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In Python NumPy arrays implement the flatten method, [note 1] while in R the desired effect can be achieved via the c() or as.vector() functions. In R , function vec() of package 'ks' allows vectorization and function vech() implemented in both packages 'ks' and 'sn' allows half-vectorization.
In C++ several linear algebra libraries exploit the language's ability to overload operators. In some cases a very terse abstraction in those languages is explicitly influenced by the array programming paradigm, as the NumPy extension library to Python , Armadillo and Blitz++ libraries do.
Here, c[i:i+3] represents the four array elements from c[i] to c[i+3] and the vector processor can perform four operations for a single vector instruction. Since the four vector operations complete in roughly the same time as one scalar instruction, the vector approach can run up to four times faster than the original code.
Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. Fastor [5] R. Poya, A. J. Gil and R. Ortigosa C++ 2016 0.6.4 / 06.2023 Free MIT License: Fastor is a high performance tensor (fixed multi-dimensional array) library for modern C++. GNU Scientific Library [6] GNU Project C, C++ 1996
By analogy with the mathematical concepts vector and matrix, array types with one and two indices are often called vector type and matrix type, respectively. More generally, a multidimensional array type can be called a tensor type , by analogy with the physical concept, tensor .
Automatic vectorization, a compiler optimization that transforms loops to vector operations; Image tracing, the creation of vector from raster graphics; Word embedding, mapping words to vectors, in natural language processing
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to speak, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression.
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication.