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Solving linear equations involving tensors #27

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ajdunlap opened this issue Apr 19, 2017 · 2 comments
Open

Solving linear equations involving tensors #27

ajdunlap opened this issue Apr 19, 2017 · 2 comments

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@ajdunlap
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If you have a fixed tensor X and fix some indices, then contracting this tensor with another tensor along the given indices is a linear map on tensors (of each fixed size). It would be nice if this package provided a way to solve linear systems of this form. Technically, this should be no more difficult than inverting a matrix -- the request is just for a way to support solving the system within the tensor notation.

@Jutho
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Jutho commented Apr 21, 2017

Do you have a good tensor notation convention for denoting this operation? I/You can of course easily write a function for that and to the necessary permutations and reshapes, but I read your request as having this supported within the @tensor macro?

@ajdunlap
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Yeah, that was my suggestion, but indeed a great notation does not come to mind. Perhaps a more achievable goal would be a nice notation for reshaping an array within the @tensor macro? E.g. a way if I have a tensor with 4 indices to "combine" the first and second indices, or the second and third, or the first and third and fourth, etc?

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