Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
RubenRanval`TensorTrainTools`
TensorTrainContract  |
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TensorTrainContract
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The input is a nonempty list of rank-3 arrays , where is the number of dimensions of the resulting array.
{,…,}
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1
A
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n
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The bond dimension refers to the size of the internal contracted indices connecting adjacent tensor cores. It effectively dictates the rank and compression level of the Tensor Train.
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Each core has dimensions where is the size of the dimension of the resulting array, and is the bond dimension between cores and .
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k
{,,}
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k-1
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th
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k+1
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The first core has =1 and the last core has =1.
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0
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Contracting the cores returned by reconstructs the original array, exactly up to floating-point error when the decomposition was exact, or up to the truncation error when a cap or nonzero was applied.
"MaxBondDimension"
Examples
(3)
Basic Examples
(1)
Decompose a tensor and contract it back to recover the original array:
In[1]:=
tensor=RandomReal[1,{2,3,4}];tensor//MatrixForm
Out[1]//MatrixForm=
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In[2]:=
tensorTrain=TensorTrainDecomposition@tensor
Out[2]=
TensorTrain
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In[3]:=
recon=TensorTrainContract@%
Out[3]=
{{{0.82289,0.370384,0.775953,0.933255},{0.393653,0.765388,0.293522,0.264758},{0.0890085,0.766846,0.725353,0.692162}},{{0.529998,0.907113,0.837152,0.237219},{0.501381,0.0981147,0.324782,0.973763},{0.222511,0.275392,0.868763,0.0271}}}
In[4]:=
%//MatrixForm
Out[4]//MatrixForm=
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The original and the reconstructed tensors are exactly equal up to floating-point error:
In[5]:=
Max[Abs[tensor-recon]]
Out[5]=
9.99201×
-16
10
Applications
(1)
Possible Issues
(1)
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""