian positive-definite matrix , is a decomposition of the form \mathbf = \mathbf^, where is a lower triangular matrix with real and positive diagonal entries, and * denotes the conjugate transpose of . Every Hermitian positive-definite matrix (and thus also every real-valued symmetric positive-definite matrix) has a unique Cholesky decomposition. The converse holds trivially: if can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singular Value Decomposition
In linear algebra, the singular value decomposition (SVD) is a Matrix decomposition, factorization of a real number, real or complex number, complex matrix (mathematics), matrix into a rotation, followed by a rescaling followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any matrix. It is related to the polar decomposition#Matrix polar decomposition, polar decomposition. Specifically, the singular value decomposition of an m \times n complex matrix is a factorization of the form \mathbf = \mathbf, where is an complex unitary matrix, \mathbf \Sigma is an m \times n rectangular diagonal matrix with non-negative real numbers on the diagonal, is an n \times n complex unitary matrix, and \mathbf V^* is the conjugate transpose of . Such decomposition always exists for any complex matrix. If is real, then and can be guaranteed to be real orthogonal matrix, orthogonal matrices; in such contexts, the SVD ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LU Decomposition
In numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix multiplication and matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix. It is also sometimes referred to as LR decomposition (factors into left and right triangular matrices). The LU decomposition was introduced by the Polish astronomer Tadeusz Banachiewicz in 1938, who first wrote product equation LU=A=h^Tg (The last form in his alternate yet equivalent matrix notation appears as g\times h. ) Definitions Let ''A'' be a square matrix. An LU factorization refers to expression of ''A'' into product of two facto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
QR Decomposition
In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix ''A'' into a product ''A'' = ''QR'' of an orthonormal matrix ''Q'' and an upper triangular matrix ''R''. QR decomposition is often used to solve the linear least squares (LLS) problem and is the basis for a particular eigenvalue algorithm, the QR algorithm. Cases and definitions Square matrix Any real square matrix ''A'' may be decomposed as : A = QR, where ''Q'' is an orthogonal matrix (its columns are orthogonal unit vectors meaning and ''R'' is an upper triangular matrix (also called right triangular matrix). If ''A'' is invertible, then the factorization is unique if we require the diagonal elements of ''R'' to be positive. If instead ''A'' is a complex square matrix, then there is a decomposition ''A'' = ''QR'' where ''Q'' is a unitary matrix (so the conjugate transpose If ''A'' has ''n'' linearly independent columns, then the first ''n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Twister
The Mersenne Twister is a general-purpose pseudorandom number generator (PRNG) developed in 1997 by and . Its name derives from the choice of a Mersenne prime as its period length. The Mersenne Twister was created specifically to address most of the flaws found in earlier PRNGs. The most commonly used version of the Mersenne Twister algorithm is based on the Mersenne prime 2^-1. The standard implementation of that, MT19937, uses a 32-bit word length. There is another implementation (with five variants) that uses a 64-bit word length, MT19937-64; it generates a different sequence. ''k''-distribution A pseudorandom sequence x_i of ''w''-bit integers of period ''P'' is said to be ''k-distributed'' to ''v''-bit accuracy if the following holds. : Let trunc''v''(''x'') denote the number formed by the leading ''v'' bits of ''x'', and consider ''P'' of the ''kv''-bit vectors :: (\operatorname_v(x_i), \operatorname_v(x_), \, \ldots, \operatorname_v(x_)) \quad (0\leq i. The Mersenn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. LAPACK was originally written in FORTRAN 77, but moved to Fortran 90 in version 3.2 (2008). The routines handle both real and complex matrices in both single and double precision. LAPACK relies on an underlying BLAS implementation to provide efficient and portable computational building blocks for its routines. LAPACK was designed as the successor to the linear equations and linear least-squares routines of LINPACK and the eigenvalue routines of EISPACK. LINPACK, written in the 1970s and 1980s, was designed to run on the then-modern vector computers with shared memory. LAPACK, in contrast, was designed to eff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
F Sharp (programming Language)
F# (pronounced F sharp) is a general-purpose, high-level, strongly typed, multi-paradigm programming language that encompasses functional, imperative, and object-oriented programming methods. It is most often used as a cross-platform Common Language Infrastructure (CLI) language on .NET, but can also generate JavaScript and graphics processing unit (GPU) code. F# is developed by the F# Software Foundation, Microsoft and open contributors. An open source, cross-platform compiler for F# is available from the F# Software Foundation. F# is a fully supported language in Visual Studio and JetBrains Rider. Plug-ins supporting F# exist for many widely used editors including Visual Studio Code, Vim, and Emacs. F# is a member of the ML language family and originated as a .NET Framework implementation of a core of the programming language OCaml. It has also been influenced by C#, Python, Haskell, Scala and Erlang. History Versions Language evolution F# uses an open deve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
