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The cross product operation is an example of a vector rank function because it operates on vectors, not scalars. Matrix multiplication is an example of a 2-rank function, because it operates on 2-dimensional objects (matrices). Collapse operators reduce the dimensionality of an input data array by one or more dimensions. For example, summing ...
The dynamic array has performance similar to an array, with the addition of new operations to add and remove elements: Getting or setting the value at a particular index (constant time) Iterating over the elements in order (linear time, good cache performance) Inserting or deleting an element in the middle of the array (linear time)
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.
Python 2001 1.11.1 / 6.2023 Free BSD: Based on Python Xtensor [12] S. Corlay, W. Vollprecht, J. Mabille et al. C++ 2016 0.21.10 / 11.2020 Free 3-clause BSD: Xtensor is a C++ library meant for numerical analysis with multi-dimensional array expressions, broadcasting and lazy computing.
Eigen is a vector mathematics library with performance comparable with Intel's Math Kernel Library; Hermes Project: C++/Python library for rapid prototyping of space- and space-time adaptive hp-FEM solvers. IML++ is a C++ library for solving linear systems of equations, capable of dealing with dense, sparse, and distributed matrices.
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It is the vector equivalent of register indirect addressing, with gather involving indexed reads, and scatter, indexed writes. Vector processors (and some SIMD units in CPUs ) have hardware support for gather and scatter operations, as do many input/output systems, allowing large data sets to be transferred to main memory more rapidly.
In computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms, an associative array is a function with finite domain. [1] It supports 'lookup', 'remove', and 'insert ...