MATLAB tensor classes for fast algorithm prototyping.

Bader, Brett William ; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)

Sandia National Laboratories

关键词: 99 General And Miscellaneous//Mathematics, Computing, And Information Science;    97 Mathematical Methods And Computing;    Calculus Of Tensors.;    Tensors Image Processing.;    Arrays.;   

DOI  :  10.2172/974890
RP-ID  :  SAND2004-5187
RP-ID  :  AC04-94AL85000
RP-ID  :  974890

美国|英语

来源: UNT Digital Library

【 摘 要 】

Tensors (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.