Mercurial > repos > pointsource_algs / changeset
changeset
New version of sliding.
Tue, 31 Dec 2024 09:25:45 -0500
- author
- Tuomo Valkonen <tuomov@iki.fi>
- date
- Tue, 31 Dec 2024 09:25:45 -0500
- branch
- dev
- changeset 35
- b087e3eab191
- parent 34
- efa60bc4f743
- child 36
- fb911f72e698
New version of sliding.
--- a/Cargo.lock Thu Aug 29 00:00:00 2024 -0500 +++ b/Cargo.lock Tue Dec 31 09:25:45 2024 -0500 @@ -4,9 +4,9 @@ [[package]] name = "GSL" -version = "6.0.0" +version = "7.0.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "c9becaf6d7d1ba36a457288e661fa6a0472e8328629276f45369eafcd48ef1ce" +checksum = "db3943d5a15b5c46e991124abee6a1bc89c7c9ffb25dbb8aeb4eab926fd9b307" dependencies = [ "GSL-sys", "paste", @@ -23,24 +23,19 @@ ] [[package]] -name = "adler" -version = "1.0.2" +name = "aho-corasick" +version = "1.1.3" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "f26201604c87b1e01bd3d98f8d5d9a8fcbb815e8cedb41ffccbeb4bf593a35fe" - -[[package]] -name = "aho-corasick" -version = "0.7.20" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "cc936419f96fa211c1b9166887b38e5e40b19958e5b895be7c1f93adec7071ac" +checksum = "8e60d3430d3a69478ad0993f19238d2df97c507009a52b3c10addcd7f6bcb916" dependencies = [ "memchr", ] [[package]] name = "alg_tools" -version = "0.2.0-dev" +version = "0.3.0-dev" dependencies = [ + "anyhow", "colored", "cpu-time", "csv", @@ -52,7 +47,7 @@ "rayon", "serde", "serde_json", - "trait-set", + "simba", ] [[package]] @@ -71,6 +66,61 @@ ] [[package]] +name = "anstream" +version = "0.6.18" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "8acc5369981196006228e28809f761875c0327210a891e941f4c683b3a99529b" +dependencies = [ + "anstyle", + "anstyle-parse", + "anstyle-query", + "anstyle-wincon", + "colorchoice", + "is_terminal_polyfill", + "utf8parse", +] + +[[package]] +name = "anstyle" +version = "1.0.10" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "55cc3b69f167a1ef2e161439aa98aed94e6028e5f9a59be9a6ffb47aef1651f9" + +[[package]] +name = "anstyle-parse" +version = "0.2.6" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "3b2d16507662817a6a20a9ea92df6652ee4f94f914589377d69f3b21bc5798a9" +dependencies = [ + "utf8parse", +] + +[[package]] +name = "anstyle-query" +version = "1.1.2" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "79947af37f4177cfead1110013d678905c37501914fba0efea834c3fe9a8d60c" +dependencies = [ + "windows-sys 0.59.0", +] + +[[package]] +name = "anstyle-wincon" +version = "3.0.6" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "2109dbce0e72be3ec00bed26e6a7479ca384ad226efdd66db8fa2e3a38c83125" +dependencies = [ + "anstyle", + "windows-sys 0.59.0", +] + +[[package]] +name = "anyhow" +version = "1.0.95" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "34ac096ce696dc2fcabef30516bb13c0a68a11d30131d3df6f04711467681b04" + +[[package]] name = "approx" version = "0.5.1" source = "registry+https://github.com/rust-lang/crates.io-index" @@ -86,60 +136,30 @@ checksum = "d468802bab17cbc0cc575e9b053f41e72aa36bfa6b7f55e3529ffa43161b97fa" [[package]] -name = "bit_field" -version = "0.10.2" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "dc827186963e592360843fb5ba4b973e145841266c1357f7180c43526f2e5b61" - -[[package]] -name = "bitflags" -version = "1.3.2" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "bef38d45163c2f1dde094a7dfd33ccf595c92905c8f8f4fdc18d06fb1037718a" - -[[package]] name = "bitflags" version = "2.4.0" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "b4682ae6287fcf752ecaabbfcc7b6f9b72aa33933dc23a554d853aea8eea8635" [[package]] -name = "bstr" -version = "0.2.17" +name = "bumpalo" +version = "3.16.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "ba3569f383e8f1598449f1a423e72e99569137b47740b1da11ef19af3d5c3223" -dependencies = [ - "lazy_static", - "memchr", - "regex-automata", - "serde", -] - -[[package]] -name = "bumpalo" -version = "3.14.0" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "7f30e7476521f6f8af1a1c4c0b8cc94f0bee37d91763d0ca2665f299b6cd8aec" +checksum = "79296716171880943b8470b5f8d03aa55eb2e645a4874bdbb28adb49162e012c" [[package]] name = "bytemuck" -version = "1.14.0" +version = "1.20.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "374d28ec25809ee0e23827c2ab573d729e293f281dfe393500e7ad618baa61c6" - -[[package]] -name = "byteorder" -version = "1.5.0" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "1fd0f2584146f6f2ef48085050886acf353beff7305ebd1ae69500e27c67f64b" +checksum = "8b37c88a63ffd85d15b406896cc343916d7cf57838a847b3a6f2ca5d39a5695a" [[package]] name = "cc" -version = "1.0.83" +version = "1.2.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "f1174fb0b6ec23863f8b971027804a42614e347eafb0a95bf0b12cdae21fc4d0" +checksum = "1aeb932158bd710538c73702db6945cb68a8fb08c519e6e12706b94263b36db8" dependencies = [ - "libc", + "shlex", ] [[package]] @@ -150,9 +170,9 @@ [[package]] name = "chrono" -version = "0.4.31" +version = "0.4.39" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "7f2c685bad3eb3d45a01354cedb7d5faa66194d1d58ba6e267a8de788f79db38" +checksum = "7e36cc9d416881d2e24f9a963be5fb1cd90966419ac844274161d10488b3e825" dependencies = [ "android-tzdata", "iana-time-zone", @@ -160,22 +180,29 @@ "num-traits", "serde", "wasm-bindgen", - "windows-targets", + "windows-targets 0.52.6", ] [[package]] name = "clap" -version = "4.0.32" +version = "4.5.23" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "a7db700bc935f9e43e88d00b0850dae18a63773cfbec6d8e070fccf7fef89a39" +checksum = "3135e7ec2ef7b10c6ed8950f0f792ed96ee093fa088608f1c76e569722700c84" dependencies = [ - "bitflags 1.3.2", + "clap_builder", "clap_derive", +] + +[[package]] +name = "clap_builder" +version = "4.5.23" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "30582fc632330df2bd26877bde0c1f4470d57c582bbc070376afcd04d8cb4838" +dependencies = [ + "anstream", + "anstyle", "clap_lex", - "is-terminal", - "once_cell", "strsim", - "termcolor", "terminal_size", "unicase", "unicode-width", @@ -183,57 +210,43 @@ [[package]] name = "clap_derive" -version = "4.0.21" +version = "4.5.18" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "0177313f9f02afc995627906bbd8967e2be069f5261954222dac78290c2b9014" +checksum = "4ac6a0c7b1a9e9a5186361f67dfa1b88213572f427fb9ab038efb2bd8c582dab" dependencies = [ "heck", - "proc-macro-error", "proc-macro2", "quote", - "syn 1.0.109", + "syn 2.0.93", ] [[package]] name = "clap_lex" -version = "0.3.3" +version = "0.7.4" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "033f6b7a4acb1f358c742aaca805c939ee73b4c6209ae4318ec7aca81c42e646" -dependencies = [ - "os_str_bytes", -] +checksum = "f46ad14479a25103f283c0f10005961cf086d8dc42205bb44c46ac563475dca6" [[package]] -name = "color_quant" -version = "1.1.0" +name = "colorchoice" +version = "1.0.3" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "3d7b894f5411737b7867f4827955924d7c254fc9f4d91a6aad6b097804b1018b" - -[[package]] -name = "colorbrewer" -version = "0.2.0" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "525be5012d97bc222e124ded87f18601e6fbd24a406761bcb1664475663919a6" -dependencies = [ - "rgb", -] +checksum = "5b63caa9aa9397e2d9480a9b13673856c78d8ac123288526c37d7839f2a86990" [[package]] name = "colored" -version = "2.0.4" +version = "2.1.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "2674ec482fbc38012cf31e6c42ba0177b431a0cb6f15fe40efa5aab1bda516f6" +checksum = "cbf2150cce219b664a8a70df7a1f933836724b503f8a413af9365b4dcc4d90b8" dependencies = [ - "is-terminal", "lazy_static", - "windows-sys", + "windows-sys 0.48.0", ] [[package]] name = "core-foundation-sys" -version = "0.8.4" +version = "0.8.7" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "e496a50fda8aacccc86d7529e2c1e0892dbd0f898a6b5645b5561b89c3210efa" +checksum = "773648b94d0e5d620f64f280777445740e61fe701025087ec8b57f45c791888b" [[package]] name = "cpu-time" @@ -246,15 +259,6 @@ ] [[package]] -name = "crc32fast" -version = "1.3.2" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "b540bd8bc810d3885c6ea91e2018302f68baba2129ab3e88f32389ee9370880d" -dependencies = [ - "cfg-if", -] - -[[package]] name = "crossbeam-deque" version = "0.8.3" source = "registry+https://github.com/rust-lang/crates.io-index" @@ -288,20 +292,13 @@ ] [[package]] -name = "crunchy" -version = "0.2.2" +name = "csv" +version = "1.3.1" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "7a81dae078cea95a014a339291cec439d2f232ebe854a9d672b796c6afafa9b7" - 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"windows", + "windows-core", ] [[package]] @@ -450,82 +378,33 @@ ] [[package]] -name = "image" -version = "0.24.7" +name = "is_terminal_polyfill" +version = "1.70.1" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "6f3dfdbdd72063086ff443e297b61695500514b1e41095b6fb9a5ab48a70a711" -dependencies = [ - "bytemuck", - "byteorder", - "color_quant", - "exr", - "gif", - "jpeg-decoder", - "num-rational", - "num-traits", - "png", - "qoi", - "tiff", -] - -[[package]] -name = "io-lifetimes" -version = "1.0.11" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "eae7b9aee968036d54dce06cebaefd919e4472e753296daccd6d344e3e2df0c2" -dependencies = [ - "hermit-abi", - "libc", - "windows-sys", -] - -[[package]] -name = "is-terminal" -version = "0.4.9" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "cb0889898416213fab133e1d33a0e5858a48177452750691bde3666d0fdbaf8b" -dependencies = [ - "hermit-abi", - "rustix 0.38.19", - "windows-sys", -] +checksum = "7943c866cc5cd64cbc25b2e01621d07fa8eb2a1a23160ee81ce38704e97b8ecf" [[package]] name = "itertools" -version = "0.10.5" +version = "0.13.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "b0fd2260e829bddf4cb6ea802289de2f86d6a7a690192fbe91b3f46e0f2c8473" +checksum = "413ee7dfc52ee1a4949ceeb7dbc8a33f2d6c088194d9f922fb8318faf1f01186" dependencies = [ "either", ] [[package]] name = "itoa" -version = "0.4.8" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "b71991ff56294aa922b450139ee08b3bfc70982c6b2c7562771375cf73542dd4" - 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--- a/Cargo.toml Thu Aug 29 00:00:00 2024 -0500 +++ b/Cargo.toml Tue Dec 31 09:25:45 2024 -0500 @@ -21,29 +21,31 @@ ] categories = ["mathematics", "science", "computer-vision"] +[dependencies.alg_tools] +version = "~0.3.0-dev" +path = "../alg_tools" +default-features = false +features = ["nightly"] + [dependencies] -alg_tools = { version = "~0.2.0-dev", path = "../alg_tools", default-features = false } serde = { version = "1.0", features = ["derive"] } num-traits = { version = "~0.2.14", features = ["std"] } rand = "~0.8.5" -colored = "~2.0.0" +colored = "~2.1.0" rand_distr = "~0.4.3" -nalgebra = { version = "~0.31.0", features = ["rand-no-std"] } -itertools = "~0.10.3" +nalgebra = { version = "~0.33.0", features = ["rand-no-std"] } +itertools = "~0.13.0" numeric_literals = "~0.2.0" -poloto = "~3.13.1" -GSL = "~6.0.0" +GSL = "~7.0.0" float_extras = "~0.1.6" -clap = { version = "~4.0.27", features = ["derive", "unicode", "wrap_help"] } -image = "~0.24.3" +clap = { version = "~4.5.0", features = ["derive", "unicode", "wrap_help"] } cpu-time = "~1.0.0" -colorbrewer = "~0.2.0" -rgb = "~0.8.33" serde_json = "~1.0.85" chrono = { version = "~0.4.23", features = ["alloc", "std", "serde"] } +anyhow = "1.0.95" [build-dependencies] -regex = "~1.7.0" +regex = "~1.11.0" [profile.release] debug = true
--- a/README.md Thu Aug 29 00:00:00 2024 -0500 +++ b/README.md Tue Dec 31 09:25:45 2024 -0500 @@ -52,35 +52,29 @@ ### Building and running the experiments -To compile the code and run the experiments in the manuscript, use +To compile and install the program, use +```console +cargo install --path=. +``` +When doing this for the first time, several dependencies will be downloaded. +Now you can run the default experiment with +``` +pointsource_algs -o results +``` +The `-o results` option tells `pointsource_algs` to write results in the +`results` directory. The option is required. + +Alternatively, you may build and run the program without installing with ```console cargo run --release -- -o results ``` -When doing this for the first time, several dependencies will be downloaded. -The double-dash (`--`) separates the arguments of Cargo and this software, -`pointsource_algs`. The `--release` option to Cargo is required for `rustc` to -build optimised high performance code. Without that flag the performance will -be significantly worse. The `-o results` option tells `pointsource_algs` to -write results in the `results` directory. The option is required. - -Alternatively, you may build the executable with -```console -cargo build --release -``` -and then run it with -``` -target/release/pointsource_algs -o results -``` +The double-dash separates the options for the Cargo build system +and `pointsource_algs`. ### Documentation Use the `--help` option to get an extensive listing of command line options to -customise algorithm parameters and the experiments performed. As above with -`-o`, if using `cargo` to run the executable, you have to pass any arguments -to `pointsource_algs` after a double-dash: -```console -cargo run --release -- --help -``` +customise algorithm parameters and the experiments performed. ## Internals
--- a/src/dataterm.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/dataterm.rs Tue Dec 31 09:25:45 2024 -0500 @@ -4,25 +4,26 @@ use numeric_literals::replace_float_literals; -use alg_tools::loc::Loc; use alg_tools::euclidean::Euclidean; use alg_tools::linops::GEMV; pub use alg_tools::norms::L1; use alg_tools::norms::Norm; +use alg_tools::instance::{Instance, Space}; use crate::types::*; pub use crate::types::L2Squared; -use crate::measures::DiscreteMeasure; +use crate::measures::RNDM; /// Calculates the residual $Aμ-b$. #[replace_float_literals(F::cast_from(literal))] pub(crate) fn calculate_residual< + X : Space, + I : Instance<X>, F : Float, V : Euclidean<F> + Clone, - A : GEMV<F, DiscreteMeasure<Loc<F, N>, F>, Codomain = V>, - const N : usize + A : GEMV<F, X, Codomain = V>, >( - μ : &DiscreteMeasure<Loc<F, N>, F>, + μ : I, opA : &A, b : &V ) -> V { @@ -35,12 +36,14 @@ #[replace_float_literals(F::cast_from(literal))] pub(crate) fn calculate_residual2< F : Float, + X : Space, + I : Instance<X>, + J : Instance<X>, V : Euclidean<F> + Clone, - A : GEMV<F, DiscreteMeasure<Loc<F, N>, F>, Codomain = V>, - const N : usize + A : GEMV<F, X, Codomain = V>, >( - μ : &DiscreteMeasure<Loc<F, N>, F>, - μ_delta : &DiscreteMeasure<Loc<F, N>, F>, + μ : I, + μ_delta : J, opA : &A, b : &V ) -> V { @@ -58,14 +61,17 @@ fn calculate_fit(&self, _residual : &V) -> F; /// Calculates $F(Aμ-b)$, where $F$ is the data fidelity. - fn calculate_fit_op<A : GEMV<F, DiscreteMeasure<Loc<F, N>, F>, Codomain = V>>( + fn calculate_fit_op<I, A : GEMV<F, RNDM<F, N>, Codomain = V>>( &self, - μ : &DiscreteMeasure<Loc<F, N>, F>, + μ : I, opA : &A, b : &V ) -> F - where V : Euclidean<F> + Clone { - let r = calculate_residual(&μ, opA, b); + where + V : Euclidean<F> + Clone, + I : Instance<RNDM<F, N>>, + { + let r = calculate_residual(μ, opA, b); self.calculate_fit(&r) } }
--- a/src/experiments.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/experiments.rs Tue Dec 31 09:25:45 2024 -0500 @@ -21,6 +21,7 @@ use crate::run::{ RunnableExperiment, ExperimentV2, + ExperimentBiased, Named, DefaultAlgorithm, AlgorithmConfig @@ -28,6 +29,10 @@ //use crate::fb::FBGenericConfig; use crate::rand_distr::{SerializableNormal, SaltAndPepper}; use crate::regularisation::Regularisation; +use alg_tools::euclidean::Euclidean; +use alg_tools::instance::Instance; +use alg_tools::mapping::Mapping; +use alg_tools::operator_arithmetic::{MappingSum, Weighted}; /// Experiments shorthands, to be used with the command line parser @@ -58,6 +63,9 @@ /// Two dimensions, “fast” spread, 1-norm data fidelity #[clap(name = "2d_l1_fast")] Experiment2D_L1_Fast, + /// One dimension, “fast” spread, 2-norm-squared data fidelity with extra TV-regularised bias + #[clap(name = "1d_tv_fast")] + Experiment1D_TV_Fast, } macro_rules! make_float_constant { @@ -92,6 +100,25 @@ ([0.30, 0.70], 5.0) ]; +/// The $\{0,1\}$-valued characteristic function of a ball as a [`Mapping`]. +#[derive(Debug,Copy,Clone,Serialize,PartialEq)] +struct BallCharacteristic<F : Float, const N : usize> { + pub center : Loc<F, N>, + pub radius : F, +} + +impl<F : Float, const N : usize> Mapping<Loc<F, N>> for BallCharacteristic<F, N> { + type Codomain =F; + + fn apply<I : Instance<Loc<F, N>>>(&self, i : I) -> F { + if self.center.dist2(i) <= self.radius { + F::ONE + } else { + F::ZERO + } + } +} + //#[replace_float_literals(F::cast_from(literal))] impl DefaultExperiment { /// Convert the experiment shorthand into a runnable experiment configuration. @@ -115,6 +142,7 @@ make_float_constant!(Variance1 = 0.05.powi(2)); make_float_constant!(CutOff1 = 0.15); make_float_constant!(Hat1 = 0.16); + make_float_constant!(HatBias = 0.05); // We use a different step length for PDPS in 2D experiments let pdps_2d = || { @@ -294,6 +322,30 @@ ]), }}) }, + Experiment1D_TV_Fast => { + let base_spread = HatConv { radius : HatBias }; + Box::new(Named { name, data : ExperimentBiased { + λ : 0.02, + bias : MappingSum::new([ + Weighted::new(1.0, BallCharacteristic{ center : 0.3.into(), radius : 0.2 }), + Weighted::new(0.5, BallCharacteristic{ center : 0.6.into(), radius : 0.3 }), + ]), + base : ExperimentV2 { + domain : [[0.0, 1.0]].into(), + sensor_count : [N_SENSORS_1D], + regularisation : Regularisation::NonnegRadon(cli.alpha.unwrap_or(0.2)), + noise_distr : SerializableNormal::new(0.0, cli.variance.unwrap_or(0.1))?, + dataterm : DataTerm::L2Squared, + μ_hat : MU_TRUE_1D_BASIC.into(), + sensor : BallIndicator { r : SensorWidth1D, exponent : Linfinity }, + spread : base_spread, + kernel : base_spread, + kernel_plot_width, + noise_seed, + algorithm_defaults: HashMap::new(), + }, + }}) + }, }) } }
--- a/src/fb.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/fb.rs Tue Dec 31 09:25:45 2024 -0500 @@ -6,10 +6,7 @@ * Valkonen T. - _Proximal methods for point source localisation_, [arXiv:2212.02991](https://arxiv.org/abs/2212.02991). -The main routine is [`pointsource_fb_reg`]. It is based on [`generic_pointsource_fb_reg`], which is -also used by our [primal-dual proximal splitting][crate::pdps] implementation. - -FISTA-type inertia can also be enabled through [`FBConfig::meta`]. +The main routine is [`pointsource_fb_reg`]. ## Problem @@ -76,7 +73,7 @@ $$ </p> -We solve this with either SSN or FB via [`quadratic_nonneg`] as determined by +We solve this with either SSN or FB as determined by [`InnerSettings`] in [`FBGenericConfig::inner`]. */ @@ -87,10 +84,11 @@ use alg_tools::iterate::{ AlgIteratorFactory, - AlgIteratorState, + AlgIteratorIteration, + AlgIterator, }; use alg_tools::euclidean::Euclidean; -use alg_tools::linops::{Apply, GEMV}; +use alg_tools::linops::{Mapping, GEMV}; use alg_tools::sets::Cube; use alg_tools::loc::Loc; use alg_tools::bisection_tree::{ @@ -107,17 +105,24 @@ }; use alg_tools::mapping::RealMapping; use alg_tools::nalgebra_support::ToNalgebraRealField; +use alg_tools::instance::Instance; +use alg_tools::norms::Linfinity; use crate::types::*; use crate::measures::{ DiscreteMeasure, + RNDM, DeltaMeasure, + Radon, }; use crate::measures::merging::{ SpikeMergingMethod, SpikeMerging, }; -use crate::forward_model::ForwardModel; +use crate::forward_model::{ + ForwardModel, + AdjointProductBoundedBy +}; use crate::seminorms::DiscreteMeasureOp; use crate::subproblem::{ InnerSettings, @@ -146,8 +151,7 @@ pub generic : FBGenericConfig<F>, } -/// Settings for the solution of the stepwise optimality condition in algorithms based on -/// [`generic_pointsource_fb_reg`]. +/// Settings for the solution of the stepwise optimality condition. #[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)] #[serde(default)] pub struct FBGenericConfig<F : Float> { @@ -188,8 +192,8 @@ /// Iterations between merging heuristic tries pub merge_every : usize, - /// Save $μ$ for postprocessing optimisation - pub postprocessing : bool + // /// Save $μ$ for postprocessing optimisation + // pub postprocessing : bool } #[replace_float_literals(F::cast_from(literal))] @@ -221,29 +225,36 @@ final_merging : Default::default(), merge_every : 10, merge_tolerance_mult : 2.0, - postprocessing : false, + // postprocessing : false, } } } +impl<F : Float> FBGenericConfig<F> { + /// Check if merging should be attempted this iteration + pub fn merge_now<I : AlgIterator>(&self, state : &AlgIteratorIteration<I>) -> bool { + state.iteration() % self.merge_every == 0 + } +} + /// TODO: document. /// `μ_base + ν_delta` is the base point, where `μ` and `μ_base` are assumed to have the same spike /// locations, while `ν_delta` may have different locations. #[replace_float_literals(F::cast_from(literal))] pub(crate) fn insert_and_reweigh< - 'a, F, GA, 𝒟, BTA, G𝒟, S, K, Reg, State, const N : usize + 'a, F, GA, 𝒟, BTA, G𝒟, S, K, Reg, I, const N : usize >( - μ : &mut DiscreteMeasure<Loc<F, N>, F>, - minus_τv : &BTFN<F, GA, BTA, N>, - μ_base : &DiscreteMeasure<Loc<F, N>, F>, - ν_delta: Option<&DiscreteMeasure<Loc<F, N>, F>>, + μ : &mut RNDM<F, N>, + τv : &BTFN<F, GA, BTA, N>, + μ_base : &RNDM<F, N>, + ν_delta: Option<&RNDM<F, N>>, op𝒟 : &'a 𝒟, op𝒟norm : F, τ : F, ε : F, config : &FBGenericConfig<F>, reg : &Reg, - state : &State, + state : &AlgIteratorIteration<I>, stats : &mut IterInfo<F, N>, ) -> (BTFN<F, BothGenerators<GA, G𝒟>, BTA, N>, bool) where F : Float + ToNalgebraRealField, @@ -255,9 +266,8 @@ S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, K: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, - DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F>, Reg : RegTerm<F, N>, - State : AlgIteratorState { + I : AlgIterator { // Maximum insertion count and measure difference calculation depend on insertion style. let (max_insertions, warn_insertions) = match (state.iteration(), config.bootstrap_insertions) { @@ -265,11 +275,10 @@ _ => (config.max_insertions, !state.is_quiet()), }; - // TODO: should avoid a copy of μ_base here. - let ω0 = op𝒟.apply(match ν_delta { - None => μ_base.clone(), - Some(ν_d) => &*μ_base + ν_d, - }); + let ω0 = match ν_delta { + None => op𝒟.apply(μ_base), + Some(ν) => op𝒟.apply(μ_base + ν), + }; // Add points to support until within error tolerance or maximum insertion count reached. let mut count = 0; @@ -277,10 +286,12 @@ if μ.len() > 0 { // Form finite-dimensional subproblem. The subproblem references to the original μ^k // from the beginning of the iteration are all contained in the immutable c and g. + // TODO: observe negation of -τv after switch from minus_τv: finite-dimensional + // problems have not yet been updated to sign change. let à = op𝒟.findim_matrix(μ.iter_locations()); let g̃ = DVector::from_iterator(μ.len(), μ.iter_locations() - .map(|ζ| minus_τv.apply(ζ) + ω0.apply(ζ)) + .map(|ζ| ω0.apply(ζ) - τv.apply(ζ)) .map(F::to_nalgebra_mixed)); let mut x = μ.masses_dvector(); @@ -298,12 +309,12 @@ μ.set_masses_dvector(&x); } - // Form d = ω0 - τv - 𝒟μ = -𝒟(μ - μ^k) - τv for checking the proximate optimality + // Form d = τv + 𝒟μ - ω0 = τv + 𝒟(μ - μ^k) for checking the proximate optimality // conditions in the predual space, and finding new points for insertion, if necessary. - let mut d = minus_τv + op𝒟.preapply(match ν_delta { - None => μ_base.sub_matching(μ), - Some(ν) => μ_base.sub_matching(μ) + ν - }); + let mut d = τv + match ν_delta { + None => op𝒟.preapply(μ.sub_matching(μ_base)), + Some(ν) => op𝒟.preapply(μ.sub_matching(μ_base) - ν) + }; // If no merging heuristic is used, let's be more conservative about spike insertion, // and skip it after first round. If merging is done, being more greedy about spike @@ -330,11 +341,9 @@ // No point in optimising the weight here; the finite-dimensional algorithm is fast. *μ += DeltaMeasure { x : ξ, α : 0.0 }; count += 1; + stats.inserted += 1; }; - // TODO: should redo everything if some transports cause a problem. - // Maybe implementation should call above loop as a closure. - if !within_tolerances && warn_insertions { // Complain (but continue) if we failed to get within tolerances // by inserting more points. @@ -346,61 +355,33 @@ (d, within_tolerances) } -#[replace_float_literals(F::cast_from(literal))] -pub(crate) fn prune_and_maybe_simple_merge< - 'a, F, GA, 𝒟, BTA, G𝒟, S, K, Reg, State, const N : usize ->( - μ : &mut DiscreteMeasure<Loc<F, N>, F>, - minus_τv : &BTFN<F, GA, BTA, N>, - μ_base : &DiscreteMeasure<Loc<F, N>, F>, - op𝒟 : &'a 𝒟, - τ : F, - ε : F, - config : &FBGenericConfig<F>, - reg : &Reg, - state : &State, - stats : &mut IterInfo<F, N>, -) -where F : Float + ToNalgebraRealField, - GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, - BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, - G𝒟 : SupportGenerator<F, N, SupportType = K, Id = usize> + Clone, - 𝒟 : DiscreteMeasureOp<Loc<F, N>, F, PreCodomain = PreBTFN<F, G𝒟, N>>, - 𝒟::Codomain : RealMapping<F, N>, - S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, - K: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, - BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, - DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F>, - Reg : RegTerm<F, N>, - State : AlgIteratorState { - if state.iteration() % config.merge_every == 0 { - stats.merged += μ.merge_spikes(config.merging, |μ_candidate| { - let mut d = minus_τv + op𝒟.preapply(μ_base.sub_matching(&μ_candidate)); - reg.verify_merge_candidate(&mut d, μ_candidate, τ, ε, &config) - }); - } - +pub(crate) fn prune_with_stats<F : Float, const N : usize>( + μ : &mut RNDM<F, N>, +) -> usize { let n_before_prune = μ.len(); μ.prune(); debug_assert!(μ.len() <= n_before_prune); - stats.pruned += n_before_prune - μ.len(); + n_before_prune - μ.len() } #[replace_float_literals(F::cast_from(literal))] pub(crate) fn postprocess< F : Float, V : Euclidean<F> + Clone, - A : GEMV<F, DiscreteMeasure<Loc<F, N>, F>, Codomain = V>, + A : GEMV<F, RNDM<F, N>, Codomain = V>, D : DataTerm<F, V, N>, const N : usize > ( - mut μ : DiscreteMeasure<Loc<F, N>, F>, + mut μ : RNDM<F, N>, config : &FBGenericConfig<F>, dataterm : D, opA : &A, b : &V, -) -> DiscreteMeasure<Loc<F, N>, F> -where DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F> { +) -> RNDM<F, N> +where + RNDM<F, N> : SpikeMerging<F>, + for<'a> &'a RNDM<F, N> : Instance<RNDM<F, N>>, +{ μ.merge_spikes_fitness(config.merging, |μ̃| dataterm.calculate_fit_op(μ̃, opA, b), |&v| v); @@ -437,15 +418,13 @@ fbconfig : &FBConfig<F>, iterator : I, mut plotter : SeqPlotter<F, N>, -) -> DiscreteMeasure<Loc<F, N>, F> +) -> RNDM<F, N> where F : Float + ToNalgebraRealField, I : AlgIteratorFactory<IterInfo<F, N>>, for<'b> &'b A::Observable : std::ops::Neg<Output=A::Observable>, - //+ std::ops::Mul<F, Output=A::Observable>, <-- FIXME: compiler overflow - A::Observable : std::ops::MulAssign<F>, GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, - A : ForwardModel<Loc<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>> - + Lipschitz<&'a 𝒟, FloatType=F>, + A : ForwardModel<RNDM<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>> + + AdjointProductBoundedBy<RNDM<F, N>, 𝒟, FloatType=F>, BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, G𝒟 : SupportGenerator<F, N, SupportType = K, Id = usize> + Clone, 𝒟 : DiscreteMeasureOp<Loc<F, N>, F, PreCodomain = PreBTFN<F, G𝒟, N>>, @@ -455,13 +434,13 @@ BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, Cube<F, N>: P2Minimise<Loc<F, N>, F>, PlotLookup : Plotting<N>, - DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F>, + RNDM<F, N> : SpikeMerging<F>, Reg : RegTerm<F, N> { // Set up parameters let config = &fbconfig.generic; - let op𝒟norm = op𝒟.opnorm_bound(); - let τ = fbconfig.τ0/opA.lipschitz_factor(&op𝒟).unwrap(); + let op𝒟norm = op𝒟.opnorm_bound(Radon, Linfinity); + let τ = fbconfig.