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Fastor is a high performance tensor (fixed multi-dimensional array) library for modern C++. GNU Scientific Library [6] GNU Project C, C++ 1996 2.7.1 / 11.2021 Free GPL: General purpose numerical analysis library. Includes some support for linear algebra. IMSL Numerical Libraries: Rogue Wave Software: C, Java, C#, Fortran, Python 1970 many ...
vmmlib [44] is a C++ linear algebra library that supports 3-way tensors, emphasizing computation and manipulation of several tensor decompositions. Spartns [45] is a Sparse Tensor framework for Common Lisp. FAstMat [46] is a thread-safe general tensor algebra library written in C++ and specially designed for FEM/FVM/BEM/FDM element/edge wise ...
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. IT++ is a C++ library for linear algebra (matrices and vectors), signal processing and communications ...
The following tables provide a comparison of computer algebra systems (CAS). [ 1 ] [ 2 ] [ 3 ] A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language.
In machine learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector ...
Version 1.0 was released in Dec 2006. [3] Eigen is implemented using the expression templates metaprogramming technique, meaning it builds expression trees at compile time and generates custom code to evaluate these. Using expression templates and a cost model of floating point operations, the library performs its own loop unrolling and ...
Tensor contraction is an operation that reduces a type (n, m) tensor to a type (n − 1, m − 1) tensor, of which the trace is a special case. It thereby reduces the total order of a tensor by two. It thereby reduces the total order of a tensor by two.
Mathematically vectors are elements of a vector space over a field, and for use in physics is usually defined with = or .Concretely, if the dimension = of is finite, then, after making a choice of basis, we can view such vector spaces as or .