Editing Array programming (section)

==Concepts of array==
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 language|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.

[[Kenneth E. Iverson]] described the rationale behind array programming (actually referring to APL) as follows:<ref>{{cite journal |last= Iverson |first=K. E. |title= Notation as a Tool of Thought |journal= Communications of the ACM |volume= 23 |issue= 8 |pages= 444–465 |year= 1980 |doi= 10.1145/358896.358899 |author-link= Kenneth E. Iverson |doi-access= free }}</ref>
{{quote|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.
The thesis is that the advantages of executability and universality found in programming languages can be effectively combined, in a single coherent language, with the advantages offered by mathematical notation. 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.

Indeed, the very suggestiveness of a notation may make it seem harder to learn because of the many properties it suggests for explorations.

[...]
Users of computers and programming languages are often concerned primarily with the efficiency of execution of algorithms, and might, therefore, summarily dismiss many of the algorithms presented here. Such dismissal would be short-sighted since a clear statement of an algorithm can usually be used as a basis from which one may easily derive a more efficient algorithm.}}

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 (computing)|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). [[Reduce (higher-order function)|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.