τ0/opA.adjoint_product_bound(&op𝒟).unwrap(); // We multiply tolerance by τ for FB since our subproblems depending on tolerances are scaled // by τ compared to the conditional gradient approach. let tolerance = config.tolerance * τ * reg.tolerance_scaling(); @@ -470,66 +449,59 @@ // Initialise iterates let mut μ = DiscreteMeasure::new(); let mut residual = -b; + + // Statistics + let full_stats = |residual : &A::Observable, + μ : &RNDM<F, N>, + ε, stats| IterInfo { + value : residual.norm2_squared_div2() + reg.apply(μ), + n_spikes : μ.len(), + ε, + //postprocessing: config.postprocessing.then(|| μ.clone()), + .. stats + }; let mut stats = IterInfo::new(); // Run the algorithm - iterator.iterate(|state| { + for state in iterator.iter_init(|| full_stats(&residual, &μ, ε, stats.clone())) { // Calculate smooth part of surrogate model. - // Using `std::mem::replace` here is not ideal, and expects that `empty_observable` - // has no significant overhead. For some reosn Rust doesn't allow us simply moving - // the residual and replacing it below before the end of this closure. - residual *= -τ; - let r = std::mem::replace(&mut residual, opA.empty_observable()); - let minus_τv = opA.preadjoint().apply(r); + let τv = opA.preadjoint().apply(residual * τ); // Save current base point let μ_base = μ.clone(); // Insert and reweigh - let (d, within_tolerances) = insert_and_reweigh( - &mut μ, &minus_τv, &μ_base, None, + let (d, _within_tolerances) = insert_and_reweigh( + &mut μ, &τv, &μ_base, None, op𝒟, op𝒟norm, τ, ε, - config, ®, state, &mut stats + config, ®, &state, &mut stats ); // Prune and possibly merge spikes - prune_and_maybe_simple_merge( - &mut μ, &minus_τv, &μ_base, - op𝒟, - τ, ε, - config, ®, state, &mut stats - ); + if config.merge_now(&state) { + stats.merged += μ.merge_spikes(config.merging, |μ_candidate| { + let mut d = &τv + op𝒟.preapply(μ_candidate.sub_matching(&μ_base)); + reg.verify_merge_candidate(&mut d, μ_candidate, τ, ε, &config) + }); + } + stats.pruned += prune_with_stats(&mut μ); // Update residual residual = calculate_residual(&μ, opA, b); - // Update main tolerance for next iteration - let ε_prev = ε; - ε = tolerance.update(ε, state.iteration()); + let iter = state.iteration(); stats.this_iters += 1; - // Give function value if needed + // Give statistics if needed state.if_verbose(|| { - // Plot if so requested - plotter.plot_spikes( - format!("iter {} end; {}", state.iteration(), within_tolerances), &d, - "start".to_string(), Some(&minus_τv), - reg.target_bounds(τ, ε_prev), &μ, - ); - // Calculate mean inner iterations and reset relevant counters. - // Return the statistics - let res = IterInfo { - value : residual.norm2_squared_div2() + reg.apply(&μ), - n_spikes : μ.len(), - ε : ε_prev, - postprocessing: config.postprocessing.then(|| μ.clone()), - .. stats - }; - stats = IterInfo::new(); - res - }) - }); + plotter.plot_spikes(iter, Some(&d), Some(&τv), &μ); + full_stats(&residual, &μ, ε, std::mem::replace(&mut stats, IterInfo::new())) + }); + + // Update main tolerance for next iteration + ε = tolerance.update(ε, iter); + } postprocess(μ, config, L2Squared, opA, b) } @@ -563,15 +535,13 @@ fbconfig : &FBConfig<F>, iterator : I, mut plotter : SeqPlotter<F, N>, -) -> DiscreteMeasure<Loc<F, N>, F> +) -> RNDM<F, N> where F : Float + ToNalgebraRealField, I : AlgIteratorFactory<IterInfo<F, N>>, for<'b> &'b A::Observable : std::ops::Neg<Output=A::Observable>, - //+ std::ops::Mul<F, Output=A::Observable>, <-- FIXME: compiler overflow - A::Observable : std::ops::MulAssign<F>, GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, - A : ForwardModel<Loc<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>> - + Lipschitz<&'a 𝒟, FloatType=F>, + A : ForwardModel<RNDM<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>> + + AdjointProductBoundedBy<RNDM<F, N>, 𝒟, FloatType=F>, BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, G𝒟 : SupportGenerator<F, N, SupportType = K, Id = usize> + Clone, 𝒟 : DiscreteMeasureOp<Loc<F, N>, F, PreCodomain = PreBTFN<F, G𝒟, N>>, @@ -581,13 +551,13 @@ BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, Cube<F, N>: P2Minimise<Loc<F, N>, F>, PlotLookup : Plotting<N>, - DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F>, + RNDM<F, N> : SpikeMerging<F>, Reg : RegTerm<F, N> { // Set up parameters let config = &fbconfig.generic; - let op𝒟norm = op𝒟.opnorm_bound(); - let τ = fbconfig.τ0/opA.lipschitz_factor(&op𝒟).unwrap(); + let op𝒟norm = op𝒟.opnorm_bound(Radon, Linfinity); + let τ = fbconfig.τ0/opA.adjoint_product_bound(&op𝒟).unwrap(); let mut λ = 1.0; // We multiply tolerance by τ for FB since our subproblems depending on tolerances are scaled // by τ compared to the conditional gradient approach. @@ -598,32 +568,36 @@ let mut μ = DiscreteMeasure::new(); let mut μ_prev = DiscreteMeasure::new(); let mut residual = -b; + let mut warned_merging = false; + + // Statistics + let full_stats = |ν : &RNDM<F, N>, ε, stats| IterInfo { + value : L2Squared.calculate_fit_op(ν, opA, b) + reg.apply(ν), + n_spikes : ν.len(), + ε, + // postprocessing: config.postprocessing.then(|| ν.clone()), + .. stats + }; let mut stats = IterInfo::new(); - let mut warned_merging = false; // Run the algorithm - iterator.iterate(|state| { + for state in iterator.iter_init(|| full_stats(&μ, ε, stats.clone())) { // Calculate smooth part of surrogate model. - // Using `std::mem::replace` here is not ideal, and expects that `empty_observable` - // has no significant overhead. For some reosn Rust doesn't allow us simply moving - // the residual and replacing it below before the end of this closure. - residual *= -τ; - let r = std::mem::replace(&mut residual, opA.empty_observable()); - let minus_τv = opA.preadjoint().apply(r); + let τv = opA.preadjoint().apply(residual * τ); // Save current base point let μ_base = μ.clone(); // Insert new spikes and reweigh - let (d, within_tolerances) = insert_and_reweigh( - &mut μ, &minus_τv, &μ_base, None, + let (d, _within_tolerances) = insert_and_reweigh( + &mut μ, &τv, &μ_base, None, op𝒟, op𝒟norm, τ, ε, - config, ®, state, &mut stats + config, ®, &state, &mut stats ); // (Do not) merge spikes. - if state.iteration() % config.merge_every == 0 { + if config.merge_now(&state) { match config.merging { SpikeMergingMethod::None => { }, _ => if !warned_merging { @@ -653,32 +627,18 @@ // Update residual residual = calculate_residual(&μ, opA, b); - // Update main tolerance for next iteration - let ε_prev = ε; - ε = tolerance.update(ε, state.iteration()); + let iter = state.iteration(); stats.this_iters += 1; - // Give function value if needed + // Give statistics if needed state.if_verbose(|| { - // Plot if so requested - plotter.plot_spikes( - format!("iter {} end; {}", state.iteration(), within_tolerances), &d, - "start".to_string(), Some(&minus_τv), - reg.target_bounds(τ, ε_prev), &μ_prev, - ); - // Calculate mean inner iterations and reset relevant counters. - // Return the statistics - let res = IterInfo { - value : L2Squared.calculate_fit_op(&μ_prev, opA, b) + reg.apply(&μ_prev), - n_spikes : μ_prev.len(), - ε : ε_prev, - postprocessing: config.postprocessing.then(|| μ_prev.clone()), - .. stats - }; - stats = IterInfo::new(); - res - }) - }); + plotter.plot_spikes(iter, Some(&d), Some(&τv), &μ_prev); + full_stats(&μ_prev, ε, std::mem::replace(&mut stats, IterInfo::new())) + }); + + // Update main tolerance for next iteration + ε = tolerance.update(ε, iter); + } postprocess(μ_prev, config, L2Squared, opA, b) }
--- a/src/forward_model.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/forward_model.rs Tue Dec 31 09:25:45 2024 -0500 @@ -2,705 +2,71 @@ Forward models from discrete measures to observations. */ -use numeric_literals::replace_float_literals; -use nalgebra::base::{ - DMatrix, - DVector -}; -use std::iter::Zip; -use std::ops::RangeFrom; -use std::marker::PhantomData; - pub use alg_tools::linops::*; use alg_tools::euclidean::Euclidean; -use alg_tools::norms::{ - L1, Linfinity, L2, Norm -}; -use alg_tools::bisection_tree::*; -use alg_tools::mapping::RealMapping; -use alg_tools::lingrid::*; -use alg_tools::iter::{MapX, Mappable}; -use alg_tools::nalgebra_support::ToNalgebraRealField; -use alg_tools::tabledump::write_csv; use alg_tools::error::DynError; -use alg_tools::maputil::map2; +use alg_tools::instance::Instance; +use alg_tools::norms::{NormExponent, L2, Norm}; use crate::types::*; -use crate::measures::*; -use crate::seminorms::{ - ConvolutionOp, - SimpleConvolutionKernel, -}; -use crate::kernels::{ - Convolution, - AutoConvolution, - BoundedBy, -}; -use crate::types::L2Squared; -use crate::transport::TransportLipschitz; - -pub type RNDM<F, const N : usize> = DiscreteMeasure<Loc<F,N>, F>; +use crate::measures::Radon; +pub mod sensor_grid; +pub mod bias; /// `ForwardeModel`s are bounded preadjointable linear operators $A ∈ 𝕃(𝒵(Ω); E)$ /// where $𝒵(Ω) ⊂ ℳ(Ω)$ is the space of sums of delta measures, presented by -/// [`DiscreteMeasure`], and $E$ is a [`Euclidean`] space. -pub trait ForwardModel<Domain, F : Float + ToNalgebraRealField> -: BoundedLinear<DiscreteMeasure<Domain, F>, Codomain=Self::Observable, FloatType=F> -+ GEMV<F, DiscreteMeasure<Domain, F>, Self::Observable> -+ Linear<DeltaMeasure<Domain, F>, Codomain=Self::Observable> -+ Preadjointable<DiscreteMeasure<Domain, F>, Self::Observable> { +/// [`crate::measures::DiscreteMeasure`], and $E$ is a [`Euclidean`] space. +pub trait ForwardModel<Domain : Space, F : Float = f64, E : NormExponent = Radon> + : BoundedLinear<Domain, E, L2, F, Codomain=Self::Observable> + + GEMV<F, Domain, Self::Observable> + + Preadjointable<Domain, Self::Observable> +where + for<'a> Self::Observable : Instance<Self::Observable>, + Domain : Norm<F, E>, +{ /// The codomain or value space (of “observables”) for this operator. /// It is assumed to be a [`Euclidean`] space, and therefore also (identified with) /// the domain of the preadjoint. type Observable : Euclidean<F, Output=Self::Observable> + AXPY<F> + + Space + Clone; - /// Return A_*A and A_* b - fn findim_quadratic_model( - &self, - μ : &DiscreteMeasure<Domain, F>, - b : &Self::Observable - ) -> (DMatrix<F::MixedType>, DVector<F::MixedType>); - /// Write an observable into a file. fn write_observable(&self, b : &Self::Observable, prefix : String) -> DynError; /// Returns a zero observable fn zero_observable(&self) -> Self::Observable; - - /// Returns an empty (uninitialised) observable. - /// - /// This is used as a placeholder for temporary [`std::mem::replace`] move operations. - fn empty_observable(&self) -> Self::Observable; -} - -pub type ShiftedSensor<F, S, P, const N : usize> = Shift<Convolution<S, P>, F, N>; - -/// Trait for physical convolution models. Has blanket implementation for all cases. -pub trait Spread<F : Float, const N : usize> -: 'static + Clone + Support<F, N> + RealMapping<F, N> + Bounded<F> {} - -impl<F, T, const N : usize> Spread<F, N> for T -where F : Float, - T : 'static + Clone + Support<F, N> + Bounded<F> + RealMapping<F, N> {} - -/// Trait for compactly supported sensors. Has blanket implementation for all cases. -pub trait Sensor<F : Float, const N : usize> : Spread<F, N> + Norm<F, L1> + Norm<F, Linfinity> {} - -impl<F, T, const N : usize> Sensor<F, N> for T -where F : Float, - T : Spread<F, N> + Norm<F, L1> + Norm<F, Linfinity> {} - - -pub trait SensorGridBT<F, S, P, const N : usize> : -Clone + BTImpl<F, N, Data=usize, Agg=Bounds<F>> -where F : Float, - S : Sensor<F, N>, - P : Spread<F, N> {} - -impl<F, S, P, T, const N : usize> -SensorGridBT<F, S, P, N> -for T -where T : Clone + BTImpl<F, N, Data=usize, Agg=Bounds<F>>, - F : Float, - S : Sensor<F, N>, - P : Spread<F, N> {} - -// We need type alias bounds to access associated types -#[allow(type_alias_bounds)] -type SensorGridBTFN<F, S, P, BT : SensorGridBT<F, S, P, N>, const N : usize> -= BTFN<F, SensorGridSupportGenerator<F, S, P, N>, BT, N>; - -/// Sensor grid forward model -#[derive(Clone)] -pub struct SensorGrid<F, S, P, BT, const N : usize> -where F : Float, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - BT : SensorGridBT<F, S, P, N>, { - domain : Cube<F, N>, - sensor_count : [usize; N], - sensor : S, - spread : P, - base_sensor : Convolution<S, P>, - bt : BT, } -impl<F, S, P, BT, const N : usize> SensorGrid<F, S, P, BT, N> -where F : Float, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N> { - - pub fn new( - domain : Cube<F, N>, - sensor_count : [usize; N], - sensor : S, - spread : P, - depth : BT::Depth - ) -> Self { - let base_sensor = Convolution(sensor.clone(), spread.clone()); - let bt = BT::new(domain, depth); - let mut sensorgrid = SensorGrid { - domain, - sensor_count, - sensor, - spread, - base_sensor, - bt, - }; - - for (x, id) in sensorgrid.grid().into_iter().zip(0usize..) { - let s = sensorgrid.shifted_sensor(x); - sensorgrid.bt.insert(id, &s); - } - - sensorgrid - } - - pub fn grid(&self) -> LinGrid<F, N> { - lingrid_centered(&self.domain, &self.sensor_count) - } - - pub fn n_sensors(&self) -> usize { - self.sensor_count.iter().product() - } - - #[inline] - fn shifted_sensor(&self, x : Loc<F, N>) -> ShiftedSensor<F, S, P, N> { - self.base_sensor.clone().shift(x) - } - - #[inline] - fn _zero_observable(&self) -> DVector<F> { - DVector::zeros(self.n_sensors()) - } -} - -impl<F, S, P, BT, const N : usize> Apply<RNDM<F, N>> for SensorGrid<F, S, P, BT, N> -where F : Float, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N> { - - type Output = DVector<F>; - - #[inline] - fn apply(&self, μ : RNDM<F, N>) -> DVector<F> { - self.apply(&μ) - } +/// Trait for operators $A$ for which $A_*A$ is bounded by some other operator. +pub trait AdjointProductBoundedBy<Domain : Space, D> : Linear<Domain> { + type FloatType : Float; + /// Return $L$ such that $A_*A ≤ LD$. + fn adjoint_product_bound(&self, other : &D) -> Option<Self::FloatType>; } -impl<'a, F, S, P, BT, const N : usize> Apply<&'a RNDM<F, N>> for SensorGrid<F, S, P, BT, N> -where F : Float, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N> { - - type Output = DVector<F>; - - fn apply(&self, μ : &'a RNDM<F, N>) -> DVector<F> { - let mut res = self._zero_observable(); - self.apply_add(&mut res, μ); - res - } -} - -impl<F, S, P, BT, const N : usize> Linear<RNDM<F, N>> for SensorGrid<F, S, P, BT, N> -where F : Float, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N> { - type Codomain = DVector<F>; -} - - -#[replace_float_literals(F::cast_from(literal))] -impl<F, S, P, BT, const N : usize> GEMV<F, RNDM<F, N>, DVector<F>> for SensorGrid<F, S, P, BT, N> -where F : Float, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N> { - - fn gemv(&self, y : &mut DVector<F>, α : F, μ : &RNDM<F, N>, β : F) { - let grid = self.grid(); - if β == 0.0 { - y.fill(0.0) - } else if β != 1.0 { - *y *= β; // Need to multiply first, as we have to be able to add to y. - } - if α == 1.0 { - self.apply_add(y, μ) - } else { - for δ in μ.iter_spikes() { - for &d in self.bt.iter_at(&δ.x) { - let sensor = self.shifted_sensor(grid.entry_linear_unchecked(d)); - y[d] += sensor.apply(&δ.x) * (α * δ.α); - } - } - } - } - - fn apply_add(&self, y : &mut DVector<F>, μ : &RNDM<F, N>) { - let grid = self.grid(); - for δ in μ.iter_spikes() { - for &d in self.bt.iter_at(&δ.x) { - let sensor = self.shifted_sensor(grid.entry_linear_unchecked(d)); - y[d] += sensor.apply(&δ.x) * δ.α; - } - } - } - +/// Trait for operators $A$ for which $A_*A$ is bounded by a diagonal operator. +pub trait AdjointProductPairBoundedBy<Domain : Space, D1, D2> : Linear<Domain> { + type FloatType : Float; + /// Return $(L, L_z)$ such that $A_*A ≤ (L_1 D_1, L_2 D_2)$. + fn adjoint_product_pair_bound(&self, other1 : &D1, other_2 : &D2) + -> Option<(Self::FloatType, Self::FloatType)>; } -impl<F, S, P, BT, const N : usize> Apply<DeltaMeasure<Loc<F, N>, F>> -for SensorGrid<F, S, P, BT, N> -where F : Float, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N> { - - type Output = DVector<F>; - - #[inline] - fn apply(&self, δ : DeltaMeasure<Loc<F, N>, F>) -> DVector<F> { - self.apply(&δ) +/// Trait for [`ForwardModel`]s whose preadjoint has Lipschitz values. +pub trait LipschitzValues { + type FloatType : Float; + /// Return (if one exists) a factor $L$ such that $A_*z$ is $L$-Lipschitz for all + /// $z$ in the unit ball. + fn value_unit_lipschitz_factor(&self) -> Option<Self::FloatType> { + None } -} - -impl<'a, F, S, P, BT, const N : usize> Apply<&'a DeltaMeasure<Loc<F, N>, F>> -for SensorGrid<F, S, P, BT, N> -where F : Float, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N> { - - type Output = DVector<F>; - - fn apply(&self, δ : &DeltaMeasure<Loc<F, N>, F>) -> DVector<F> { - let mut res = DVector::zeros(self.n_sensors()); - let grid = self.grid(); - for &d in self.bt.iter_at(&δ.x) { - let sensor = self.shifted_sensor(grid.entry_linear_unchecked(d)); - res[d] += sensor.apply(&δ.x) * δ.α; - } - res - } -} -impl<F, S, P, BT, const N : usize> Linear<DeltaMeasure<Loc<F, N>, F>> for SensorGrid<F, S, P, BT, N> -where F : Float, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N> { - type Codomain = DVector<F>; -} - -impl<F, S, P, BT, const N : usize> BoundedLinear<RNDM<F, N>> for SensorGrid<F, S, P, BT, N> -where F : Float, - BT : SensorGridBT<F, S, P, N, Agg=Bounds<F>>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N> { - type FloatType = F; - - /// An estimate on the operator norm in $𝕃(ℳ(Ω); ℝ^n)$ with $ℳ(Ω)$ equipped - /// with the Radon norm, and $ℝ^n$ with the Euclidean norm. - fn opnorm_bound(&self) -> F { - // With {x_i}_{i=1}^n the grid centres and φ the kernel, we have - // |Aμ|_2 = sup_{|z|_2 ≤ 1} ⟨z,Αμ⟩ = sup_{|z|_2 ≤ 1} ⟨A^*z|μ⟩ - // ≤ sup_{|z|_2 ≤ 1} |A^*z|_∞ |μ|_ℳ - // = sup_{|z|_2 ≤ 1} |∑ φ(· - x_i)z_i|_∞ |μ|_ℳ - // ≤ sup_{|z|_2 ≤ 1} |φ|_∞ ∑ |z_i| |μ|_ℳ - // ≤ sup_{|z|_2 ≤ 1} |φ|_∞ √n |z|_2 |μ|_ℳ - // = |φ|_∞ √n |μ|_ℳ. - // Hence - let n = F::cast_from(self.n_sensors()); - self.base_sensor.bounds().uniform() * n.sqrt() - } -} - -type SensorGridPreadjoint<'a, A, F, const N : usize> = PreadjointHelper<'a, A, RNDM<F,N>>; - - -impl<F, S, P, BT, const N : usize> -Preadjointable<RNDM<F, N>, DVector<F>> -for SensorGrid<F, S, P, BT, N> -where F : Float, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N>, - Weighted<ShiftedSensor<F, S, P, N>, F> : LocalAnalysis<F, BT::Agg, N> { - type PreadjointCodomain = BTFN<F, SensorGridSupportGenerator<F, S, P, N>, BT, N>; - type Preadjoint<'a> = SensorGridPreadjoint<'a, Self, F, N> where Self : 'a; - - fn preadjoint(&self) -> Self::Preadjoint<'_> { - PreadjointHelper::new(self) + /// Return (if one exists) a factor $L$ such that $∇A_*z$ is $L$-Lipschitz for all + /// $z$ in the unit ball. + fn value_diff_unit_lipschitz_factor(&self) -> Option<Self::FloatType> { + None } } -#[derive(Clone,Debug)] -pub struct SensorGridSupportGenerator<F, S, P, const N : usize> -where F : Float, - S : Sensor<F, N>, - P : Spread<F, N> { - base_sensor : Convolution<S, P>, - grid : LinGrid<F, N>, - weights : DVector<F> -} - -impl<F, S, P, const N : usize> SensorGridSupportGenerator<F, S, P, N> -where F : Float, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N> { - - #[inline] - fn construct_sensor(&self, id : usize, w : F) -> Weighted<ShiftedSensor<F, S, P, N>, F> { - let x = self.grid.entry_linear_unchecked(id); - self.base_sensor.clone().shift(x).weigh(w) - } - - #[inline] - fn construct_sensor_and_id<'a>(&'a self, (id, w) : (usize, &'a F)) - -> (usize, Weighted<ShiftedSensor<F, S, P, N>, F>) { - (id.into(), self.construct_sensor(id, *w)) - } -} - -impl<F, S, P, const N : usize> SupportGenerator<F, N> -for SensorGridSupportGenerator<F, S, P, N> -where F : Float, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N> { - type Id = usize; - type SupportType = Weighted<ShiftedSensor<F, S, P, N>, F>; - type AllDataIter<'a> = MapX<'a, Zip<RangeFrom<usize>, - std::slice::Iter<'a, F>>, - Self, - (Self::Id, Self::SupportType)> - where Self : 'a; - - #[inline] - fn support_for(&self, d : Self::Id) -> Self::SupportType { - self.construct_sensor(d, self.weights[d]) - } - - #[inline] - fn support_count(&self) -> usize { - self.weights.len() - } - - #[inline] - fn all_data(&self) -> Self::AllDataIter<'_> { - (0..).zip(self.weights.as_slice().iter()).mapX(self, Self::construct_sensor_and_id) - } -} - -/// Helper structure for constructing preadjoints of `S` where `S : Linear<X>`. -/// [`Linear`] needs to be implemented for each instance, but [`Adjointable`] -/// and [`BoundedLinear`] have blanket implementations. -#[derive(Clone,Debug)] -pub struct PreadjointHelper<'a, S : 'a, X> { - forward_op : &'a S, - _domain : PhantomData<X> -} - -impl<'a, S : 'a, X> PreadjointHelper<'a, S, X> { - pub fn new(forward_op : &'a S) -> Self { - PreadjointHelper { forward_op, _domain: PhantomData } - } -} - -impl<'a, X, Ypre, S> Adjointable<Ypre, X> -for PreadjointHelper<'a, S, X> -where Self : Linear<Ypre>, - S : Clone + Linear<X> { - type AdjointCodomain = S::Codomain; - type Adjoint<'b> = S where Self : 'b; - fn adjoint(&self) -> Self::Adjoint<'_> { - self.forward_op.clone() - } -} - -impl<'a, X, Ypre, S> BoundedLinear<Ypre> -for PreadjointHelper<'a, S, X> -where Self : Linear<Ypre>, - S : 'a + Clone + BoundedLinear<X> { - type FloatType = S::FloatType; - fn opnorm_bound(&self) -> Self::FloatType { - self.forward_op.opnorm_bound() - } -} - - -impl<'a, 'b, F, S, P, BT, const N : usize> Apply<&'b DVector<F>> -for PreadjointHelper<'a, SensorGrid<F, S, P, BT, N>, RNDM<F,N>> -where F : Float, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N>, - Weighted<ShiftedSensor<F, S, P, N>, F> : LocalAnalysis<F, BT::Agg, N> { - - type Output = SensorGridBTFN<F, S, P, BT, N>; - - fn apply(&self, x : &'b DVector<F>) -> Self::Output { - self.apply(x.clone()) - } -} - -impl<'a, F, S, P, BT, const N : usize> Apply<DVector<F>> -for PreadjointHelper<'a, SensorGrid<F, S, P, BT, N>, RNDM<F,N>> -where F : Float, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N>, - Weighted<ShiftedSensor<F, S, P, N>, F> : LocalAnalysis<F, BT::Agg, N> { - - type Output = SensorGridBTFN<F, S, P, BT, N>; - - fn apply(&self, x : DVector<F>) -> Self::Output { - let fwd = &self.forward_op; - let generator = SensorGridSupportGenerator{ - base_sensor : fwd.base_sensor.clone(), - grid : fwd.grid(), - weights : x - }; - BTFN::new_refresh(&fwd.bt, generator) - } -} - -impl<'a, F, S, P, BT, const N : usize> Linear<DVector<F>> -for PreadjointHelper<'a, SensorGrid<F, S, P, BT, N>, RNDM<F,N>> -where F : Float, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N>, - Weighted<ShiftedSensor<F, S, P, N>, F> : LocalAnalysis<F, BT::Agg, N> { - - type Codomain = SensorGridBTFN<F, S, P, BT, N>; -} - -impl<F, S, P, BT, const N : usize> ForwardModel<Loc<F, N>, F> -for SensorGrid<F, S, P, BT, N> -where F : Float + ToNalgebraRealField<MixedType=F> + nalgebra::RealField, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N>, - Weighted<ShiftedSensor<F, S, P, N>, F> : LocalAnalysis<F, BT::Agg, N> { - type Observable = DVector<F>; - - fn findim_quadratic_model( - &self, - μ : &DiscreteMeasure<Loc<F, N>, F>, - b : &Self::Observable - ) -> (DMatrix<F::MixedType>, DVector<F::MixedType>) { - assert_eq!(b.len(), self.n_sensors()); - let mut mA = DMatrix::zeros(self.n_sensors(), μ.len()); - let grid = self.grid(); - for (mut mAcol, δ) in mA.column_iter_mut().zip(μ.iter_spikes()) { - for &d in self.bt.iter_at(&δ.x) { - let sensor = self.shifted_sensor(grid.entry_linear_unchecked(d)); - mAcol[d] += sensor.apply(&δ.x); - } - } - let mAt = mA.transpose(); - (&mAt * mA, &mAt * b) - } - - fn write_observable(&self, b : &Self::Observable, prefix : String) -> DynError { - let it = self.grid().into_iter().zip(b.iter()).map(|(x, &v)| (x, v)); - write_csv(it, prefix + ".txt") - } - - #[inline] - fn zero_observable(&self) -> Self::Observable { - self._zero_observable() - } - - #[inline] - fn empty_observable(&self) -> Self::Observable { - DVector::zeros(0) - } - -} - -/// Implements the calculation a factor $L$ such that $A_*A ≤ L 𝒟$ for $A$ the forward model -/// and $𝒟$ a seminorm of suitable form. -/// -/// **This assumes (but does not check) that the sensors are not overlapping.** -#[replace_float_literals(F::cast_from(literal))] -impl<'a, F, BT, S, P, K, const N : usize> Lipschitz<&'a ConvolutionOp<F, K, BT, N>> -for SensorGrid<F, S, P, BT, N> -where F : Float + nalgebra::RealField + ToNalgebraRealField, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N>, - K : SimpleConvolutionKernel<F, N>, - AutoConvolution<P> : BoundedBy<F, K> { - - type FloatType = F; - - fn lipschitz_factor(&self, seminorm : &'a ConvolutionOp<F, K, BT, N>) -> Option<F> { - // Sensors should not take on negative values to allow - // A_*A to be upper bounded by a simple convolution of `spread`. - if self.sensor.bounds().lower() < 0.0 { - return None - } - - // Calculate the factor $L_1$ for betwee $ℱ[ψ * ψ] ≤ L_1 ℱ[ρ]$ for $ψ$ the base spread - // and $ρ$ the kernel of the seminorm. - let l1 = AutoConvolution(self.spread.clone()).bounding_factor(seminorm.kernel())?; - - // Calculate the factor for transitioning from $A_*A$ to `AutoConvolution<P>`, where A - // consists of several `Convolution<S, P>` for the physical model `P` and the sensor `S`. - let l0 = self.sensor.norm(Linfinity) * self.sensor.norm(L1); - - // The final transition factor is: - Some(l0 * l1) - } -} - -#[replace_float_literals(F::cast_from(literal))] -impl<F, BT, S, P, const N : usize> TransportLipschitz<L2Squared> -for SensorGrid<F, S, P, BT, N> -where F : Float + ToNalgebraRealField, - BT : SensorGridBT<F, S, P, N>, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N> + Lipschitz<L2, FloatType = F> { - type FloatType = F; - - fn transport_lipschitz_factor(&self, L2Squared : L2Squared) -> Self::FloatType { - // We estimate the factor by N_ψL^2, where L is the 2-norm Lipschitz factor of - // the base sensor (sensor * base_spread), and N_ψ the maximum overlap. - let l = self.base_sensor.lipschitz_factor(L2).unwrap(); - let w = self.base_sensor.support_hint().width(); - let d = map2(self.domain.width(), &self.sensor_count, |wi, &i| wi/F::cast_from(i)); - let n = w.iter() - .zip(d.iter()) - .map(|(&wi, &di)| (wi/di).ceil()) - .reduce(F::mul) - .unwrap(); - 2.0 * n * l.powi(2) - } -} - - -macro_rules! make_sensorgridsupportgenerator_scalarop_rhs { - ($trait:ident, $fn:ident, $trait_assign:ident, $fn_assign:ident) => { - impl<F, S, P, const N : usize> - std::ops::$trait_assign<F> - for SensorGridSupportGenerator<F, S, P, N> - where F : Float, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N> { - fn $fn_assign(&mut self, t : F) { - self.weights.$fn_assign(t); - } - } - - impl<F, S, P, const N : usize> - std::ops::$trait<F> - for SensorGridSupportGenerator<F, S, P, N> - where F : Float, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N> { - type Output = SensorGridSupportGenerator<F, S, P, N>; - fn $fn(mut self, t : F) -> Self::Output { - std::ops::$trait_assign::$fn_assign(&mut self.weights, t); - self - } - } - - impl<'a, F, S, P, const N : usize> - std::ops::$trait<F> - for &'a SensorGridSupportGenerator<F, S, P, N> - where F : Float, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N> { - type Output = SensorGridSupportGenerator<F, S, P, N>; - fn $fn(self, t : F) -> Self::Output { - SensorGridSupportGenerator{ - base_sensor : self.base_sensor.clone(), - grid : self.grid, - weights : (&self.weights).$fn(t) - } - } - } - } -} - -make_sensorgridsupportgenerator_scalarop_rhs!(Mul, mul, MulAssign, mul_assign); -make_sensorgridsupportgenerator_scalarop_rhs!(Div, div, DivAssign, div_assign); - -macro_rules! make_sensorgridsupportgenerator_unaryop { - ($trait:ident, $fn:ident) => { - impl<F, S, P, const N : usize> - std::ops::$trait - for SensorGridSupportGenerator<F, S, P, N> - where F : Float, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N> { - type Output = SensorGridSupportGenerator<F, S, P, N>; - fn $fn(mut self) -> Self::Output { - self.weights = self.weights.$fn(); - self - } - } - - impl<'a, F, S, P, const N : usize> - std::ops::$trait - for &'a SensorGridSupportGenerator<F, S, P, N> - where F : Float, - S : Sensor<F, N>, - P : Spread<F, N>, - Convolution<S, P> : Spread<F, N> { - type Output = SensorGridSupportGenerator<F, S, P, N>; - fn $fn(self) -> Self::Output { - SensorGridSupportGenerator{ - base_sensor : self.base_sensor.clone(), - grid : self.grid, - weights : (&self.weights).$fn() - } - } - } - } -} - -make_sensorgridsupportgenerator_unaryop!(Neg, neg);
