Use this tag for questions that involve tensors. Tensors are fundamental tools for linear computations, generalizing vectors and matrices to higher ranks. Mathematica 9 introduces powerful methods to algebraically manipulate tensors with any rank and symmetry.

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7
votes
1answer
246 views

Compiling Map over expression that yields a ragged array

I'm trying to speed up a function that looks in the neighborhood of each 3D point in a large dataset and finds all the points within 1 unit in each direction, x, y, z. I've started by using ...
6
votes
1answer
324 views

Solving antisymmetric tensorial equation

Assume we have the following Tensor objects: \begin{equation} F_{i}{}^{j}\;and\;S_{ij}{}^{k}, \end{equation} where the components of $F$ are known, and we would like to solve for the components of $S$ ...
16
votes
4answers
5k views

How to calculate scalar curvature Ricci tensor and Christoffel symbols in Mathematica?

I am seeking a convenient and effective way to calculate such geometric quantities. I've used packages like TensoriaCalc, but they don't work at all time. ...
5
votes
3answers
466 views

Multidimensional array reduction through summation over one of its dimensions

1. Introduction I am using an array of dimension 3 (might become more) to store some values. I would like to implement a function that takes as argument the array and a couple of numbers smaller than ...
13
votes
2answers
749 views

Higher order SVD

Does anyone know how to do a higher order SVD in Mathematica ? A good reference seems to be here http://www.sandia.gov/~tgkolda/pubs/pubfiles/SAND2007-6702.pdf but I don't understand their formalism ...
5
votes
1answer
225 views

Problems with CircleTimes and infix notation

I am trying to create a function called TensorBasis that takes as input a list (thought of as a list of names of basis vectors of a vector space) and an integer ...
10
votes
1answer
577 views

Nesting Parallel processes

I just attempted to run code that had nested ParallelMap[] functions. It generates the error message: ParallelMap::subpar: Parallel computations cannot be nested; proceeding with sequential ...
40
votes
2answers
2k views

Internal`Bag inside Compile

Since Internal`Bag, Internal`StuffBag and Internal`BagPart can be compiled down, it is a ...
14
votes
2answers
2k views

How to represent and manipulate abstract indexed vector (or tensor) expressions?

I have a couple abstract indexed quantities, both differential elements $dx = dx^\mu e_\mu + x^\mu de_\mu$ $du = du^\mu e_\mu + u^\mu de_\mu$ I can compute the expression $(dx + du) \cdot (dx + du) ...