[Numpy-discussion] Software Capabilities of NumPy in Our Tensor Survey Paper

[Li Jiajia]

Hi all,
	I’m a PhD student in Georgia Tech. Recently, we’re working on a survey paper about tensor algorithms: basic tensor operations, tensor decomposition and some tensor applications. We are making a table to compare the capabilities of different software and planning to include NumPy. We’d like to make sure these parameters are correct to make a fair compare. Although we have looked into the related documents, please help us to confirm these. Besides, if you think there are more features of your software and a more preferred citation, please let us know. We’ll consider to update them. We want to show NumPy supports tensors, and we also include "scikit-tensor” in our survey, which is based on NumPy.
	Please let me know any confusion or any advice! 
	Thanks a lot! :-)

Notice: 
1. “YES/NO” to show whether or not the software supports the operation or has the feature.
2. “?” means we’re not sure of the feature, and please help us out. 
3. “Tensor order” means the maximum number of tensor dimensions that users can do with this software. 
4. For computational cores, 
	1) "Element-wise Tensor Operation (A * B)” includes element-wise add/minus/multiply/divide, also Kronecker, outer and Katri-Rao products. If the software contains one of them, we mark “YES”.
	2) “TTM” means tensor-times-matrix multiplication. We distinguish TTM from tensor contraction. If the software includes tensor contraction, it can also support TTM.
	3) For “MTTKRP”, we know most software can realize it through the above two operations. We mark it “YES”, only if an specified optimization for the whole operation.

 <> <>Software Name <>	
NumPy

Computational Cores

Element-wise Tensor Operation (A * B)

YES

Tensor Contraction (A Xmn B)

NO

TTM ( A Xn B)

NO

Matriced Tensor Times Khatri-Rao Product (MTTKRP)

NO

Tensor Decomposition

CP

NO

Tucker

NO

Hierarchical Tucker (HT)

NO

Tensor Train (TT)

NO

Tensor Features

Tensor Order

Arbitrary

Dense Tensors

YES

Sparse Tensors

NO ?

Parallelized

NO ?

Software Information

Application Domain

General 

Programming Environment

Python

Latest Version

1.10.4
Release Date

2016

Citation: 
1. AN DER WALT, S., COLBERT, S., AND VAROQUAUX, G. The NumPy array: A structure for efficient numerical computation. Computing in Science Engineering 13, 2 (March 2011), 22–30.
2. OLIPHANT, T. E. Python for scientific computing. Computing in Science Engineering 9, 3 (May 2007), 10–20.
3. NumPy (Version1.10.4).Available from http://www.numpy.org, Jan <http://www.numpy.org, Jan> 2016.

Best regards!
Jiajia Li

------------------------------------------
E-mail: jiajiali at gatech.edu
Tel: +1 (404)9404603
Computational Science & Engineering
Georgia Institute of Technology

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