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/forward_model/bias.rs Tue Dec 31 09:25:45 2024 -0500 @@ -0,0 +1,110 @@ +/*! +Simple parametric forward model. + */ + +use numeric_literals::replace_float_literals; +use alg_tools::types::{Float, ClosedAdd}; +use alg_tools::mapping::Space; +use alg_tools::direct_product::Pair; +use alg_tools::linops::{Linear, RowOp, ColOp, IdOp, ZeroOp, AXPY}; +use alg_tools::error::DynError; +use alg_tools::norms::{L2, Norm, PairNorm, NormExponent}; +use crate::types::L2Squared; +use crate::measures::RNDM; +use super::{ForwardModel, AdjointProductBoundedBy, AdjointProductPairBoundedBy, LipschitzValues}; +use crate::transport::TransportLipschitz; + +impl<Domain, F, A, E> ForwardModel<Pair<Domain, A::Observable>, F, PairNorm<E, L2, L2>> +for RowOp<A, IdOp<A::Observable>> +where + E : NormExponent, + Domain : Space + Norm<F, E>, + F : Float, + A::Observable : ClosedAdd + Norm<F, L2> + 'static, + A : ForwardModel<Domain, F, E> + 'static +{ + type Observable = A::Observable; + + fn write_observable(&self, b : &Self::Observable, prefix : String) -> DynError { + self.0.write_observable(b, prefix) + } + + /// Returns a zero observable + fn zero_observable(&self) -> Self::Observable { + self.0.zero_observable() + } +} + +#[replace_float_literals(F::cast_from(literal))] +impl<Domain, F, A, D, Z> AdjointProductPairBoundedBy<Pair<Domain, Z>, D, IdOp<Z>> +for RowOp<A, IdOp<Z>> +where + Domain : Space, + F : Float, + Z : Clone + Space + ClosedAdd, + A : AdjointProductBoundedBy<Domain, D, FloatType=F, Codomain = Z>, + D : Linear<Domain>, + A::Codomain : ClosedAdd, +{ + type FloatType = F; + + fn adjoint_product_pair_bound(&self, d : &D, _ : &IdOp<Z>) -> Option<(F, F)> { + self.0.adjoint_product_bound(d).map(|l_0| { + // [A_*; B_*][A, B] = [A_*A, A_* B; B_* A, B_* B] ≤ diag(2A_*A, 2B_*B) + // ≤ diag(2l_A𝒟_A, 2l_B𝒟_B), where now 𝒟_B=Id and l_B=1. + (2.0 * l_0, 2.0) + }) + } +} + +/// This `impl` is bit of an abuse as the codomain of `Apre` is a [`Pair`] of a measure predual, +/// to which this `impl` applies, and another space. +impl<F, Apre, Z> LipschitzValues +for ColOp<Apre, IdOp<Z>> +where + F : Float, + Z : Clone + Space + ClosedAdd, + Apre : LipschitzValues<FloatType = F>, +{ + type FloatType = F; + /// Return (if one exists) a factor $L$ such that $A_*z$ is $L$-Lipschitz for all + /// $z$ in the unit ball. + fn value_unit_lipschitz_factor(&self) -> Option<Self::FloatType> { + self.0.value_unit_lipschitz_factor() + } + + /// Return (if one exists) a factor $L$ such that $∇A_*z$ is $L$-Lipschitz for all + /// $z$ in the unit ball. + fn value_diff_unit_lipschitz_factor(&self) -> Option<Self::FloatType> { + self.0.value_diff_unit_lipschitz_factor() + } +} + + + +impl<'a, F : Float, Y : Space, XD, const N : usize> TransportLipschitz<L2Squared> for +ZeroOp<'a, RNDM<F, N>, XD, Y, F> { + type FloatType = F; + + fn transport_lipschitz_factor(&self, _ : L2Squared) -> Self::FloatType { + F::ZERO + } +} + + +/// TODO: should assume `D` to be positive semi-definite and self-adjoint. +#[replace_float_literals(F::cast_from(literal))] +impl<'a, F, D, XD, Y, const N : usize> AdjointProductBoundedBy<RNDM<F, N>, D> +for ZeroOp<'a, RNDM<F, N>, XD, Y, F> +where + F : Float, + Y : AXPY<F> + Clone, + D : Linear<RNDM<F, N>>, +{ + type FloatType = F; + /// Return $L$ such that $A_*A ≤ L𝒟$ is bounded by some `other` operator $𝒟$. + fn adjoint_product_bound(&self, _ : &D) -> Option<F> { + Some(0.0) + } +} +
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/forward_model/sensor_grid.rs Tue Dec 31 09:25:45 2024 -0500 @@ -0,0 +1,634 @@ +/*! +Sensor grid forward model +*/ + +use numeric_literals::replace_float_literals; +use nalgebra::base::{ + DMatrix, + DVector +}; +use std::iter::Zip; +use std::ops::RangeFrom; + +pub use alg_tools::linops::*; +use alg_tools::norms::{ + L1, Linfinity, L2, Norm +}; +use alg_tools::bisection_tree::*; +use alg_tools::mapping::{ + RealMapping, + DifferentiableMapping +}; +use alg_tools::lingrid::*; +use alg_tools::iter::{MapX, Mappable}; +use alg_tools::nalgebra_support::ToNalgebraRealField; +use alg_tools::tabledump::write_csv; +use alg_tools::error::DynError; +use alg_tools::maputil::map2; +use alg_tools::instance::Instance; + +use crate::types::*; +use crate::measures::{DiscreteMeasure, Radon}; +use crate::seminorms::{ + ConvolutionOp, + SimpleConvolutionKernel, +}; +use crate::kernels::{ + Convolution, + AutoConvolution, + BoundedBy, +}; +use crate::types::L2Squared; +use crate::transport::TransportLipschitz; +use crate::preadjoint_helper::PreadjointHelper; +use super::{ + ForwardModel, + LipschitzValues, + AdjointProductBoundedBy +}; +use crate::frank_wolfe::FindimQuadraticModel; + +type RNDM<F, const N : usize> = DiscreteMeasure<Loc<F,N>, F>; + +pub type ShiftedSensor<F, S, P, const N : usize> = Shift<Convolution<S, P>, F, N>; + +/// Trait for physical convolution models. Has blanket implementation for all cases. +pub trait Spread<F : Float, const N : usize> +: 'static + Clone + Support<F, N> + RealMapping<F, N> + Bounded<F> {} + +impl<F, T, const N : usize> Spread<F, N> for T +where F : Float, + T : 'static + Clone + Support<F, N> + Bounded<F> + RealMapping<F, N> {} + +/// Trait for compactly supported sensors. Has blanket implementation for all cases. +pub trait Sensor<F : Float, const N : usize> : Spread<F, N> + Norm<F, L1> + Norm<F, Linfinity> {} + +impl<F, T, const N : usize> Sensor<F, N> for T +where F : Float, + T : Spread<F, N> + Norm<F, L1> + Norm<F, Linfinity> {} + + +pub trait SensorGridBT<F, S, P, const N : usize> : +Clone + BTImpl<F, N, Data=usize, Agg=Bounds<F>> +where F : Float, + S : Sensor<F, N>, + P : Spread<F, N> {} + +impl<F, S, P, T, const N : usize> +SensorGridBT<F, S, P, N> +for T +where T : Clone + BTImpl<F, N, Data=usize, Agg=Bounds<F>>, + F : Float, + S : Sensor<F, N>, + P : Spread<F, N> {} + +// We need type alias bounds to access associated types +#[allow(type_alias_bounds)] +pub type SensorGridBTFN<F, S, P, BT : SensorGridBT<F, S, P, N>, const N : usize> += BTFN<F, SensorGridSupportGenerator<F, S, P, N>, BT, N>; + +/// Sensor grid forward model +#[derive(Clone)] +pub struct SensorGrid<F, S, P, BT, const N : usize> +where F : Float, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N>, + BT : SensorGridBT<F, S, P, N>, { + domain : Cube<F, N>, + sensor_count : [usize; N], + sensor : S, + spread : P, + base_sensor : Convolution<S, P>, + bt : BT, +} + +impl<F, S, P, BT, const N : usize> SensorGrid<F, S, P, BT, N> +where F : Float, + BT : SensorGridBT<F, S, P, N>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> + LocalAnalysis<F, BT::Agg, N>, + /*ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N>*/ { + + /// Create a new sensor grid. + /// + /// The parameter `depth` indicates the search depth of the created [`BT`]s + /// for the adjoint values. + pub fn new( + domain : Cube<F, N>, + sensor_count : [usize; N], + sensor : S, + spread : P, + depth : BT::Depth + ) -> Self { + let base_sensor = Convolution(sensor.clone(), spread.clone()); + let bt = BT::new(domain, depth); + let mut sensorgrid = SensorGrid { + domain, + sensor_count, + sensor, + spread, + base_sensor, + bt, + }; + + for (x, id) in sensorgrid.grid().into_iter().zip(0usize..) { + let s = sensorgrid.shifted_sensor(x); + sensorgrid.bt.insert(id, &s); + } + + sensorgrid + } +} + + +impl<F, S, P, BT, const N : usize> SensorGrid<F, S, P, BT, N> +where F : Float, + BT : SensorGridBT<F, S, P, N>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> { + + /// Return the grid of sensor locations. + pub fn grid(&self) -> LinGrid<F, N> { + lingrid_centered(&self.domain, &self.sensor_count) + } + + /// Returns the number of sensors (number of grid points) + pub fn n_sensors(&self) -> usize { + self.sensor_count.iter().product() + } + + /// Constructs a sensor shifted by `x`. + #[inline] + fn shifted_sensor(&self, x : Loc<F, N>) -> ShiftedSensor<F, S, P, N> { + self.base_sensor.clone().shift(x) + } + + #[inline] + fn _zero_observable(&self) -> DVector<F> { + DVector::zeros(self.n_sensors()) + } + + /// Returns the maximum number of overlapping sensors $N_\psi$. + pub fn max_overlapping(&self) -> F { + let w = self.base_sensor.support_hint().width(); + let d = map2(self.domain.width(), &self.sensor_count, |wi, &i| wi/F::cast_from(i)); + w.iter() + .zip(d.iter()) + .map(|(&wi, &di)| (wi/di).ceil()) + .reduce(F::mul) + .unwrap() + } +} + +impl<F, S, P, BT, const N : usize> Mapping<RNDM<F, N>> for SensorGrid<F, S, P, BT, N> +where + F : Float, + BT : SensorGridBT<F, S, P, N>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N>, + //ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N>, +{ + + type Codomain = DVector<F>; + + #[inline] + fn apply<I : Instance<RNDM<F, N>>>(&self, μ : I) -> DVector<F> { + let mut y = self._zero_observable(); + self.apply_add(&mut y, μ); + y + } +} + + +impl<F, S, P, BT, const N : usize> Linear<RNDM<F, N>> for SensorGrid<F, S, P, BT, N> +where + F : Float, + BT : SensorGridBT<F, S, P, N>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N>, + //ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N> +{ } + + +#[replace_float_literals(F::cast_from(literal))] +impl<F, S, P, BT, const N : usize> GEMV<F, RNDM<F, N>, DVector<F>> for SensorGrid<F, S, P, BT, N> +where F : Float, + BT : SensorGridBT<F, S, P, N>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N>, + //ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N> +{ + + fn gemv<I : Instance<RNDM<F, N>>>( + &self, y : &mut DVector<F>, α : F, μ : I, β : F + ) { + let grid = self.grid(); + if β == 0.0 { + y.fill(0.0) + } else if β != 1.0 { + *y *= β; // Need to multiply first, as we have to be able to add to y. + } + if α == 1.0 { + self.apply_add(y, μ) + } else { + for δ in μ.ref_instance() { + for &d in self.bt.iter_at(&δ.x) { + let sensor = self.shifted_sensor(grid.entry_linear_unchecked(d)); + y[d] += sensor.apply(&δ.x) * (α * δ.α); + } + } + } + } + + fn apply_add<I : Instance<RNDM<F, N>>>( + &self, y : &mut DVector<F>, μ : I + ) { + let grid = self.grid(); + for δ in μ.ref_instance() { + for &d in self.bt.iter_at(&δ.x) { + let sensor = self.shifted_sensor(grid.entry_linear_unchecked(d)); + y[d] += sensor.apply(&δ.x) * δ.α; + } + } + } + +} + + +impl<F, S, P, BT, const N : usize> +BoundedLinear<RNDM<F, N>, Radon, L2, F> +for SensorGrid<F, S, P, BT, N> +where F : Float, + BT : SensorGridBT<F, S, P, N, Agg=Bounds<F>>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N>, + ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N> { + + /// An estimate on the operator norm in $𝕃(ℳ(Ω); ℝ^n)$ with $ℳ(Ω)$ equipped + /// with the Radon norm, and $ℝ^n$ with the Euclidean norm. + fn opnorm_bound(&self, _ : Radon, _ : L2) -> F { + // With {x_i}_{i=1}^n the grid centres and φ the kernel, we have + // |Aμ|_2 = sup_{|z|_2 ≤ 1} ⟨z,Αμ⟩ = sup_{|z|_2 ≤ 1} ⟨A^*z|μ⟩ + // ≤ sup_{|z|_2 ≤ 1} |A^*z|_∞ |μ|_ℳ + // = sup_{|z|_2 ≤ 1} |∑ φ(· - x_i)z_i|_∞ |μ|_ℳ + // ≤ sup_{|z|_2 ≤ 1} |φ|_∞ ∑ |z_i| |μ|_ℳ + // ≤ sup_{|z|_2 ≤ 1} |φ|_∞ √n |z|_2 |μ|_ℳ + // = |φ|_∞ √n |μ|_ℳ. + // Hence + let n = F::cast_from(self.n_sensors()); + self.base_sensor.bounds().uniform() * n.sqrt() + } +} + +type SensorGridPreadjoint<'a, A, F, const N : usize> = PreadjointHelper<'a, A, RNDM<F,N>>; + + +impl<F, S, P, BT, const N : usize> +Preadjointable<RNDM<F, N>, DVector<F>> +for SensorGrid<F, S, P, BT, N> +where F : Float, + BT : SensorGridBT<F, S, P, N>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> + LocalAnalysis<F, BT::Agg, N>, + /*ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N>, + Weighted<ShiftedSensor<F, S, P, N>, F> : LocalAnalysis<F, BT::Agg, N>*/ { + type PreadjointCodomain = BTFN<F, SensorGridSupportGenerator<F, S, P, N>, BT, N>; + type Preadjoint<'a> = SensorGridPreadjoint<'a, Self, F, N> where Self : 'a; + + fn preadjoint(&self) -> Self::Preadjoint<'_> { + PreadjointHelper::new(self) + } +} + +#[replace_float_literals(F::cast_from(literal))] +impl<'a, F, S, P, BT, const N : usize> LipschitzValues +for SensorGridPreadjoint<'a, SensorGrid<F, S, P, BT, N>, F, N> +where F : Float, + BT : SensorGridBT<F, S, P, N>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> + Lipschitz<L2, FloatType=F> + DifferentiableMapping<Loc<F,N>> + LocalAnalysis<F, BT::Agg, N>, + for<'b> <Convolution<S, P> as DifferentiableMapping<Loc<F,N>>>::Differential<'b> : Lipschitz<L2, FloatType=F>, + /*ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N>, + Weighted<ShiftedSensor<F, S, P, N>, F> : LocalAnalysis<F, BT::Agg, N>*/ { + + type FloatType = F; + + fn value_unit_lipschitz_factor(&self) -> Option<F> { + // The Lipschitz factor of the sensors has to be scaled by the square root of twice + // the number of overlapping sensors at a single ponit, as Lipschitz estimates involve + // two points. + let fw = self.forward_op; + let n = fw.max_overlapping(); + fw.base_sensor.lipschitz_factor(L2).map(|l| (2.0 * n).sqrt() * l) + } + + fn value_diff_unit_lipschitz_factor(&self) -> Option<F> { + // The Lipschitz factor of the sensors has to be scaled by the square root of twice + // the number of overlapping sensors at a single ponit, as Lipschitz estimates involve + // two points. + let fw = self.forward_op; + let n = fw.max_overlapping(); + fw.base_sensor.diff_ref().lipschitz_factor(L2).map(|l| (2.0 * n).sqrt() * l) + } +} + +#[derive(Clone,Debug)] +pub struct SensorGridSupportGenerator<F, S, P, const N : usize> +where F : Float, + S : Sensor<F, N>, + P : Spread<F, N> { + base_sensor : Convolution<S, P>, + grid : LinGrid<F, N>, + weights : DVector<F> +} + +impl<F, S, P, const N : usize> SensorGridSupportGenerator<F, S, P, N> +where F : Float, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> { + + #[inline] + fn construct_sensor(&self, id : usize, w : F) -> Weighted<ShiftedSensor<F, S, P, N>, F> { + let x = self.grid.entry_linear_unchecked(id); + self.base_sensor.clone().shift(x).weigh(w) + } + + #[inline] + fn construct_sensor_and_id<'a>(&'a self, (id, w) : (usize, &'a F)) + -> (usize, Weighted<ShiftedSensor<F, S, P, N>, F>) { + (id.into(), self.construct_sensor(id, *w)) + } +} + +impl<F, S, P, const N : usize> SupportGenerator<F, N> +for SensorGridSupportGenerator<F, S, P, N> +where F : Float, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> { + type Id = usize; + type SupportType = Weighted<ShiftedSensor<F, S, P, N>, F>; + type AllDataIter<'a> = MapX<'a, Zip<RangeFrom<usize>, + std::slice::Iter<'a, F>>, + Self, + (Self::Id, Self::SupportType)> + where Self : 'a; + + #[inline] + fn support_for(&self, d : Self::Id) -> Self::SupportType { + self.construct_sensor(d, self.weights[d]) + } + + #[inline] + fn support_count(&self) -> usize { + self.weights.len() + } + + #[inline] + fn all_data(&self) -> Self::AllDataIter<'_> { + (0..).zip(self.weights.as_slice().iter()).mapX(self, Self::construct_sensor_and_id) + } +} + +impl<F, S, P, BT, const N : usize> ForwardModel<DiscreteMeasure<Loc<F, N>, F>, F> +for SensorGrid<F, S, P, BT, N> +where F : Float + ToNalgebraRealField<MixedType=F> + nalgebra::RealField, + BT : SensorGridBT<F, S, P, N>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> + LocalAnalysis<F, BT::Agg, N>, + /*ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N>, + Weighted<ShiftedSensor<F, S, P, N>, F> : LocalAnalysis<F, BT::Agg, N>*/ { + type Observable = DVector<F>; + + fn write_observable(&self, b : &Self::Observable, prefix : String) -> DynError { + let it = self.grid().into_iter().zip(b.iter()).map(|(x, &v)| (x, v)); + write_csv(it, prefix + ".txt") + } + + #[inline] + fn zero_observable(&self) -> Self::Observable { + self._zero_observable() + } +} + +impl<F, S, P, BT, const N : usize> FindimQuadraticModel<Loc<F, N>, F> +for SensorGrid<F, S, P, BT, N> +where F : Float + ToNalgebraRealField<MixedType=F> + nalgebra::RealField, + BT : SensorGridBT<F, S, P, N>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> + LocalAnalysis<F, BT::Agg, N>, + /*ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N>, + Weighted<ShiftedSensor<F, S, P, N>, F> : LocalAnalysis<F, BT::Agg, N>*/ { + + fn findim_quadratic_model( + &self, + μ : &DiscreteMeasure<Loc<F, N>, F>, + b : &Self::Observable + ) -> (DMatrix<F::MixedType>, DVector<F::MixedType>) { + assert_eq!(b.len(), self.n_sensors()); + let mut mA = DMatrix::zeros(self.n_sensors(), μ.len()); + let grid = self.grid(); + for (mut mAcol, δ) in mA.column_iter_mut().zip(μ.iter_spikes()) { + for &d in self.bt.iter_at(&δ.x) { + let sensor = self.shifted_sensor(grid.entry_linear_unchecked(d)); + mAcol[d] += sensor.apply(&δ.x); + } + } + let mAt = mA.transpose(); + (&mAt * mA, &mAt * b) + } +} + +/// Implements the calculation a factor $L$ such that $A_*A ≤ L 𝒟$ for $A$ the forward model +/// and $𝒟$ a seminorm of suitable form. +/// +/// **This assumes (but does not check) that the sensors are not overlapping.** +#[replace_float_literals(F::cast_from(literal))] +impl<F, BT, S, P, K, const N : usize> +AdjointProductBoundedBy<RNDM<F, N>, ConvolutionOp<F, K, BT, N>> +for SensorGrid<F, S, P, BT, N> +where F : Float + nalgebra::RealField + ToNalgebraRealField, + BT : SensorGridBT<F, S, P, N>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N>, + K : SimpleConvolutionKernel<F, N>, + AutoConvolution<P> : BoundedBy<F, K> { + + type FloatType = F; + + fn adjoint_product_bound(&self, seminorm : &ConvolutionOp<F, K, BT, N>) -> Option<F> { + // Sensors should not take on negative values to allow + // A_*A to be upper bounded by a simple convolution of `spread`. + if self.sensor.bounds().lower() < 0.0 { + return None + } + + // Calculate the factor $L_1$ for betwee $ℱ[ψ * ψ] ≤ L_1 ℱ[ρ]$ for $ψ$ the base spread + // and $ρ$ the kernel of the seminorm. + let l1 = AutoConvolution(self.spread.clone()).bounding_factor(seminorm.kernel())?; + + // Calculate the factor for transitioning from $A_*A$ to `AutoConvolution<P>`, where A + // consists of several `Convolution<S, P>` for the physical model `P` and the sensor `S`. + let l0 = self.sensor.norm(Linfinity) * self.sensor.norm(L1); + + // The final transition factor is: + Some(l0 * l1) + } +} + +#[replace_float_literals(F::cast_from(literal))] +impl<F, BT, S, P, const N : usize> TransportLipschitz<L2Squared> +for SensorGrid<F, S, P, BT, N> +where F : Float + ToNalgebraRealField, + BT : SensorGridBT<F, S, P, N>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> + Lipschitz<L2, FloatType = F> { + type FloatType = F; + + fn transport_lipschitz_factor(&self, L2Squared : L2Squared) -> Self::FloatType { + // We estimate the factor by N_ψL^2, where L is the 2-norm Lipschitz factor of + // the base sensor (sensor * base_spread), and N_ψ the maximum overlap. + // The factors two comes from Lipschitz estimates having two possible + // points of overlap. + let l = self.base_sensor.lipschitz_factor(L2).unwrap(); + 2.0 * self.max_overlapping() * l.powi(2) + } +} + + +macro_rules! make_sensorgridsupportgenerator_scalarop_rhs { + ($trait:ident, $fn:ident, $trait_assign:ident, $fn_assign:ident) => { + impl<F, S, P, const N : usize> + std::ops::$trait_assign<F> + for SensorGridSupportGenerator<F, S, P, N> + where F : Float, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> { + fn $fn_assign(&mut self, t : F) { + self.weights.$fn_assign(t); + } + } + + impl<F, S, P, const N : usize> + std::ops::$trait<F> + for SensorGridSupportGenerator<F, S, P, N> + where F : Float, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> { + type Output = SensorGridSupportGenerator<F, S, P, N>; + fn $fn(mut self, t : F) -> Self::Output { + std::ops::$trait_assign::$fn_assign(&mut self.weights, t); + self + } + } + + impl<'a, F, S, P, const N : usize> + std::ops::$trait<F> + for &'a SensorGridSupportGenerator<F, S, P, N> + where F : Float, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> { + type Output = SensorGridSupportGenerator<F, S, P, N>; + fn $fn(self, t : F) -> Self::Output { + SensorGridSupportGenerator{ + base_sensor : self.base_sensor.clone(), + grid : self.grid, + weights : (&self.weights).$fn(t) + } + } + } + } +} + +make_sensorgridsupportgenerator_scalarop_rhs!(Mul, mul, MulAssign, mul_assign); +make_sensorgridsupportgenerator_scalarop_rhs!(Div, div, DivAssign, div_assign); + +macro_rules! make_sensorgridsupportgenerator_unaryop { + ($trait:ident, $fn:ident) => { + impl<F, S, P, const N : usize> + std::ops::$trait + for SensorGridSupportGenerator<F, S, P, N> + where F : Float, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> { + type Output = SensorGridSupportGenerator<F, S, P, N>; + fn $fn(mut self) -> Self::Output { + self.weights = self.weights.$fn(); + self + } + } + + impl<'a, F, S, P, const N : usize> + std::ops::$trait + for &'a SensorGridSupportGenerator<F, S, P, N> + where F : Float, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> { + type Output = SensorGridSupportGenerator<F, S, P, N>; + fn $fn(self) -> Self::Output { + SensorGridSupportGenerator{ + base_sensor : self.base_sensor.clone(), + grid : self.grid, + weights : (&self.weights).$fn() + } + } + } + } +} + +make_sensorgridsupportgenerator_unaryop!(Neg, neg); + +impl<'a, F, S, P, BT, const N : usize> Mapping<DVector<F>> +for PreadjointHelper<'a, SensorGrid<F, S, P, BT, N>, RNDM<F,N>> +where F : Float, + BT : SensorGridBT<F, S, P, N>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> + LocalAnalysis<F, Bounds<F>, N>, + //ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N>, + /*Weighted<ShiftedSensor<F, S, P, N>, F> : LocalAnalysis<F, BT::Agg, N>*/ { + + type Codomain = SensorGridBTFN<F, S, P, BT, N>; + + fn apply<I : Instance<DVector<F>>>(&self, x : I) -> Self::Codomain { + let fwd = &self.forward_op; + let generator = SensorGridSupportGenerator{ + base_sensor : fwd.base_sensor.clone(), + grid : fwd.grid(), + weights : x.own() + }; + BTFN::new_refresh(&fwd.bt, generator) + } +} + +impl<'a, F, S, P, BT, const N : usize> Linear<DVector<F>> +for PreadjointHelper<'a, SensorGrid<F, S, P, BT, N>, RNDM<F,N>> +where F : Float, + BT : SensorGridBT<F, S, P, N>, + S : Sensor<F, N>, + P : Spread<F, N>, + Convolution<S, P> : Spread<F, N> + LocalAnalysis<F, Bounds<F>, N>, + /*ShiftedSensor<F, S, P, N> : LocalAnalysis<F, BT::Agg, N>, + Weighted<ShiftedSensor<F, S, P, N>, F> : LocalAnalysis<F, BT::Agg, N>*/ { + +} +
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/forward_pdps.rs Tue Dec 31 09:25:45 2024 -0500 @@ -0,0 +1,268 @@ +/*! +Solver for the point source localisation problem using a +primal-dual proximal splitting with a forward step. +*/ + +use numeric_literals::replace_float_literals; +use serde::{Serialize, Deserialize}; + +use alg_tools::iterate::AlgIteratorFactory; +use alg_tools::euclidean::Euclidean; +use alg_tools::sets::Cube; +use alg_tools::loc::Loc; +use alg_tools::mapping::{Mapping, Instance}; +use alg_tools::norms::Norm; +use alg_tools::direct_product::Pair; +use alg_tools::bisection_tree::{ + BTFN, + PreBTFN, + Bounds, + BTNodeLookup, + BTNode, + BTSearch, + P2Minimise, + SupportGenerator, + LocalAnalysis, + //Bounded, +}; +use alg_tools::mapping::RealMapping; +use alg_tools::nalgebra_support::ToNalgebraRealField; +use alg_tools::linops::{ + BoundedLinear, AXPY, GEMV, Adjointable, IdOp, +}; +use alg_tools::convex::{Conjugable, Prox}; +use alg_tools::norms::{L2, Linfinity, PairNorm}; + +use crate::types::*; +use crate::measures::{DiscreteMeasure, Radon, RNDM}; +use crate::measures::merging::SpikeMerging; +use crate::forward_model::{ + ForwardModel, + AdjointProductPairBoundedBy, +}; +use crate::seminorms::DiscreteMeasureOp; +use crate::plot::{ + SeqPlotter, + Plotting, + PlotLookup +}; +use crate::fb::*; +use crate::regularisation::RegTerm; +use crate::dataterm::calculate_residual; + +/// Settings for [`pointsource_forward_pdps_pair`]. +#[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)] +#[serde(default)] +pub struct ForwardPDPSConfig<F : Float> { + /// Primal step length scaling. + pub τ0 : F, + /// Primal step length scaling. + pub σp0 : F, + /// Dual step length scaling. + pub σd0 : F, + /// Generic parameters + pub insertion : FBGenericConfig<F>, +} + +#[replace_float_literals(F::cast_from(literal))] +impl<F : Float> Default for ForwardPDPSConfig<F> { + fn default() -> Self { + let τ0 = 0.99; + ForwardPDPSConfig { + τ0, + σd0 : 0.1, + σp0 : 0.99, + insertion : Default::default() + } + } +} + +type MeasureZ<F, Z, const N : usize> = Pair<RNDM<F, N>, Z>; + +/// Iteratively solve the pointsource localisation with an additional variable +/// using primal-dual proximal splitting with a forward step. +#[replace_float_literals(F::cast_from(literal))] +pub fn pointsource_forward_pdps_pair< + 'a, F, I, A, GA, 𝒟, BTA, BT𝒟, G𝒟, S, K, Reg, Z, R, Y, /*KOpM, */ KOpZ, H, const N : usize +>( + opA : &'a A, + b : &A::Observable, + reg : Reg, + op𝒟 : &'a 𝒟, + config : &ForwardPDPSConfig<F>, + iterator : I, + mut plotter : SeqPlotter<F, N>, + //opKμ : KOpM, + opKz : &KOpZ, + fnR : &R, + fnH : &H, + mut z : Z, + mut y : Y, +) -> MeasureZ<F, Z, N> +where + F : Float + ToNalgebraRealField, + I : AlgIteratorFactory<IterInfo<F, N>>, + for<'b> &'b A::Observable : std::ops::Neg<Output=A::Observable> + Instance<A::Observable>, + GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, + A : ForwardModel< + MeasureZ<F, Z, N>, + F, + PairNorm<Radon, L2, L2>, + PreadjointCodomain = Pair<BTFN<F, GA, BTA, N>, Z>, + > + + AdjointProductPairBoundedBy<MeasureZ<F, Z, N>, 𝒟, IdOp<Z>, FloatType=F>, + BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, + G𝒟 : SupportGenerator<F, N, SupportType = K, Id = usize> + Clone, + 𝒟 : DiscreteMeasureOp<Loc<F, N>, F, PreCodomain = PreBTFN<F, G𝒟, N>, + Codomain = BTFN<F, G𝒟, BT𝒟, N>>, + BT𝒟 : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, + S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, + K: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, + BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, + Cube<F, N>: P2Minimise<Loc<F, N>, F>, + PlotLookup : Plotting<N>, + RNDM<F, N> : SpikeMerging<F>, + Reg : RegTerm<F, N>, + KOpZ : BoundedLinear<Z, L2, L2, F, Codomain=Y> + + GEMV<F, Z> + + Adjointable<Z, Y, AdjointCodomain = Z>, + for<'b> KOpZ::Adjoint<'b> : GEMV<F, Y>, + Y : AXPY<F> + Euclidean<F, Output=Y> + Clone + ClosedAdd, + for<'b> &'b Y : Instance<Y>, + Z : AXPY<F, Owned=Z> + Euclidean<F, Output=Z> + Clone + Norm<F, L2>, + for<'b> &'b Z : Instance<Z>, + R : Prox<Z, Codomain=F>, + H : Conjugable<Y, F, Codomain=F>, + for<'b> H::Conjugate<'b> : Prox<Y>, +{ + + // Check parameters + assert!(config.τ0 > 0.0 && + config.τ0 < 1.0 && + config.σp0 > 0.0 && + config.σp0 < 1.0 && + config.σd0 > 0.0 && + config.σp0 * config.σd0 <= 1.0, + "Invalid step length parameters"); + + // Initialise iterates + let mut μ = DiscreteMeasure::new(); + let mut residual = calculate_residual(Pair(&μ, &z), opA, b); + + // Set up parameters + let op𝒟norm = op𝒟.opnorm_bound(Radon, Linfinity); + let bigM = 0.0; //opKμ.adjoint_product_bound(&op𝒟).unwrap().sqrt(); + let nKz = opKz.opnorm_bound(L2, L2); + let opIdZ = IdOp::new(); + let (l, l_z) = opA.adjoint_product_pair_bound(&op𝒟, &opIdZ).unwrap(); + // We need to satisfy + // + // τσ_dM(1-σ_p L_z)/(1 - τ L) + [σ_p L_z + σ_pσ_d‖K_z‖^2] < 1 + // ^^^^^^^^^^^^^^^^^^^^^^^^^ + // with 1 > σ_p L_z and 1 > τ L. + // + // To do so, we first solve σ_p and σ_d from standard PDPS step length condition + // ^^^^^ < 1. then we solve τ from the rest. + let σ_d = config.σd0 / nKz; + let σ_p = config.σp0 / (l_z + config.σd0 * nKz); + // Observe that = 1 - ^^^^^^^^^^^^^^^^^^^^^ = 1 - σ_{p,0} + // We get the condition τσ_d M (1-σ_p L_z) < (1-σ_{p,0})*(1-τ L) + // ⟺ τ [ σ_d M (1-σ_p L_z) + (1-σ_{p,0}) L ] < (1-σ_{p,0}) + let φ = 1.0 - config.σp0; + let a = 1.0 - σ_p * l_z; + let τ = config.τ0 * φ / ( σ_d * bigM * a + φ * l ); + // Acceleration is not currently supported + // let γ = dataterm.factor_of_strong_convexity(); + let ω = 1.0; + + // We multiply tolerance by τ for FB since our subproblems depending on tolerances are scaled + // by τ compared to the conditional gradient approach. + let tolerance = config.insertion.tolerance * τ * reg.tolerance_scaling(); + let mut ε = tolerance.initial(); + + let starH = fnH.conjugate(); + + // Statistics + let full_stats = |residual : &A::Observable, μ : &RNDM<F, N>, z : &Z, ε, stats| IterInfo { + value : residual.norm2_squared_div2() + fnR.apply(z) + + reg.apply(μ) + fnH.apply(/* opKμ.apply(μ) + */ opKz.apply(z)), + n_spikes : μ.len(), + ε, + // postprocessing: config.insertion.postprocessing.then(|| μ.clone()), + .. stats + }; + let mut stats = IterInfo::new(); + + // Run the algorithm + for state in iterator.iter_init(|| full_stats(&residual, &μ, &z, ε, stats.clone())) { + // Calculate initial transport + let Pair(τv, τz) = opA.preadjoint().apply(residual * τ); + let z_base = z.clone(); + let μ_base = μ.clone(); + + // Construct μ^{k+1} by solving finite-dimensional subproblems and insert new spikes. + let (d, _within_tolerances) = insert_and_reweigh( + &mut μ, &τv, &μ_base, None, + op𝒟, op𝒟norm, + τ, ε, &config.insertion, + ®, &state, &mut stats, + ); + + // // Merge spikes. + // // This expects the prune below to prune γ. + // // TODO: This may not work correctly in all cases. + // let ins = &config.insertion; + // if ins.merge_now(&state) { + // if let SpikeMergingMethod::None = ins.merging { + // } else { + // stats.merged += μ.merge_spikes(ins.merging, |μ_candidate| { + // let ν = μ_candidate.sub_matching(&γ1)-&μ_base_minus_γ0; + // let mut d = &τv̆ + op𝒟.preapply(ν); + // reg.verify_merge_candidate(&mut d, μ_candidate, τ, ε, ins) + // }); + // } + // } + + // Prune spikes with zero weight. + stats.pruned += prune_with_stats(&mut μ); + + // Do z variable primal update + z.axpy(-σ_p/τ, τz, 1.0); // TODO: simplify nasty factors + opKz.adjoint().gemv(&mut z, -σ_p, &y, 1.0); + z = fnR.prox(σ_p, z); + // Do dual update + // opKμ.gemv(&mut y, σ_d*(1.0 + ω), &μ, 1.0); // y = y + σ_d K[(1+ω)(μ,z)^{k+1}] + opKz.gemv(&mut y, σ_d*(1.0 + ω), &z, 1.0); + // opKμ.gemv(&mut y, -σ_d*ω, μ_base, 1.0);// y = y + σ_d K[(1+ω)(μ,z)^{k+1} - ω (μ,z)^k]-b + opKz.gemv(&mut y, -σ_d*ω, z_base, 1.0);// y = y + σ_d K[(1+ω)(μ,z)^{k+1} - ω (μ,z)^k]-b + y = starH.prox(σ_d, y); + + // Update residual + residual = calculate_residual(Pair(&μ, &z), opA, b); + + // Update step length parameters + // let ω = pdpsconfig.acceleration.accelerate(&mut τ, &mut σ, γ); + + // Give statistics if requested + let iter = state.iteration(); + stats.this_iters += 1; + + state.if_verbose(|| { + plotter.plot_spikes(iter, Some(&d), Some(&τv), &μ); + full_stats(&residual, &μ, &z, ε, std::mem::replace(&mut stats, IterInfo::new())) + }); + + // Update main tolerance for next iteration + ε = tolerance.update(ε, iter); + } + + let fit = |μ̃ : &RNDM<F, N>| { + (opA.apply(Pair(μ̃, &z))-b).norm2_squared_div2() + //+ fnR.apply(z) + reg.apply(μ) + + fnH.apply(/* opKμ.apply(&μ̃) + */ opKz.apply(&z)) + }; + + μ.merge_spikes_fitness(config.insertion.merging, fit, |&v| v); + μ.prune(); + Pair(μ, z) +}
