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For example, a container defined as std::vector<Shape*> does not work because Shape is not a class, but a template needing specialization. A container defined as std::vector<Shape<Circle>*> can only store Circles, not Squares. This is because each of the classes derived from the CRTP base class Shape is a unique type.
[10] [11] vector<bool> does not meet the requirements for a C++ Standard Library container. For instance, a container<T>::reference must be a true lvalue of type T. This is not the case with vector<bool>::reference, which is a proxy class convertible to bool. [12] Similarly, the vector<bool>::iterator does not yield a bool& when dereferenced.
LAPACK++, a C++ wrapper library for LAPACK and BLAS; MFEM is a free, lightweight, scalable C++ library for finite element methods. Intel MKL, Intel Math Kernel Library (in C and C++), a library of optimized math routines for science, engineering, and financial applications, written in C/C++ and Fortran. Core math functions include BLAS, LAPACK ...
Automatic vectorization, in parallel computing, is a special case of automatic parallelization, where a computer program is converted from a scalar implementation, which processes a single pair of operands at a time, to a vector implementation, which processes one operation on multiple pairs of operands at once.
Given an n × n square matrix A of real or complex numbers, an eigenvalue λ and its associated generalized eigenvector v are a pair obeying the relation [1] =,where v is a nonzero n × 1 column vector, I is the n × n identity matrix, k is a positive integer, and both λ and v are allowed to be complex even when A is real.l When k = 1, the vector is called simply an eigenvector, and the pair ...
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.
In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix, the algorithm will produce a number , which is the greatest (in absolute value) eigenvalue of , and a nonzero vector , which is a corresponding eigenvector of , that is, =.
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.