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| name: CI | ||
| on: | ||
| push: | ||
| branches: | ||
| - main | ||
| pull_request: | ||
| branches: | ||
| - main | ||
| concurrency: | ||
| # Skip intermediate builds: always. | ||
| # Cancel intermediate builds: only if it is a pull request build. | ||
| group: ${{ github.workflow }}-${{ github.ref }} | ||
| cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }} | ||
| jobs: | ||
| test: | ||
| name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }} | ||
| runs-on: ${{ matrix.os }} | ||
| strategy: | ||
| fail-fast: false | ||
| matrix: | ||
| version: | ||
| - '1.9' | ||
| - '1' | ||
| os: | ||
| - ubuntu-latest | ||
| #- macOS-latest | ||
| #- windows-latest | ||
| arch: | ||
| - x64 | ||
| steps: | ||
| - uses: actions/checkout@v4 | ||
| - uses: julia-actions/setup-julia@v2 | ||
| with: | ||
| version: ${{ matrix.version }} | ||
| arch: ${{ matrix.arch }} | ||
| - uses: julia-actions/cache@v1 | ||
| - uses: julia-actions/julia-buildpkg@v1 | ||
| - uses: julia-actions/julia-runtest@v1 | ||
| continue-on-error: ${{ matrix.version == 'nightly' }} | ||
| - uses: julia-actions/julia-processcoverage@v1 | ||
| - uses: codecov/codecov-action@v3 | ||
| docs: | ||
| name: Documentation | ||
| runs-on: ubuntu-latest | ||
| steps: | ||
| - uses: actions/checkout@v4 | ||
| - uses: julia-actions/setup-julia@v2 | ||
| with: | ||
| version: '1' | ||
| - uses: julia-actions/julia-buildpkg@v1 | ||
| - uses: julia-actions/julia-docdeploy@v1 | ||
| env: | ||
| GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} | ||
| DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }} |
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| @@ -0,0 +1,33 @@ | ||
| name: TagBot | ||
| on: | ||
| issue_comment: | ||
| types: | ||
| - created | ||
| workflow_dispatch: | ||
| inputs: | ||
| lookback: | ||
| default: "3" | ||
| permissions: | ||
| actions: read | ||
| checks: read | ||
| contents: write | ||
| deployments: read | ||
| issues: read | ||
| discussions: read | ||
| packages: read | ||
| pages: read | ||
| pull-requests: read | ||
| repository-projects: read | ||
| security-events: read | ||
| statuses: read | ||
| jobs: | ||
| TagBot: | ||
| if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot' | ||
| runs-on: ubuntu-latest | ||
| steps: | ||
| - uses: JuliaRegistries/TagBot@v1 | ||
| with: | ||
| token: ${{ secrets.GITHUB_TOKEN }} | ||
| # Edit the following line to reflect the actual name of the GitHub Secret containing your private key | ||
| ssh: ${{ secrets.DOCUMENTER_KEY }} | ||
| # ssh: ${{ secrets.NAME_OF_MY_SSH_PRIVATE_KEY_SECRET }} |
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| # QuanticsGrids | ||
|
|
||
| [](https://tensors4fields.gitlab.io/QuanticsGrids.jl/dev/index.html) | ||
| [](https://gitlab.com/tensors4fields/QuanticsGrids.jl/-/commits/main) | ||
| [](https://gitlab.com/tensors4fields/QuanticsGrids.jl/-/commits/main) | ||
| [](https://tensor4all.github.io/QuanticsGrids.jl/dev) | ||
| [](https://github.com/tensor4all/QuanticsGrids.jl/actions/workflows/CI.yml) | ||
|
|
||
| This module contains utilities for interpolations of functions in the quantics TCI / quantics tensor train (QTT) format. | ||
| This library provides utilities for interpolations of functions in the quantics TCI / quantics tensor train (QTT) format. | ||
|
|
||
| ## Installation | ||
|
|
||
| This module has been registered in the General registry. It can be installed by typing the following in a Julia REPL: | ||
| The following will install QuanticsGrids.jl: | ||
|
|
||
| ```julia | ||
| julia> using Pkg; Pkg.add("QuanticsGrids.jl") | ||
| ``` | ||
|
|
||
| ## Definition | ||
| We first introduce a $B$-base presentation ($B=2, 3, 4, \cdots$). | ||
| To avoid confusing, we will use the 1-based indexing of Julia below. | ||
| We represent a positive integer $X~(\ge 1)$ as | ||
|
|
||
| $$ | ||
| X= \sum_{i=1}^R (x_i-1) \times B^{R-i+1} + 1, | ||