--- a/src/fourier.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/fourier.rs Tue Dec 31 09:25:45 2024 -0500 @@ -3,14 +3,14 @@ */ use alg_tools::types::{Num, Float}; -use alg_tools::mapping::{RealMapping, Mapping}; +use alg_tools::mapping::{RealMapping, Mapping, Space}; use alg_tools::bisection_tree::Weighted; use alg_tools::loc::Loc; /// Trait for Fourier transforms. When F is a non-complex number, the transform /// also has to be non-complex, i.e., the function itself symmetric. pub trait Fourier<F : Num> : Mapping<Self::Domain, Codomain=F> { - type Domain; + type Domain : Space; type Transformed : Mapping<Self::Domain, Codomain=F>; fn fourier(&self) -> Self::Transformed;
--- a/src/frank_wolfe.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/frank_wolfe.rs Tue Dec 31 09:25:45 2024 -0500 @@ -14,18 +14,18 @@ */ use numeric_literals::replace_float_literals; +use nalgebra::{DMatrix, DVector}; use serde::{Serialize, Deserialize}; //use colored::Colorize; use alg_tools::iterate::{ AlgIteratorFactory, - AlgIteratorState, AlgIteratorOptions, ValueIteratorFactory, }; use alg_tools::euclidean::Euclidean; use alg_tools::norms::Norm; -use alg_tools::linops::Apply; +use alg_tools::linops::Mapping; use alg_tools::sets::Cube; use alg_tools::loc::Loc; use alg_tools::bisection_tree::{ @@ -40,9 +40,11 @@ }; use alg_tools::mapping::RealMapping; use alg_tools::nalgebra_support::ToNalgebraRealField; +use alg_tools::norms::L2; use crate::types::*; use crate::measures::{ + RNDM, DiscreteMeasure, DeltaMeasure, Radon, @@ -71,7 +73,7 @@ RegTerm }; -/// Settings for [`pointsource_fw`]. +/// Settings for [`pointsource_fw_reg`]. #[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)] #[serde(default)] pub struct FWConfig<F : Float> { @@ -111,10 +113,20 @@ } } -/// Helper struct for pre-initialising the finite-dimensional subproblems solver -/// [`prepare_optimise_weights`]. -/// -/// The pre-initialisation is done by [`prepare_optimise_weights`]. +pub trait FindimQuadraticModel<Domain, F> : ForwardModel<DiscreteMeasure<Domain, F>, F> +where + F : Float + ToNalgebraRealField, + Domain : Clone + PartialEq, +{ + /// Return A_*A and A_* b + fn findim_quadratic_model( + &self, + μ : &DiscreteMeasure<Domain, F>, + b : &Self::Observable + ) -> (DMatrix<F::MixedType>, DVector<F::MixedType>); +} + +/// Helper struct for pre-initialising the finite-dimensional subproblem solver. pub struct FindimData<F : Float> { /// ‖A‖^2 opAnorm_squared : F, @@ -125,7 +137,7 @@ /// Trait for finite dimensional weight optimisation. pub trait WeightOptim< F : Float + ToNalgebraRealField, - A : ForwardModel<Loc<F, N>, F>, + A : ForwardModel<RNDM<F, N>, F>, I : AlgIteratorFactory<F>, const N : usize > { @@ -154,7 +166,7 @@ /// Returns the number of iterations taken by the method configured in `inner`. fn optimise_weights<'a>( &self, - μ : &mut DiscreteMeasure<Loc<F, N>, F>, + μ : &mut RNDM<F, N>, opA : &'a A, b : &A::Observable, findim_data : &FindimData<F>, @@ -166,12 +178,12 @@ /// Trait for regularisation terms supported by [`pointsource_fw_reg`]. pub trait RegTermFW< F : Float + ToNalgebraRealField, - A : ForwardModel<Loc<F, N>, F>, + A : ForwardModel<RNDM<F, N>, F>, I : AlgIteratorFactory<F>, const N : usize > : RegTerm<F, N> + WeightOptim<F, A, I, N> - + for<'a> Apply<&'a DiscreteMeasure<Loc<F, N>, F>, Output = F> { + + Mapping<RNDM<F, N>, Codomain = F> { /// With $g = A\_\*(Aμ-b)$, returns $(x, g(x))$ for $x$ a new point to be inserted /// into $μ$, as determined by the regulariser. @@ -188,7 +200,7 @@ /// Insert point `ξ` into `μ` for the relaxed algorithm from Bredies–Pikkarainen. fn relaxed_insert<'a>( &self, - μ : &mut DiscreteMeasure<Loc<F, N>, F>, + μ : &mut RNDM<F, N>, g : &A::PreadjointCodomain, opA : &'a A, ξ : Loc<F, N>, @@ -201,18 +213,18 @@ impl<F : Float + ToNalgebraRealField, A, I, const N : usize> WeightOptim<F, A, I, N> for RadonRegTerm<F> where I : AlgIteratorFactory<F>, - A : ForwardModel<Loc<F, N>, F> { + A : FindimQuadraticModel<Loc<F, N>, F> { fn prepare_optimise_weights(&self, opA : &A, b : &A::Observable) -> FindimData<F> { FindimData{ - opAnorm_squared : opA.opnorm_bound().powi(2), + opAnorm_squared : opA.opnorm_bound(Radon, L2).powi(2), m0 : b.norm2_squared() / (2.0 * self.α()), } } fn optimise_weights<'a>( &self, - μ : &mut DiscreteMeasure<Loc<F, N>, F>, + μ : &mut RNDM<F, N>, opA : &'a A, b : &A::Observable, findim_data : &FindimData<F>, @@ -245,12 +257,19 @@ #[replace_float_literals(F::cast_from(literal))] impl<F : Float + ToNalgebraRealField, A, I, S, GA, BTA, const N : usize> RegTermFW<F, A, I, N> for RadonRegTerm<F> -where Cube<F, N> : P2Minimise<Loc<F, N>, F>, - I : AlgIteratorFactory<F>, - S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, - GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, - A : ForwardModel<Loc<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>>, - BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>> { +where + Cube<F, N> : P2Minimise<Loc<F, N>, F>, + I : AlgIteratorFactory<F>, + S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, + GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, + A : FindimQuadraticModel<Loc<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>>, + BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, + // FIXME: the following *should not* be needed, they are already implied + RNDM<F, N> : Mapping<A::PreadjointCodomain, Codomain = F>, + DeltaMeasure<Loc<F, N>, F> : Mapping<A::PreadjointCodomain, Codomain = F>, + //A : Mapping<RNDM<F, N>, Codomain = A::Observable>, + //A : Mapping<DeltaMeasure<Loc<F, N>, F>, Codomain = A::Observable>, +{ fn find_insertion( &self, @@ -269,7 +288,7 @@ fn relaxed_insert<'a>( &self, - μ : &mut DiscreteMeasure<Loc<F, N>, F>, + μ : &mut RNDM<F, N>, g : &A::PreadjointCodomain, opA : &'a A, ξ : Loc<F, N>, @@ -282,7 +301,7 @@ let v = if v_ξ.abs() <= α { 0.0 } else { m0 / α * v_ξ }; let δ = DeltaMeasure { x : ξ, α : v }; let dp = μ.apply(g) - δ.apply(g); - let d = opA.apply(&*μ) - opA.apply(&δ); + let d = opA.apply(&*μ) - opA.apply(δ); let r = d.norm2_squared(); let s = if r == 0.0 { 1.0 @@ -298,18 +317,18 @@ impl<F : Float + ToNalgebraRealField, A, I, const N : usize> WeightOptim<F, A, I, N> for NonnegRadonRegTerm<F> where I : AlgIteratorFactory<F>, - A : ForwardModel<Loc<F, N>, F> { + A : FindimQuadraticModel<Loc<F, N>, F> { fn prepare_optimise_weights(&self, opA : &A, b : &A::Observable) -> FindimData<F> { FindimData{ - opAnorm_squared : opA.opnorm_bound().powi(2), + opAnorm_squared : opA.opnorm_bound(Radon, L2).powi(2), m0 : b.norm2_squared() / (2.0 * self.α()), } } fn optimise_weights<'a>( &self, - μ : &mut DiscreteMeasure<Loc<F, N>, F>, + μ : &mut RNDM<F, N>, opA : &'a A, b : &A::Observable, findim_data : &FindimData<F>, @@ -342,12 +361,17 @@ #[replace_float_literals(F::cast_from(literal))] impl<F : Float + ToNalgebraRealField, A, I, S, GA, BTA, const N : usize> RegTermFW<F, A, I, N> for NonnegRadonRegTerm<F> -where Cube<F, N> : P2Minimise<Loc<F, N>, F>, - I : AlgIteratorFactory<F>, - S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, - GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, - A : ForwardModel<Loc<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>>, - BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>> { +where + Cube<F, N> : P2Minimise<Loc<F, N>, F>, + I : AlgIteratorFactory<F>, + S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, + GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, + A : FindimQuadraticModel<Loc<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>>, + BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, + // FIXME: the following *should not* be needed, they are already implied + RNDM<F, N> : Mapping<A::PreadjointCodomain, Codomain = F>, + DeltaMeasure<Loc<F, N>, F> : Mapping<A::PreadjointCodomain, Codomain = F>, +{ fn find_insertion( &self, @@ -361,7 +385,7 @@ fn relaxed_insert<'a>( &self, - μ : &mut DiscreteMeasure<Loc<F, N>, F>, + μ : &mut RNDM<F, N>, g : &A::PreadjointCodomain, opA : &'a A, ξ : Loc<F, N>, @@ -409,20 +433,18 @@ config : &FWConfig<F>, iterator : I, mut plotter : SeqPlotter<F, N>, -) -> DiscreteMeasure<Loc<F, N>, F> +) -> RNDM<F, N> where F : Float + ToNalgebraRealField, I : AlgIteratorFactory<IterInfo<F, N>>, for<'b> &'b A::Observable : std::ops::Neg<Output=A::Observable>, - //+ std::ops::Mul<F, Output=A::Observable>, <-- FIXME: compiler overflow - A::Observable : std::ops::MulAssign<F>, GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, - A : ForwardModel<Loc<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>>, + A : ForwardModel<RNDM<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>>, BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, Cube<F, N>: P2Minimise<Loc<F, N>, F>, PlotLookup : Plotting<N>, - DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F>, + RNDM<F, N> : SpikeMerging<F>, Reg : RegTermFW<F, A, ValueIteratorFactory<F, AlgIteratorOptions>, N> { // Set up parameters @@ -438,26 +460,24 @@ let mut μ = DiscreteMeasure::new(); let mut residual = -b; - let mut inner_iters = 0; - let mut this_iters = 0; - let mut pruned = 0; - let mut merged = 0; + // Statistics + let full_stats = |residual : &A::Observable, + ν : &RNDM<F, N>, + ε, stats| IterInfo { + value : residual.norm2_squared_div2() + reg.apply(ν), + n_spikes : ν.len(), + ε, + .. stats + }; + let mut stats = IterInfo::new(); // Run the algorithm - iterator.iterate(|state| { - // Update tolerance + for state in iterator.iter_init(|| full_stats(&residual, &μ, ε, stats.clone())) { let inner_tolerance = ε * config.inner.tolerance_mult; let refinement_tolerance = ε * config.refinement.tolerance_mult; - let ε_prev = ε; - ε = tolerance.update(ε, state.iteration()); // Calculate smooth part of surrogate model. - // - // Using `std::mem::replace` here is not ideal, and expects that `empty_observable` - // has no significant overhead. For some reosn Rust doesn't allow us simply moving - // the residual and replacing it below before the end of this closure. - let r = std::mem::replace(&mut residual, opA.empty_observable()); - let mut g = -preadjA.apply(r); + let mut g = preadjA.apply(residual * (-1.0)); // Find absolute value maximising point let (ξ, v_ξ) = reg.find_insertion(&mut g, refinement_tolerance, @@ -467,60 +487,46 @@ FWVariant::FullyCorrective => { // No point in optimising the weight here: the finite-dimensional algorithm is fast. μ += DeltaMeasure { x : ξ, α : 0.0 }; + stats.inserted += 1; config.inner.iterator_options.stop_target(inner_tolerance) }, FWVariant::Relaxed => { // Perform a relaxed initialisation of μ reg.relaxed_insert(&mut μ, &g, opA, ξ, v_ξ, &findim_data); + stats.inserted += 1; // The stop_target is only needed for the type system. AlgIteratorOptions{ max_iter : 1, .. config.inner.iterator_options}.stop_target(0.0) } }; - inner_iters += reg.optimise_weights(&mut μ, opA, b, &findim_data, &config.inner, inner_it); + stats.inner_iters += reg.optimise_weights(&mut μ, opA, b, &findim_data, + &config.inner, inner_it); // Merge spikes and update residual for next step and `if_verbose` below. let (r, count) = μ.merge_spikes_fitness(config.merging, |μ̃| opA.apply(μ̃) - b, A::Observable::norm2_squared); residual = r; - merged += count; - + stats.merged += count; // Prune points with zero mass let n_before_prune = μ.len(); μ.prune(); debug_assert!(μ.len() <= n_before_prune); - pruned += n_before_prune - μ.len(); + stats.pruned += n_before_prune - μ.len(); - this_iters +=1; + stats.this_iters += 1; + let iter = state.iteration(); - // Give function value if needed + // Give statistics if needed state.if_verbose(|| { - plotter.plot_spikes( - format!("iter {} start", state.iteration()), &g, - "".to_string(), None::<&A::PreadjointCodomain>, - None, &μ - ); - let res = IterInfo { - value : residual.norm2_squared_div2() + reg.apply(&μ), - n_spikes : μ.len(), - inner_iters, - this_iters, - merged, - pruned, - ε : ε_prev, - postprocessing : None, - untransported_fraction : None, - transport_error : None, - }; - inner_iters = 0; - this_iters = 0; - merged = 0; - pruned = 0; - res - }) - }); + plotter.plot_spikes(iter, Some(&g), Option::<&S>::None, &μ); + full_stats(&residual, &μ, ε, std::mem::replace(&mut stats, IterInfo::new())) + }); + + // Update tolerance + ε = tolerance.update(ε, iter); + } // Return final iterate μ
--- a/src/kernels.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/kernels.rs Tue Dec 31 09:25:45 2024 -0500 @@ -24,4 +24,7 @@ pub use ball_indicator::*; mod hat_convolution; pub use hat_convolution::*; +mod linear; +pub use linear::*; +
--- a/src/kernels/ball_indicator.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/kernels/ball_indicator.rs Tue Dec 31 09:25:45 2024 -0500 @@ -1,6 +1,6 @@ //! Implementation of the indicator function of a ball with respect to various norms. -use float_extras::f64::{tgamma as gamma}; +use float_extras::f64::tgamma as gamma; use numeric_literals::replace_float_literals; use serde::Serialize; use alg_tools::types::*; @@ -14,10 +14,16 @@ LocalAnalysis, GlobalAnalysis, }; -use alg_tools::mapping::Apply; +use alg_tools::mapping::{ + Mapping, + Differential, + DifferentiableImpl, +}; +use alg_tools::instance::Instance; +use alg_tools::euclidean::StaticEuclidean; use alg_tools::maputil::array_init; use alg_tools::coefficients::factorial; - +use crate::types::*; use super::base::*; /// Representation of the indicator of the ball $𝔹_q = \\{ x ∈ ℝ^N \mid \\|x\\|\_q ≤ r \\}$, @@ -36,14 +42,17 @@ #[replace_float_literals(C::Type::cast_from(literal))] impl<'a, F : Float, C : Constant<Type=F>, Exponent : NormExponent, const N : usize> -Apply<&'a Loc<C::Type, N>> +Mapping<Loc<C::Type, N>> for BallIndicator<C, Exponent, N> -where Loc<F, N> : Norm<F, Exponent> { - type Output = C::Type; +where + Loc<F, N> : Norm<F, Exponent> +{ + type Codomain = C::Type; + #[inline] - fn apply(&self, x : &'a Loc<C::Type, N>) -> Self::Output { + fn apply<I : Instance<Loc<C::Type, N>>>(&self, x : I) -> Self::Codomain { let r = self.r.value(); - let n = x.norm(self.exponent); + let n = x.eval(|x| x.norm(self.exponent)); if n <= r { 1.0 } else { @@ -52,14 +61,79 @@ } } +impl<'a, F : Float, C : Constant<Type=F>, Exponent : NormExponent, const N : usize> +DifferentiableImpl<Loc<C::Type, N>> +for BallIndicator<C, Exponent, N> +where + C : Constant, + Loc<F, N> : Norm<F, Exponent> +{ + type Derivative = Loc<C::Type, N>; + + #[inline] + fn differential_impl<I : Instance<Loc<C::Type, N>>>(&self, _x : I) -> Self::Derivative { + Self::Derivative::origin() + } +} + impl<F : Float, C : Constant<Type=F>, Exponent : NormExponent, const N : usize> -Apply<Loc<C::Type, N>> +Lipschitz<L2> for BallIndicator<C, Exponent, N> -where Loc<F, N> : Norm<F, Exponent> { - type Output = C::Type; - #[inline] - fn apply(&self, x : Loc<C::Type, N>) -> Self::Output { - self.apply(&x) +where C : Constant, + Loc<F, N> : Norm<F, Exponent> { + type FloatType = C::Type; + + fn lipschitz_factor(&self, _l2 : L2) -> Option<C::Type> { + None + } +} + +impl<'b, F : Float, C : Constant<Type=F>, Exponent : NormExponent, const N : usize> +Lipschitz<L2> +for Differential<'b, Loc<F, N>, BallIndicator<C, Exponent, N>> +where C : Constant, + Loc<F, N> : Norm<F, Exponent> { + type FloatType = C::Type; + + fn lipschitz_factor(&self, _l2 : L2) -> Option<C::Type> { + None + } +} + +impl<'a, 'b, F : Float, C : Constant<Type=F>, Exponent : NormExponent, const N : usize> +Lipschitz<L2> +for Differential<'b, Loc<F, N>, &'a BallIndicator<C, Exponent, N>> +where C : Constant, + Loc<F, N> : Norm<F, Exponent> { + type FloatType = C::Type; + + fn lipschitz_factor(&self, _l2 : L2) -> Option<C::Type> { + None + } +} + + +impl<'b, F : Float, C : Constant<Type=F>, Exponent : NormExponent, const N : usize> +NormBounded<L2> +for Differential<'b, Loc<F, N>, BallIndicator<C, Exponent, N>> +where C : Constant, + Loc<F, N> : Norm<F, Exponent> { + type FloatType = C::Type; + + fn norm_bound(&self, _l2 : L2) -> C::Type { + F::INFINITY + } +} + +impl<'a, 'b, F : Float, C : Constant<Type=F>, Exponent : NormExponent, const N : usize> +NormBounded<L2> +for Differential<'b, Loc<F, N>, &'a BallIndicator<C, Exponent, N>> +where C : Constant, + Loc<F, N> : Norm<F, Exponent> { + type FloatType = C::Type; + + fn norm_bound(&self, _l2 : L2) -> C::Type { + F::INFINITY } } @@ -188,32 +262,21 @@ #[replace_float_literals(F::cast_from(literal))] -impl<'a, F : Float, R, const N : usize> Apply<&'a Loc<F, N>> +impl<'a, F : Float, R, const N : usize> Mapping<Loc<F, N>> for AutoConvolution<CubeIndicator<R, N>> where R : Constant<Type=F> { - type Output = F; + type Codomain = F; #[inline] - fn apply(&self, y : &'a Loc<F, N>) -> F { + fn apply<I : Instance<Loc<F, N>>>(&self, y : I) -> F { let two_r = 2.0 * self.0.r.value(); // This is just a product of one-dimensional versions - y.iter().map(|&x| { + y.cow().iter().map(|&x| { 0.0.max(two_r - x.abs()) }).product() } } -impl<F : Float, R, const N : usize> Apply<Loc<F, N>> -for AutoConvolution<CubeIndicator<R, N>> -where R : Constant<Type=F> { - type Output = F; - - #[inline] - fn apply(&self, y : Loc<F, N>) -> F { - self.apply(&y) - } -} - #[replace_float_literals(F::cast_from(literal))] impl<F : Float, R, const N : usize> Support<F, N> for AutoConvolution<CubeIndicator<R, N>>
--- a/src/kernels/base.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/kernels/base.rs Tue Dec 31 09:25:45 2024 -0500 @@ -14,16 +14,22 @@ GlobalAnalysis, Bounded, }; -use alg_tools::mapping::{Apply, Differentiable}; +use alg_tools::mapping::{ + Mapping, + DifferentiableImpl, + DifferentiableMapping, + Differential, +}; +use alg_tools::instance::{Instance, Space}; use alg_tools::maputil::{array_init, map2, map1_indexed}; use alg_tools::sets::SetOrd; use crate::fourier::Fourier; -use crate::types::Lipschitz; +use crate::types::*; /// Representation of the product of two kernels. /// -/// The kernels typically implement [`Support`] and [`Mapping`][alg_tools::mapping::Mapping]. +/// The kernels typically implement [`Support`] and [`Mapping`]. /// /// The implementation [`Support`] only uses the [`Support::support_hint`] of the first parameter! #[derive(Copy,Clone,Serialize,Debug)] @@ -34,59 +40,94 @@ pub B ); -impl<A, B, F : Float, const N : usize> Apply<Loc<F, N>> +impl<A, B, F : Float, const N : usize> Mapping<Loc<F, N>> for SupportProductFirst<A, B> -where A : for<'a> Apply<&'a Loc<F, N>, Output=F>, - B : for<'a> Apply<&'a Loc<F, N>, Output=F> { - type Output = F; +where + A : Mapping<Loc<F, N>, Codomain = F>, + B : Mapping<Loc<F, N>, Codomain = F>, +{ + type Codomain = F; + #[inline] - fn apply(&self, x : Loc<F, N>) -> Self::Output { - self.0.apply(&x) * self.1.apply(&x) + fn apply<I : Instance<Loc<F, N>>>(&self, x : I) -> Self::Codomain { + self.0.apply(x.ref_instance()) * self.1.apply(x) } } -impl<'a, A, B, F : Float, const N : usize> Apply<&'a Loc<F, N>> +impl<A, B, F : Float, const N : usize> DifferentiableImpl<Loc<F, N>> for SupportProductFirst<A, B> -where A : Apply<&'a Loc<F, N>, Output=F>, - B : Apply<&'a Loc<F, N>, Output=F> { - type Output = F; +where + A : DifferentiableMapping< + Loc<F, N>, + DerivativeDomain=Loc<F, N>, + Codomain = F + >, + B : DifferentiableMapping< + Loc<F, N>, + DerivativeDomain=Loc<F, N>, + Codomain = F, + > +{ + type Derivative = Loc<F, N>; + #[inline] - fn apply(&self, x : &'a Loc<F, N>) -> Self::Output { - self.0.apply(x) * self.1.apply(x) + fn differential_impl<I : Instance<Loc<F, N>>>(&self, x : I) -> Self::Derivative { + let xr = x.ref_instance(); + self.0.differential(xr) * self.1.apply(xr) + self.1.differential(xr) * self.0.apply(x) } } -impl<A, B, F : Float, const N : usize> Differentiable<Loc<F, N>> +impl<A, B, M : Copy, F : Float> Lipschitz<M> for SupportProductFirst<A, B> -where A : for<'a> Apply<&'a Loc<F, N>, Output=F> - + for<'a> Differentiable<&'a Loc<F, N>, Output=Loc<F, N>>, - B : for<'a> Apply<&'a Loc<F, N>, Output=F> - + for<'a> Differentiable<&'a Loc<F, N>, Output=Loc<F, N>> { - type Output = Loc<F, N>; +where A : Lipschitz<M, FloatType = F> + Bounded<F>, + B : Lipschitz<M, FloatType = F> + Bounded<F> { + type FloatType = F; #[inline] - fn differential(&self, x : Loc<F, N>) -> Self::Output { - self.0.differential(&x) * self.1.apply(&x) + self.1.differential(&x) * self.0.apply(&x) + fn lipschitz_factor(&self, m : M) -> Option<F> { + // f(x)g(x) - f(y)g(y) = f(x)[g(x)-g(y)] - [f(y)-f(x)]g(y) + let &SupportProductFirst(ref f, ref g) = self; + f.lipschitz_factor(m).map(|l| l * g.bounds().uniform()) + .zip(g.lipschitz_factor(m).map(|l| l * f.bounds().uniform())) + .map(|(a, b)| a + b) } } -impl<'a, A, B, F : Float, const N : usize> Differentiable<&'a Loc<F, N>> -for SupportProductFirst<A, B> -where A : Apply<&'a Loc<F, N>, Output=F> - + Differentiable<&'a Loc<F, N>, Output=Loc<F, N>>, - B : Apply<&'a Loc<F, N>, Output=F> - + Differentiable<&'a Loc<F, N>, Output=Loc<F, N>> { - type Output = Loc<F, N>; +impl<'a, A, B, M : Copy, Domain, F : Float> Lipschitz<M> +for Differential<'a, Domain, SupportProductFirst<A, B>> +where + Domain : Space, + A : Clone + DifferentiableMapping<Domain> + Lipschitz<M, FloatType = F> + Bounded<F>, + B : Clone + DifferentiableMapping<Domain> + Lipschitz<M, FloatType = F> + Bounded<F>, + SupportProductFirst<A, B> : DifferentiableMapping<Domain>, + for<'b> A::Differential<'b> : Lipschitz<M, FloatType = F> + NormBounded<L2, FloatType=F>, + for<'b> B::Differential<'b> : Lipschitz<M, FloatType = F> + NormBounded<L2, FloatType=F> +{ + type FloatType = F; #[inline] - fn differential(&self, x : &'a Loc<F, N>) -> Self::Output { - self.0.differential(&x) * self.1.apply(&x) + self.1.differential(&x) * self.0.apply(&x) + fn lipschitz_factor(&self, m : M) -> Option<F> { + // ∇[gf] = f∇g + g∇f + // ⟹ ∇[gf](x) - ∇[gf](y) = f(x)∇g(x) + g(x)∇f(x) - f(y)∇g(y) + g(y)∇f(y) + // = f(x)[∇g(x)-∇g(y)] + g(x)∇f(x) - [f(y)-f(x)]∇g(y) + g(y)∇f(y) + // = f(x)[∇g(x)-∇g(y)] + g(x)[∇f(x)-∇f(y)] + // - [f(y)-f(x)]∇g(y) + [g(y)-g(x)]∇f(y) + let &SupportProductFirst(ref f, ref g) = self.base_fn(); + let (df, dg) = (f.diff_ref(), g.diff_ref()); + [ + df.lipschitz_factor(m).map(|l| l * g.bounds().uniform()), + dg.lipschitz_factor(m).map(|l| l * f.bounds().uniform()), + f.lipschitz_factor(m).map(|l| l * dg.norm_bound(L2)), + g.lipschitz_factor(m).map(|l| l * df.norm_bound(L2)) + ].into_iter().sum() } } impl<'a, A, B, F : Float, const N : usize> Support<F, N> for SupportProductFirst<A, B> -where A : Support<F, N>, - B : Support<F, N> { +where + A : Support<F, N>, + B : Support<F, N> +{ #[inline] fn support_hint(&self) -> Cube<F, N> { self.0.support_hint() @@ -125,7 +166,7 @@ /// Representation of the sum of two kernels /// -/// The kernels typically implement [`Support`] and [`Mapping`][alg_tools::mapping::Mapping]. +/// The kernels typically implement [`Support`] and [`Mapping`]. /// /// The implementation [`Support`] only uses the [`Support::support_hint`] of the first parameter! #[derive(Copy,Clone,Serialize,Debug)] @@ -136,55 +177,48 @@ pub B ); -impl<'a, A, B, F : Float, const N : usize> Apply<&'a Loc<F, N>> +impl<'a, A, B, F : Float, const N : usize> Mapping<Loc<F, N>> for SupportSum<A, B> -where A : Apply<&'a Loc<F, N>, Output=F>, - B : Apply<&'a Loc<F, N>, Output=F> { - type Output = F; +where + A : Mapping<Loc<F, N>, Codomain = F>, + B : Mapping<Loc<F, N>, Codomain = F>, +{ + type Codomain = F; + #[inline] - fn apply(&self, x : &'a Loc<F, N>) -> Self::Output { - self.0.apply(x) + self.1.apply(x) - } -} - -impl<A, B, F : Float, const N : usize> Apply<Loc<F, N>> -for SupportSum<A, B> -where A : for<'a> Apply<&'a Loc<F, N>, Output=F>, - B : for<'a> Apply<&'a Loc<F, N>, Output=F> { - type Output = F; - #[inline] - fn apply(&self, x : Loc<F, N>) -> Self::Output { - self.0.apply(&x) + self.1.apply(&x) + fn apply<I : Instance<Loc<F, N>>>(&self, x : I) -> Self::Codomain { + self.0.apply(x.ref_instance()) + self.1.apply(x) } } -impl<'a, A, B, F : Float, const N : usize> Differentiable<&'a Loc<F, N>> +impl<'a, A, B, F : Float, const N : usize> DifferentiableImpl<Loc<F, N>> for SupportSum<A, B> -where A : Differentiable<&'a Loc<F, N>, Output=Loc<F, N>>, - B : Differentiable<&'a Loc<F, N>, Output=Loc<F, N>> { - type Output = Loc<F, N>; +where + A : DifferentiableMapping< + Loc<F, N>, + DerivativeDomain = Loc<F, N> + >, + B : DifferentiableMapping< + Loc<F, N>, + DerivativeDomain = Loc<F, N>, + > +{ + + type Derivative = Loc<F, N>; + #[inline] - fn differential(&self, x : &'a Loc<F, N>) -> Self::Output { - self.0.differential(x) + self.1.differential(x) + fn differential_impl<I : Instance<Loc<F, N>>>(&self, x : I) -> Self::Derivative { + self.0.differential(x.ref_instance()) + self.1.differential(x) } } -impl<A, B, F : Float, const N : usize> Differentiable<Loc<F, N>> -for SupportSum<A, B> -where A : for<'a> Differentiable<&'a Loc<F, N>, Output=Loc<F, N>>, - B : for<'a> Differentiable<&'a Loc<F, N>, Output=Loc<F, N>> { - type Output = Loc<F, N>; - #[inline] - fn differential(&self, x : Loc<F, N>) -> Self::Output { - self.0.differential(&x) + self.1.differential(&x) - } -} impl<'a, A, B, F : Float, const N : usize> Support<F, N> for SupportSum<A, B> where A : Support<F, N>, B : Support<F, N>, Cube<F, N> : SetOrd { + #[inline] fn support_hint(&self) -> Cube<F, N> { self.0.support_hint().common(&self.1.support_hint()) @@ -237,10 +271,29 @@ } } +impl<'b, F : Float, M : Copy, A, B, Domain> Lipschitz<M> +for Differential<'b, Domain, SupportSum<A, B>> +where + Domain : Space, + A : Clone + DifferentiableMapping<Domain, Codomain=F>, + B : Clone + DifferentiableMapping<Domain, Codomain=F>, + SupportSum<A, B> : DifferentiableMapping<Domain, Codomain=F>, + for<'a> A :: Differential<'a> : Lipschitz<M, FloatType = F>, + for<'a> B :: Differential<'a> : Lipschitz<M, FloatType = F> +{ + type FloatType = F; + + fn lipschitz_factor(&self, m : M) -> Option<F> { + let base = self.base_fn(); + base.0.diff_ref().lipschitz_factor(m) + .zip(base.1.diff_ref().lipschitz_factor(m)) + .map(|(a, b)| a + b) + } +} /// Representation of the convolution of two kernels. /// -/// The kernels typically implement [`Support`]s and [`Mapping`][alg_tools::mapping::Mapping]. +/// The kernels typically implement [`Support`]s and [`Mapping`]. // /// Trait implementations have to be on a case-by-case basis. #[derive(Copy,Clone,Serialize,Debug,Eq,PartialEq)] @@ -252,18 +305,45 @@ ); impl<F : Float, M, A, B> Lipschitz<M> for Convolution<A, B> -where A : Bounded<F> , +where A : Norm<F, L1> , B : Lipschitz<M, FloatType = F> { type FloatType = F; fn lipschitz_factor(&self, m : M) -> Option<F> { - self.1.lipschitz_factor(m).map(|l| l * self.0.bounds().uniform()) + // For [f * g](x) = ∫ f(x-y)g(y) dy we have + // [f * g](x) - [f * g](z) = ∫ [f(x-y)-f(z-y)]g(y) dy. + // Hence |[f * g](x) - [f * g](z)| ≤ ∫ |f(x-y)-f(z-y)|g(y)| dy. + // ≤ L|x-z| ∫ |g(y)| dy, + // where L is the Lipschitz factor of f. + self.1.lipschitz_factor(m).map(|l| l * self.0.norm(L1)) + } +} + +impl<'b, F : Float, M, A, B, Domain> Lipschitz<M> +for Differential<'b, Domain, Convolution<A, B>> +where + Domain : Space, + A : Clone + Norm<F, L1> , + Convolution<A, B> : DifferentiableMapping<Domain, Codomain=F>, + B : Clone + DifferentiableMapping<Domain, Codomain=F>, + for<'a> B :: Differential<'a> : Lipschitz<M, FloatType = F> +{ + type FloatType = F; + + fn lipschitz_factor(&self, m : M) -> Option<F> { + // For [f * g](x) = ∫ f(x-y)g(y) dy we have + // ∇[f * g](x) - ∇[f * g](z) = ∫ [∇f(x-y)-∇f(z-y)]g(y) dy. + // Hence |∇[f * g](x) - ∇[f * g](z)| ≤ ∫ |∇f(x-y)-∇f(z-y)|g(y)| dy. + // ≤ L|x-z| ∫ |g(y)| dy, + // where L is the Lipschitz factor of ∇f. + let base = self.base_fn(); + base.1.diff_ref().lipschitz_factor(m).map(|l| l * base.0.norm(L1)) } } /// Representation of the autoconvolution of a kernel. /// -/// The kernel typically implements [`Support`] and [`Mapping`][alg_tools::mapping::Mapping]. +/// The kernel typically implements [`Support`] and [`Mapping`]. /// /// Trait implementations have to be on a case-by-case basis. #[derive(Copy,Clone,Serialize,Debug,Eq,PartialEq)] @@ -273,11 +353,27 @@ ); impl<F : Float, M, C> Lipschitz<M> for AutoConvolution<C> -where C : Lipschitz<M, FloatType = F> + Bounded<F> { +where C : Lipschitz<M, FloatType = F> + Norm<F, L1> { type FloatType = F; fn lipschitz_factor(&self, m : M) -> Option<F> { - self.0.lipschitz_factor(m).map(|l| l * self.0.bounds().uniform()) + self.0.lipschitz_factor(m).map(|l| l * self.0.norm(L1)) + } +} + +impl<'b, F : Float, M, C, Domain> Lipschitz<M> +for Differential<'b, Domain, AutoConvolution<C>> +where + Domain : Space, + C : Clone + Norm<F, L1> + DifferentiableMapping<Domain, Codomain=F>, + AutoConvolution<C> : DifferentiableMapping<Domain, Codomain=F>, + for<'a> C :: Differential<'a> : Lipschitz<M, FloatType = F> +{ + type FloatType = F; + + fn lipschitz_factor(&self, m : M) -> Option<F> { + let base = self.base_fn(); + base.0.diff_ref().lipschitz_factor(m).map(|l| l * base.0.norm(L1)) } } @@ -285,42 +381,47 @@ /// Representation a multi-dimensional product of a one-dimensional kernel. /// /// For $G: ℝ → ℝ$, this is the function $F(x\_1, …, x\_n) := \prod_{i=1}^n G(x\_i)$. -/// The kernel $G$ typically implements [`Support`] and [`Mapping`][alg_tools::mapping::Mapping] +/// The kernel $G$ typically implements [`Support`] and [`Mapping`] /// on [`Loc<F, 1>`]. Then the product implements them on [`Loc<F, N>`]. #[derive(Copy,Clone,Serialize,Debug,Eq,PartialEq)] +#[allow(dead_code)] struct UniformProduct<G, const N : usize>( /// The one-dimensional kernel G ); -impl<'a, G, F : Float, const N : usize> Apply<&'a Loc<F, N>> +impl<'a, G, F : Float, const N : usize> Mapping<Loc<F, N>> for UniformProduct<G, N> -where G : Apply<Loc<F, 1>, Output=F> { - type Output = F; +where + G : Mapping<Loc<F, 1>, Codomain = F> +{ + type Codomain = F; + #[inline] - fn apply(&self, x : &'a Loc<F, N>) -> F { - x.iter().map(|&y| self.0.apply(Loc([y]))).product() + fn apply<I : Instance<Loc<F, N>>>(&self, x : I) -> F { + x.cow().iter().map(|&y| self.0.apply(Loc([y]))).product() } } -impl<G, F : Float, const N : usize> Apply<Loc<F, N>> + + +impl<'a, G, F : Float, const N : usize> DifferentiableImpl<Loc<F, N>> for UniformProduct<G, N> -where G : Apply<Loc<F, 1>, Output=F> { - type Output = F; +where + G : DifferentiableMapping< + Loc<F, 1>, + DerivativeDomain = F, + Codomain = F, + > +{ + type Derivative = Loc<F, N>; + #[inline] - fn apply(&self, x : Loc<F, N>) -> F { - x.into_iter().map(|y| self.0.apply(Loc([y]))).product() - } -} - -impl<'a, G, F : Float, const N : usize> Differentiable<&'a Loc<F, N>> -for UniformProduct<G, N> -where G : Apply<Loc<F, 1>, Output=F> + Differentiable<Loc<F, 1>, Output=F> { - type Output = Loc<F, N>; - #[inline] - fn differential(&self, x : &'a Loc<F, N>) -> Loc<F, N> { - let vs = x.map(|y| self.0.apply(Loc([y]))); - product_differential(x, &vs, |y| self.0.differential(Loc([y]))) + fn differential_impl<I : Instance<Loc<F, N>>>(&self, x0 : I) -> Loc<F, N> { + x0.eval(|x| { + let vs = x.map(|y| self.0.apply(Loc([y]))); + product_differential(x, &vs, |y| self.0.differential(Loc([y]))) + }) } } @@ -342,13 +443,39 @@ }).into() } -impl<G, F : Float, const N : usize> Differentiable<Loc<F, N>> -for UniformProduct<G, N> -where G : Apply<Loc<F, 1>, Output=F> + Differentiable<Loc<F, 1>, Output=F> { - type Output = Loc<F, N>; - #[inline] - fn differential(&self, x : Loc<F, N>) -> Loc<F, N> { - self.differential(&x) +/// Helper function to calulate the Lipschitz factor of $∇f$ for $f(x)=∏_{i=1}^N g(x_i)$. +/// +/// The parameter `bound` is a bound on $|g|_∞$, `lip` is a Lipschitz factor for $g$, +/// `dbound` is a bound on $|∇g|_∞$, and `dlip` a Lipschitz factor for $∇g$. +#[inline] +pub(crate) fn product_differential_lipschitz_factor<F : Float, const N : usize>( + bound : F, + lip : F, + dbound : F, + dlip : F +) -> F { + // For arbitrary ψ(x) = ∏_{i=1}^n ψ_i(x_i), we have + // ψ(x) - ψ(y) = ∑_i [ψ_i(x_i)-ψ_i(y_i)] ∏_{j ≠ i} ψ_j(x_j) + // by a simple recursive argument. In particular, if ψ_i=g for all i, j, we have + // |ψ(x) - ψ(y)| ≤ ∑_i L_g M_g^{n-1}|x-y|, where L_g is the Lipschitz factor of g, and + // M_g a bound on it. + // + // We also have in the general case ∇ψ(x) = ∑_i ∇ψ_i(x_i) ∏_{j ≠ i} ψ_j(x_j), whence + // using the previous formula for each i with f_i=∇ψ_i and f_j=ψ_j for j ≠ i, we get + // ∇ψ(x) - ∇ψ(y) = ∑_i[ ∇ψ_i(x_i)∏_{j ≠ i} ψ_j(x_j) - ∇ψ_i(y_i)∏_{j ≠ i} ψ_j(y_j)] + // = ∑_i[ [∇ψ_i(x_i) - ∇ψ_j(x_j)] ∏_{j ≠ i}ψ_j(x_j) + // + [∑_{k ≠ i} [ψ_k(x_k) - ∇ψ_k(x_k)] ∏_{j ≠ i, k}ψ_j(x_j)]∇ψ_i(x_i)]. + // With $ψ_i=g for all i, j, it follows that + // |∇ψ(x) - ∇ψ(y)| ≤ ∑_i L_{∇g} M_g^{n-1} + ∑_{k ≠ i} L_g M_g^{n-2} M_{∇g} + // = n [L_{∇g} M_g^{n-1} + (n-1) L_g M_g^{n-2} M_{∇g}]. + // = n M_g^{n-2}[L_{∇g} M_g + (n-1) L_g M_{∇g}]. + if N >= 2 { + F::cast_from(N) * bound.powi((N-2) as i32) + * (dlip * bound + F::cast_from(N-1) * lip * dbound) + } else if N==1 { + dlip + } else { + panic!("Invalid dimension") } }
--- a/src/kernels/gaussian.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/kernels/gaussian.rs Tue Dec 31 09:25:45 2024 -0500 @@ -17,10 +17,15 @@ Weighted, Bounded, }; -use alg_tools::mapping::{Apply, Differentiable}; +use alg_tools::mapping::{ + Mapping, + Instance, + Differential, + DifferentiableImpl, +}; use alg_tools::maputil::array_init; -use crate::types::Lipschitz; +use crate::types::*; use crate::fourier::Fourier; use super::base::*; use super::ball_indicator::CubeIndicator; @@ -59,63 +64,108 @@ #[replace_float_literals(S::Type::cast_from(literal))] -impl<'a, S, const N : usize> Apply<&'a Loc<S::Type, N>> for Gaussian<S, N> -where S : Constant { - type Output = S::Type; +impl<'a, S, const N : usize> Mapping<Loc<S::Type, N>> for Gaussian<S, N> +where + S : Constant +{ + type Codomain = S::Type; + // This is not normalised to neither to have value 1 at zero or integral 1 // (unless the cut-off ε=0). #[inline] - fn apply(&self, x : &'a Loc<S::Type, N>) -> Self::Output { - let d_squared = x.norm2_squared(); + fn apply<I : Instance<Loc<S::Type, N>>>(&self, x : I) -> Self::Codomain { + let d_squared = x.eval(|x| x.norm2_squared()); let σ2 = self.variance.value(); let scale = self.scale(); (-d_squared / (2.0 * σ2)).exp() / scale } } -impl<S, const N : usize> Apply<Loc<S::Type, N>> for Gaussian<S, N> +#[replace_float_literals(S::Type::cast_from(literal))] +impl<'a, S, const N : usize> DifferentiableImpl<Loc<S::Type, N>> for Gaussian<S, N> where S : Constant { - type Output = S::Type; + type Derivative = Loc<S::Type, N>; + #[inline] - fn apply(&self, x : Loc<S::Type, N>) -> Self::Output { - self.apply(&x) + fn differential_impl<I : Instance<Loc<S::Type, N>>>(&self, x0 : I) -> Self::Derivative { + let x = x0.cow(); + let f = -self.apply(&*x) / self.variance.value(); + *x * f } } -#[replace_float_literals(S::Type::cast_from(literal))] -impl<'a, S, const N : usize> Differentiable<&'a Loc<S::Type, N>> for Gaussian<S, N> -where S : Constant { - type Output = Loc<S::Type, N>; - #[inline] - fn differential(&self, x : &'a Loc<S::Type, N>) -> Self::Output { - x * (self.apply(x) / self.variance.value()) - } -} -impl<S, const N : usize> Differentiable<Loc<S::Type, N>> for Gaussian<S, N> -where S : Constant { - type Output = Loc<S::Type, N>; - // This is not normalised to neither to have value 1 at zero or integral 1 - // (unless the cut-off ε=0). - #[inline] - fn differential(&self, x : Loc<S::Type, N>) -> Self::Output { - x * (self.apply(&x) / self.variance.value()) - } -} +// To calculate the the Lipschitz factors, we consider +// f(t) = e^{-t²/2} +// f'(t) = -t f(t) which has max at t=1 by f''(t)=0 +// f''(t) = (t²-1)f(t) which has max at t=√3 by f'''(t)=0 +// f'''(t) = -(t³-3t) +// So f has the Lipschitz factor L=f'(1), and f' has the Lipschitz factor L'=f''(√3). +// +// Now g(x) = Cf(‖x‖/σ) for a scaling factor C is the Gaussian. +// Thus ‖g(x)-g(y)‖ = C‖f(‖x‖/σ)-f(‖y‖/σ)‖ ≤ (C/σ)L‖x-y‖, +// so g has the Lipschitz factor (C/σ)f'(1) = (C/σ)exp(-0.5). +// +// Also ∇g(x)= Cx/(σ‖x‖)f'(‖x‖/σ) (*) +// = -(C/σ²)xf(‖x‖/σ) +// = -C/σ (x/σ) f(‖x/σ‖) +// ∇²g(x) = -(C/σ)[Id/σ f(‖x‖/σ) + x ⊗ x/(σ²‖x‖) f'(‖x‖/σ)] +// = (C/σ²)[-Id + x ⊗ x/σ²]f(‖x‖/σ). +// Thus ‖∇²g(x)‖ = (C/σ²)‖-Id + x ⊗ x/σ²‖f(‖x‖/σ), where +// ‖-Id + x ⊗ x/σ²‖ = ‖[-Id + x ⊗ x/σ²](x/‖x‖)‖ = |-1 + ‖x²/σ^2‖|. +// This means that ‖∇²g(x)‖ = (C/σ²)|f''(‖x‖/σ)|, which is maximised with ‖x‖/σ=√3. +// Hence the Lipschitz factor of ∇g is (C/σ²)f''(√3) = (C/σ²)2e^{-3/2}. #[replace_float_literals(S::Type::cast_from(literal))] impl<S, const N : usize> Lipschitz<L2> for Gaussian<S, N> where S : Constant { type FloatType = S::Type; fn lipschitz_factor(&self, L2 : L2) -> Option<Self::FloatType> { - // f(x)=f_1(‖x‖_2/σ) * √(2π) / √(2πσ)^N, where f_1 is one-dimensional Gaussian with - // variance 1. The Lipschitz factor of f_1 is e^{-1/2}/√(2π), see, e.g., - // https://math.stackexchange.com/questions/3630967/is-the-gaussian-density-lipschitz-continuous - // Thus the Lipschitz factor we want is e^{-1/2} / (√(2πσ)^N * σ). Some((-0.5).exp() / (self.scale() * self.variance.value().sqrt())) } } + +#[replace_float_literals(S::Type::cast_from(literal))] +impl<'a, S : Constant, const N : usize> Lipschitz<L2> +for Differential<'a, Loc<S::Type, N>, Gaussian<S, N>> { + type FloatType = S::Type; + + fn lipschitz_factor(&self, _l2 : L2) -> Option<S::Type> { + let g = self.base_fn(); + let σ2 = g.variance.value(); + let scale = g.scale(); + Some(2.0*(-3.0/2.0).exp()/(σ2*scale)) + } +} + +// From above, norm bounds on the differnential can be calculated as achieved +// for f' at t=1, i.e., the bound is |f'(1)|. +// For g then |C/σ f'(1)|. +// It follows that the norm bounds on the differential are just the Lipschitz +// factors of the undifferentiated function, given how the latter is calculed above. + +#[replace_float_literals(S::Type::cast_from(literal))] +impl<'b, S : Constant, const N : usize> NormBounded<L2> +for Differential<'b, Loc<S::Type, N>, Gaussian<S, N>> { + type FloatType = S::Type; + + fn norm_bound(&self, _l2 : L2) -> S::Type { + self.base_fn().lipschitz_factor(L2).unwrap() + } +} + +#[replace_float_literals(S::Type::cast_from(literal))] +impl<'b, 'a, S : Constant, const N : usize> NormBounded<L2> +for Differential<'b, Loc<S::Type, N>, &'a Gaussian<S, N>> { + type FloatType = S::Type; + + fn norm_bound(&self, _l2 : L2) -> S::Type { + self.base_fn().lipschitz_factor(L2).unwrap() + } +} + + #[replace_float_literals(S::Type::cast_from(literal))] impl<'a, S, const N : usize> Gaussian<S, N> where S : Constant { @@ -204,16 +254,16 @@ /// This implements $g := χ\_{[-b, b]^n} \* (f χ\_{[-a, a]^n})$ where $a,b>0$ and $f$ is /// a gaussian kernel on $ℝ^n$. For an expression for $g$, see Lemma 3.9 in the manuscript. #[replace_float_literals(F::cast_from(literal))] -impl<'a, F : Float, R, C, S, const N : usize> Apply<&'a Loc<F, N>> +impl<'a, F : Float, R, C, S, const N : usize> Mapping<Loc<F, N>> for Convolution<CubeIndicator<R, N>, BasicCutGaussian<C, S, N>> where R : Constant<Type=F>, C : Constant<Type=F>, S : Constant<Type=F> { - type Output = F; + type Codomain = F; #[inline] - fn apply(&self, y : &'a Loc<F, N>) -> F { + fn apply<I : Instance<Loc<F, N>>>(&self, y : I) -> F { let Convolution(ref ind, SupportProductFirst(ref cut, ref gaussian)) = self; @@ -224,7 +274,7 @@ let c = 0.5; // 1/(σ√(2π) * σ√(π/2) = 1/2 // This is just a product of one-dimensional versions - y.product_map(|x| { + y.cow().product_map(|x| { let c1 = -(a.min(b + x)); //(-a).max(-x-b); let c2 = a.min(b - x); if c1 >= c2 { @@ -239,43 +289,31 @@ } } -impl<F : Float, R, C, S, const N : usize> Apply<Loc<F, N>> +/// This implements the differential of $g := χ\_{[-b, b]^n} \* (f χ\_{[-a, a]^n})$ where $a,b>0$ +/// and $f$ is a gaussian kernel on $ℝ^n$. For an expression for the value of $g$, from which the +/// derivative readily arises (at points of differentiability), see Lemma 3.9 in the manuscript. +#[replace_float_literals(F::cast_from(literal))] +impl<'a, F : Float, R, C, S, const N : usize> DifferentiableImpl<Loc<F, N>> for Convolution<CubeIndicator<R, N>, BasicCutGaussian<C, S, N>> where R : Constant<Type=F>, C : Constant<Type=F>, S : Constant<Type=F> { - type Output = F; - - #[inline] - fn apply(&self, y : Loc<F, N>) -> F { - self.apply(&y) - } -} + type Derivative = Loc<F, N>; -/// This implements the differential of $g := χ\_{[-b, b]^n} \* (f χ\_{[-a, a]^n})$ where $a,b>0$ -/// and $f$ is a gaussian kernel on $ℝ^n$. For an expression for the value of $g$, from which the -/// derivative readily arises (at points of differentiability), see Lemma 3.9 in the manuscript. -#[replace_float_literals(F::cast_from(literal))] -impl<'a, F : Float, R, C, S, const N : usize> Differentiable<&'a Loc<F, N>> -for Convolution<CubeIndicator<R, N>, BasicCutGaussian<C, S, N>> -where R : Constant<Type=F>, - C : Constant<Type=F>, - S : Constant<Type=F> { - - type Output = Loc<F, N>; - + /// Although implemented, this function is not differentiable. #[inline] - fn differential(&self, y : &'a Loc<F, N>) -> Loc<F, N> { + fn differential_impl<I : Instance<Loc<F, N>>>(&self, y0 : I) -> Loc<F, N> { let Convolution(ref ind, SupportProductFirst(ref cut, ref gaussian)) = self; + let y = y0.cow(); let a = cut.r.value(); let b = ind.r.value(); let σ = gaussian.variance.value().sqrt(); let t = F::SQRT_2 * σ; let c = 0.5; // 1/(σ√(2π) * σ√(π/2) = 1/2 - let c_div_t = c / t; + let c_mul_erf_scale_div_t = c * F::FRAC_2_SQRT_PI / t; // Calculate the values for all component functions of the // product. This is just the loop from apply above. @@ -292,35 +330,31 @@ } }); // This computes the gradient for each coordinate - product_differential(y, &unscaled_vs, |x| { + product_differential(&*y, &unscaled_vs, |x| { let c1 = -(a.min(b + x)); //(-a).max(-x-b); let c2 = a.min(b - x); if c1 >= c2 { 0.0 } else { - // erf'(z) = (2/√π)*exp(-z^2), and we get extra factor -1/(√2*σ) = -1/t - // from the chain rule (the minus comes from inside c_1 or c_2). - let de1 = (-(c1/t).powi(2)).exp(); - let de2 = (-(c2/t).powi(2)).exp(); - c_div_t * (de1 - de2) + // erf'(z) = (2/√π)*exp(-z^2), and we get extra factor 1/(√2*σ) = -1/t + // from the chain rule (the minus comes from inside c_1 or c_2, and changes the + // order of de2 and de1 in the final calculation). + let de1 = if b + x < a { + (-((b+x)/t).powi(2)).exp() + } else { + 0.0 + }; + let de2 = if b - x < a { + (-((b-x)/t).powi(2)).exp() + } else { + 0.0 + }; + c_mul_erf_scale_div_t * (de1 - de2) } }) } } -impl<F : Float, R, C, S, const N : usize> Differentiable<Loc<F, N>> -for Convolution<CubeIndicator<R, N>, BasicCutGaussian<C, S, N>> -where R : Constant<Type=F>, - C : Constant<Type=F>, - S : Constant<Type=F> { - - type Output = Loc<F, N>; - - #[inline] - fn differential(&self, y : Loc<F, N>) -> Loc<F, N> { - self.differential(&y) - } -} #[replace_float_literals(F::cast_from(literal))] impl<'a, F : Float, R, C, S, const N : usize> Lipschitz<L1> @@ -378,6 +412,7 @@ } } +/* impl<'a, F : Float, R, C, S, const N : usize> Lipschitz<L2> for Convolution<CubeIndicator<R, N>, BasicCutGaussian<C, S, N>> where R : Constant<Type=F>, @@ -389,6 +424,7 @@ self.lipschitz_factor(L1).map(|l1| l1 * <S::Type>::cast_from(N).sqrt()) } } +*/ impl<F : Float, R, C, S, const N : usize> Convolution<CubeIndicator<R, N>, BasicCutGaussian<C, S, N>>
--- a/src/kernels/hat.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/kernels/hat.rs Tue Dec 31 09:25:45 2024 -0500 @@ -14,8 +14,9 @@ GlobalAnalysis, Bounded, }; -use alg_tools::mapping::Apply; -use alg_tools::maputil::{array_init}; +use alg_tools::mapping::{Mapping, Instance}; +use alg_tools::maputil::array_init; +use crate::types::Lipschitz; /// Representation of the hat function $f(x)=1-\\|x\\|\_1/ε$ of `width` $ε$ on $ℝ^N$. #[derive(Copy,Clone,Serialize,Debug,Eq,PartialEq)] @@ -25,26 +26,17 @@ } #[replace_float_literals(C::Type::cast_from(literal))] -impl<'a, C : Constant, const N : usize> Apply<&'a Loc<C::Type, N>> for Hat<C, N> { - type Output = C::Type; +impl<'a, C : Constant, const N : usize> Mapping<Loc<C::Type, N>> for Hat<C, N> { + type Codomain = C::Type; + #[inline] - fn apply(&self, x : &'a Loc<C::Type, N>) -> Self::Output { + fn apply<I : Instance<Loc<C::Type, N>>>(&self, x : I) -> Self::Codomain { let ε = self.width.value(); - 0.0.max(1.0-x.norm(L1)/ε) + 0.0.max(1.0-x.cow().norm(L1)/ε) } } #[replace_float_literals(C::Type::cast_from(literal))] -impl<C : Constant, const N : usize> Apply<Loc<C::Type, N>> for Hat<C, N> { - type Output = C::Type; - #[inline] - fn apply(&self, x : Loc<C::Type, N>) -> Self::Output { - self.apply(&x) - } -} - - -#[replace_float_literals(C::Type::cast_from(literal))] impl<'a, C : Constant, const N : usize> Support<C::Type, N> for Hat<C, N> { #[inline] fn support_hint(&self) -> Cube<C::Type,N> { @@ -94,6 +86,26 @@ } } +#[replace_float_literals(C::Type::cast_from(literal))] +impl<'a, C : Constant, const N : usize> Lipschitz<L1> for Hat<C, N> { + type FloatType = C::Type; + + fn lipschitz_factor(&self, _l1 : L1) -> Option<C::Type> { + Some(1.0/self.width.value()) + } +} + +#[replace_float_literals(C::Type::cast_from(literal))] +impl<'a, C : Constant, const N : usize> Lipschitz<L2> for Hat<C, N> { + type FloatType = C::Type; + + fn lipschitz_factor(&self, _l2 : L2) -> Option<C::Type> { + self.lipschitz_factor(L1).map(|l1| + <L2 as Dominated<C::Type, L1, Loc<C::Type,N>>>::from_norm(&L2, l1, L1) + ) + } +} + impl<'a, C : Constant, const N : usize> LocalAnalysis<C::Type, Bounds<C::Type>, N> for Hat<C, N> {
--- a/src/kernels/hat_convolution.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/kernels/hat_convolution.rs Tue Dec 31 09:25:45 2024 -0500 @@ -14,7 +14,12 @@ GlobalAnalysis, Bounded, }; -use alg_tools::mapping::{Apply, Differentiable}; +use alg_tools::mapping::{ + Mapping, + Instance, + DifferentiableImpl, + Differential, +}; use alg_tools::maputil::array_init; use crate::types::Lipschitz; @@ -39,6 +44,31 @@ /// -\frac{2}{3} (y-1)^3 & \frac{1}{2}\leq y<1. \\\\ /// \end{cases} /// $$ +// Hence +// $$ +// (h\*h)'(y) = +// \begin{cases} +// 2 (y+1)^2 & -1<y\leq -\frac{1}{2}, \\\\ +// -6 y^2-4 y & -\frac{1}{2}<y\leq 0, \\\\ +// 6 y^2-4 y & 0<y<\frac{1}{2}, \\\\ +// -2 (y-1)^2 & \frac{1}{2}\leq y<1. \\\\ +// \end{cases} +// $$ +// as well as +// $$ +// (h\*h)''(y) = +// \begin{cases} +// 4 (y+1) & -1<y\leq -\frac{1}{2}, \\\\ +// -12 y-4 & -\frac{1}{2}<y\leq 0, \\\\ +// 12 y-4 & 0<y<\frac{1}{2}, \\\\ +// -4 (y-1) & \frac{1}{2}\leq y<1. \\\\ +// \end{cases} +// $$ +// This is maximised at y=±1/2 with value 2, and minimised at y=0 with value -4. +// Now observe that +// $$ +// [∇f(x\_1, …, x\_n)]_j = \frac{4}{σ} (h\*h)'(x\_j/σ) \prod\_{j ≠ i} \frac{4}{σ} (h\*h)(x\_i/σ) +// $$ #[derive(Copy,Clone,Debug,Serialize,Eq)] pub struct HatConv<S : Constant, const N : usize> { /// The parameter $σ$ of the kernel. @@ -61,27 +91,19 @@ } } -impl<'a, S, const N : usize> Apply<&'a Loc<S::Type, N>> for HatConv<S, N> +impl<'a, S, const N : usize> Mapping<Loc<S::Type, N>> for HatConv<S, N> where S : Constant { - type Output = S::Type; + type Codomain = S::Type; + #[inline] - fn apply(&self, y : &'a Loc<S::Type, N>) -> Self::Output { + fn apply<I : Instance<Loc<S::Type, N>>>(&self, y : I) -> Self::Codomain { let σ = self.radius(); - y.product_map(|x| { + y.cow().product_map(|x| { self.value_1d_σ1(x / σ) / σ }) } } -impl<'a, S, const N : usize> Apply<Loc<S::Type, N>> for HatConv<S, N> -where S : Constant { - type Output = S::Type; - #[inline] - fn apply(&self, y : Loc<S::Type, N>) -> Self::Output { - self.apply(&y) - } -} - #[replace_float_literals(S::Type::cast_from(literal))] impl<S, const N : usize> Lipschitz<L1> for HatConv<S, N> where S : Constant { @@ -95,7 +117,7 @@ // = ∑_{j=1}^N [ψ_j(x_j)-ψ_j(y_j)]∏_{i > j} ψ_i(x_i) ∏_{i < j} ψ_i(y_i) // Thus // |∏_{i=1}^N ψ_i(x_i) - ∏_{i=1}^N ψ_i(y_i)| - // ≤ ∑_{j=1}^N |ψ_j(x_j)-ψ_j(y_j)| ∏_{j ≠ i} \max_i |ψ_i| + // ≤ ∑_{j=1}^N |ψ_j(x_j)-ψ_j(y_j)| ∏_{j ≠ i} \max_j |ψ_j| let σ = self.radius(); let l1d = self.lipschitz_1d_σ1() / (σ*σ); let m1d = self.value_1d_σ1(0.0) / σ; @@ -113,31 +135,45 @@ } -impl<'a, S, const N : usize> Differentiable<&'a Loc<S::Type, N>> for HatConv<S, N> +impl<'a, S, const N : usize> DifferentiableImpl<Loc<S::Type, N>> for HatConv<S, N> where S : Constant { - type Output = Loc<S::Type, N>; + type Derivative = Loc<S::Type, N>; + #[inline] - fn differential(&self, y : &'a Loc<S::Type, N>) -> Self::Output { + fn differential_impl<I : Instance<Loc<S::Type, N>>>(&self, y0 : I) -> Self::Derivative { + let y = y0.cow(); let σ = self.radius(); let σ2 = σ * σ; let vs = y.map(|x| { self.value_1d_σ1(x / σ) / σ }); - product_differential(y, &vs, |x| { + product_differential(&*y, &vs, |x| { self.diff_1d_σ1(x / σ) / σ2 }) } } -impl<'a, S, const N : usize> Differentiable<Loc<S::Type, N>> for HatConv<S, N> -where S : Constant { - type Output = Loc<S::Type, N>; + +#[replace_float_literals(S::Type::cast_from(literal))] +impl<'a, F : Float, S, const N : usize> Lipschitz<L2> +for Differential<'a, Loc<F, N>, HatConv<S, N>> +where S : Constant<Type=F> { + type FloatType = F; + #[inline] - fn differential(&self, y : Loc<S::Type, N>) -> Self::Output { - self.differential(&y) + fn lipschitz_factor(&self, _l2 : L2) -> Option<F> { + let h = self.base_fn(); + let σ = h.radius(); + Some(product_differential_lipschitz_factor::<F, N>( + h.value_1d_σ1(0.0) / σ, + h.lipschitz_1d_σ1() / (σ*σ), + h.maxabsdiff_1d_σ1() / (σ*σ), + h.lipschitz_diff_1d_σ1() / (σ*σ), + )) } } + #[replace_float_literals(S::Type::cast_from(literal))] impl<'a, F : Float, S, const N : usize> HatConv<S, N> where S : Constant<Type=F> { @@ -173,6 +209,34 @@ // Maximal absolute differential achieved at ±0.5 by diff_1d_σ1 analysis 2.0 } + + /// Computes the maximum absolute differential of the kernel for $n=1$ with $σ=1$. + #[inline] + fn maxabsdiff_1d_σ1(&self) -> F { + // Maximal absolute differential achieved at ±0.5 by diff_1d_σ1 analysis + 2.0 + } + + /// Computes the second differential of the kernel for $n=1$ with $σ=1$. + #[inline] + #[allow(dead_code)] + fn diff2_1d_σ1(&self, x : F) -> F { + let y = x.abs(); + if y >= 1.0 { + 0.0 + } else if y > 0.5 { + - 16.0 * (y - 1.0) + } else /* 0 ≤ y ≤ 0.5 */ { + 48.0 * y - 16.0 + } + } + + /// Computes the differential of the kernel for $n=1$ with $σ=1$. + #[inline] + fn lipschitz_diff_1d_σ1(&self) -> F { + // Maximal absolute second differential achieved at 0 by diff2_1d_σ1 analysis + 16.0 + } } impl<'a, S, const N : usize> Support<S::Type, N> for HatConv<S, N> @@ -235,21 +299,21 @@ } #[replace_float_literals(F::cast_from(literal))] -impl<'a, F : Float, R, C, const N : usize> Apply<&'a Loc<F, N>> +impl<'a, F : Float, R, C, const N : usize> Mapping<Loc<F, N>> for Convolution<CubeIndicator<R, N>, HatConv<C, N>> where R : Constant<Type=F>, C : Constant<Type=F> { - type Output = F; + type Codomain = F; #[inline] - fn apply(&self, y : &'a Loc<F, N>) -> F { + fn apply<I : Instance<Loc<F, N>>>(&self, y : I) -> F { let Convolution(ref ind, ref hatconv) = self; let β = ind.r.value(); let σ = hatconv.radius(); // This is just a product of one-dimensional versions - y.product_map(|x| { + y.cow().product_map(|x| { // With $u_σ(x) = u_1(x/σ)/σ$ the normalised hat convolution // we have // $$ @@ -264,29 +328,17 @@ } } -impl<'a, F : Float, R, C, const N : usize> Apply<Loc<F, N>> +#[replace_float_literals(F::cast_from(literal))] +impl<'a, F : Float, R, C, const N : usize> DifferentiableImpl<Loc<F, N>> for Convolution<CubeIndicator<R, N>, HatConv<C, N>> where R : Constant<Type=F>, C : Constant<Type=F> { - type Output = F; + type Derivative = Loc<F, N>; #[inline] - fn apply(&self, y : Loc<F, N>) -> F { - self.apply(&y) - } -} - -#[replace_float_literals(F::cast_from(literal))] -impl<'a, F : Float, R, C, const N : usize> Differentiable<&'a Loc<F, N>> -for Convolution<CubeIndicator<R, N>, HatConv<C, N>> -where R : Constant<Type=F>, - C : Constant<Type=F> { - - type Output = Loc<F, N>; - - #[inline] - fn differential(&self, y : &'a Loc<F, N>) -> Loc<F, N> { + fn differential_impl<I : Instance<Loc<F, N>>>(&self, y0 : I) -> Loc<F, N> { + let y = y0.cow(); let Convolution(ref ind, ref hatconv) = self; let β = ind.r.value(); let σ = hatconv.radius(); @@ -295,24 +347,12 @@ let vs = y.map(|x| { self.value_1d_σ1(x / σ, β / σ) }); - product_differential(y, &vs, |x| { + product_differential(&*y, &vs, |x| { self.diff_1d_σ1(x / σ, β / σ) / σ2 }) } } -impl<'a, F : Float, R, C, const N : usize> Differentiable<Loc<F, N>> -for Convolution<CubeIndicator<R, N>, HatConv<C, N>> -where R : Constant<Type=F>, - C : Constant<Type=F> { - - type Output = Loc<F, N>; - - #[inline] - fn differential(&self, y : Loc<F, N>) -> Loc<F, N> { - self.differential(&y) - } -} /// Integrate $f$, whose support is $[c, d]$, on $[a, b]$. /// If $b > d$, add $g()$ to the result. @@ -415,6 +455,22 @@ } } +/* +impl<'a, F : Float, R, C, const N : usize> Lipschitz<L2> +for Differential<Loc<F, N>, Convolution<CubeIndicator<R, N>, HatConv<C, N>>> +where R : Constant<Type=F>, + C : Constant<Type=F> { + + type FloatType = F; + + #[inline] + fn lipschitz_factor(&self, _l2 : L2) -> Option<F> { + dbg!("unimplemented"); + None + } +} +*/ + impl<F : Float, R, C, const N : usize> Convolution<CubeIndicator<R, N>, HatConv<C, N>> where R : Constant<Type=F>, @@ -556,7 +612,7 @@ #[cfg(test)] mod tests { use alg_tools::lingrid::linspace; - use alg_tools::mapping::Apply; + use alg_tools::mapping::Mapping; use alg_tools::norms::Linfinity; use alg_tools::loc::Loc; use crate::kernels::{BallIndicator, CubeIndicator, Convolution};
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/kernels/linear.rs Tue Dec 31 09:25:45 2024 -0500 @@ -0,0 +1,94 @@ +//! Implementation of the linear function + +use numeric_literals::replace_float_literals; +use serde::Serialize; +use alg_tools::types::*; +use alg_tools::norms::*; +use alg_tools::loc::Loc; +use alg_tools::sets::Cube; +use alg_tools::bisection_tree::{ + Support, + Bounds, + LocalAnalysis, + GlobalAnalysis, + Bounded, +}; +use alg_tools::mapping::{Mapping, Instance}; +use alg_tools::maputil::array_init; +use alg_tools::euclidean::Euclidean; + +/// Representation of the hat function $f(x)=1-\\|x\\|\_1/ε$ of `width` $ε$ on $ℝ^N$. +#[derive(Copy,Clone,Serialize,Debug,Eq,PartialEq)] +pub struct Linear<F : Float, const N : usize> { + /// The parameter $ε>0$. + pub v : Loc<F, N>, +} + +#[replace_float_literals(F::cast_from(literal))] +impl<F : Float, const N : usize> Mapping<Loc<F, N>> for Linear<F, N> { + type Codomain = F; + + #[inline] + fn apply<I : Instance<Loc<F, N>>>(&self, x : I) -> Self::Codomain { + x.eval(|x| self.v.dot(x)) + } +} + + +#[replace_float_literals(F::cast_from(literal))] +impl<'a, F : Float, const N : usize> Support<F, N> for Linear<F, N> { + #[inline] + fn support_hint(&self) -> Cube<F,N> { + array_init(|| [F::NEG_INFINITY, F::INFINITY]).into() + } + + #[inline] + fn in_support(&self, _x : &Loc<F,N>) -> bool { + true + } + + /*fn fully_in_support(&self, _cube : &Cube<F,N>) -> bool { + todo!("Not implemented, but not used at the moment") + }*/ + + #[inline] + fn bisection_hint(&self, _cube : &Cube<F,N>) -> [Option<F>; N] { + [None; N] + } +} + + +#[replace_float_literals(F::cast_from(literal))] +impl<'a, F : Float, const N : usize> +GlobalAnalysis<F, Bounds<F>> +for Linear<F, N> { + #[inline] + fn global_analysis(&self) -> Bounds<F> { + Bounds(F::NEG_INFINITY, F::INFINITY) + } +} + +impl<'a, F : Float, const N : usize> +LocalAnalysis<F, Bounds<F>, N> +for Linear<F, N> { + #[inline] + fn local_analysis(&self, cube : &Cube<F, N>) -> Bounds<F> { + let (lower, upper) = cube.iter_corners() + .map(|x| self.apply(x)) + .fold((F::INFINITY, F::NEG_INFINITY), |(lower, upper), v| { + (lower.min(v), upper.max(v)) + }); + Bounds(lower, upper) + } +} + +#[replace_float_literals(F::cast_from(literal))] +impl<'a, F : Float, const N : usize> +Norm<F, Linfinity> +for Linear<F, N> { + #[inline] + fn norm(&self, _ : Linfinity) -> F { + self.bounds().upper() + } +} +
