TensorNetwork

Tenet.AbstractTensorNetwork Type

AbstractTensorNetwork

Abstract type for TensorNetwork-derived types. Its subtypes must implement conversion or extraction of the underlying TensorNetwork by overloading the TensorNetwork constructor.

Implementors interface

Any implementor of the AbstractTensorNetwork interface (currently only TensorNetwork) must define the following methods:

• inds

• tensors

• size

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Tenet.TensorNetwork Type

TensorNetwork

Hypergraph of interconnected tensors, representing a multilinear equation aka Tensor Network. Vertices represent tensors and edges, tensor indices.

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Base.append! Method

append!(tn::TensorNetwork, tensors::AbstractVecOrTuple{<:Tensor})

Add a list of tensors to a TensorNetwork.

See also: push!, merge!.

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Base.collect Method

Base.collect(tn::AbstractTensorNetwork)

Return a list of the Tensors in the TensorNetwork. It is equivalent to tensors(tn).

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Base.conj Method

conj(tn::AbstractTensorNetwork)

Return a copy of the AbstractTensorNetwork with all tensors conjugated.

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Base.copy Method

copy(tn::TensorNetwork)

Return a shallow copy of a TensorNetwork; i.e. changes to the copied TensorNetwork won't affect the original one, but changes to the tensors will.

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Base.delete! Method

delete!(tn::TensorNetwork, x)

Like pop! but return the TensorNetwork instead.

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Base.in Method

in(tensor::Tensor, tn::TensorNetwork)
in(index::Symbol, tn::TensorNetwork)

Return true if there is a Tensor in tn for which == evaluates to true. This method is equivalent to tensor ∈ tensors(tn) code, but it's faster on large amount of tensors.

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Base.merge! Method

merge!(self::TensorNetwork, others::TensorNetwork...)
merge(self::TensorNetwork, others::TensorNetwork...)

Fuse various TensorNetworks into one.

See also: append!.

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Base.pop! Method

pop!(tn::TensorNetwork, tensor::Tensor)
pop!(tn::TensorNetwork, i::Union{Symbol,AbstractVecOrTuple{Symbol}})

Remove a tensor from the Tensor Network and returns it. If a Tensor is passed, then the first tensor satisfies egality (i.e. ≡ or ===) will be removed. If a Symbol or a list of Symbols is passed, then remove and return the tensors that contain all the indices.

See also: push!, delete!.

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Base.push! Method

push!(tn::AbstractTensorNetwork, tensor::Tensor)

Add a new tensor to the Tensor Network.

See also: append!, pop!.

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Base.rand Method

rand(TensorNetwork, n::Integer, regularity::Integer; out = 0, dim = 2:9, seed = nothing, globalind = false)

Generate a random tensor network.

Arguments

• n Number of tensors.

• regularity Average number of indices per tensor.

• out Number of open indices.

• dim Range of dimension sizes.

• seed If not nothing, seed random generator with this value.

• globalind Add a global 'broadcast' dimension to every tensor.

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Base.replace! Method

replace!(tn::AbstractTensorNetwork, old => new...)
replace(tn::AbstractTensorNetwork, old => new...)

Replace the element in old with the one in new. Depending on the types of old and new, the following behaviour is expected:

• If Symbols, it will correspond to a index renaming.

• If Tensors, first element that satisfies egality (≡ or ===) will be replaced.

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Base.selectdim Method

selectdim(tn::AbstractTensorNetwork, index::Symbol, i)

Return a copy of the AbstractTensorNetwork where index has been projected to dimension i.

See also: view, slice!.

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Base.size Method

size(tn::AbstractTensorNetwork)
size(tn::AbstractTensorNetwork, index)

Return a mapping from indices to their dimensionalities.

If index is set, return the dimensionality of index. This is equivalent to size(tn)[index].

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Base.view Method

view(tn::AbstractTensorNetwork, index => i...)

Return a copy of the AbstractTensorNetwork where each index has been projected to dimension i. It is equivalent to a recursive call of selectdim.

See also: selectdim, slice!.

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EinExprs.einexpr Method

einexpr(tn::AbstractTensorNetwork; optimizer = EinExprs.Greedy, output = inds(tn, :open), kwargs...)

Search a contraction path for the given AbstractTensorNetwork and return it as a EinExpr.

Keyword Arguments

• optimizer Contraction path optimizer. Check EinExprs documentation for more info.

• outputs Indices that won't be contracted. Defaults to open indices.

• kwargs Options to be passed to the optimizer.

See also: contract.

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EinExprs.inds Function

inds(tn::AbstractTensorNetwork, set = :all)

Return the names of the indices in the AbstractTensorNetwork.

Keyword Arguments

• set

  • :all (default) All indices.

  • :open Indices only mentioned in one tensor.

  • :inner Indices mentioned at least twice.

  • :hyper Indices mentioned at least in three tensors.

  • :parallelto Indices parallel to i in the graph (i included).

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Tenet.arrays Method

arrays(tn::AbstractTensorNetwork; kwargs...)

Return a list of the arrays of in the TensorNetwork. It is equivalent to parent.(tensors(tn; kwargs...)).

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Tenet.contract! Method

contract!(tn::AbstractTensorNetwork, index)

In-place contraction of tensors connected to index.

See also: contract.

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Tenet.contract! Method

contract!(tn::AbstractTensorNetwork; path=einexpr(tn))

Same as contract but in-place.

See also: einexpr.

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Tenet.contract Method

contract(tn::AbstractTensorNetwork; path=einexpr(tn))

Contract a AbstractTensorNetwork. If path is not specified, the contraction order will be computed by einexpr.

See also: einexpr, contract!.

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Tenet.fuse! Method

fuse!(tn::AbstractTensorNetwork, i::Symbol)

Group indices parallel to i and reshape the tensors accordingly.

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Tenet.ninds Method

ninds(tn::TensorNetwork; kwargs...)

Return the number of indices in the TensorNetwork. It accepts the same keyword arguments as inds.

See also: ntensors

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Tenet.ntensors Method

ntensors(tn::AbstractTensorNetwork)

Return the number of tensors in the TensorNetwork. It accepts the same keyword arguments as tensors.

See also: ninds

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Tenet.resetinds! Method

resetinds!(tn::AbstractTensorNetwork; init::Int=1)

Rename all indices in the TensorNetwork to a new set of indices starting from initth Unicode character.

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Tenet.slice! Method

slice!(tn::AbstractTensorNetwork, index::Symbol, i)

In-place projection of index on dimension i.

See also: selectdim, view.

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Tenet.tensors Function

tensors(tn::AbstractTensorNetwork)

Return a list of the Tensors in the AbstractTensorNetwork.

Implementation details

• As the tensors of a AbstractTensorNetwork are stored as keys of the .tensormap dictionary and it uses objectid as hash, order is not stable so it sorts for repeated evaluations.

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