| $$ | ||
|
|
||
| where $x_i$ is either 1 or 2 and $R$ is the number of digits. | ||
| In this library, the $B$-base representation of $X$ is represented by the vector | ||
|
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| $$[x_1, \cdots, x_R].$$ | ||
|
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| This library supports two unfolding schemes (interleaved and fused representations) for handling multiple variables. | ||
| As an example, we consider three variables $X$, $Y$ and $Z$. | ||
| Their $B$-base representations are given by | ||
|
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| $$[x_1, \cdots, x_R], [y_1, \cdots, y_R], [z_1, \cdots, z_R],$$ | ||
|
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| respectively. | ||
| The interleaved representation of these variables reads | ||
|
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| $$[x_1, y_1, z_1, x_2, y_2, z_2, \cdots, x_R, y_R, z_R].$$ | ||
|
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| The fused representation is given by | ||
|
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| $$[\alpha_1, \alpha_2, \cdots, \alpha_R],$$ | ||
|
|
||
| where | ||
|
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| $$ | ||
| \alpha_i = (x_i-1) + B(y_i-1) + B^2 (z_i-1) + 1 | ||
| $$ | ||
|
|
||
| with | ||
|
|
||
| $$ | ||
| 1 \le \alpha_i \le B^3. | ||
| $$ | ||
|
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||
| This convention is consistent with the column major used in Julia: At each digit level $i$, the bit for $x$ runs fastest. | ||
| The fused representaion generalizes to any number of variables. | ||
|
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||
|
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| ## Usage | ||
| This package contains two main functionalities: | ||
|
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| 1. Low-level functions for converting betwen linear and quantics representations | ||
| 2. High-level interface for creating a grid | ||
|
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| The normal users will use the second high-level interface. | ||
| We will describe its usage. | ||
|
|
||
| ## Discretized grid | ||
| `DiscretizedGrid` can be used to discretize a $d$-dimensional space. | ||
|
|
||
| ## Creating a one-dimensional grid | ||
|
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| We can create a one-dimensional grid by discretizing $x$ axis on $[0, 1)$ with $R$ bits as | ||
|
|
||
| ```julia | ||
| import QuanticsGrids as QD | ||
| xmin = 0.0 | ||
| xmax = 1.0 | ||
| R = 4 | ||
| grid = QD.DiscretizedGrid{1}(R, xmin, xmax) | ||
| ```` | ||
|
|
||
| Here, `DiscretizedGrid` takes one parameter `1`, which denotes the dimension of the grid. | ||
| There are six functions for translating between different reprenstations: | ||
| `grididx` (1-based linear index), `quantics` and `origcoord` (original coordiate, i.e., $x$). | ||
|
|
||
| Example: | ||
| ```julia | ||
| quantics = fill(1, R) | ||
| origcoord = 0.0 | ||
| grididx = 1 | ||
| @assert QD.quantics_to_grididx(grid, quantics) == grididx | ||
| @assert QD.quantics_to_origcoord(grid, quantics) == origcoord | ||
| @assert QD.grididx_to_quantics(grid, grididx) == quantics | ||
| @assert QD.grididx_to_origcoord(grid, grididx) == origcoord | ||
| @assert QD.origcoord_to_quantics(grid, origcoord) == quantics | ||
| @assert QD.origcoord_to_grididx(grid, origcoord) == grididx | ||
| quantics = fill(2, R) | ||
| origcoord = 1-1/2^R | ||
| grididx = 2^R | ||
| @assert QD.quantics_to_grididx(grid, quantics) == grididx | ||
| @assert QD.quantics_to_origcoord(grid, quantics) == origcoord | ||
| @assert QD.grididx_to_quantics(grid, grididx) == quantics | ||
| @assert QD.grididx_to_origcoord(grid, grididx) == origcoord | ||
| @assert QD.origcoord_to_quantics(grid, origcoord) == quantics | ||
| @assert QD.origcoord_to_grididx(grid, origcoord) == grididx | ||
| ``` | ||
|
|
||