--- a/src/kernels/mollifier.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/kernels/mollifier.rs Tue Dec 31 09:25:45 2024 -0500 @@ -2,7 +2,7 @@ //! Implementation of the standard mollifier use rgsl::hypergeometric::hyperg_U; -use float_extras::f64::{tgamma as gamma}; +use float_extras::f64::tgamma as gamma; use numeric_literals::replace_float_literals; use serde::Serialize; use alg_tools::types::*; @@ -17,7 +17,7 @@ LocalAnalysis, GlobalAnalysis }; -use alg_tools::mapping::Apply; +use alg_tools::mapping::{Mapping, Instance}; use alg_tools::maputil::array_init; /// Reresentation of the (unnormalised) standard mollifier. @@ -36,13 +36,14 @@ } #[replace_float_literals(C::Type::cast_from(literal))] -impl<'a, C : Constant, const N : usize> Apply<&'a Loc<C::Type, N>> for Mollifier<C, N> { - type Output = C::Type; +impl<C : Constant, const N : usize> Mapping<Loc<C::Type, N>> for Mollifier<C, N> { + type Codomain = C::Type; + #[inline] - fn apply(&self, x : &'a Loc<C::Type, N>) -> Self::Output { + fn apply<I : Instance<Loc<C::Type, N>>>(&self, x : I) -> Self::Codomain { let ε = self.width.value(); let ε2 = ε*ε; - let n2 = x.norm2_squared(); + let n2 = x.eval(|x| x.norm2_squared()); if n2 < ε2 { (n2 / (n2 - ε2)).exp() } else { @@ -51,13 +52,6 @@ } } -impl<C : Constant, const N : usize> Apply<Loc<C::Type, N>> for Mollifier<C, N> { - type Output = C::Type; - #[inline] - fn apply(&self, x : Loc<C::Type, N>) -> Self::Output { - self.apply(&x) - } -} impl<'a, C : Constant, const N : usize> Support<C::Type, N> for Mollifier<C, N> { #[inline]
--- a/src/main.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/main.rs Tue Dec 31 09:25:45 2024 -0500 @@ -31,6 +31,7 @@ pub mod seminorms; pub mod transport; pub mod forward_model; +pub mod preadjoint_helper; pub mod plot; pub mod subproblem; pub mod tolerance; @@ -39,6 +40,8 @@ pub mod fb; pub mod radon_fb; pub mod sliding_fb; +pub mod sliding_pdps; +pub mod forward_pdps; pub mod frank_wolfe; pub mod pdps; pub mod run; @@ -166,6 +169,13 @@ tau0 : Option<F>, #[arg(long, requires = "algorithm")] + /// Second primal step length parameter override for SlidingPDPS. + /// + /// Only use if running just a single algorithm, as different algorithms have different + /// regularisation parameters. + sigmap0 : Option<F>, + + #[arg(long, requires = "algorithm")] /// Dual step length parameter override for --algorithm. /// /// Only use if running just a single algorithm, as different algorithms have different @@ -173,7 +183,7 @@ sigma0 : Option<F>, #[arg(long)] - /// Normalised transport step length for sliding_fb. + /// Normalised transport step length for sliding methods. theta0 : Option<F>, #[arg(long)] @@ -184,15 +194,23 @@ /// Transport toleranced wrt. ∇v transport_tolerance_dv : Option<F>, + #[arg(long)] + /// Transport adaptation factor. Must be in (0, 1). + transport_adaptation : Option<F>, + + #[arg(long)] + /// Minimal step length parameter for sliding methods. + tau0_min : Option<F>, + #[arg(value_enum, long)] /// PDPS acceleration, when available. acceleration : Option<pdps::Acceleration>, - #[arg(long)] - /// Perform postprocess weight optimisation for saved iterations - /// - /// Only affects FB, FISTA, and PDPS. - postprocessing : Option<bool>, + // #[arg(long)] + // /// Perform postprocess weight optimisation for saved iterations + // /// + // /// Only affects FB, FISTA, and PDPS. + // postprocessing : Option<bool>, #[arg(value_name = "n", long)] /// Merging frequency, if merging enabled (every n iterations) @@ -246,9 +264,14 @@ for experiment_shorthand in cli.experiments.iter().unique() { let experiment = experiment_shorthand.get_experiment(&cli.experiment_overrides).unwrap(); let mut algs : Vec<Named<AlgorithmConfig<float>>> - = cli.algorithm.iter() - .map(|alg| experiment.algorithm_defaults(*alg, &cli.algoritm_overrides)) - .collect(); + = cli.algorithm + .iter() + .map(|alg| alg.to_named( + experiment.algorithm_defaults(*alg) + .unwrap_or_else(|| alg.default_config()) + .cli_override(&cli.algoritm_overrides) + )) + .collect(); for filename in cli.saved_algorithm.iter() { let f = std::fs::File::open(filename).unwrap(); let alg = serde_json::from_reader(f).unwrap();
--- a/src/measures.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/measures.rs Tue Dec 31 09:25:45 2024 -0500 @@ -7,3 +7,4 @@ mod discrete; pub use discrete::*; pub mod merging; +
--- a/src/measures/base.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/measures/base.rs Tue Dec 31 09:25:45 2024 -0500 @@ -16,3 +16,6 @@ type Domain; } +/// Decomposition of measures +pub struct MeasureDecomp; +
--- a/src/measures/delta.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/measures/delta.rs Tue Dec 31 09:25:45 2024 -0500 @@ -7,8 +7,9 @@ use crate::types::*; use std::ops::{Div, Mul, DivAssign, MulAssign, Neg}; use serde::ser::{Serialize, Serializer, SerializeStruct}; -use alg_tools::norms::{Norm, Dist}; -use alg_tools::linops::{Apply, Linear}; +use alg_tools::norms::Norm; +use alg_tools::linops::{Mapping, Linear}; +use alg_tools::instance::{Instance, Space}; /// Representation of a delta measure. /// @@ -50,43 +51,50 @@ } -impl<Domain : PartialEq, F : Float> Measure<F> for DeltaMeasure<Domain, F> { +impl<Domain, F : Float> Measure<F> for DeltaMeasure<Domain, F> { type Domain = Domain; } -impl<Domain : PartialEq, F : Float> Norm<F, Radon> for DeltaMeasure<Domain, F> { +impl<Domain, F : Float> Norm<F, Radon> for DeltaMeasure<Domain, F> { #[inline] fn norm(&self, _ : Radon) -> F { self.α.abs() } } -impl<Domain : PartialEq, F : Float> Dist<F, Radon> for DeltaMeasure<Domain, F> { +// impl<Domain : PartialEq, F : Float> Dist<F, Radon> for DeltaMeasure<Domain, F> { +// #[inline] +// fn dist(&self, other : &Self, _ : Radon) -> F { +// if self.x == other. x { +// (self.α - other.α).abs() +// } else { +// self.α.abs() + other.α.abs() +// } +// } +// } + +impl<Domain, G, F : Num> Mapping<G> for DeltaMeasure<Domain, F> +where + Domain : Space, + G::Codomain : Mul<F, Output=G::Codomain>, + G : Mapping<Domain> + Clone + Space, + for<'b> &'b Domain : Instance<Domain>, +{ + type Codomain = G::Codomain; + #[inline] - fn dist(&self, other : &Self, _ : Radon) -> F { - if self.x == other. x { - (self.α - other.α).abs() - } else { - self.α.abs() + other.α.abs() - } + fn apply<I : Instance<G>>(&self, g : I) -> Self::Codomain { + g.eval(|g̃| g̃.apply(&self.x) * self.α) } } -impl<'b, Domain, G, F : Num, V : Mul<F, Output=V>> Apply<G> for DeltaMeasure<Domain, F> -where G: for<'a> Apply<&'a Domain, Output = V>, - V : Mul<F> { - type Output = V; - - #[inline] - fn apply(&self, g : G) -> Self::Output { - g.apply(&self.x) * self.α - } -} - -impl<Domain, G, F : Num, V : Mul<F, Output=V>> Linear<G> for DeltaMeasure<Domain, F> -where G: for<'a> Apply<&'a Domain, Output = V> { - type Codomain = V; -} +impl<Domain, G, F : Num> Linear<G> for DeltaMeasure<Domain, F> +where + Domain : Space, + G::Codomain : Mul<F, Output=G::Codomain>, + G : Mapping<Domain> + Clone + Space, + for<'b> &'b Domain : Instance<Domain>, +{ } // /// Partial blanket implementation of [`DeltaMeasure`] as a linear functional of [`Mapping`]s. // /// A full blanket implementation is not possible due to annoying Rust limitations: only [`Apply`] @@ -141,12 +149,13 @@ } } -/*impl<F : Num> From<(F, F)> for DeltaMeasure<Loc<F, 1>, F> { +impl<'a, Domain : Clone, F : Num> From<&'a DeltaMeasure<Domain, F>> for DeltaMeasure<Domain, F> { #[inline] - fn from((x, α) : (F, F)) -> Self { - DeltaMeasure{x: Loc([x]), α: α} + fn from(d : &'a DeltaMeasure<Domain, F>) -> Self { + d.clone() } -}*/ +} + impl<Domain, F : Num> DeltaMeasure<Domain, F> { /// Set the mass of the spike. @@ -186,6 +195,26 @@ } } +impl<Domain, F : Num> IntoIterator for DeltaMeasure<Domain, F> { + type Item = Self; + type IntoIter = std::iter::Once<Self>; + + #[inline] + fn into_iter(self) -> Self::IntoIter { + std::iter::once(self) + } +} + +impl<'a, Domain, F : Num> IntoIterator for &'a DeltaMeasure<Domain, F> { + type Item = Self; + type IntoIter = std::iter::Once<Self>; + + #[inline] + fn into_iter(self) -> Self::IntoIter { + std::iter::once(self) + } +} + macro_rules! make_delta_scalarop_rhs { ($trait:ident, $fn:ident, $trait_assign:ident, $fn_assign:ident) => {
--- a/src/measures/discrete.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/measures/discrete.rs Tue Dec 31 09:25:45 2024 -0500 @@ -11,9 +11,11 @@ use alg_tools::norms::Norm; use alg_tools::tabledump::TableDump; -use alg_tools::linops::{Apply, Linear}; +use alg_tools::linops::{Mapping, Linear}; use alg_tools::iter::{MapF,Mappable}; use alg_tools::nalgebra_support::ToNalgebraRealField; +use alg_tools::collection::Collection; +use alg_tools::instance::{Instance, Decomposition, MyCow, EitherDecomp, Space}; use crate::types::*; use super::base::*; @@ -29,6 +31,8 @@ pub(super) spikes : Vec<DeltaMeasure<Domain, F>>, } +pub type RNDM<F, const N : usize> = DiscreteMeasure<Loc<F, N>, F>; + /// Iterator over the [`DeltaMeasure`] spikes of a [`DiscreteMeasure`]. pub type SpikeIter<'a, Domain, F> = std::slice::Iter<'a, DeltaMeasure<Domain, F>>; @@ -109,6 +113,13 @@ self.spikes.iter_mut().zip(iter).for_each(|(δ, α)| δ.set_mass(α)); } + /// Update the locations of all the spikes to those produced by an iterator. + #[inline] + pub fn set_locations<'a, I : Iterator<Item=&'a Domain>>(&mut self, iter : I) + where Domain : 'static + Clone { + self.spikes.iter_mut().zip(iter.cloned()).for_each(|(δ, α)| δ.set_location(α)); + } + // /// Map the masses of all the spikes using a function and an iterator // #[inline] // pub fn zipmap_masses< @@ -190,7 +201,7 @@ impl<Domain, F : Num> IntoIterator for DiscreteMeasure<Domain, F> { type Item = DeltaMeasure<Domain, F>; - type IntoIter = <Vec<DeltaMeasure<Domain, F>> as IntoIterator>::IntoIter; + type IntoIter = std::vec::IntoIter<DeltaMeasure<Domain, F>>; #[inline] fn into_iter(self) -> Self::IntoIter { @@ -198,6 +209,60 @@ } } +impl<'a, Domain, F : Num> IntoIterator for &'a DiscreteMeasure<Domain, F> { + type Item = &'a DeltaMeasure<Domain, F>; + type IntoIter = SpikeIter<'a, Domain, F>; + + #[inline] + fn into_iter(self) -> Self::IntoIter { + self.spikes.iter() + } +} + +impl<Domain, F : Num> Sum<DeltaMeasure<Domain, F>> for DiscreteMeasure<Domain, F> { + // Required method + fn sum<I>(iter: I) -> Self + where + I : Iterator<Item = DeltaMeasure<Domain, F>> + { + Self::from_iter(iter) + } +} + +impl<'a, Domain : Clone, F : Num> Sum<&'a DeltaMeasure<Domain, F>> + for DiscreteMeasure<Domain, F> +{ + // Required method + fn sum<I>(iter: I) -> Self + where + I : Iterator<Item = &'a DeltaMeasure<Domain, F>> + { + Self::from_iter(iter.cloned()) + } +} + +impl<Domain, F : Num> Sum<DiscreteMeasure<Domain, F>> for DiscreteMeasure<Domain, F> { + // Required method + fn sum<I>(iter: I) -> Self + where + I : Iterator<Item = DiscreteMeasure<Domain, F>> + { + Self::from_iter(iter.map(|μ| μ.into_iter()).flatten()) + } +} + +impl<'a, Domain : Clone, F : Num> Sum<&'a DiscreteMeasure<Domain, F>> + for DiscreteMeasure<Domain, F> +{ + // Required method + fn sum<I>(iter: I) -> Self + where + I : Iterator<Item = &'a DiscreteMeasure<Domain, F>> + { + Self::from_iter(iter.map(|μ| μ.iter_spikes()).flatten().cloned()) + } +} + impl<Domain : Clone, F : Float> DiscreteMeasure<Domain, F> { /// Computes `μ1 ← θ * μ1 - ζ * μ2`, pruning entries where both `μ1` (`self`) and `μ2` have // zero weight. `μ2` will contain copy of pruned original `μ1` without arithmetic performed. @@ -312,6 +377,45 @@ } } +impl<Domain, F : Num> From<Vec<DeltaMeasure<Domain, F>>> +for DiscreteMeasure<Domain, F> { + #[inline] + fn from(spikes : Vec<DeltaMeasure<Domain, F>>) -> Self { + DiscreteMeasure{ spikes } + } +} + +impl<'a, Domain, F : Num, D> From<&'a [D]> +for DiscreteMeasure<Domain, F> +where &'a D : Into<DeltaMeasure<Domain, F>> { + #[inline] + fn from(list : &'a [D]) -> Self { + list.into_iter().map(|d| d.into()).collect() + } +} + + +impl<Domain, F : Num> From<DeltaMeasure<Domain, F>> +for DiscreteMeasure<Domain, F> { + #[inline] + fn from(δ : DeltaMeasure<Domain, F>) -> Self { + DiscreteMeasure{ + spikes : vec!(δ) + } + } +} + +impl<'a, Domain : Clone, F : Num> From<&'a DeltaMeasure<Domain, F>> +for DiscreteMeasure<Domain, F> { + #[inline] + fn from(δ : &'a DeltaMeasure<Domain, F>) -> Self { + DiscreteMeasure{ + spikes : vec!(δ.clone()) + } + } +} + + impl<Domain, F : Num, D : Into<DeltaMeasure<Domain, F>>> FromIterator<D> for DiscreteMeasure<Domain, F> { #[inline] @@ -371,19 +475,28 @@ } } -impl<Domain, G, F : Num, Y : Sum + Mul<F, Output=Y>> Apply<G> for DiscreteMeasure<Domain, F> -where G: for<'a> Apply<&'a Domain, Output = Y> { - type Output = Y; +impl<Domain, G, F : Num> Mapping<G> for DiscreteMeasure<Domain, F> +where + Domain : Space, + G::Codomain : Sum + Mul<F, Output=G::Codomain>, + G : Mapping<Domain, Codomain=F> + Clone + Space, + for<'b> &'b Domain : Instance<Domain>, +{ + type Codomain = G::Codomain; + #[inline] - fn apply(&self, g : G) -> Y { - self.spikes.iter().map(|m| g.apply(&m.x) * m.α).sum() + fn apply<I : Instance<G>>(&self, g : I) -> Self::Codomain { + g.eval(|g| self.spikes.iter().map(|m| g.apply(&m.x) * m.α).sum()) } } -impl<Domain, G, F : Num, Y : Sum + Mul<F, Output=Y>> Linear<G> for DiscreteMeasure<Domain, F> -where G : for<'a> Apply<&'a Domain, Output = Y> { - type Codomain = Y; -} +impl<Domain, G, F : Num> Linear<G> for DiscreteMeasure<Domain, F> +where + Domain : Space, + G::Codomain : Sum + Mul<F, Output=G::Codomain>, + G : Mapping<Domain, Codomain=F> + Clone + Space, + for<'b> &'b Domain : Instance<Domain>, +{ } /// Helper trait for constructing arithmetic operations for combinations @@ -391,6 +504,7 @@ trait Lift<F : Num, Domain> { type Producer : Iterator<Item=DeltaMeasure<Domain, F>>; + #[allow(dead_code)] /// Lifts `self` into a [`DiscreteMeasure`]. fn lift(self) -> DiscreteMeasure<Domain, F>; @@ -687,3 +801,217 @@ make_discrete_scalarop_lhs!(Mul, mul; f32 f64 i8 i16 i32 i64 isize u8 u16 u32 u64 usize); make_discrete_scalarop_lhs!(Div, div; f32 f64 i8 i16 i32 i64 isize u8 u16 u32 u64 usize); + +impl<F : Num, Domain> Collection for DiscreteMeasure<Domain, F> { + type Element = DeltaMeasure<Domain, F>; + type RefsIter<'a> = std::slice::Iter<'a, Self::Element> where Self : 'a; + + #[inline] + fn iter_refs(&self) -> Self::RefsIter<'_> { + self.iter_spikes() + } +} + +impl<Domain : Clone, F : Num> Space for DiscreteMeasure<Domain, F> { + type Decomp = MeasureDecomp; +} + +pub type SpikeSlice<'b, Domain, F> = &'b [DeltaMeasure<Domain, F>]; + +pub type EitherSlice<'b, Domain, F> = EitherDecomp< + Vec<DeltaMeasure<Domain, F>>, + SpikeSlice<'b, Domain, F> +>; + +impl<F : Num, Domain : Clone> Decomposition<DiscreteMeasure<Domain, F>> for MeasureDecomp { + type Decomposition<'b> = EitherSlice<'b, Domain, F> where DiscreteMeasure<Domain, F> : 'b; + type Reference<'b> = SpikeSlice<'b, Domain, F> where DiscreteMeasure<Domain, F> : 'b; + + /// Left the lightweight reference type into a full decomposition type. + fn lift<'b>(r : Self::Reference<'b>) -> Self::Decomposition<'b> { + EitherDecomp::Borrowed(r) + } +} + +impl<F : Num, Domain : Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp> +for DiscreteMeasure<Domain, F> +{ + fn decompose<'b>(self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b> + where Self : 'b, DiscreteMeasure<Domain, F> : 'b { + EitherDecomp::Owned(self.spikes) + } + + fn ref_instance(&self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_> + { + self.spikes.as_slice() + } + + fn cow<'b>(self) -> MyCow<'b, DiscreteMeasure<Domain, F>> where Self : 'b { + MyCow::Owned(self) + } + + fn own(self) -> DiscreteMeasure<Domain, F> { + self + } +} + +impl<'a, F : Num, Domain : Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp> +for &'a DiscreteMeasure<Domain, F> +{ + fn decompose<'b>(self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b> + where Self : 'b, DiscreteMeasure<Domain, F> : 'b { + EitherDecomp::Borrowed(self.spikes.as_slice()) + } + + fn ref_instance(&self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_> + { + self.spikes.as_slice() + } + + fn cow<'b>(self) -> MyCow<'b, DiscreteMeasure<Domain, F>> where Self : 'b { + MyCow::Borrowed(self) + } + + fn own(self) -> DiscreteMeasure<Domain, F> { + self.clone() + } +} + +impl<'a, F : Num, Domain : Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp> +for EitherSlice<'a, Domain, F> +{ + fn decompose<'b>(self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b> + where Self : 'b, DiscreteMeasure<Domain, F> : 'b { + self + } + + fn ref_instance(&self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_> + { + match self { + EitherDecomp::Owned(v) => v.as_slice(), + EitherDecomp::Borrowed(s) => s, + } + } + + fn own(self) -> DiscreteMeasure<Domain, F> { + match self { + EitherDecomp::Owned(v) => v.into(), + EitherDecomp::Borrowed(s) => s.into(), + } + } +} + +impl<'a, F : Num, Domain : Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp> +for &'a EitherSlice<'a, Domain, F> +{ + fn decompose<'b>(self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b> + where Self : 'b, DiscreteMeasure<Domain, F> : 'b { + match self { + EitherDecomp::Owned(v) => EitherDecomp::Borrowed(v.as_slice()), + EitherDecomp::Borrowed(s) => EitherDecomp::Borrowed(s), + } + } + + fn ref_instance(&self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_> + { + match self { + EitherDecomp::Owned(v) => v.as_slice(), + EitherDecomp::Borrowed(s) => s, + } + } + + fn own(self) -> DiscreteMeasure<Domain, F> { + match self { + EitherDecomp::Owned(v) => v.as_slice(), + EitherDecomp::Borrowed(s) => s + }.into() + } +} + +impl<'a, F : Num, Domain : Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp> +for SpikeSlice<'a, Domain, F> +{ + fn decompose<'b>(self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b> + where Self : 'b, DiscreteMeasure<Domain, F> : 'b { + EitherDecomp::Borrowed(self) + } + + fn ref_instance(&self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_> + { + self + } + + fn own(self) -> DiscreteMeasure<Domain, F> { + self.into() + } +} + +impl<'a, F : Num, Domain : Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp> +for &'a SpikeSlice<'a, Domain, F> +{ + fn decompose<'b>(self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b> + where Self : 'b, DiscreteMeasure<Domain, F> : 'b { + EitherDecomp::Borrowed(*self) + } + + fn ref_instance(&self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_> + { + *self + } + + fn own(self) -> DiscreteMeasure<Domain, F> { + (*self).into() + } +} + +impl<F : Num, Domain : Clone > Instance<DiscreteMeasure<Domain, F>, MeasureDecomp> +for DeltaMeasure<Domain, F> +{ + fn decompose<'b>(self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b> + where Self : 'b, DiscreteMeasure<Domain, F> : 'b { + EitherDecomp::Owned(vec![self]) + } + + fn ref_instance(&self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_> + { + std::slice::from_ref(self) + } + + fn own(self) -> DiscreteMeasure<Domain, F> { + self.into() + } +} + +impl<'a, F : Num, Domain : Clone> Instance<DiscreteMeasure<Domain, F>, MeasureDecomp> +for &'a DeltaMeasure<Domain, F> +{ + fn decompose<'b>(self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Decomposition<'b> + where Self : 'b, DiscreteMeasure<Domain, F> : 'b { + EitherDecomp::Borrowed(std::slice::from_ref(self)) + } + + fn ref_instance(&self) + -> <MeasureDecomp as Decomposition<DiscreteMeasure<Domain, F>>>::Reference<'_> + { + std::slice::from_ref(*self) + } + + fn own(self) -> DiscreteMeasure<Domain, F> { + self.into() + } +}
--- a/src/pdps.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/pdps.rs Tue Dec 31 09:25:45 2024 -0500 @@ -6,8 +6,7 @@ * Valkonen T. - _Proximal methods for point source localisation_, [arXiv:2212.02991](https://arxiv.org/abs/2212.02991). -The main routine is [`pointsource_pdps`]. It is based on specilisatinn of -[`generic_pointsource_fb_reg`] through relevant [`FBSpecialisation`] implementations. +The main routine is [`pointsource_pdps_reg`]. Both norm-2-squared and norm-1 data terms are supported. That is, implemented are solvers for <div> $$ @@ -37,10 +36,6 @@ For $F_0(y)=\frac{1}{2}\|y\|_2^2$ the second part reads $y = Aμ -b$. For $F_0(y)=\|y\|_1$ the second part reads $y ∈ ∂\|·\|_1(Aμ - b)$. </p> - -Based on zero initialisation for $μ$, we use the [`Subdifferentiable`] trait to make an -initialisation corresponding to the second part of the optimality conditions. -In the algorithm itself, standard proximal steps are taking with respect to $F\_0^* + ⟨b, ·⟩$. */ use numeric_literals::replace_float_literals; @@ -48,13 +43,10 @@ use nalgebra::DVector; use clap::ValueEnum; -use alg_tools::iterate::{ - AlgIteratorFactory, - AlgIteratorState, -}; +use alg_tools::iterate::AlgIteratorFactory; use alg_tools::loc::Loc; use alg_tools::euclidean::Euclidean; -use alg_tools::linops::Apply; +use alg_tools::linops::Mapping; use alg_tools::norms::{ Linfinity, Projection, @@ -69,14 +61,17 @@ SupportGenerator, LocalAnalysis, }; -use alg_tools::mapping::RealMapping; +use alg_tools::mapping::{RealMapping, Instance}; use alg_tools::nalgebra_support::ToNalgebraRealField; use alg_tools::linops::AXPY; use crate::types::*; -use crate::measures::DiscreteMeasure; +use crate::measures::{DiscreteMeasure, RNDM, Radon}; use crate::measures::merging::SpikeMerging; -use crate::forward_model::ForwardModel; +use crate::forward_model::{ + AdjointProductBoundedBy, + ForwardModel +}; use crate::seminorms::DiscreteMeasureOp; use crate::plot::{ SeqPlotter, @@ -87,7 +82,7 @@ FBGenericConfig, insert_and_reweigh, postprocess, - prune_and_maybe_simple_merge + prune_with_stats }; use crate::regularisation::RegTerm; use crate::dataterm::{ @@ -110,7 +105,30 @@ Full } -/// Settings for [`pointsource_pdps`]. +#[replace_float_literals(F::cast_from(literal))] +impl Acceleration { + /// PDPS parameter acceleration. Updates τ and σ and returns ω. + /// This uses dual strong convexity, not primal. + fn accelerate<F : Float>(self, τ : &mut F, σ : &mut F, γ : F) -> F { + match self { + Acceleration::None => 1.0, + Acceleration::Partial => { + let ω = 1.0 / (1.0 + γ * (*σ)).sqrt(); + *σ *= ω; + *τ /= ω; + ω + }, + Acceleration::Full => { + let ω = 1.0 / (1.0 + 2.0 * γ * (*σ)).sqrt(); + *σ *= ω; + *τ /= ω; + ω + }, + } + } +} + +/// Settings for [`pointsource_pdps_reg`]. #[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)] #[serde(default)] pub struct PDPSConfig<F : Float> { @@ -155,9 +173,13 @@ #[replace_float_literals(F::cast_from(literal))] -impl<F : Float, V : Euclidean<F> + AXPY<F>, const N : usize> -PDPSDataTerm<F, V, N> -for L2Squared { +impl<F, V, const N : usize> PDPSDataTerm<F, V, N> +for L2Squared +where + F : Float, + V : Euclidean<F> + AXPY<F>, + for<'b> &'b V : Instance<V>, +{ fn some_subdifferential(&self, x : V) -> V { x } fn factor_of_strong_convexity(&self) -> F { @@ -166,7 +188,7 @@ #[inline] fn dual_update(&self, y : &mut V, y_prev : &V, σ : F) { - y.axpy(1.0 / (1.0 + σ), &y_prev, σ / (1.0 + σ)); + y.axpy(1.0 / (1.0 + σ), y_prev, σ / (1.0 + σ)); } } @@ -210,16 +232,13 @@ iterator : I, mut plotter : SeqPlotter<F, N>, dataterm : D, -) -> DiscreteMeasure<Loc<F, N>, F> +) -> RNDM<F, N> where F : Float + ToNalgebraRealField, I : AlgIteratorFactory<IterInfo<F, N>>, - for<'b> &'b A::Observable : std::ops::Neg<Output=A::Observable> - + std::ops::Add<A::Observable, Output=A::Observable>, - //+ std::ops::Mul<F, Output=A::Observable>, // <-- FIXME: compiler overflow - A::Observable : std::ops::MulAssign<F>, + for<'b> &'b A::Observable : std::ops::Neg<Output=A::Observable> + Instance<A::Observable>, GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, - A : ForwardModel<Loc<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>> - + Lipschitz<&'a 𝒟, FloatType=F>, + A : ForwardModel<RNDM<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>> + + AdjointProductBoundedBy<RNDM<F, N>, 𝒟, FloatType=F>, BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, G𝒟 : SupportGenerator<F, N, SupportType = K, Id = usize> + Clone, 𝒟 : DiscreteMeasureOp<Loc<F, N>, F, PreCodomain = PreBTFN<F, G𝒟, N>>, @@ -228,14 +247,20 @@ K: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, PlotLookup : Plotting<N>, - DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F>, + RNDM<F, N> : SpikeMerging<F>, D : PDPSDataTerm<F, A::Observable, N>, Reg : RegTerm<F, N> { + // Check parameters + assert!(pdpsconfig.τ0 > 0.0 && + pdpsconfig.σ0 > 0.0 && + pdpsconfig.τ0 * pdpsconfig.σ0 <= 1.0, + "Invalid step length parameters"); + // Set up parameters let config = &pdpsconfig.generic; - let op𝒟norm = op𝒟.opnorm_bound(); - let l = opA.lipschitz_factor(&op𝒟).unwrap().sqrt(); + let op𝒟norm = op𝒟.opnorm_bound(Radon, Linfinity); + let l = opA.adjoint_product_bound(&op𝒟).unwrap().sqrt(); let mut τ = pdpsconfig.τ0 / l; let mut σ = pdpsconfig.σ0 / l; let γ = dataterm.factor_of_strong_convexity(); @@ -249,53 +274,42 @@ let mut μ = DiscreteMeasure::new(); let mut y = dataterm.some_subdifferential(-b); let mut y_prev = y.clone(); + let full_stats = |μ : &RNDM<F, N>, ε, stats| IterInfo { + value : dataterm.calculate_fit_op(μ, opA, b) + reg.apply(μ), + n_spikes : μ.len(), + ε, + // postprocessing: config.postprocessing.then(|| μ.clone()), + .. stats + }; let mut stats = IterInfo::new(); // Run the algorithm - iterator.iterate(|state| { + for state in iterator.iter_init(|| full_stats(&μ, ε, stats.clone())) { // Calculate smooth part of surrogate model. - // Using `std::mem::replace` here is not ideal, and expects that `empty_observable` - // has no significant overhead. For some reosn Rust doesn't allow us simply moving - // the residual and replacing it below before the end of this closure. - y *= -τ; - let r = std::mem::replace(&mut y, opA.empty_observable()); - let minus_τv = opA.preadjoint().apply(r); + let τv = opA.preadjoint().apply(y * τ); // Save current base point let μ_base = μ.clone(); // Insert and reweigh - let (d, within_tolerances) = insert_and_reweigh( - &mut μ, &minus_τv, &μ_base, None, + let (d, _within_tolerances) = insert_and_reweigh( + &mut μ, &τv, &μ_base, None, op𝒟, op𝒟norm, τ, ε, - config, ®, state, &mut stats + config, ®, &state, &mut stats ); // Prune and possibly merge spikes - prune_and_maybe_simple_merge( - &mut μ, &minus_τv, &μ_base, - op𝒟, - τ, ε, - config, ®, state, &mut stats - ); + if config.merge_now(&state) { + stats.merged += μ.merge_spikes(config.merging, |μ_candidate| { + let mut d = &τv + op𝒟.preapply(μ_candidate.sub_matching(&μ_base)); + reg.verify_merge_candidate(&mut d, μ_candidate, τ, ε, &config) + }); + } + stats.pruned += prune_with_stats(&mut μ); // Update step length parameters - let ω = match pdpsconfig.acceleration { - Acceleration::None => 1.0, - Acceleration::Partial => { - let ω = 1.0 / (1.0 + γ * σ).sqrt(); - σ = σ * ω; - τ = τ / ω; - ω - }, - Acceleration::Full => { - let ω = 1.0 / (1.0 + 2.0 * γ * σ).sqrt(); - σ = σ * ω; - τ = τ / ω; - ω - }, - }; + let ω = pdpsconfig.acceleration.accelerate(&mut τ, &mut σ, γ); // Do dual update y = b.clone(); // y = b @@ -304,32 +318,17 @@ dataterm.dual_update(&mut y, &y_prev, σ); y_prev.copy_from(&y); - // Update main tolerance for next iteration - let ε_prev = ε; - ε = tolerance.update(ε, state.iteration()); + // Give statistics if requested + let iter = state.iteration(); stats.this_iters += 1; - // Give function value if needed state.if_verbose(|| { - // Plot if so requested - plotter.plot_spikes( - format!("iter {} end; {}", state.iteration(), within_tolerances), &d, - "start".to_string(), Some(&minus_τv), - reg.target_bounds(τ, ε_prev), &μ, - ); - // Calculate mean inner iterations and reset relevant counters. - // Return the statistics - let res = IterInfo { - value : dataterm.calculate_fit_op(&μ, opA, b) + reg.apply(&μ), - n_spikes : μ.len(), - ε : ε_prev, - postprocessing: config.postprocessing.then(|| μ.clone()), - .. stats - }; - stats = IterInfo::new(); - res - }) - }); + plotter.plot_spikes(iter, Some(&d), Some(&τv), &μ); + full_stats(&μ, ε, std::mem::replace(&mut stats, IterInfo::new())) + }); + + ε = tolerance.update(ε, iter); + } postprocess(μ, config, dataterm, opA, b) }
