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README.md

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# TensorCrossInterpolation
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[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://tensors4fields.gitlab.io/tensorcrossinterpolation.jl/dev/index.html)
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[![Build Status](https://gitlab.com/tensors4fields/tensorcrossinterpolation.jl/badges/main/pipeline.svg)](https://gitlab.com/tensors4fields/tensorcrossinterpolation.jl/-/pipelines)
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[![Coverage](https://gitlab.com/tensors4fields/tensorcrossinterpolation.jl/badges/main/coverage.svg)](https://gitlab.com/tensors4fields/tensorcrossinterpolation.jl/-/commits/main)
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[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://tensor4all.github.io/TensorCrossInterpolation.jl/dev)
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[![CI](https://github.com/tensor4all/TensorCrossInterpolation.jl/actions/workflows/CI.yml/badge.svg)](https://github.com/tensor4all/TensorCrossInterpolation.jl/actions/workflows/CI.yml)
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The [TensorCrossInterpolation module](https://gitlab.com/tensors4fields/tensorcrossinterpolation.jl) implements the *tensor cross interpolation* algorithm for efficient interpolation of multi-index tensors and multivariate functions.
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The [TensorCrossInterpolation module](https://github.com/tensor4all/TensorCrossInterpolation.jl) implements the *tensor cross interpolation* algorithm for efficient interpolation of multi-index tensors and multivariate functions.
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This algorithm is used in the *quantics tensor cross interpolation* (QTCI) method for exponentially efficient interpolation of functions with scale separation. QTCI is implemented in the [QuanticsTCI.jl](https://gitlab.com/tensors4fields/quanticstci.jl) module.
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This algorithm is used in the *quantics tensor cross interpolation* (QTCI) method for exponentially efficient interpolation of functions with scale separation. QTCI is implemented in the [QuanticsTCI.jl](https://github.com/tensor4all/quanticstci.jl) module.
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## Installation
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## Related modules
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### [TCIITensorConversion.jl](https://gitlab.com/tensors4fields/tciitensorconversion.jl)
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### [TCIITensorConversion.jl](https://github.com/tensor4all/tciitensorconversion.jl)
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A small helper module for easy conversion of `TensorCI1`, `TensorCI2` and `TensorTrain` objects into ITensors `MPS` objects. This should be helpful for those integrating TCI into a larger tensor network algorithm.
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For this conversion, simply call the `MPS` constructor on the object:
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```julia
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mps = MPS(tci)
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```
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### [QuanticsTCI.jl](https://gitlab.com/tensors4fields/QuanticsTCI.jl)
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### [QuanticsTCI.jl](https://github.com/tensor4all/QuanticsTCI.jl)
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A module that implements the *quantics representation* and combines it with TCI for exponentially efficient interpolation of functions with scale separation.
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## Contributions
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- If you are having have technical trouble, feel free to contact me directly.
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- Feature requests and bug reports are always welcome, feel free to open an [issue](https://gitlab.com/tensors4fields/TensorCrossInterpolation.jl/-/issues) for those.
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- If you have implemented something that might be useful for others, we'd appreciate a [merge request](https://gitlab.com/tensors4fields/TensorCrossInterpolation.jl/-/merge_requests)!
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- Feature requests and bug reports are always welcome, feel free to open an [issue](https://github.com/tensor4all/TensorCrossInterpolation.jl/-/issues) for those.
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- If you have implemented something that might be useful for others, we'd appreciate a [merge request](https://github.com/tensor4all/TensorCrossInterpolation.jl/-/merge_requests)!
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## Authors
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docs/make.jl

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using Documenter
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push!(LOAD_PATH, "../src/")
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using TensorCrossInterpolation
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using Documenter
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DocMeta.setdocmeta!(TensorCrossInterpolation, :DocTestSetup, :(using TensorCrossInterpolation); recursive=true)
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makedocs(;
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modules=[TensorCrossInterpolation],
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authors="Ritter.Marc <[email protected]> and contributors",
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repo="https://gitlab.com/tensors4fields/tensorcrossinterpolation.jl/blob/{commit}{path}#{line}",
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sitename="TensorCrossInterpolation.jl",
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format=Documenter.HTML(;
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prettyurls=get(ENV, "CI", "false") == "true",
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canonical="https://gitlab.com/tensors4fields/tensorcrossinterpolation.jl",
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canonical="https://github.com/tensor4all/TensorCrossInterpolation.jl",
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edit_link="main",
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assets=String[],
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repolink="https://gitlab.com/tensors4fields/tensorcrossinterpolation.jl"
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),
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assets=String[]),
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pages=[
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"Home" => "index.md",
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"Documentation" => "documentation.md",

docs/src/documentation.md

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# Documentation
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Documentation of all types and methods in module [TensorCrossInterpolation](https://gitlab.com/tensors4fields/TensorCrossInterpolation.jl).
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Documentation of all types and methods in module [TensorCrossInterpolation](https://github.com/tensor4all/TensorCrossInterpolation.jl).
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## Matrix approximation
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docs/src/index.md

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# TensorCrossInterpolation
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This is the documentation for [TensorCrossInterpolation](https://gitlab.com/tensors4fields/TensorCrossInterpolation.jl).
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This is the documentation for [TensorCrossInterpolation](https://github.com/tensor4all/TensorCrossInterpolation.jl).
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With the user manual and usage examples below, users should be able to use this library as a "black box" in most cases. Detailed documentation of (almost) all methods can be found in the [Documentation](@ref) section, and [Implementation](@ref) contains a detailed explanation of this implementation of TCI.
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println("TCI approximation: $(tci([1, 2, 3, 4, 5]))")
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```
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For easy integration into tensor network algorithms, the tensor train can be converted to ITensors MPS format. If you're using julia version 1.9 or later, an extension is automatically loaded if both `TensorCrossInterpolation.jl` and `ITensors.jl` are present.
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For older versions of julia, use the package using [TCIITensorConversion.jl](https://gitlab.com/tensors4fields/tciitensorconversion.jl).
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For older versions of julia, use the package using [TCIITensorConversion.jl](https://github.com/tensor4all/tciitensorconversion.jl).
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## Sums and Integrals
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