Homepage of "tensorA",
an R package for tensor algebra

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Disclaimer

Current version

Future versions

• The discussion on further necessary functionality is hereby opened.
• Whoever might find himself able to provide a more detailed and mathematically found explanation of tensors and their operations - maybe including informative English references - for the help files, is warmly invited for honorable contribution.
• A the thing with tensorial derivatives in missing in the package. However it is not clear how to implement such a thing in a numerical package, since derivatives are symbolic concept. I am looking for suggestions.
• The package currently only provides basic statistical procedures for tensors (mean and variance). General non-centered, centered and factorial moments are planned. Can anybody provide tensorial datasets? What models are most used?

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What is "tensorA"?

Simply speaking a tensor is multidimensional array. And seen from this point of view the package just provides some additional operations of arrays. All those who want to do computations on arrays that are most naturally expressed in operations of tensors, vectors and matrices of vectors or matrices will find this package useful for several reasons:

• The package organizes the dimensions by names, such that there is no need reordering dimensions or keeping track of the sequence of dimensions.
• The package supports parallelized computations on datasets of vectors, matrices and tensors just as R provides for numbers, e.g. inversion, solving of equation system, decompositions. The resulting computation is typically substantially faster, transparent, and faster to code than any sapply constructs computing the same results.
• The package provides a direct implementation of the calculus of tensor algebra including co- and contravariate basis, Einsteins and Riemanns summing convention, dragging rule and named indices.