--- a/src/plot.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/plot.rs Tue Dec 31 09:25:45 2024 -0500 @@ -1,33 +1,14 @@ //! Plotting helper utilities use numeric_literals::replace_float_literals; -use std::io::Write; -use image::{ - ImageFormat, - ImageBuffer, - Rgb -}; -use itertools::izip; -use colorbrewer::Palette as CbPalette; - +use serde::Serialize; use alg_tools::types::*; use alg_tools::lingrid::LinGrid; -use alg_tools::mapping::{ - RealMapping, - DifferentiableRealMapping, - SliceCodomain -}; +use alg_tools::mapping::RealMapping; use alg_tools::loc::Loc; -use alg_tools::bisection_tree::Bounds; -use alg_tools::maputil::map4; use alg_tools::tabledump::write_csv; use crate::measures::*; -/// Default RGB ramp from [`colorbrewer`]. -/// -/// This is a tuple of parameters to [`colorbrewer::get_color_ramp`]. -const RAMP : (CbPalette, u32) = (CbPalette::RdBu, 11); - /// Helper trait for implementing dimension-dependent plotting routines. pub trait Plotting<const N : usize> { /// Plot several mappings and a discrete measure into a file. @@ -36,13 +17,10 @@ T1 : RealMapping<F, N>, T2 : RealMapping<F, N> > ( - g_explanation : String, - g : &T1, - ω_explanation : String, + g : Option<&T1>, ω : Option<&T2>, grid : LinGrid<F, N>, - bnd : Option<Bounds<F>>, - μ : &DiscreteMeasure<Loc<F, N>, F>, + μ : &RNDM<F, N>, filename : String, ); @@ -54,98 +32,57 @@ g : &T1, grid : LinGrid<F, N>, filename : String, - explanation : String ); - - /// Plot a differentiable mapping into several file, sampling values on a given grid. - fn plot_into_file_diff< - F : Float, - T1 : DifferentiableRealMapping<F, N>, - > ( - g : &T1, - grid : LinGrid<F, N>, - base_filename : String, - explanation : String - ) { - Self::plot_into_file(g, grid, base_filename.clone(), explanation.clone()); - let d = g.diff_ref(); - for i in 0..N { - Self::plot_into_file(&d.slice_codomain_ref(i), - grid, - format!("{base_filename}_diff{i}"), - format!("{explanation} differential, dimension {i}")); - } - } } /// Helper type for looking up a [`Plotting`] based on dimension. pub struct PlotLookup; +#[derive(Serialize)] +struct CSVHelper1<F : Float> { + x : F, + f : F, +} + +#[derive(Serialize)] +struct CSVHelper1_2<F : Float>{ + x : F, + g : Option<F>, + omega : Option<F> +} + +#[derive(Serialize)] +struct CSVSpike1<F : Float> { + x : F, + alpha : F, +} + impl Plotting<1> for PlotLookup { fn plot_into_file_spikes< F : Float, T1 : RealMapping<F, 1>, T2 : RealMapping<F, 1> > ( - g_explanation : String, - g : &T1, - ω_explanation : String, + g0 : Option<&T1>, ω0 : Option<&T2>, grid : LinGrid<F, 1>, - bnd0 : Option<Bounds<F>>, μ : &DiscreteMeasure<Loc<F, 1>, F>, filename : String, ) { - let start = grid.start[0].as_(); - let end = grid.end[0].as_(); - let m = μ.iter_masses().fold(F::ZERO, |m, α| m.max(α)); - let s = μ.iter_masses().fold(F::ZERO, |m, α| m.add(α)); - let mut spike_scale = F::ONE; - - let mut plotter = poloto::plot( - "f", "x", - format!("f(x); spike max={:.4}, n={}, ∑={:.4}", m, μ.len(), s) - ).move_into(); - - if let Some(ω) = ω0 { - let graph_ω = grid.into_iter().map(|x@Loc([x0]) : Loc<F, 1>| { - [x0.as_(), ω.apply(&x).as_()] - }); - plotter.line(ω_explanation.as_str(), graph_ω.clone()); - // let csv_f = format!("{}.txt", filename); - // write_csv(graph_ω, csv_f).expect("CSV save error"); - } - - let graph_g = grid.into_iter().map(|x@Loc([x0]) : Loc<F, 1>| { - [x0.as_(), g.apply(&x).as_()] + let data = grid.into_iter().map(|p@Loc([x]) : Loc<F, 1>| CSVHelper1_2 { + x, + g : g0.map(|g| g.apply(&p)), + omega : ω0.map(|ω| ω.apply(&p)) }); - plotter.line(g_explanation.as_str(), graph_g.clone()); - // let csv_f = format!("{}.txt", filename); - // write_csv(graph_g, csv_f).expect("CSV save error"); - - bnd0.map(|bnd| { - let upperb = bnd.upper().as_(); - let lowerb = bnd.lower().as_(); - let upper : [[f64; 2]; 2] = [[start, upperb], [end, upperb]]; - let lower = [[start, lowerb], [end, lowerb]]; - spike_scale *= bnd.upper(); + let csv_f = format!("{}_functions.csv", filename); + write_csv(data, csv_f).expect("CSV save error"); - plotter.line("upper bound", upper) - .line("lower bound", lower) - .ymarker(lowerb) - .ymarker(upperb); + let spikes = μ.iter_spikes().map(|δ| { + let Loc([x]) = δ.x; + CSVSpike1 { x, alpha : δ.α } }); - - for &DeltaMeasure{ α, x : Loc([x]) } in μ.iter_spikes() { - let spike = [[x.as_(), 0.0], [x.as_(), (α/m * spike_scale).as_()]]; - plotter.line("", spike); - } - - let svg = format!("{}", poloto::disp(|a| poloto::simple_theme(a, plotter))); - - std::fs::File::create(filename + ".svg").and_then(|mut file| - file.write_all(svg.as_bytes()) - ).expect("SVG save error"); + let csv_f = format!("{}_spikes.csv", filename); + write_csv(spikes, csv_f).expect("CSV save error"); } fn plot_into_file< @@ -155,150 +92,37 @@ g : &T1, grid : LinGrid<F, 1>, filename : String, - explanation : String ) { - let graph_g = grid.into_iter().map(|x@Loc([x0]) : Loc<F, 1>| { - [x0.as_(), g.apply(&x).as_()] + let data = grid.into_iter().map(|p@Loc([x]) : Loc<F, 1>| CSVHelper1 { + x, + f : g.apply(&p), }); - - let plotter: poloto::Plotter<'_, float, float> = poloto::plot("f", "x", "f(x)") - .line(explanation.as_str(), graph_g.clone()) - .move_into(); - - let svg = format!("{}", poloto::disp(|a| poloto::simple_theme(a, plotter))); - - let svg_f = format!("{}.svg", filename); - std::fs::File::create(svg_f).and_then(|mut file| - file.write_all(svg.as_bytes()) - ).expect("SVG save error"); - let csv_f = format!("{}.txt", filename); - write_csv(graph_g, csv_f).expect("CSV save error"); + write_csv(data, csv_f).expect("CSV save error"); } } -/// Convert $[0, 1] ∈ F$ to $\\\{0, …, M\\\} ∈ F$ where $M=$`F::RANGE_MAX`. -#[inline] -fn scale_uint<F, U>(v : F) -> U -where F : Float + CastFrom<U> + num_traits::cast::AsPrimitive<U>, - U : Unsigned { - (v*F::cast_from(U::RANGE_MAX)).as_() -} - -/// Convert $[a, b] ∈ F$ to $\\\{0, …, M\\\} ∈ F$ where $M=$`F::RANGE_MAX`. -#[replace_float_literals(F::cast_from(literal))] -#[inline] -fn scale_range_uint<F, U>(v : F, &Bounds(a, b) : &Bounds<F>) -> U -where F : Float + CastFrom<U> + num_traits::cast::AsPrimitive<U>, - U : Unsigned { - debug_assert!(a < b); - scale_uint(((v - a)/(b - a)).max(0.0).min(1.0)) -} - - -/// Sample a mapping on a grid. -/// -/// Returns a vector of values as well as upper and lower bounds of the values. -fn rawdata_and_range<F, T>(grid : &LinGrid<F, 2>, g :&T) -> (Vec<F>, Bounds<F>) -where F : Float, - T : RealMapping<F, 2> { - let rawdata : Vec<F> = grid.into_iter().map(|x| g.apply(&x)).collect(); - let range = rawdata.iter() - .map(|&v| Bounds(v, v)) - .reduce(|b1, b2| b1.common(&b2)) - .unwrap(); - (rawdata, range) +#[derive(Serialize)] +struct CSVHelper2<F : Float> { + x : F, + y : F, + f : F, } -/*fn to_range<'a, F, U>(rawdata : &'a Vec<F>, range : &'a Bounds<F>) --> std::iter::Map<std::slice::Iter<'a, F>, impl FnMut(&'a F) -> U> -where F : Float + CastFrom<U> + num_traits::cast::AsPrimitive<U>, - U : Unsigned { - rawdata.iter().map(move |&v| scale_range_uint(v, range)) -}*/ - -/// Convert a scalar value to an RGB triplet. -/// -/// Converts the value `v` supposed to be within the range `[a, b]` to an rgb value according -/// to the given `ramp` of equally-spaced rgb interpolation points. -#[replace_float_literals(F::cast_from(literal))] -fn one_to_ramp<F, U>( - &Bounds(a, b) : &Bounds<F>, - ramp : &Vec<Loc<F, 3>>, - v : F, -) -> Rgb<U> -where F : Float + CastFrom<U> + num_traits::cast::AsPrimitive<U>, - U : Unsigned { - - let n = ramp.len() - 1; - let m = F::cast_from(U::RANGE_MAX); - let ramprange = move |v : F| {let m : usize = v.as_(); m.min(n).max(0) }; - - let w = F::cast_from(n) * (v - a) / (b - a); // convert [0, 1] to [0, n] - let (l, u) = (w.floor(), w.ceil()); // Find closest integers - let (rl, ru) = (ramprange(l), ramprange(u)); - let (cl, cu) = (ramp[rl], ramp[ru]); // Get corresponding colours - let λ = match rl==ru { // Interpolation factor - true => 0.0, - false => (u - w) / (u - l), - }; - let Loc(rgb) = cl * λ + cu * (1.0 - λ); // Interpolate - - Rgb(rgb.map(|v| (v * m).round().min(m).max(0.0).as_())) +#[derive(Serialize)] +struct CSVHelper2_2<F : Float>{ + x : F, + y : F, + g : Option<F>, + omega : Option<F> } -/// Convert a an iterator over scalar values to an iterator over RGB triplets. -/// -/// The conversion is that performed by [`one_to_ramp`]. -#[replace_float_literals(F::cast_from(literal))] -fn to_ramp<'a, F, U, I>( - bounds : &'a Bounds<F>, - ramp : &'a Vec<Loc<F, 3>>, - iter : I, -) -> std::iter::Map<I, impl FnMut(F) -> Rgb<U> + 'a> -where F : Float + CastFrom<U> + num_traits::cast::AsPrimitive<U>, - U : Unsigned, - I : Iterator<Item = F> + 'a { - iter.map(move |v| one_to_ramp(bounds, ramp, v)) -} - -/// Convert a [`colorbrewer`] sepcification to a ramp of rgb triplets. -fn get_ramp<F : Float>((palette, nb) : (CbPalette, u32)) -> Vec<Loc<F, 3>> { - let m = F::cast_from(u8::MAX); - colorbrewer::get_color_ramp(palette, nb) - .expect("Invalid colorbrewer ramp") - .into_iter() - .map(|rgb::RGB{r, g, b}| { - [r, g, b].map(|c| F::cast_from(c) / m).into() - }).collect() -} - -/// Perform hue shifting of an RGB value. -/// -// The hue `ω` is in radians. -#[replace_float_literals(F::cast_from(literal))] -fn hueshift<F, U>(ω : F, Rgb([r_in, g_in, b_in]) : Rgb<U>) -> Rgb<U> -where F : Float + CastFrom<U>, - U : Unsigned { - let m = F::cast_from(U::RANGE_MAX); - let r = F::cast_from(r_in) / m; - let g = F::cast_from(g_in) / m; - let b = F::cast_from(b_in) / m; - let u = ω.cos(); - let w = ω.sin(); - - let nr = (0.299 + 0.701*u + 0.168*w) * r - + (0.587 - 0.587*u + 0.330*w) * g - + (0.114 - 0.114*u - 0.497*w) * b; - let ng = (0.299 - 0.299*u - 0.328*w) * r - + (0.587 + 0.413*u + 0.035*w) * g - + (0.114 - 0.114*u + 0.292*w) *b; - let nb = (0.299 - 0.3*u + 1.25*w) * r - + (0.587 - 0.588*u - 1.05*w) * g - + (0.114 + 0.886*u - 0.203*w) * b; - - Rgb([nr, ng, nb].map(scale_uint)) +#[derive(Serialize)] +struct CSVSpike2<F : Float> { + x : F, + y : F, + alpha : F, } @@ -309,55 +133,27 @@ T1 : RealMapping<F, 2>, T2 : RealMapping<F, 2> > ( - _g_explanation : String, - g : &T1, - _ω_explanation : String, + g0 : Option<&T1>, ω0 : Option<&T2>, grid : LinGrid<F, 2>, - _bnd0 : Option<Bounds<F>>, μ : &DiscreteMeasure<Loc<F, 2>, F>, filename : String, ) { - let [w, h] = grid.count; - let (rawdata_g, range_g) = rawdata_and_range(&grid, g); - let (rawdata_ω, range) = match ω0 { - Some(ω) => { - let (rawdata_ω, range_ω) = rawdata_and_range(&grid, ω); - (rawdata_ω, range_g.common(&range_ω)) - }, - None => { - let mut zeros = Vec::new(); - zeros.resize(rawdata_g.len(), 0.0); - (zeros, range_g) - } - }; - let ramp = get_ramp(RAMP); - let base_im_iter = to_ramp::<F, u16, _>(&range_g, &ramp, rawdata_g.iter().cloned()); - let im_iter = izip!(base_im_iter, rawdata_g.iter(), rawdata_ω.iter()) - .map(|(rgb, &v, &w)| { - hueshift(2.0 * F::PI * (v - w).abs() / range.upper(), rgb) - }); - let mut img = ImageBuffer::new(w as u32, h as u32); - img.pixels_mut() - .zip(im_iter) - .for_each(|(p, v)| *p = v); + let data = grid.into_iter().map(|p@Loc([x, y]) : Loc<F, 2>| CSVHelper2_2 { + x, + y, + g : g0.map(|g| g.apply(&p)), + omega : ω0.map(|ω| ω.apply(&p)) + }); + let csv_f = format!("{}_functions.csv", filename); + write_csv(data, csv_f).expect("CSV save error"); - // Add spikes - let m = μ.iter_masses().fold(F::ZERO, |m, α| m.max(α)); - let μ_range = Bounds(F::ZERO, m); - for &DeltaMeasure{ ref x, α } in μ.iter_spikes() { - let [a, b] = map4(x, &grid.start, &grid.end, &grid.count, |&ξ, &a, &b, &n| { - ((ξ-a)/(b-a)*F::cast_from(n)).as_() - }); - if a < w.as_() && b < h.as_() { - let sc : u16 = scale_range_uint(α, &μ_range); - // TODO: use max of points that map to this pixel. - img[(a, b)] = Rgb([u16::MAX, u16::MAX, sc/2]); - } - } - - img.save_with_format(filename + ".png", ImageFormat::Png) - .expect("Image save error"); + let spikes = μ.iter_spikes().map(|δ| { + let Loc([x, y]) = δ.x; + CSVSpike2 { x, y, alpha : δ.α } + }); + let csv_f = format!("{}_spikes.csv", filename); + write_csv(spikes, csv_f).expect("CSV save error"); } fn plot_into_file< @@ -367,22 +163,14 @@ g : &T1, grid : LinGrid<F, 2>, filename : String, - _explanation : String ) { - let [w, h] = grid.count; - let (rawdata, range) = rawdata_and_range(&grid, g); - let ramp = get_ramp(RAMP); - let im_iter = to_ramp::<F, u16, _>(&range, &ramp, rawdata.iter().cloned()); - let mut img = ImageBuffer::new(w as u32, h as u32); - img.pixels_mut() - .zip(im_iter) - .for_each(|(p, v)| *p = v); - img.save_with_format(filename.clone() + ".png", ImageFormat::Png) - .expect("Image save error"); - - let csv_iter = grid.into_iter().zip(rawdata.iter()).map(|(Loc(x), &v)| (x, v)); - let csv_f = filename + ".txt"; - write_csv(csv_iter, csv_f).expect("CSV save error"); + let data = grid.into_iter().map(|p@Loc([x, y]) : Loc<F, 2>| CSVHelper2 { + x, + y, + f : g.apply(&p), + }); + let csv_f = format!("{}.txt", filename); + write_csv(data, csv_f).expect("CSV save error"); } } @@ -410,12 +198,10 @@ /// This calls [`PlotLookup::plot_into_file_spikes`] with a sequentially numbered file name. pub fn plot_spikes<T1, T2>( &mut self, - g_explanation : String, - g : &T1, - ω_explanation : String, + iter : usize, + g : Option<&T1>, ω : Option<&T2>, - tol : Option<Bounds<F>>, - μ : &DiscreteMeasure<Loc<F, N>, F>, + μ : &RNDM<F, N>, ) where T1 : RealMapping<F, N>, T2 : RealMapping<F, N> { @@ -424,12 +210,11 @@ } if self.plot_count < self.max_plots { PlotLookup::plot_into_file_spikes( - g_explanation, g, - ω_explanation, ω, + g, + ω, self.grid, - tol, μ, - format!("{}out{:03}", self.prefix, self.plot_count) + format!("{}out{:03}", self.prefix, iter) ); self.plot_count += 1; }
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/preadjoint_helper.rs Tue Dec 31 09:25:45 2024 -0500 @@ -0,0 +1,55 @@ +/*! +Preadjoint construction helper +*/ + +use std::marker::PhantomData; +use alg_tools::types::*; +pub use alg_tools::linops::*; +use alg_tools::norms::{Norm, HasDualExponent}; + +/// Helper structure for constructing preadjoints of `S` where `S : Linear<X>`. +/// [`Linear`] needs to be implemented for each instance, but [`Adjointable`] +/// and [`BoundedLinear`] have blanket implementations. +#[derive(Clone,Debug)] +pub struct PreadjointHelper<'a, S : 'a, X> { + pub forward_op : &'a S, + _domain : PhantomData<X> +} + +impl<'a, S : 'a, X> PreadjointHelper<'a, S, X> { + pub fn new(forward_op : &'a S) -> Self { + PreadjointHelper { forward_op, _domain: PhantomData } + } +} + +impl<'a, X, Ypre, S> Adjointable<Ypre, X> +for PreadjointHelper<'a, S, X> +where + X : Space, + Ypre : Space, + Self : Linear<Ypre>, + S : Clone + Linear<X> +{ + type AdjointCodomain = S::Codomain; + type Adjoint<'b> = S where Self : 'b; + + fn adjoint(&self) -> Self::Adjoint<'_> { + self.forward_op.clone() + } +} + +impl<'a, F, X, Ypre, ExpXpre, ExpYpre, S> BoundedLinear<Ypre, ExpYpre, ExpXpre, F> +for PreadjointHelper<'a, S, X> +where + ExpXpre : HasDualExponent, + ExpYpre : HasDualExponent, + F : Float, + X : Space + Norm<F, ExpXpre::DualExp>, + Ypre : Space + Norm<F, ExpYpre>, + Self : Linear<Ypre>, + S : 'a + Clone + BoundedLinear<X, ExpXpre::DualExp, ExpYpre::DualExp, F> +{ + fn opnorm_bound(&self, expy : ExpYpre, expx : ExpXpre) -> F { + self.forward_op.opnorm_bound(expx.dual_exponent(), expy.dual_exponent()) + } +}
--- a/src/radon_fb.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/radon_fb.rs Tue Dec 31 09:25:45 2024 -0500 @@ -11,10 +11,11 @@ use alg_tools::iterate::{ AlgIteratorFactory, - AlgIteratorState, + AlgIteratorIteration, + AlgIterator }; use alg_tools::euclidean::Euclidean; -use alg_tools::linops::Apply; +use alg_tools::linops::Mapping; use alg_tools::sets::Cube; use alg_tools::loc::Loc; use alg_tools::bisection_tree::{ @@ -29,11 +30,14 @@ }; use alg_tools::mapping::RealMapping; use alg_tools::nalgebra_support::ToNalgebraRealField; +use alg_tools::norms::L2; use crate::types::*; use crate::measures::{ + RNDM, DiscreteMeasure, DeltaMeasure, + Radon, }; use crate::measures::merging::{ SpikeMergingMethod, @@ -54,10 +58,11 @@ use crate::fb::{ FBGenericConfig, - postprocess + postprocess, + prune_with_stats }; -/// Settings for [`pointsource_fb_reg`]. +/// Settings for [`pointsource_radon_fb_reg`]. #[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)] #[serde(default)] pub struct RadonFBConfig<F : Float> { @@ -79,17 +84,17 @@ #[replace_float_literals(F::cast_from(literal))] pub(crate) fn insert_and_reweigh< - 'a, F, GA, BTA, S, Reg, State, const N : usize + 'a, F, GA, BTA, S, Reg, I, const N : usize >( - μ : &mut DiscreteMeasure<Loc<F, N>, F>, - minus_τv : &mut BTFN<F, GA, BTA, N>, - μ_base : &mut DiscreteMeasure<Loc<F, N>, F>, - _ν_delta: Option<&DiscreteMeasure<Loc<F, N>, F>>, + μ : &mut RNDM<F, N>, + τv : &mut BTFN<F, GA, BTA, N>, + μ_base : &mut RNDM<F, N>, + //_ν_delta: Option<&RNDM<F, N>>, τ : F, ε : F, config : &FBGenericConfig<F>, reg : &Reg, - _state : &State, + _state : &AlgIteratorIteration<I>, stats : &mut IterInfo<F, N>, ) where F : Float + ToNalgebraRealField, @@ -97,18 +102,20 @@ BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, - DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F>, + RNDM<F, N> : SpikeMerging<F>, Reg : RegTerm<F, N>, - State : AlgIteratorState { + I : AlgIterator { 'i_and_w: for i in 0..=1 { // Optimise weights if μ.len() > 0 { // Form finite-dimensional subproblem. The subproblem references to the original μ^k // from the beginning of the iteration are all contained in the immutable c and g. + // TODO: observe negation of -τv after switch from minus_τv: finite-dimensional + // problems have not yet been updated to sign change. let g̃ = DVector::from_iterator(μ.len(), μ.iter_locations() - .map(|ζ| F::to_nalgebra_mixed(minus_τv.apply(ζ)))); + .map(|ζ| - F::to_nalgebra_mixed(τv.apply(ζ)))); let mut x = μ.masses_dvector(); let y = μ_base.masses_dvector(); @@ -122,7 +129,7 @@ if i>0 { // Simple debugging test to see if more inserts would be needed. Doesn't seem so. //let n = μ.dist_matching(μ_base); - //println!("{:?}", reg.find_tolerance_violation_slack(minus_τv, τ, ε, false, config, n)); + //println!("{:?}", reg.find_tolerance_violation_slack(τv, τ, ε, false, config, n)); break 'i_and_w } @@ -132,69 +139,23 @@ // Find a spike to insert, if needed. // This only check the overall tolerances, not tolerances on support of μ-μ_base or μ, // which are supposed to have been guaranteed by the finite-dimensional weight optimisation. - match reg.find_tolerance_violation_slack(minus_τv, τ, ε, false, config, n) { + match reg.find_tolerance_violation_slack(τv, τ, ε, false, config, n) { None => { break 'i_and_w }, Some((ξ, _v_ξ, _in_bounds)) => { // Weight is found out by running the finite-dimensional optimisation algorithm // above *μ += DeltaMeasure { x : ξ, α : 0.0 }; *μ_base += DeltaMeasure { x : ξ, α : 0.0 }; + stats.inserted += 1; } }; } } -#[replace_float_literals(F::cast_from(literal))] -pub(crate) fn prune_and_maybe_simple_merge< - 'a, F, GA, BTA, S, Reg, State, const N : usize ->( - μ : &mut DiscreteMeasure<Loc<F, N>, F>, - minus_τv : &mut BTFN<F, GA, BTA, N>, - μ_base : &DiscreteMeasure<Loc<F, N>, F>, - τ : F, - ε : F, - config : &FBGenericConfig<F>, - reg : &Reg, - state : &State, - stats : &mut IterInfo<F, N>, -) -where F : Float + ToNalgebraRealField, - GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, - BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, - S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, - BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, - DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F>, - Reg : RegTerm<F, N>, - State : AlgIteratorState { - - assert!(μ_base.len() <= μ.len()); - - if state.iteration() % config.merge_every == 0 { - stats.merged += μ.merge_spikes(config.merging, |μ_candidate| { - // Important: μ_candidate's new points are afterwards, - // and do not conflict with μ_base. - // TODO: could simplify to requiring μ_base instead of μ_radon. - // but may complicate with sliding base's exgtra points that need to be - // after μ_candidate's extra points. - // TODO: doesn't seem to work, maybe need to merge μ_base as well? - // Although that doesn't seem to make sense. - let μ_radon = μ_candidate.sub_matching(μ_base); - reg.verify_merge_candidate_radonsq(minus_τv, μ_candidate, τ, ε, &config, &μ_radon) - //let n = μ_candidate.dist_matching(μ_base); - //reg.find_tolerance_violation_slack(minus_τv, τ, ε, false, config, n).is_none() - }); - } - - let n_before_prune = μ.len(); - μ.prune(); - debug_assert!(μ.len() <= n_before_prune); - stats.pruned += n_before_prune - μ.len(); -} - /// Iteratively solve the pointsource localisation problem using simplified forward-backward splitting. /// -/// The settings in `config` have their [respective documentation](FBConfig). `opA` is the +/// The settings in `config` have their [respective documentation][RadonFBConfig]. `opA` is the /// forward operator $A$, $b$ the observable, and $\lambda$ the regularisation weight. /// Finally, the `iterator` is an outer loop verbosity and iteration count control /// as documented in [`alg_tools::iterate`]. @@ -219,20 +180,17 @@ fbconfig : &RadonFBConfig<F>, iterator : I, mut _plotter : SeqPlotter<F, N>, -) -> DiscreteMeasure<Loc<F, N>, F> +) -> RNDM<F, N> where F : Float + ToNalgebraRealField, I : AlgIteratorFactory<IterInfo<F, N>>, for<'b> &'b A::Observable : std::ops::Neg<Output=A::Observable>, - //+ std::ops::Mul<F, Output=A::Observable>, <-- FIXME: compiler overflow - A::Observable : std::ops::MulAssign<F>, GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, - A : ForwardModel<Loc<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>>, + A : ForwardModel<RNDM<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>>, BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, Cube<F, N>: P2Minimise<Loc<F, N>, F>, - PlotLookup : Plotting<N>, - DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F>, + RNDM<F, N> : SpikeMerging<F>, Reg : RegTerm<F, N> { // Set up parameters @@ -240,7 +198,7 @@ // We need L such that the descent inequality F(ν) - F(μ) - ⟨F'(μ),ν-μ⟩ ≤ (L/2)‖ν-μ‖²_ℳ ∀ ν,μ // holds. Since the left hand side expands as (1/2)‖A(ν-μ)‖₂², this is to say, we need L such // that ‖Aμ‖₂² ≤ L ‖μ‖²_ℳ ∀ μ. Thus `opnorm_bound` gives the square root of L. - let τ = fbconfig.τ0/opA.opnorm_bound().powi(2); + let τ = fbconfig.τ0/opA.opnorm_bound(Radon, L2).powi(2); // We multiply tolerance by τ for FB since our subproblems depending on tolerances are scaled // by τ compared to the conditional gradient approach. let tolerance = config.tolerance * τ * reg.tolerance_scaling(); @@ -249,71 +207,74 @@ // Initialise iterates let mut μ = DiscreteMeasure::new(); let mut residual = -b; + + // Statistics + let full_stats = |residual : &A::Observable, + μ : &RNDM<F, N>, + ε, stats| IterInfo { + value : residual.norm2_squared_div2() + reg.apply(μ), + n_spikes : μ.len(), + ε, + // postprocessing: config.postprocessing.then(|| μ.clone()), + .. stats + }; let mut stats = IterInfo::new(); // Run the algorithm - iterator.iterate(|state| { + for state in iterator.iter_init(|| full_stats(&residual, &μ, ε, stats.clone())) { // Calculate smooth part of surrogate model. - // Using `std::mem::replace` here is not ideal, and expects that `empty_observable` - // has no significant overhead. For some reosn Rust doesn't allow us simply moving - // the residual and replacing it below before the end of this closure. - residual *= -τ; - let r = std::mem::replace(&mut residual, opA.empty_observable()); - let mut minus_τv = opA.preadjoint().apply(r); + let mut τv = opA.preadjoint().apply(residual * τ); // Save current base point let mut μ_base = μ.clone(); // Insert and reweigh insert_and_reweigh( - &mut μ, &mut minus_τv, &mut μ_base, None, + &mut μ, &mut τv, &mut μ_base, //None, τ, ε, - config, ®, state, &mut stats + config, ®, &state, &mut stats ); // Prune and possibly merge spikes - prune_and_maybe_simple_merge( - &mut μ, &mut minus_τv, &μ_base, - τ, ε, - config, ®, state, &mut stats - ); + assert!(μ_base.len() <= μ.len()); + if config.merge_now(&state) { + stats.merged += μ.merge_spikes(config.merging, |μ_candidate| { + // Important: μ_candidate's new points are afterwards, + // and do not conflict with μ_base. + // TODO: could simplify to requiring μ_base instead of μ_radon. + // but may complicate with sliding base's exgtra points that need to be + // after μ_candidate's extra points. + // TODO: doesn't seem to work, maybe need to merge μ_base as well? + // Although that doesn't seem to make sense. + let μ_radon = μ_candidate.sub_matching(&μ_base); + reg.verify_merge_candidate_radonsq(&mut τv, μ_candidate, τ, ε, &config, &μ_radon) + //let n = μ_candidate.dist_matching(μ_base); + //reg.find_tolerance_violation_slack(τv, τ, ε, false, config, n).is_none() + }); + } + stats.pruned += prune_with_stats(&mut μ); // Update residual residual = calculate_residual(&μ, opA, b); - // Update main tolerance for next iteration - let ε_prev = ε; - ε = tolerance.update(ε, state.iteration()); + let iter = state.iteration(); stats.this_iters += 1; - // Give function value if needed + // Give statistics if needed state.if_verbose(|| { - // Plot if so requested - // plotter.plot_spikes( - // format!("iter {} end;", state.iteration()), &d, - // "start".to_string(), Some(&minus_τv), - // reg.target_bounds(τ, ε_prev), &μ, - // ); - // Calculate mean inner iterations and reset relevant counters. - // Return the statistics - let res = IterInfo { - value : residual.norm2_squared_div2() + reg.apply(&μ), - n_spikes : μ.len(), - ε : ε_prev, - postprocessing: config.postprocessing.then(|| μ.clone()), - .. stats - }; - stats = IterInfo::new(); - res - }) - }); + full_stats(&residual, &μ, ε, std::mem::replace(&mut stats, IterInfo::new())) + }); + + // Update main tolerance for next iteration + ε = tolerance.update(ε, iter); + } postprocess(μ, config, L2Squared, opA, b) } /// Iteratively solve the pointsource localisation problem using simplified inertial forward-backward splitting. /// -/// The settings in `config` have their [respective documentation](FBConfig). `opA` is the +/// The settings in `config` have their [respective documentation][RadonFBConfig]. `opA` is the /// forward operator $A$, $b$ the observable, and $\lambda$ the regularisation weight. /// Finally, the `iterator` is an outer loop verbosity and iteration count control /// as documented in [`alg_tools::iterate`]. @@ -337,21 +298,19 @@ reg : Reg, fbconfig : &RadonFBConfig<F>, iterator : I, - mut _plotter : SeqPlotter<F, N>, -) -> DiscreteMeasure<Loc<F, N>, F> + mut plotter : SeqPlotter<F, N>, +) -> RNDM<F, N> where F : Float + ToNalgebraRealField, I : AlgIteratorFactory<IterInfo<F, N>>, for<'b> &'b A::Observable : std::ops::Neg<Output=A::Observable>, - //+ std::ops::Mul<F, Output=A::Observable>, <-- FIXME: compiler overflow - A::Observable : std::ops::MulAssign<F>, GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, - A : ForwardModel<Loc<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>>, + A : ForwardModel<RNDM<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>>, BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, Cube<F, N>: P2Minimise<Loc<F, N>, F>, PlotLookup : Plotting<N>, - DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F>, + RNDM<F, N> : SpikeMerging<F>, Reg : RegTerm<F, N> { // Set up parameters @@ -359,7 +318,7 @@ // We need L such that the descent inequality F(ν) - F(μ) - ⟨F'(μ),ν-μ⟩ ≤ (L/2)‖ν-μ‖²_ℳ ∀ ν,μ // holds. Since the left hand side expands as (1/2)‖A(ν-μ)‖₂², this is to say, we need L such // that ‖Aμ‖₂² ≤ L ‖μ‖²_ℳ ∀ μ. Thus `opnorm_bound` gives the square root of L. - let τ = fbconfig.τ0/opA.opnorm_bound().powi(2); + let τ = fbconfig.τ0/opA.opnorm_bound(Radon, L2).powi(2); let mut λ = 1.0; // We multiply tolerance by τ for FB since our subproblems depending on tolerances are scaled // by τ compared to the conditional gradient approach. @@ -370,31 +329,35 @@ let mut μ = DiscreteMeasure::new(); let mut μ_prev = DiscreteMeasure::new(); let mut residual = -b; + let mut warned_merging = false; + + // Statistics + let full_stats = |ν : &RNDM<F, N>, ε, stats| IterInfo { + value : L2Squared.calculate_fit_op(ν, opA, b) + reg.apply(ν), + n_spikes : ν.len(), + ε, + // postprocessing: config.postprocessing.then(|| ν.clone()), + .. stats + }; let mut stats = IterInfo::new(); - let mut warned_merging = false; // Run the algorithm - iterator.iterate(|state| { + for state in iterator.iter_init(|| full_stats(&μ, ε, stats.clone())) { // Calculate smooth part of surrogate model. - // Using `std::mem::replace` here is not ideal, and expects that `empty_observable` - // has no significant overhead. For some reosn Rust doesn't allow us simply moving - // the residual and replacing it below before the end of this closure. - residual *= -τ; - let r = std::mem::replace(&mut residual, opA.empty_observable()); - let mut minus_τv = opA.preadjoint().apply(r); + let mut τv = opA.preadjoint().apply(residual * τ); // Save current base point let mut μ_base = μ.clone(); // Insert new spikes and reweigh insert_and_reweigh( - &mut μ, &mut minus_τv, &mut μ_base, None, + &mut μ, &mut τv, &mut μ_base, //None, τ, ε, - config, ®, state, &mut stats + config, ®, &state, &mut stats ); // (Do not) merge spikes. - if state.iteration() % config.merge_every == 0 { + if config.merge_now(&state) { match config.merging { SpikeMergingMethod::None => { }, _ => if !warned_merging { @@ -423,33 +386,19 @@ // Update residual residual = calculate_residual(&μ, opA, b); - - // Update main tolerance for next iteration - let ε_prev = ε; - ε = tolerance.update(ε, state.iteration()); + + let iter = state.iteration(); stats.this_iters += 1; - // Give function value if needed + // Give statistics if needed state.if_verbose(|| { - // Plot if so requested - // plotter.plot_spikes( - // format!("iter {} end;", state.iteration()), &d, - // "start".to_string(), Some(&minus_τv), - // reg.target_bounds(τ, ε_prev), &μ_prev, - // ); - // Calculate mean inner iterations and reset relevant counters. - // Return the statistics - let res = IterInfo { - value : L2Squared.calculate_fit_op(&μ_prev, opA, b) + reg.apply(&μ_prev), - n_spikes : μ_prev.len(), - ε : ε_prev, - postprocessing: config.postprocessing.then(|| μ_prev.clone()), - .. stats - }; - stats = IterInfo::new(); - res - }) - }); + plotter.plot_spikes(iter, Option::<&S>::None, Some(&τv), &μ_prev); + full_stats(&μ_prev, ε, std::mem::replace(&mut stats, IterInfo::new())) + }); + + // Update main tolerance for next iteration + ε = tolerance.update(ε, iter); + } postprocess(μ_prev, config, L2Squared, opA, b) }
