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MapReduce is a programming model and an associated implementation for processing and generating big data sets with a parallel and distributed algorithm on a cluster. [1] [2] [3]A MapReduce program is composed of a map procedure, which performs filtering and sorting (such as sorting students by first name into queues, one queue for each name), and a reduce method, which performs a summary ...
In Haskell, the polymorphic function map :: (a -> b) -> [a] -> [b] is generalized to a polytypic function fmap :: Functor f => (a -> b) -> f a -> f b, which applies to any type belonging the Functor type class. The type constructor of lists [] can be defined as an instance of the Functor type class using the map function from the previous example:
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
A typical example of RDD-centric functional programming is the following Scala program that computes the frequencies of all words occurring in a set of text files and prints the most common ones. Each map , flatMap (a variant of map ) and reduceByKey takes an anonymous function that performs a simple operation on a single data item (or a pair ...
The term map may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial. [3] [4] In category theory, a map may refer to a morphism. [2]
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.
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Graph of tent map function Example of iterating the initial condition x 0 = 0.4 over the tent map with μ = 1.9. In mathematics, the tent map with parameter μ is the real-valued function f μ defined by ():= {,}, the name being due to the tent-like shape of the graph of f μ.