Multiplication between tensor and vectors

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giordano de marzo
giordano de marzo 2019-5-11
回答： Matthew Paluszak 2020-5-29
I've a big tensor M_{abc}, let's say 500*200*500, and 3 vectors X, Y and Z whose dimensions are 500, 200 and 500. I've to perform the following operations
  • X_a=M_{abc}Y_bZ_c
  • Y_b=M_{abc}X_aZ_c
  • Z_c=M_{abc}X_aY_b
  • X=X/mean(X)
  • Y=Y/mean(Y)
  • Z=Z/mean(Z)
where the repeated indices are to be summed (M_{abc}Y_bZ_c=\sum_{b, c} M_{abc}Y_bZ_c). In the two dimensional case (matrix and two vectors) I would simply use matrix multiplications, considering that I've to repeat the procedure something between 5 and 50 times, till the 3 vectors converge stopping to vary under a new application of the algorithm, which is the best way to perform this procedure (hopefully without for loops)?

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回答（1 个）

Matthew Paluszak
Matthew Paluszak 2020-5-29
I don’t know the answer, but I also would like to know!

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