RubenRanval/TensorTrainTools | Paclet Repository

RubenRanval`TensorTrainTools`

TensorTrain

TensorTrain [{ A 1 , A 2 ,…, A n }]
	represents a tensor in tensor train format with rank-3 cores A i

Details and Options

▪

A tensor train (also called a matrix product state, MPS) expresses a tensor of rank

as a chain of

rank-3 cores, typically storing far fewer elements than the dense tensor.

▪

Each core

must be a rank-3 array with dimensions

{

i-1

}

, where

is the

dimension of the represented tensor and

are the bond dimensions.

▪

The boundary bond dimensions

and

must both equal 1, and the last dimension of each core must equal the first dimension of the following core.

▪

validates its cores, issuing a message and returning

if they do not form a valid tensor train.

▪

[…]["Properties"]

gives a list of all available properties.

	"Cores"	the list of rank-3 cores
	"CoreCount"	the number of cores
	"TensorDimensions"	the dimensions of the original tensor
	"BondDimensions"	the internal bond dimensions of the tensor train
	"ParameterCount"	the total number of stored core elements
	"FullElementCount"	the number of elements of the represented dense tensor
	"CompressionRatio"	ratio of dense element count to stored paramater count
	"Tensor"	the original input tensor
	"Diagram"	a tensor network diagram of the train