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TensorTrainTools

Guides

  • TensorTrainTools Overview

Symbols

  • RandomTensorTrain
  • TensorTrainCompress
  • TensorTrainContract
  • TensorTrainDecomposition
  • TensorTrainHadamard
  • TensorTrainInnerProduct
  • TensorTrain
  • TensorTrainNorm
  • TensorTrainOrthogonalize
  • TensorTrainPlus
  • TensorTrainScale
RubenRanval`TensorTrainTools`
TensorTrainNorm
​
TensorTrainNorm
[tt]
gives the Frobenius norm of the tensor represented by the tensor train
tt
​
Details and Options
▪
The norm is computed without forming the dense tensor: the train is left-orthogonalized, after which the norm equals the Euclidean norm of the single non-orthonormal core.
▪
TensorTrainNorm
[tt]
produce the same result up to the rounding error as
Sqrt
[
TensorTrainInnerProduct
[tt,tt]]
.
Examples  
(1)
Basic Examples  
(1)
Get the norm of a random tensor train:
In[1]:=
tt=TensorTrainDecomposition[RandomReal[1,{1,2,3}]];​​TensorTrainNorm[tt]
Out[1]=
1.75589
This gives the same result as
Sqrt
[
TensorTrainInnerProduct
[tt,tt]]
:
In[2]:=
TensorTrainNorm[tt]Sqrt[TensorTrainInnerProduct[tt,tt]]
Out[2]=
True
RelatedGuides
▪
TensorTrainTools Overview
""

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