Array programming

In computer science, array programming refers to solutions which allow the application of operations to an entire set of values at once. Such solutions are commonly used in scientific and engineering settings. most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered significant by, say, an applied mathematician.it is important to distinguish the difficulty of describing and of learning a piece of notation from the difficulty of mastering its implications. For example, learning the rules for computing a matrix product is easy, but a mastery of its implications (such as its associativity, its distributivity over addition, and its ability to represent linear functions and geometric operations) is a different and much more difficult matter. In computer science, array programming refers to solutions which allow the application of operations to an entire set of values at once. Such solutions are commonly used in scientific and engineering settings. Modern programming languages that support array programming (also known as vector or multidimensional languages) have been engineered specifically to generalize operations on scalars to apply transparently to vectors, matrices, and higher-dimensional arrays. These include APL, Fortran 90, Mata, MATLAB, Analytica, TK Solver (as lists), Octave, R, Cilk Plus, Julia, Perl Data Language (PDL), Wolfram Language, and the NumPy extension to Python. In these languages, an operation that operates on entire arrays can be called a vectorized operation, regardless of whether it is executed on a vector processor (which implements vector instructions) or not. Array programming primitives concisely express broad ideas about data manipulation. The level of concision can be dramatic in certain cases: it is not uncommon to find array programming language one-liners that require more than a couple of pages of Java code. The fundamental idea behind array programming is that operations apply at once to an entire set of values. This makes it a high-level programming model as it allows the programmer to think and operate on whole aggregates of data, without having to resort to explicit loops of individual scalar operations. Iverson described the rationale behind array programming (actually referring to APL) as follows: The basis behind array programming and thinking is to find and exploit the properties of data where individual elements are similar or adjacent. Unlike object orientation which implicitly breaks down data to its constituent parts (or scalar quantities), array orientation looks to group data and apply a uniform handling. Function rank is an important concept to array programming languages in general, by analogy to tensor rank in mathematics: functions that operate on data may be classified by the number of dimensions they act on. Ordinary multiplication, for example, is a scalar ranked function because it operates on zero-dimensional data (individual numbers). The cross product operation is an example of a vector rank function because it operates on vectors, not scalars. Matrix multiplication is an example of a 2-rank function, because it operates on 2-dimensional objects (matrices). Collapse operators reduce the dimensionality of an input data array by one or more dimensions. For example, summing over elements collapses the input array by 1 dimension. Array programming is very well suited to implicit parallelization; a topic of much research nowadays. Further, Intel and compatible CPUs developed and produced after 1997 contained various instruction set extensions, starting from MMX and continuing through SSSE3 and 3DNow!, which include rudimentary SIMD array capabilities. Array processing is distinct from parallel processing in that one physical processor performs operations on a group of items simultaneously while parallel processing aims to split a larger problem into smaller ones (MIMD) to be solved piecemeal by numerous processors. Processors with two or more cores are increasingly common today. The canonical examples of array programming languages are Fortran, APL, and J. Others include: A+, Analytica, Chapel, IDL, Julia, K, Klong, Q, Mata, Wolfram Language, MATLAB, MOLSF, NumPy, GNU Octave, PDL, R, S-Lang, SAC, Nial and ZPL.