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These include APL, J, Fortran, MATLAB, Analytica, Octave, R, Cilk Plus, Julia, Perl Data Language (PDL), Raku (programming language). In these languages, an operation that operates on entire arrays can be called a vectorized operation, [1] regardless of whether it is executed on a vector processor, which implements vector instructions. Array ...
The elementary functions are constructed by composing arithmetic operations, the exponential function (), the natural logarithm (), trigonometric functions (,), and their inverses. The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's ...
These operations and associated laws qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space. Vectors play an important role in physics : the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors. [ 7 ]
Algebraic expressions were written in reverse Polish notation; thus, + was written a b +, and similarly for the other arithmetic operations of subtraction, multiplication, and division. The algebraic expression a x 2 + b x + c {\displaystyle ax^{2}+bx+c} was written a x dup × × b x × + c + , where ' dup ' meant 'duplicate the value'.
R is a programming language for statistical computing and data visualization. It has been adopted in the fields of data mining, bioinformatics and data analysis. [9] The core R language is augmented by a large number of extension packages, containing reusable code, documentation, and sample data. R software is open-source and free software.
In mathematics, the dot product or scalar product [note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry , the dot product of the Cartesian coordinates of two vectors is widely used.
Programming languages that implement matrices may have easy means for vectorization. In Matlab/GNU Octave a matrix A can be vectorized by A(:). GNU Octave also allows vectorization and half-vectorization with vec(A) and vech(A) respectively. Julia has the vec(A) function as well.
An n-ary operation ω: X n → X is called an internal operation. An n-ary operation ω: X i × S × X n − i − 1 → X where 0 ≤ i < n is called an external operation by the scalar set or operator set S. In particular for a binary operation, ω: S × X → X is called a left-external operation by S, and ω: X × S → X is called a right ...