| Optionally, one can include the end point `grid_max` in a grid as | ||
|
|
||
| ```julia | ||
| import QuanticsGrids as QD | ||
| xmin = 0.0 | ||
| xmax = 1.0 | ||
| R = 4 | ||
| grid = QD.DiscretizedGrid{1}(R, xmin, xmax; includeendpoint=true) | ||
| @assert QD.grididx_to_origcoord(grid, 1) == xmin | ||
| @assert QD.grididx_to_origcoord(grid, 2^R) == xmax | ||
| ```` | ||
|
|
||
| ## Creating a $d$-dimensional grid | ||
| A $d$-dimensional grid, where each axis is discretized with $R$ bits, can be generated in a similar way as follows. | ||
| As an option, you can choose the fused representation (`:fused`) or the interleaved representation (`:interleaved`). | ||
|
|
||
| ### fused representation | ||
| ```julia | ||
| import QuanticsGrids as QD | ||
| xmin, xmax = 0.0, 1.0 | ||
| ymin, ymax = 0.0, 1.0 | ||
| zmin, zmax = 0.0, 1.0 | ||
| R = 4 | ||
| grid = QD.DiscretizedGrid{3}(R, (xmin,ymin,zmin), (xmax,ymax,zmax); unfoldingscheme=:fused) | ||
| quantics = fill(1, R) | ||
| origcoord = (0.0, 0.0, 0.0) | ||
| grididx = (1, 1, 1) | ||
| @assert QD.quantics_to_grididx(grid, quantics) == grididx | ||
| @assert QD.quantics_to_origcoord(grid, quantics) == origcoord | ||
| @assert QD.grididx_to_quantics(grid, grididx) == quantics | ||
| @assert QD.grididx_to_origcoord(grid, grididx) == origcoord | ||
| @assert QD.origcoord_to_quantics(grid, origcoord) == quantics | ||
| @assert QD.origcoord_to_grididx(grid, origcoord) == grididx | ||
| # Incrementing the least significant fused bits increments the $x$ index. | ||
| quantics = vcat(fill(1, R-1), 2) # [1, 1, ..., 1, 2] | ||
| origcoord = (1/2^R, 0.0, 0.0) | ||
| grididx = (2, 1, 1) | ||
| @assert QD.quantics_to_grididx(grid, quantics) == grididx | ||
| @assert QD.quantics_to_origcoord(grid, quantics) == origcoord | ||
| @assert QD.grididx_to_quantics(grid, grididx) == quantics | ||
| @assert QD.grididx_to_origcoord(grid, grididx) == origcoord | ||
| @assert QD.origcoord_to_quantics(grid, origcoord) == quantics | ||
| @assert QD.origcoord_to_grididx(grid, origcoord) == grididx | ||
| ``` | ||
|
|
||
| ### Interleaved representation | ||
| ```julia | ||
| import QuanticsGrids as QD | ||
| xmin, xmax = 0.0, 1.0 | ||
| ymin, ymax = 0.0, 1.0 | ||
| zmin, zmax = 0.0, 1.0 | ||
| R = 4 | ||
| grid = QD.DiscretizedGrid{3}(R, (xmin,ymin,zmin), (xmax,ymax,zmax); unfoldingscheme=QD.UnfoldingSchemes.interleaved) | ||
| # (x1, y1, z1, ...., xR, yR, zR) | ||
| quantics = fill(1, 3R) # length is 3R | ||
| origcoord = (0.0, 0.0, 0.0) | ||
| grididx = (1, 1, 1) | ||
| @assert QD.quantics_to_grididx(grid, quantics) == grididx | ||
| @assert QD.quantics_to_origcoord(grid, quantics) == origcoord | ||
| @assert QD.grididx_to_quantics(grid, grididx) == quantics | ||
| @assert QD.grididx_to_origcoord(grid, grididx) == origcoord | ||
| @assert QD.origcoord_to_quantics(grid, origcoord) == quantics | ||
| @assert QD.origcoord_to_grididx(grid, origcoord) == grididx | ||
| quantics = vcat(fill(1, 3R-3), [2, 1, 1]) # [1, 1, 1, ..., 2, 1, 1] | ||
| origcoord = (1/2^R, 0.0, 0.0) | ||
| grididx = (2, 1, 1) | ||
| @assert QD.quantics_to_grididx(grid, quantics) == grididx | ||
| @assert QD.quantics_to_origcoord(grid, quantics) == origcoord | ||
| @assert QD.grididx_to_quantics(grid, grididx) == quantics | ||
| @assert QD.grididx_to_origcoord(grid, grididx) == origcoord | ||
| @assert QD.origcoord_to_quantics(grid, origcoord) == quantics | ||
| @assert QD.origcoord_to_grididx(grid, origcoord) == grididx | ||
| ``` | ||
|
|
||
| ## Inherent discrete grid | ||
| `InherentDiscreteGrid` can be used if the target space is discrete. | ||
| `InherentDiscreteGrid` has a very similar interface to `DiscretizedGrid`. | ||
| We provide one example. | ||
|
|
||
| ```julia | ||
| import QuanticsGrids as QD | ||
| R = 4 | ||
| # Grid: [0, 1, ..., 2^R-1]. The second argument (0,) specifies the origin. | ||
| grid = QD.InherentDiscreteGrid{1}(R, 0; step=1) | ||
| quantics = fill(1, R) | ||
| origcoord = 0 | ||
| grididx = 1 | ||
