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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.
After flattening, arrays are represented as single-dimensional value vector V containing scalar elements, alongside auxiliary information recording the nested structure, typically in the form of a boolean flag vector F. The flag vector indicates, for the corresponding element in the value vector, whether it is the beginning of a new segment.
NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
Support for multi-dimensional arrays may also be provided by external libraries, which may even support arbitrary orderings, where each dimension has a stride value, and row-major or column-major are just two possible resulting interpretations. Row-major order is the default in NumPy [19] (for Python).
The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b.
There are three variants: the flattening , [1] sometimes called the first flattening, [2] as well as two other "flattenings" ′ and , each sometimes called the second flattening, [3] sometimes only given a symbol, [4] or sometimes called the second flattening and third flattening, respectively.
Gauss-Legendre (1D and tensor product rules in 2D and 3D) tabulated up to 44th-order to high precision, best available rules for triangles and tetrahedra to very high order, best available monomial rules for quadrilaterals and hexahedra.
The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [5] [6] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [7] or they can be used to build a pointer based quadtree.