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array_reduce(array, func, initval) array_reduce(array_reverse(array), func, initval) array_reduce(array, func) array_reduce(array_reverse(array), func) When initval is not supplied, NULL is used, so this is not a true foldl1. Before PHP 5.3, initval can only be integer. func is a callback Archived 2020-11-28 at the Wayback Machine. Try array ...
Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.
map function, found in many functional programming languages, is one example of a higher-order function. It takes as arguments a function f and a collection of elements, and as the result, returns a new collection with f applied to each element from the collection.
var c = 0.0 // The array input has elements indexed for i = 1 to input.length do // c is zero the first time around. var y = input[i] + c // sum + c is an approximation to the exact sum. (sum,c) = Fast2Sum(sum,y) // Next time around, the lost low part will be added to y in a fresh attempt. next i return sum
An Array is a JavaScript object prototyped from the Array constructor specifically designed to store data values indexed by integer keys. Arrays, unlike the basic Object type, are prototyped with methods and properties to aid the programmer in routine tasks (for example, join , slice , and push ).
Starting the summation from the beginning of the array yields: (((((+) +) +) +) +) +) + = Since '+' is both commutative and associative, it is a reduction operator. Therefore this reduction can be performed in parallel using several cores, where each core computes the sum of a subset of the array, and the reduction operator merges the results.
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
Given a function that accepts an array, a range query (,) on an array = [,..,] takes two indices and and returns the result of when applied to the subarray [, …,].For example, for a function that returns the sum of all values in an array, the range query (,) returns the sum of all values in the range [,].