| @assert QD.quantics_to_grididx(grid, quantics) == grididx | ||
| @assert QD.quantics_to_origcoord(grid, quantics) == origcoord | ||
| @assert QD.grididx_to_quantics(grid, grididx) == quantics | ||
| @assert QD.grididx_to_origcoord(grid, grididx) == origcoord | ||
| @assert QD.origcoord_to_quantics(grid, origcoord) == quantics | ||
| @assert QD.origcoord_to_grididx(grid, origcoord) == grididx | ||
| quantics = fill(2, R) | ||
| origcoord = 2^R-1 | ||
| grididx = 2^R | ||
| @assert QD.quantics_to_grididx(grid, quantics) == grididx | ||
| @assert QD.quantics_to_origcoord(grid, quantics) == origcoord | ||
| @assert QD.grididx_to_quantics(grid, grididx) == quantics | ||
| @assert QD.grididx_to_origcoord(grid, grididx) == origcoord | ||
| @assert QD.origcoord_to_quantics(grid, origcoord) == quantics | ||
| @assert QD.origcoord_to_grididx(grid, origcoord) == grididx | ||
| ``` | ||
|
|
||
| ## Use a base other than `2` | ||
| When creating a grid, we may want to choose a different base other than 2. | ||
|
|
||
| ```julia | ||
| import QuanticsGrids as QD | ||
| R = 4 | ||
| base = 10 | ||
| # Grid: [0, 1, ..., 10^R-1] | ||
| grid = QD.InherentDiscreteGrid{1}(R, (0,); base=10) | ||
| quantics = fill(base, R) | ||
| origcoord = base^R-1 | ||
| grididx = base^R | ||
| @assert QD.quantics_to_grididx(grid, quantics) == grididx | ||
| @assert QD.quantics_to_origcoord(grid, quantics) == origcoord | ||
| @assert QD.grididx_to_quantics(grid, grididx) == quantics | ||
| @assert QD.grididx_to_origcoord(grid, grididx) == origcoord | ||
| @assert QD.origcoord_to_quantics(grid, origcoord) == quantics | ||
| @assert QD.origcoord_to_grididx(grid, origcoord) == grididx | ||
| ``` | ||
|
|
||
| ## Create a function that takes a quantics index as its input | ||
| When using `QuanticsGrids.jl` in combination with `TensorCrossInterpolation.jl`, | ||
| one can wrap a function to be interpolated to make a fuction that takes a quantics index: | ||
|
|
||
| ```julia | ||
| import QuanticsGrids as QD | ||
| import TensorCrossInterpolation as TCI | ||
| R = 4 | ||
| grid = QD.DiscretizedGrid{2}(R, (0.0, 0.0), (1.0, 1.0)) | ||
| f(x, y) = sin(x + y) # Function to be interpolated | ||
| initialpivots = [fill(1, R)] | ||
| localdims = fill(2^2, R) | ||
| fq = QD.quanticsfunction(Float64, grid, f) # fq takes an quantics index as an input | ||
| tci, ranks, errors = TCI.crossinterpolate2(Float64, fq, localdims, initialpivots; tolerance=1e-8) | ||
| ```` | ||
|
|
||
| ## References | ||
| - M. K. Ritter, Y. N. Fernández, M. Wallerberger, J. von Delft, H. Shinaoka, and X. Waintal, *Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond*, [Phys. Rev. Lett. <b>132</b>, 056501 (2024)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.056501)/[arXiv:2303.11819](http://arxiv.org/abs/2303.11819). | ||
| Please refer to the [documentation](https://tensor4all.github.io/QuanticsGrids.jl/) for usage. |
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| Original file line number | Diff line number | Diff line change |
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|
|
@@ -6,14 +6,17 @@ DocMeta.setdocmeta!(QuanticsGrids, :DocTestSetup, :(using QuanticsGrids); recurs | |
| makedocs(; | ||
| modules=[QuanticsGrids], | ||
| authors="Ritter.Marc <[email protected]> and contributors", | ||
| repo="https://gitlab.com/tensors4fields/QuanticsGrids.jl/blob/{commit}{path}#{line}", | ||
| sitename="QuanticsGrids.jl", | ||
| format=Documenter.HTML(; | ||
| prettyurls=get(ENV, "CI", "false") == "true", | ||
| repolink="https://gitlab.com/tensors4fields/QuanticsGrids.jl", | ||
| canonical="https://github.com/tensor4all/QuanticsGrids.jl", | ||
| edit_link="main", | ||
| assets=String[]), | ||
| pages=[ | ||
| "Home" => "index.md", | ||
| "API Reference" => "apireference.md", | ||
| ]) | ||
|
|
||
| deploydocs(; | ||
| repo="github.com/tensor4all/QuanticsGrids.jl.git", | ||
| devbranch="main", | ||
| ) | ||
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