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Rank (computer Programming)
In computer programming, rank with no further specifications is usually a synonym for (or refers to) "number of dimensions"; thus, a two-dimensional array has rank ''two'', a three-dimensional array has rank ''three'' and so on. Strictly, no formal definition can be provided which applies to every programming language, since each of them has its own concepts, semantics and terminology; the term may not even be applicable or, to the contrary, applied with a very specific meaning in the context of a given language. In the case of APL the notion applies to every operand; and dyads ("binary functions") have a ''left rank'' and a ''right rank''. The box below instead shows how ''rank of a type'' and ''rank of an array expression'' could be defined (in a semi-formal style) for C++ and illustrates a simple way to calculate them at compile time. #include #include /* Rank of a type * ------------- * * Let the rank of a type T be the number of its dimensions if * it is an array; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Programming
Computer programming or coding is the composition of sequences of instructions, called computer program, programs, that computers can follow to perform tasks. It involves designing and implementing algorithms, step-by-step specifications of procedures, by writing source code, code in one or more programming languages. Programmers typically use high-level programming languages that are more easily intelligible to humans than machine code, which is directly executed by the central processing unit. Proficient programming usually requires expertise in several different subjects, including knowledge of the Domain (software engineering), application domain, details of programming languages and generic code library (computing), libraries, specialized algorithms, and Logic#Formal logic, formal logic. Auxiliary tasks accompanying and related to programming include Requirements analysis, analyzing requirements, Software testing, testing, debugging (investigating and fixing problems), imple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Programming Language
A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually defined by a formal language. Languages usually provide features such as a type system, Variable (computer science), variables, and mechanisms for Exception handling (programming), error handling. An Programming language implementation, implementation of a programming language is required in order to Execution (computing), execute programs, namely an Interpreter (computing), interpreter or a compiler. An interpreter directly executes the source code, while a compiler produces an executable program. Computer architecture has strongly influenced the design of programming languages, with the most common type (imperative languages—which implement operations in a specified order) developed to perform well on the popular von Neumann architecture. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Semantics Of Programming Languages
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid string (computer science), strings in a programming language syntax. It is closely related to, and often crosses over with, the Semantics of logic, semantics of mathematical proofs. Semantics describes the processes a computer follows when Execution (computing), executing a program in that specific language. This can be done by describing the relationship between the input and output of a program, or giving an explanation of how the program will be executed on a certain computer platform, platform, thereby creating a model of computation. History In 1967, Robert W. Floyd published the paper ''Assigning meanings to programs''; his chief aim was "a rigorous standard for proofs about computer programs, including formal verification, proofs of correctness, equivalence, and termination". Floyd further wrote: A semant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
APL Programming Language
APL (named after the book ''A Programming Language'') is a programming language developed in the 1960s by Kenneth E. Iverson. Its central datatype is the multidimensional array. It uses a large range of special graphic symbols to represent most functions and operators, leading to very concise code. It has been an important influence on the development of concept modeling, spreadsheets, functional programming, and computer math packages. It has also inspired several other programming languages. History Mathematical notation A mathematical notation for manipulating arrays was developed by Kenneth E. Iverson, starting in 1957 at Harvard University. In 1960, he began work for IBM where he developed this notation with Adin Falkoff and published it in his book ''A Programming Language'' in 1962. The preface states its premise: This notation was used inside IBM for short research reports on computer systems, such as the Burroughs B5000 and its stack mechanism when stack mach ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Function
In mathematics, a binary function (also called bivariate function, or function of two variables) is a function that takes two inputs. Precisely stated, a function f is binary if there exists sets X, Y, Z such that :\,f \colon X \times Y \rightarrow Z where X \times Y is the Cartesian product of X and Y. Alternative definitions Set-theoretically, a binary function can be represented as a subset of the Cartesian product X \times Y \times Z, where (x,y,z) belongs to the subset if and only if f(x,y) = z. Conversely, a subset R defines a binary function if and only if for any x \in X and y \in Y, there exists a unique z \in Z such that (x,y,z) belongs to R. f(x,y) is then defined to be this z. Alternatively, a binary function may be interpreted as simply a function from X \times Y to Z. Even when thought of this way, however, one generally writes f(x,y) instead of f((x,y)). (That is, the same pair of parentheses is used to indicate both function application and the formation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rank (linear Algebra)
In linear algebra, the rank of a matrix is the dimension of the vector space generated (or spanned) by its columns. p. 48, § 1.16 This corresponds to the maximal number of linearly independent columns of . This, in turn, is identical to the dimension of the vector space spanned by its rows. Rank is thus a measure of the " nondegenerateness" of the system of linear equations and linear transformation encoded by . There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics. The rank is commonly denoted by or ; sometimes the parentheses are not written, as in .Alternative notation includes \rho (\Phi) from and . Main definitions In this section, we give some definitions of the rank of a matrix. Many definitions are possible; see Alternative definitions for several of these. The column rank of is the dimension of the column space of , while the row rank of is the dimension of the row space of . A fundamental resul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (: matrices) is a rectangle, rectangular array or table of numbers, symbol (formal), symbols, or expression (mathematics), expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two-by-three matrix", a " matrix", or a matrix of dimension . Matrices are commonly used in linear algebra, where they represent linear maps. In geometry, matrices are widely used for specifying and representing geometric transformations (for example rotation (mathematics), rotations) and coordinate changes. In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimensions. Matrices are used in most areas of mathematics and scientific fields, either directly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rank (J Programming Language)
Rank is a generalization of looping as used in scalar (non- array-oriented) programming languages. It is also a generalization of '' mapcar'' in the language ''Lisp'' and ''map'' in modern functional programming languages, and a generalization of scalar extension, inner (matrix) product, and outer product in APL\360. The canonical implementation of rank may be the language '' J'', but it is also available in Dyalog APL, the International Organization for Standardization (ISO) technical standard on Extended APL, and NARS2000. Rank has several different meanings. In general, the concept of ''rank'' is used to treat an orthogonal array in terms of its subarrays. For example, a two-dimensional array may be dealt with at rank 2 as the entire matrix, or at rank 1 to work with its implicit one-dimensional columns or rows, or at rank 0 to work at the level of its individual atoms. *''Noun rank'' – The rank of a noun is a nonnegative integer. *''Verb rank'' – The rank of a verb is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
J (programming Language)
The J programming language, developed in the early 1990s by Kenneth E. Iverson and Roger Hui, is an array programming language based primarily on APL (also by Iverson). To avoid repeating the APL special-character problem, J uses only the basic ASCII character set, resorting to the use of the dot and colon as ''inflections'' to form short words similar to '' digraphs''. Most such ''primary'' (or ''primitive'') J words serve as mathematical symbols, with the dot or colon extending the meaning of the basic characters available. Also, many characters which in other languages often must be paired (such as [] "" `` or ) are treated by J as stand-alone words or, when inflected, as single-character roots of multi-character words. J is a very terse array programming language, and is most suited to mathematical and statistical programming, especially when performing operations on matrices. It has also been used in extreme programming and network performance analysis. Like John B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 sums of their horizontal segments form a succession of twelve-tone aggregates * Array mbira, a musical instrument * Spiral array model, a music pitch space Science Astronomy A telescope array, also called astronomical interferometer. Biology * Various kinds of multiple biological arrays called microarrays * Visual feature array, a model for the visual cortex Computer science Generally, a collection of same type data items that can be selected by indices computed at run-time, including: * Array (data structure), an arrangement of items at equally spaced addresses in computer memory * Array (data type), used in a programming language to specify a variable that can be indexed * Associative array, an abstract data structure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
