Tensor

Tenet.Tensor Type

Tensor{T,N,A<:AbstractArray{T,N}} <: AbstractArray{T,N}

An array-like object with named dimensions.

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Tenet.Tensor Method

Tensor(data::AbstractArray{T,N}, inds::AbstractVector{Symbol})
Tensor(data::AbstractArray{T,N}, inds::NTuple{N,Symbol}) where {T,N}
Tensor(data::AbstractArray{T,0}) where {T}
Tensor(data::Number)

Construct a tensor with the given data and indices.

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Base.adjoint Method

Base.adjoint(::Tensor)

Return the adjoint of the tensor.

Note

This method doesn't transpose the array. It is equivalent to conj.

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Base.conj Method

Base.conj(::Tensor)

Return the conjugate of the tensor.

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Base.dropdims Method

Base.dropdims(tensor::Tensor; dims)

Return a tensor where the dimensions specified by dims are removed. size(tensor, dim) == 1 for each dimension in dims.

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Base.getindex Method

Base.getindex(::Tensor, i...)
Base.getindex(::Tensor; i...)
(::Tensor)[index=i...]

Return the element of the tensor at the given indices. If kwargs are provided, then it is equivalent to calling view.

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Base.length Method

Base.length(::Tensor)

Return the length of the underlying array.

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Base.parent Method

Base.parent(::Tensor)

Return the underlying array of the tensor.

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Base.permutedims Method

Base.permutedims(tensor::Tensor, perm)

Permute the dimensions of tensor according to the given permutation perm. The inds will be permuted accordingly.

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Base.replace Method

Base.replace(::Tensor, old_new::Pair{Symbol,Symbol}...)

Replace the indices of the tensor according to the given pairs of old and new indices.

Warning

This method does not support cyclic replacements.

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Base.selectdim Method

Base.selectdim(tensor::Tensor, dim::Symbol, i)
Base.selectdim(tensor::Tensor, dim::Integer, i)

Return a view of the tensor where the index for dimension dim equals i.

Note

This method doesn't return a SubArray, but a Tensor wrapping a SubArray.

See also: selectdim

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Base.setindex! Method

Base.setindex!(t::Tensor, v, i...)
Base.setindex(::Tensor; i...)
(::Tensor)[index=i...]

Set the element of the tensor at the given indices to v. If kwargs are provided, then it is equivalent to calling .= on view.

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Base.similar Method

Base.similar(::Tensor{T,N}[, S::Type, dims::Base.Dims{N}; inds])

Return a uninitialize tensor of the same size, eltype and inds as tensor. If S is provided, the eltype of the tensor will be S. If dims is provided, the size of the tensor will be dims.

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Base.size Method

Base.size(::Tensor[, i::Symbol])

Return the size of the underlying array. If the dimension i (specified by Symbol or Integer) is specified, then the size of the corresponding dimension is returned.

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Base.view Method

Base.view(tensor::Tensor, i...)
Base.view(tensor::Tensor, inds::Pair{Symbol,<:Any}...)

Return a view of the tensor with the given indices. If a Pair is given, the index is replaced by the value of the pair.

Note

This method doesn't return a SubArray, but a Tensor wrapping a SubArray.

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Base.zero Method

Base.zero(tensor::Tensor)

Return a tensor of the same size, eltype and inds as tensor but filled with zeros.

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EinExprs.inds Method

inds(tensor::Tensor)

Return the indices of the tensor in the order of the dimensions.

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Tenet.dim Method

dim(tensor::Tensor, i::Symbol)

Return the location of the dimension of tensor corresponding to the given index i.

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Tenet.expand Method

expand(tensor::Tensor; label[, axis=1, size=1, method=:zeros])

Expand the tensor by adding a new dimension label with the given size at the specified axis. Currently the supported methods are :zeros and :repeat.

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Tenet.fuse Method

fuse(tensor, parinds; ind=first(parinds))

Fuses parinds, leaves them on the right-side internally permuted with permutator and names it as ind.

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Base.:* Method

*(::Tensor, ::Tensor)
*(::Tensor, ::Number)
*(::Number, ::Tensor)

Alias for contract.

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Base.:+ Method

+(::Tensor, ::Tensor)

Add two tensors element-wise. The tensors must have the same indices, alghough the order of the indices can be different.

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Base.:- Method

-(::Tensor, ::Tensor)

Subtract two tensors element-wise. The tensors must have the same indices, alghough the order of the indices can be different.

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LinearAlgebra.lu Method

LinearAlgebra.lu(tensor::Tensor; left_inds, right_inds, virtualind, kwargs...)

Perform LU factorization on a tensor. Either left_inds or right_inds must be specified, unless ndims(tensor) == 2 in which case no indices need to be specified.

Keyword arguments

• left_inds: left indices to be used in the LU factorization. Defaults to all indices of t except right_inds.

• right_inds: right indices to be used in the LU factorization. Defaults to all indices of t except left_inds.

• virtualind: name of the virtual bond. Defaults to a random Symbol.

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LinearAlgebra.qr Method

LinearAlgebra.qr(tensor::Tensor; left_inds, right_inds, virtualind, kwargs...)

Perform QR factorization on a tensor. Either left_inds or right_inds must be specified, unless ndims(tensor) == 2 in which case no indices need to be specified.

Keyword arguments

• left_inds: left indices to be used in the QR factorization. Defaults to all indices of t except right_inds.

• right_inds: right indices to be used in the QR factorization. Defaults to all indices of t except left_inds.

• virtualind: name of the virtual bond. Defaults to a random Symbol.

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LinearAlgebra.svd Method

LinearAlgebra.svd(tensor::Tensor; left_inds, right_inds, virtualind, kwargs...)

Perform SVD factorization on a tensor. Either left_inds or right_inds must be specified, unless ndims(tensor) == 2 in which case no indices need to be specified.

Keyword arguments

• left_inds: left indices to be used in the SVD factorization. Defaults to all indices of t except right_inds.

• right_inds: right indices to be used in the SVD factorization. Defaults to all indices of t except left_inds.

• virtualind: name of the virtual bond. Defaults to a random Symbol.

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Tenet.contract! Method

contract!(c::Tensor, a::Tensor, b::Tensor)

Perform a binary tensor contraction operation between a and b and store the result in c.

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Tenet.contract! Method

contract!(c::Tensor, a::Tensor)

Perform a unary tensor contraction operation on a and store the result in c.

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Tenet.contract Method

contract(a::Tensor, b::Tensor; dims=∩(inds(a), inds(b)), out=nothing)

Perform a binary tensor contraction operation.

Keyword arguments

- `dims`: indices to contract over. Defaults to the set intersection of the indices of `a` and `b`.
- `out`: indices of the output tensor. Defaults to the set difference of the indices of `a` and `b`.

Todo

We are in the process of making contract multi-backend; i.e. let the user choose between different einsum libraries as the engine powering contract. Currently, we use OMEinsum.jl, but it has proven to be slow when used dynamically like we do.

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Tenet.contract Method

contract(a::Tensor; dims=∩(inds(a), inds(b)), out=nothing)

Perform a unary tensor contraction operation.

Keyword arguments

- `dims`: indices to contract over. Defaults to the repeated indices.
- `out`: indices of the output tensor. Defaults to the unique indices.

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