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TensorTrainTools

Guides

  • TensorTrainTools Overview

Symbols

  • RandomTensorTrain
  • TensorTrainCompress
  • TensorTrainContract
  • TensorTrainDecomposition
  • TensorTrainHadamard
  • TensorTrainInnerProduct
  • TensorTrain
  • TensorTrainNorm
  • TensorTrainOrthogonalize
  • TensorTrainPlus
  • TensorTrainScale
RubenRanval`TensorTrainTools`
TensorTrainHadamard
​
TensorTrainHadamard
[
t
1
,
t
2
,…]
gives the elementwise (Hadamard) product of the tensor trains
t
i
​
Details and Options
▪
The product is exact: cores are combined by Kronecker products of the bond spaces, so the bond dimensions of the result are the products of the operands' bond dimensions.
▪
Bond growth is therefore multiplicative. Compress with
TensorTrainCompress
when chaining products to reduce the overall bond dimension.
▪
t
1
⊙
t
2
…
is equivalent to
TensorTrainHadamard
[
t
1
,
t
2
,…]
.
Examples  
(1)
Basic Examples  
(1)
Notice the bond dimensions of the result are the products of the operands' bond dimensions:
In[1]:=
a=TensorTrainDecomposition[RandomReal[1,{2,3,4}]]​​b=TensorTrainDecomposition[RandomReal[1,{2,3,4}]]
Out[1]=
TensorTrain
Cores: 3
Max χ: 4
Tensor dims: {2,3,4}

Out[1]=
TensorTrain
Cores: 3
Max χ: 4
Tensor dims: {2,3,4}

In[2]:=
TensorTrainHadamard[a,b]
Out[2]=
TensorTrain
Cores: 3
Max χ: 16
Tensor dims: {2,3,4}

Use
TensorTrainCompress
after each operation to reduce the overall bond dimension:
In[3]:=
%//TensorTrainCompress
Out[3]=
TensorTrain
Cores: 3
Max χ: 4
Tensor dims: {2,3,4}

RelatedGuides
▪
TensorTrainTools Overview
""

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