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README.md

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2 # Proximal methods for point source localisation: the implementation 2 # Proximal methods for point source localisation: the implementation
3 3
4 This package contains [Rust] codes for the manuscript “_Proximal methods for 4 This package contains the [Rust] codes for the numerical experiments in the articles
5 point source localisation_” ([arXiv:2212.02991]) by Tuomo Valkonen 5 * T. Valkonen, “_Proximal methods for
6 ⟨tuomov@iki.fi⟩. It concerns solution of problems of the type 6 point source localisation_”, Journal of Nonsmooth Analysis and Optimization 4 (2023), 10433, [doi:10.46298/jnsao-2023-10433] ([arXiv:2212.02991])
7 * T. Valkonen, “_Point source localisation with unbalanced optimal transport_” (2025), submitted.
8
9 It concerns solution of problems of the type
7 $$ 10 $$
8 \min_{μ ∈ ℳ(Ω)}~ F(μ) + λ \|μ\|_{ℳ(Ω)} + δ_{≥ 0}(μ), 11 \min_{μ ∈ ℳ(Ω)}~ F(μ) + λ \|μ\|_{ℳ(Ω)} + δ_{≥ 0}(μ),
9 $$ 12 $$
10 where $F$ is a data term, and $ℳ(Ω)$ is the space of Radon measures on the 13 where $F$ is a data term, and $ℳ(Ω)$ is the space of Radon measures on the
11 (rectangular) domain $Ω ⊂ ℝ^n$. Implemented are $F(μ)=\frac12\|Aμ-b\|_2^2$ and 14 (rectangular) domain $Ω ⊂ ℝ^n$. Implemented are $F(μ)=\frac12\|Aμ-b\|_2^2$ and
12 $F(μ)=\|Aμ-b\|_1$ for the forward operator $A \in 𝕃(ℳ(Ω); ℝ^m)$ modelling a 15 $F(μ)=\|Aμ-b\|_1$ for the forward operator $A \in 𝕃(ℳ(Ω); ℝ^m)$ modelling a
13 simple sensor grid. For the 2-norm-squared data term implemented are the 16 simple sensor grid.
14 algorithms μFB, μFISTA, and μPDPS from the aforementioned manuscript along with
15 comparison relaxed and fully corrective conditional gradient methods from the
16 literature. For the 1-norm data term only the μPDPS is applicable.
17 17
18 ## Installation and usage 18 ## Installation and usage
19 19
20 ### Installing dependencies 20 ### Installing dependencies
21 21
34 this can be done with 34 this can be done with
35 ```console 35 ```console
36 brew install gsl 36 brew install gsl
37 ``` 37 ```
38 For other operating systems, suggestions are available in the [rust-GSL] 38 For other operating systems, suggestions are available in the [rust-GSL]
39 crate documentation. On Windows, you will likely need to pass extra 39 crate documentation. You may need to pass extra `RUSTFLAGS` options to
40 `RUSTFLAGS` options to Cargo in the following steps to locate the library. 40 Cargo in the following steps to locate the library.
41 41
42 4. Download [alg_tools] and unpack it under the same directory as this 42 4. Download [alg_tools] and unpack it under the same directory as this
43 package. 43 package.
44 44
45 [rustup]: https://rustup.rs 45 [rustup]: https://rustup.rs
47 [Rust]: https://www.rust-lang.org/ 47 [Rust]: https://www.rust-lang.org/
48 [GNU Scientific Library]: https://www.gnu.org/software/gsl/ 48 [GNU Scientific Library]: https://www.gnu.org/software/gsl/
49 [rust-GSL]: https://docs.rs/GSL/6.0.0/rgsl/ 49 [rust-GSL]: https://docs.rs/GSL/6.0.0/rgsl/
50 [Homebrew]: https://brew.sh 50 [Homebrew]: https://brew.sh
51 [arXiv:2212.02991]: https://arxiv.org/abs/2212.02991 51 [arXiv:2212.02991]: https://arxiv.org/abs/2212.02991
52 [doi:10.46298/jnsao-2023-10433]: http://doi.org/10.46298/jnsao-2023-10433
52 53
53 ### Building and running the experiments 54 ### Building and running the experiments
54 55
55 To compile the code and run the experiments in the manuscript, use 56 To compile and install the program, use
57 ```console
58 cargo install --path=.
59 ```
60 When doing this for the first time, several dependencies will be downloaded.
61 Now you can run the default set of experiments with
62 ```
63 pointsource_algs -o results
64 ```
65 The `-o results` option tells `pointsource_algs` to write results in the
66 `results` directory. The option is required.
67
68 Alternatively, you may build and run the program without installing with
56 ```console 69 ```console
57 cargo run --release -- -o results 70 cargo run --release -- -o results
58 ``` 71 ```
59 When doing this for the first time, several dependencies will be downloaded. 72 The double-dash separates the options for the Cargo build system
60 The double-dash (`--`) separates the arguments of Cargo and this software, 73 and `pointsource_algs`.
61 `pointsource_algs`. The `--release` option to Cargo is required for `rustc` to
62 build optimised high performance code. Without that flag the performance will
63 be significantly worse. The `-o results` option tells `pointsource_algs` to
64 write results in the `results` directory. The option is required.
65
66 Alternatively, you may build the executable with
67 ```console
68 cargo build --release
69 ```
70 and then run it with
71 ```
72 target/release/pointsource_algs -o results
73 ```
74 74
75 ### Documentation 75 ### Documentation
76 76
77 Use the `--help` option to get an extensive listing of command line options to 77 Use the `--help` option to get an extensive listing of command line options to
78 customise algorithm parameters and the experiments performed. As above with 78 customise algorithm parameters and the experiments performed.
79 `-o`, if using `cargo` to run the executable, you have to pass any arguments
80 to `pointsource_algs` after a double-dash:
81 ```console
82 cargo run --release -- --help
83 ```
84 79
85 ## Internals 80 ## Internals
86 81
87 If you are interested in the program internals, the integrated source code 82 If you are interested in the program internals, the integrated source code
88 documentation may be built and opened with 83 documentation may be built and opened with

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