--- a/src/regularisation.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/regularisation.rs Tue Dec 31 09:25:45 2024 -0500 @@ -5,13 +5,14 @@ use numeric_literals::replace_float_literals; use serde::{Serialize, Deserialize}; use alg_tools::norms::Norm; -use alg_tools::linops::Apply; +use alg_tools::linops::Mapping; +use alg_tools::instance::Instance; use alg_tools::loc::Loc; use crate::types::*; use crate::measures::{ - DiscreteMeasure, + RNDM, DeltaMeasure, - Radon + Radon, }; use crate::fb::FBGenericConfig; #[allow(unused_imports)] // Used by documentation. @@ -21,7 +22,6 @@ use nalgebra::{DVector, DMatrix}; use alg_tools::nalgebra_support::ToNalgebraRealField; -use alg_tools::mapping::Mapping; use alg_tools::bisection_tree::{ BTFN, Bounds, @@ -56,12 +56,13 @@ } } -impl<'a, F : Float, const N : usize> Apply<&'a DiscreteMeasure<Loc<F, N>, F>> +impl<'a, F : Float, const N : usize> Mapping<RNDM<F, N>> for NonnegRadonRegTerm<F> { - type Output = F; + type Codomain = F; - fn apply(&self, μ : &'a DiscreteMeasure<Loc<F, N>, F>) -> F { - self.α() * μ.norm(Radon) + fn apply<I>(&self, μ : I) -> F + where I : Instance<RNDM<F, N>> { + self.α() * μ.eval(|x| x.norm(Radon)) } } @@ -81,12 +82,13 @@ } } -impl<'a, F : Float, const N : usize> Apply<&'a DiscreteMeasure<Loc<F, N>, F>> +impl<'a, F : Float, const N : usize> Mapping<RNDM<F, N>> for RadonRegTerm<F> { - type Output = F; + type Codomain = F; - fn apply(&self, μ : &'a DiscreteMeasure<Loc<F, N>, F>) -> F { - self.α() * μ.norm(Radon) + fn apply<I>(&self, μ : I) -> F + where I : Instance<RNDM<F, N>> { + self.α() * μ.eval(|x| x.norm(Radon)) } } @@ -99,11 +101,12 @@ NonnegRadon(F), } -impl<'a, F : Float, const N : usize> Apply<&'a DiscreteMeasure<Loc<F, N>, F>> +impl<'a, F : Float, const N : usize> Mapping<RNDM<F, N>> for Regularisation<F> { - type Output = F; - - fn apply(&self, μ : &'a DiscreteMeasure<Loc<F, N>, F>) -> F { + type Codomain = F; + + fn apply<I>(&self, μ : I) -> F + where I : Instance<RNDM<F, N>> { match *self { Self::Radon(α) => RadonRegTerm(α).apply(μ), Self::NonnegRadon(α) => NonnegRadonRegTerm(α).apply(μ), @@ -111,9 +114,9 @@ } } -/// Abstraction of regularisation terms for [`generic_pointsource_fb_reg`]. +/// Abstraction of regularisation terms. pub trait RegTerm<F : Float + ToNalgebraRealField, const N : usize> -: for<'a> Apply<&'a DiscreteMeasure<Loc<F, N>, F>, Output = F> { +: Mapping<RNDM<F, N>, Codomain = F> { /// Approximately solve the problem /// <div>$$ /// \min_{x ∈ ℝ^n} \frac{1}{2} x^⊤Ax - g^⊤ x + τ G(x) @@ -171,8 +174,7 @@ ) -> Option<(Loc<F, N>, F, bool)> where BT : BTSearch<F, N, Agg=Bounds<F>>, G : SupportGenerator<F, N, Id=BT::Data>, - G::SupportType : Mapping<Loc<F, N>,Codomain=F> - + LocalAnalysis<F, Bounds<F>, N> { + G::SupportType : Mapping<Loc<F, N>, Codomain=F> + LocalAnalysis<F, Bounds<F>, N> { self.find_tolerance_violation_slack(d, τ, ε, skip_by_rough_check, config, F::ZERO) } @@ -199,8 +201,7 @@ ) -> Option<(Loc<F, N>, F, bool)> where BT : BTSearch<F, N, Agg=Bounds<F>>, G : SupportGenerator<F, N, Id=BT::Data>, - G::SupportType : Mapping<Loc<F, N>,Codomain=F> - + LocalAnalysis<F, Bounds<F>, N>; + G::SupportType : Mapping<Loc<F, N>, Codomain=F> + LocalAnalysis<F, Bounds<F>, N>; /// Verify that `d` is in bounds `ε` for a merge candidate `μ` @@ -209,36 +210,34 @@ fn verify_merge_candidate<G, BT>( &self, d : &mut BTFN<F, G, BT, N>, - μ : &DiscreteMeasure<Loc<F, N>, F>, + μ : &RNDM<F, N>, τ : F, ε : F, config : &FBGenericConfig<F>, ) -> bool where BT : BTSearch<F, N, Agg=Bounds<F>>, G : SupportGenerator<F, N, Id=BT::Data>, - G::SupportType : Mapping<Loc<F, N>,Codomain=F> - + LocalAnalysis<F, Bounds<F>, N>; + G::SupportType : Mapping<Loc<F, N>, Codomain=F> + LocalAnalysis<F, Bounds<F>, N>; /// Verify that `d` is in bounds `ε` for a merge candidate `μ` /// /// This version is s used for Radon-norm squared proximal term in [`crate::radon_fb`]. - /// The [`DiscreteMeasure`]s `μ` and `radon_μ` are supposed to have same coordinates at - /// same agreeing indices. + /// The [measures][crate::measures::DiscreteMeasure] `μ` and `radon_μ` are supposed to have + /// same coordinates at same agreeing indices. /// /// `ε` is the current main tolerance and `τ` a scaling factor for the regulariser. fn verify_merge_candidate_radonsq<G, BT>( &self, d : &mut BTFN<F, G, BT, N>, - μ : &DiscreteMeasure<Loc<F, N>, F>, + μ : &RNDM<F, N>, τ : F, ε : F, config : &FBGenericConfig<F>, - radon_μ :&DiscreteMeasure<Loc<F, N>, F>, + radon_μ :&RNDM<F, N>, ) -> bool where BT : BTSearch<F, N, Agg=Bounds<F>>, G : SupportGenerator<F, N, Id=BT::Data>, - G::SupportType : Mapping<Loc<F, N>,Codomain=F> - + LocalAnalysis<F, Bounds<F>, N>; + G::SupportType : Mapping<Loc<F, N>, Codomain=F> + LocalAnalysis<F, Bounds<F>, N>; /// TODO: document this @@ -258,7 +257,7 @@ fn goodness<G, BT>( &self, d : &mut BTFN<F, G, BT, N>, - μ : &DiscreteMeasure<Loc<F, N>, F>, + μ : &RNDM<F, N>, y : &Loc<F, N>, z : &Loc<F, N>, τ : F, @@ -267,8 +266,7 @@ ) -> F where BT : BTSearch<F, N, Agg=Bounds<F>>, G : SupportGenerator<F, N, Id=BT::Data>, - G::SupportType : Mapping<Loc<F, N>,Codomain=F> - + LocalAnalysis<F, Bounds<F>, N>; + G::SupportType : Mapping<Loc<F, N>, Codomain=F> + LocalAnalysis<F, Bounds<F>, N>; /// Convert bound on the regulariser to a bond on the Radon norm fn radon_norm_bound(&self, b : F) -> F; @@ -323,69 +321,66 @@ ) -> Option<(Loc<F, N>, F, bool)> where BT : BTSearch<F, N, Agg=Bounds<F>>, G : SupportGenerator<F, N, Id=BT::Data>, - G::SupportType : Mapping<Loc<F, N>,Codomain=F> - + LocalAnalysis<F, Bounds<F>, N> { + G::SupportType : Mapping<Loc<F, N>, Codomain=F> + LocalAnalysis<F, Bounds<F>, N> { let τα = τ * self.α(); - let keep_below = τα + slack + ε; - let maximise_above = τα + slack + ε * config.insertion_cutoff_factor; + let keep_above = -τα - slack - ε; + let minimise_below = -τα - slack - ε * config.insertion_cutoff_factor; let refinement_tolerance = ε * config.refinement.tolerance_mult; // If preliminary check indicates that we are in bounds, and if it otherwise matches // the insertion strategy, skip insertion. - if skip_by_rough_check && d.bounds().upper() <= keep_below { + if skip_by_rough_check && d.bounds().lower() >= keep_above { None } else { - // If the rough check didn't indicate no insertion needed, find maximising point. - d.maximise_above(maximise_above, refinement_tolerance, config.refinement.max_steps) - .map(|(ξ, v_ξ)| (ξ, v_ξ, v_ξ <= keep_below)) + // If the rough check didn't indicate no insertion needed, find minimising point. + d.minimise_below(minimise_below, refinement_tolerance, config.refinement.max_steps) + .map(|(ξ, v_ξ)| (ξ, v_ξ, v_ξ >= keep_above)) } } fn verify_merge_candidate<G, BT>( &self, d : &mut BTFN<F, G, BT, N>, - μ : &DiscreteMeasure<Loc<F, N>, F>, + μ : &RNDM<F, N>, τ : F, ε : F, config : &FBGenericConfig<F>, ) -> bool where BT : BTSearch<F, N, Agg=Bounds<F>>, G : SupportGenerator<F, N, Id=BT::Data>, - G::SupportType : Mapping<Loc<F, N>,Codomain=F> - + LocalAnalysis<F, Bounds<F>, N> { + G::SupportType : Mapping<Loc<F, N>, Codomain=F> + LocalAnalysis<F, Bounds<F>, N> { let τα = τ * self.α(); let refinement_tolerance = ε * config.refinement.tolerance_mult; let merge_tolerance = config.merge_tolerance_mult * ε; - let keep_below = τα + merge_tolerance; - let keep_supp_above = τα - merge_tolerance; + let keep_above = -τα - merge_tolerance; + let keep_supp_below = -τα + merge_tolerance; let bnd = d.bounds(); return ( - bnd.lower() >= keep_supp_above + bnd.upper() <= keep_supp_below || μ.iter_spikes().all(|&DeltaMeasure{ α, ref x }| { - (α == 0.0) || d.apply(x) >= keep_supp_above + (α == 0.0) || d.apply(x) <= keep_supp_below }) ) && ( - bnd.upper() <= keep_below + bnd.lower() >= keep_above || - d.has_upper_bound(keep_below, refinement_tolerance, config.refinement.max_steps) + d.has_lower_bound(keep_above, refinement_tolerance, config.refinement.max_steps) ) } fn verify_merge_candidate_radonsq<G, BT>( &self, d : &mut BTFN<F, G, BT, N>, - μ : &DiscreteMeasure<Loc<F, N>, F>, + μ : &RNDM<F, N>, τ : F, ε : F, config : &FBGenericConfig<F>, - radon_μ :&DiscreteMeasure<Loc<F, N>, F>, + radon_μ :&RNDM<F, N>, ) -> bool where BT : BTSearch<F, N, Agg=Bounds<F>>, G : SupportGenerator<F, N, Id=BT::Data>, - G::SupportType : Mapping<Loc<F, N>,Codomain=F> - + LocalAnalysis<F, Bounds<F>, N> { + G::SupportType : Mapping<Loc<F, N>, Codomain=F> + LocalAnalysis<F, Bounds<F>, N> { let τα = τ * self.α(); let refinement_tolerance = ε * config.refinement.tolerance_mult; let merge_tolerance = config.merge_tolerance_mult * ε; @@ -395,7 +390,8 @@ return { μ.both_matching(radon_μ) .all(|(α, rα, x)| { - let v = d.apply(x); + let v = -d.apply(x); // TODO: observe ad hoc negation here, after minus_τv + // switch to τv. let (l1, u1) = match α.partial_cmp(&0.0).unwrap_or(Equal) { Greater => (τα, τα), _ => (F::NEG_INFINITY, τα), @@ -410,10 +406,10 @@ (l1 + l2 - merge_tolerance <= v) && (v <= u1 + u2 + merge_tolerance) }) } && { - let keep_below = τα + slack + merge_tolerance; - bnd.upper() <= keep_below + let keep_above = -τα - slack - merge_tolerance; + bnd.lower() <= keep_above || - d.has_upper_bound(keep_below, refinement_tolerance, config.refinement.max_steps) + d.has_lower_bound(keep_above, refinement_tolerance, config.refinement.max_steps) } } @@ -435,7 +431,7 @@ fn goodness<G, BT>( &self, d : &mut BTFN<F, G, BT, N>, - _μ : &DiscreteMeasure<Loc<F, N>, F>, + _μ : &RNDM<F, N>, y : &Loc<F, N>, z : &Loc<F, N>, τ : F, @@ -444,8 +440,7 @@ ) -> F where BT : BTSearch<F, N, Agg=Bounds<F>>, G : SupportGenerator<F, N, Id=BT::Data>, - G::SupportType : Mapping<Loc<F, N>,Codomain=F> - + LocalAnalysis<F, Bounds<F>, N> { + G::SupportType : Mapping<Loc<F, N>, Codomain=F> + LocalAnalysis<F, Bounds<F>, N> { let w = |x| 1.0.min((ε + d.apply(x))/(τ * self.α())); w(z) - w(y) } @@ -500,8 +495,7 @@ ) -> Option<(Loc<F, N>, F, bool)> where BT : BTSearch<F, N, Agg=Bounds<F>>, G : SupportGenerator<F, N, Id=BT::Data>, - G::SupportType : Mapping<Loc<F, N>,Codomain=F> - + LocalAnalysis<F, Bounds<F>, N> { + G::SupportType : Mapping<Loc<F, N>, Codomain=F> + LocalAnalysis<F, Bounds<F>, N> { let τα = τ * self.α(); let keep_below = τα + slack + ε; let keep_above = -(τα + slack) - ε; @@ -538,15 +532,14 @@ fn verify_merge_candidate<G, BT>( &self, d : &mut BTFN<F, G, BT, N>, - μ : &DiscreteMeasure<Loc<F, N>, F>, + μ : &RNDM<F, N>, τ : F, ε : F, config : &FBGenericConfig<F>, ) -> bool where BT : BTSearch<F, N, Agg=Bounds<F>>, G : SupportGenerator<F, N, Id=BT::Data>, - G::SupportType : Mapping<Loc<F, N>,Codomain=F> - + LocalAnalysis<F, Bounds<F>, N> { + G::SupportType : Mapping<Loc<F, N>,Codomain=F> + LocalAnalysis<F, Bounds<F>, N> { let τα = τ * self.α(); let refinement_tolerance = ε * config.refinement.tolerance_mult; let merge_tolerance = config.merge_tolerance_mult * ε; @@ -582,16 +575,15 @@ fn verify_merge_candidate_radonsq<G, BT>( &self, d : &mut BTFN<F, G, BT, N>, - μ : &DiscreteMeasure<Loc<F, N>, F>, + μ : &RNDM<F, N>, τ : F, ε : F, config : &FBGenericConfig<F>, - radon_μ : &DiscreteMeasure<Loc<F, N>, F>, + radon_μ : &RNDM<F, N>, ) -> bool where BT : BTSearch<F, N, Agg=Bounds<F>>, G : SupportGenerator<F, N, Id=BT::Data>, - G::SupportType : Mapping<Loc<F, N>,Codomain=F> - + LocalAnalysis<F, Bounds<F>, N> { + G::SupportType : Mapping<Loc<F, N>,Codomain=F> + LocalAnalysis<F, Bounds<F>, N> { let τα = τ * self.α(); let refinement_tolerance = ε * config.refinement.tolerance_mult; let merge_tolerance = config.merge_tolerance_mult * ε; @@ -647,7 +639,7 @@ fn goodness<G, BT>( &self, d : &mut BTFN<F, G, BT, N>, - _μ : &DiscreteMeasure<Loc<F, N>, F>, + _μ : &RNDM<F, N>, y : &Loc<F, N>, z : &Loc<F, N>, τ : F,
--- a/src/run.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/run.rs Tue Dec 31 09:25:45 2024 -0500 @@ -26,25 +26,46 @@ AlgIteratorOptions, Verbose, AlgIteratorFactory, + LoggingIteratorFactory, + TimingIteratorFactory, + BasicAlgIteratorFactory, }; use alg_tools::logger::Logger; -use alg_tools::error::DynError; +use alg_tools::error::{ + DynError, + DynResult, +}; use alg_tools::tabledump::TableDump; use alg_tools::sets::Cube; use alg_tools::mapping::{ RealMapping, - DifferentiableRealMapping + DifferentiableMapping, + DifferentiableRealMapping, + Instance }; use alg_tools::nalgebra_support::ToNalgebraRealField; use alg_tools::euclidean::Euclidean; -use alg_tools::lingrid::lingrid; +use alg_tools::lingrid::{lingrid, LinSpace}; use alg_tools::sets::SetOrd; +use alg_tools::linops::{RowOp, IdOp /*, ZeroOp*/}; +use alg_tools::discrete_gradient::{Grad, ForwardNeumann}; +use alg_tools::convex::Zero; +use alg_tools::maputil::map3; +use alg_tools::direct_product::Pair; use crate::kernels::*; use crate::types::*; use crate::measures::*; use crate::measures::merging::SpikeMerging; use crate::forward_model::*; +use crate::forward_model::sensor_grid::{ + SensorGrid, + SensorGridBT, + //SensorGridBTFN, + Sensor, + Spread, +}; + use crate::fb::{ FBConfig, FBGenericConfig, @@ -58,8 +79,17 @@ }; use crate::sliding_fb::{ SlidingFBConfig, + TransportConfig, pointsource_sliding_fb_reg }; +use crate::sliding_pdps::{ + SlidingPDPSConfig, + pointsource_sliding_pdps_pair +}; +use crate::forward_pdps::{ + ForwardPDPSConfig, + pointsource_forward_pdps_pair +}; use crate::pdps::{ PDPSConfig, pointsource_pdps_reg, @@ -68,9 +98,9 @@ FWConfig, FWVariant, pointsource_fw_reg, - WeightOptim, + //WeightOptim, }; -use crate::subproblem::InnerSettings; +//use crate::subproblem::InnerSettings; use crate::seminorms::*; use crate::plot::*; use crate::{AlgorithmOverrides, CommandLineArgs}; @@ -82,9 +112,11 @@ }; use crate::dataterm::{ L1, - L2Squared + L2Squared, }; -use alg_tools::norms::L2; +use alg_tools::norms::{L2, NormExponent}; +use alg_tools::operator_arithmetic::Weighted; +use anyhow::anyhow; /// Available algorithms and their configurations #[derive(Copy, Clone, Debug, Serialize, Deserialize)] @@ -96,6 +128,8 @@ RadonFB(RadonFBConfig<F>), RadonFISTA(RadonFBConfig<F>), SlidingFB(SlidingFBConfig<F>), + ForwardPDPS(ForwardPDPSConfig<F>), + SlidingPDPS(SlidingPDPSConfig<F>), } fn unpack_tolerance<F : Float>(v : &Vec<F>) -> Tolerance<F> { @@ -119,6 +153,15 @@ .. g } }; + let override_transport = |g : TransportConfig<F>| { + TransportConfig { + θ0 : cli.theta0.unwrap_or(g.θ0), + tolerance_ω: cli.transport_tolerance_omega.unwrap_or(g.tolerance_ω), + tolerance_dv: cli.transport_tolerance_dv.unwrap_or(g.tolerance_dv), + adaptation: cli.transport_adaptation.unwrap_or(g.adaptation), + .. g + } + }; use AlgorithmConfig::*; match self { @@ -156,17 +199,32 @@ }), SlidingFB(sfb) => SlidingFB(SlidingFBConfig { τ0 : cli.tau0.unwrap_or(sfb.τ0), - θ0 : cli.theta0.unwrap_or(sfb.θ0), - transport_tolerance_ω: cli.transport_tolerance_omega.unwrap_or(sfb.transport_tolerance_ω), - transport_tolerance_dv: cli.transport_tolerance_dv.unwrap_or(sfb.transport_tolerance_dv), + transport : override_transport(sfb.transport), insertion : override_fb_generic(sfb.insertion), .. sfb }), + SlidingPDPS(spdps) => SlidingPDPS(SlidingPDPSConfig { + τ0 : cli.tau0.unwrap_or(spdps.τ0), + σp0 : cli.sigmap0.unwrap_or(spdps.σp0), + σd0 : cli.sigma0.unwrap_or(spdps.σd0), + //acceleration : cli.acceleration.unwrap_or(pdps.acceleration), + transport : override_transport(spdps.transport), + insertion : override_fb_generic(spdps.insertion), + .. spdps + }), + ForwardPDPS(fpdps) => ForwardPDPS(ForwardPDPSConfig { + τ0 : cli.tau0.unwrap_or(fpdps.τ0), + σp0 : cli.sigmap0.unwrap_or(fpdps.σp0), + σd0 : cli.sigma0.unwrap_or(fpdps.σd0), + //acceleration : cli.acceleration.unwrap_or(pdps.acceleration), + insertion : override_fb_generic(fpdps.insertion), + .. fpdps + }), } } } -/// Helper struct for tagging and [`AlgorithmConfig`] or [`Experiment`] with a name. +/// Helper struct for tagging and [`AlgorithmConfig`] or [`ExperimentV2`] with a name. #[derive(Clone, Debug, Serialize, Deserialize)] pub struct Named<Data> { pub name : String, @@ -198,9 +256,15 @@ /// The RadonFISTA inertial forward-backward method #[clap(name = "radon_fista")] RadonFISTA, - /// The Sliding FB method + /// The sliding FB method #[clap(name = "sliding_fb", alias = "sfb")] SlidingFB, + /// The sliding PDPS method + #[clap(name = "sliding_pdps", alias = "spdps")] + SlidingPDPS, + /// The PDPS method with a forward step for the smooth function + #[clap(name = "forward_pdps", alias = "fpdps")] + ForwardPDPS, } impl DefaultAlgorithm { @@ -219,6 +283,8 @@ RadonFB => AlgorithmConfig::RadonFB(Default::default()), RadonFISTA => AlgorithmConfig::RadonFISTA(Default::default()), SlidingFB => AlgorithmConfig::SlidingFB(Default::default()), + SlidingPDPS => AlgorithmConfig::SlidingPDPS(Default::default()), + ForwardPDPS => AlgorithmConfig::ForwardPDPS(Default::default()), } } @@ -278,7 +344,8 @@ iter : usize, cpu_time : f64, value : F, - post_value : F, + relative_value : F, + //post_value : F, n_spikes : usize, inner_iters : usize, merged : usize, @@ -355,7 +422,7 @@ /// Kernel $ρ$ of $𝒟$. pub kernel : K, /// True point sources - pub μ_hat : DiscreteMeasure<Loc<F, N>, F>, + pub μ_hat : RNDM<F, N>, /// Regularisation term and parameter pub regularisation : Regularisation<F>, /// For plotting : how wide should the kernels be plotted @@ -367,6 +434,24 @@ pub algorithm_defaults : HashMap<DefaultAlgorithm, AlgorithmConfig<F>>, } +#[derive(Debug, Clone, Serialize)] +pub struct ExperimentBiased<F, NoiseDistr, S, K, P, B, const N : usize> +where F : Float, + [usize; N] : Serialize, + NoiseDistr : Distribution<F>, + S : Sensor<F, N>, + P : Spread<F, N>, + K : SimpleConvolutionKernel<F, N>, + B : Mapping<Loc<F, N>, Codomain = F> + Serialize + std::fmt::Debug, +{ + /// Basic setup + pub base : ExperimentV2<F, NoiseDistr, S, K, P, N>, + /// Weight of TV term + pub λ : F, + /// Bias function + pub bias : B, +} + /// Trait for runnable experiments pub trait RunnableExperiment<F : ClapFloat> { /// Run all algorithms provided, or default algorithms if none provided, on the experiment. @@ -374,51 +459,180 @@ algs : Option<Vec<Named<AlgorithmConfig<F>>>>) -> DynError; /// Return algorithm default config - fn algorithm_defaults(&self, alg : DefaultAlgorithm, cli : &AlgorithmOverrides<F>) - -> Named<AlgorithmConfig<F>>; + fn algorithm_defaults(&self, alg : DefaultAlgorithm) -> Option<AlgorithmConfig<F>>; +} + +/// Helper function to print experiment start message and save setup. +/// Returns saving prefix. +fn start_experiment<E, S>( + experiment : &Named<E>, + cli : &CommandLineArgs, + stats : S, +) -> DynResult<String> +where + E : Serialize + std::fmt::Debug, + S : Serialize, +{ + let Named { name : experiment_name, data } = experiment; + + println!("{}\n{}", + format!("Performing experiment {}…", experiment_name).cyan(), + format!("{:?}", data).bright_black()); + + // Set up output directory + let prefix = format!("{}/{}/", cli.outdir, experiment_name); + + // Save experiment configuration and statistics + let mkname_e = |t| format!("{prefix}{t}.json", prefix = prefix, t = t); + std::fs::create_dir_all(&prefix)?; + write_json(mkname_e("experiment"), experiment)?; + write_json(mkname_e("config"), cli)?; + write_json(mkname_e("stats"), &stats)?; + + Ok(prefix) +} + +/// Error codes for running an algorithm on an experiment. +enum RunError { + /// Algorithm not implemented for this experiment + NotImplemented, } -// *** macro boilerplate *** -macro_rules! impl_experiment { -($type:ident, $reg_field:ident, $reg_convert:path) => { -// *** macro *** +use RunError::*; + +type DoRunAllIt<'a, F, const N : usize> = LoggingIteratorFactory< + 'a, + Timed<IterInfo<F, N>>, + TimingIteratorFactory<BasicAlgIteratorFactory<IterInfo<F, N>>> +>; + +/// Helper function to run all algorithms on an experiment. +fn do_runall<F : Float, Z, const N : usize>( + experiment_name : &String, + prefix : &String, + cli : &CommandLineArgs, + algorithms : Vec<Named<AlgorithmConfig<F>>>, + plotgrid : LinSpace<Loc<F, N>, [usize; N]>, + mut save_extra : impl FnMut(String, Z) -> DynError, + mut do_alg : impl FnMut( + &AlgorithmConfig<F>, + DoRunAllIt<F, N>, + SeqPlotter<F, N>, + String, + ) -> Result<(RNDM<F, N>, Z), RunError>, +) -> DynError +where + PlotLookup : Plotting<N>, +{ + let mut logs = Vec::new(); + + let iterator_options = AlgIteratorOptions{ + max_iter : cli.max_iter, + verbose_iter : cli.verbose_iter + .map_or(Verbose::Logarithmic(10), + |n| Verbose::Every(n)), + quiet : cli.quiet, + }; + + // Run the algorithm(s) + for named @ Named { name : alg_name, data : alg } in algorithms.iter() { + let this_prefix = format!("{}{}/", prefix, alg_name); + + // Create Logger and IteratorFactory + let mut logger = Logger::new(); + let iterator = iterator_options.instantiate() + .timed() + .into_log(&mut logger); + + let running = if !cli.quiet { + format!("{}\n{}\n{}\n", + format!("Running {} on experiment {}…", alg_name, experiment_name).cyan(), + format!("{:?}", iterator_options).bright_black(), + format!("{:?}", alg).bright_black()) + } else { + "".to_string() + }; + // + // The following is for postprocessing, which has been disabled anyway. + // + // let reg : Box<dyn WeightOptim<_, _, _, N>> = match regularisation { + // Regularisation::Radon(α) => Box::new(RadonRegTerm(α)), + // Regularisation::NonnegRadon(α) => Box::new(NonnegRadonRegTerm(α)), + // }; + //let findim_data = reg.prepare_optimise_weights(&opA, &b); + //let inner_config : InnerSettings<F> = Default::default(); + //let inner_it = inner_config.iterator_options; + + // Create plotter and directory if needed. + let plot_count = if cli.plot >= PlotLevel::Iter { 2000 } else { 0 }; + let plotter = SeqPlotter::new(this_prefix, plot_count, plotgrid.clone()); + + let start = Instant::now(); + let start_cpu = ProcessTime::now(); + + let (μ, z) = match do_alg(alg, iterator, plotter, running) { + Ok(μ) => μ, + Err(RunError::NotImplemented) => { + let msg = format!("Algorithm “{alg_name}” not implemented for {experiment_name}. \ + Skipping.").red(); + eprintln!("{}", msg); + continue + } + }; + + let elapsed = start.elapsed().as_secs_f64(); + let cpu_time = start_cpu.elapsed().as_secs_f64(); + + println!("{}", format!("Elapsed {elapsed}s (CPU time {cpu_time}s)… ").yellow()); + + // Save results + println!("{}", "Saving results …".green()); + + let mkname = |t| format!("{prefix}{alg_name}_{t}"); + + write_json(mkname("config.json"), &named)?; + write_json(mkname("stats.json"), &AlgorithmStats { cpu_time, elapsed })?; + μ.write_csv(mkname("reco.txt"))?; + save_extra(mkname(""), z)?; + //logger.write_csv(mkname("log.txt"))?; + logs.push((mkname("log.txt"), logger)); + } + + save_logs(logs) +} + +#[replace_float_literals(F::cast_from(literal))] impl<F, NoiseDistr, S, K, P, const N : usize> RunnableExperiment<F> for -Named<$type<F, NoiseDistr, S, K, P, N>> -where F : ClapFloat + nalgebra::RealField + ToNalgebraRealField<MixedType=F>, - [usize; N] : Serialize, - S : Sensor<F, N> + Copy + Serialize + std::fmt::Debug, - P : Spread<F, N> + Copy + Serialize + std::fmt::Debug, - Convolution<S, P>: Spread<F, N> + Bounded<F> + LocalAnalysis<F, Bounds<F>, N> + Copy - // TODO: shold not have differentiability as a requirement, but - // decide availability of sliding based on it. - //+ for<'b> Differentiable<&'b Loc<F, N>, Output = Loc<F, N>>, - // TODO: very weird that rust only compiles with Differentiable - // instead of the above one on references, which is required by - // poitsource_sliding_fb_reg. - + DifferentiableRealMapping<F, N> - + Lipschitz<L2, FloatType=F>, - // <DefaultSG<F, S, P, N> as ForwardModel<Loc<F, N>, F>::PreadjointCodomain : for<'b> Differentiable<&'b Loc<F, N>, Output = Loc<F, N>>, - AutoConvolution<P> : BoundedBy<F, K>, - K : SimpleConvolutionKernel<F, N> - + LocalAnalysis<F, Bounds<F>, N> - + Copy + Serialize + std::fmt::Debug, - Cube<F, N>: P2Minimise<Loc<F, N>, F> + SetOrd, - PlotLookup : Plotting<N>, - DefaultBT<F, N> : SensorGridBT<F, S, P, N, Depth=DynamicDepth> + BTSearch<F, N>, - BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, - DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F>, - NoiseDistr : Distribution<F> + Serialize + std::fmt::Debug { +Named<ExperimentV2<F, NoiseDistr, S, K, P, N>> +where + F : ClapFloat + nalgebra::RealField + ToNalgebraRealField<MixedType=F>, + [usize; N] : Serialize, + S : Sensor<F, N> + Copy + Serialize + std::fmt::Debug, + P : Spread<F, N> + Copy + Serialize + std::fmt::Debug, + Convolution<S, P>: Spread<F, N> + Bounded<F> + LocalAnalysis<F, Bounds<F>, N> + Copy + // TODO: shold not have differentiability as a requirement, but + // decide availability of sliding based on it. + //+ for<'b> Differentiable<&'b Loc<F, N>, Output = Loc<F, N>>, + // TODO: very weird that rust only compiles with Differentiable + // instead of the above one on references, which is required by + // poitsource_sliding_fb_reg. + + DifferentiableRealMapping<F, N> + + Lipschitz<L2, FloatType=F>, + for<'b> <Convolution<S, P> as DifferentiableMapping<Loc<F,N>>>::Differential<'b> : Lipschitz<L2, FloatType=F>, // TODO: should not be required generally, only for sliding_fb. + AutoConvolution<P> : BoundedBy<F, K>, + K : SimpleConvolutionKernel<F, N> + + LocalAnalysis<F, Bounds<F>, N> + + Copy + Serialize + std::fmt::Debug, + Cube<F, N>: P2Minimise<Loc<F, N>, F> + SetOrd, + PlotLookup : Plotting<N>, + DefaultBT<F, N> : SensorGridBT<F, S, P, N, Depth=DynamicDepth> + BTSearch<F, N>, + BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, + RNDM<F, N> : SpikeMerging<F>, + NoiseDistr : Distribution<F> + Serialize + std::fmt::Debug +{ - fn algorithm_defaults(&self, alg : DefaultAlgorithm, cli : &AlgorithmOverrides<F>) - -> Named<AlgorithmConfig<F>> { - alg.to_named( - self.data - .algorithm_defaults - .get(&alg) - .map_or_else(|| alg.default_config(), - |config| config.clone()) - .cli_override(cli) - ) + fn algorithm_defaults(&self, alg : DefaultAlgorithm) -> Option<AlgorithmConfig<F>> { + self.data.algorithm_defaults.get(&alg).cloned() } fn runall(&self, cli : &CommandLineArgs, @@ -426,30 +640,15 @@ // Get experiment configuration let &Named { name : ref experiment_name, - data : $type { + data : ExperimentV2 { domain, sensor_count, ref noise_distr, sensor, spread, kernel, - ref μ_hat, /*regularisation,*/ kernel_plot_width, dataterm, noise_seed, + ref μ_hat, regularisation, kernel_plot_width, dataterm, noise_seed, .. } } = self; - let regularisation = $reg_convert(self.data.$reg_field); - - println!("{}\n{}", - format!("Performing experiment {}…", experiment_name).cyan(), - format!("{:?}", &self.data).bright_black()); - - // Set up output directory - let prefix = format!("{}/{}/", cli.outdir, self.name); // Set up algorithms - let iterator_options = AlgIteratorOptions{ - max_iter : cli.max_iter, - verbose_iter : cli.verbose_iter - .map_or(Verbose::Logarithmic(10), - |n| Verbose::Every(n)), - quiet : cli.quiet, - }; - let algorithms = match (algs, self.data.dataterm) { + let algorithms = match (algs, dataterm) { (Some(algs), _) => algs, (None, DataTerm::L2Squared) => vec![DefaultAlgorithm::FB.get_named()], (None, DataTerm::L1) => vec![DefaultAlgorithm::PDPS.get_named()], @@ -464,281 +663,404 @@ let mut rng = StdRng::seed_from_u64(noise_seed); // Generate the data and calculate SSNR statistic - let b_hat = opA.apply(μ_hat); + let b_hat : DVector<_> = opA.apply(μ_hat); let noise = DVector::from_distribution(b_hat.len(), &noise_distr, &mut rng); let b = &b_hat + &noise; // Need to wrap calc_ssnr into a function to hide ultra-lame nalgebra::RealField // overloading log10 and conflicting with standard NumTraits one. let stats = ExperimentStats::new(&b, &noise); - // Save experiment configuration and statistics - let mkname_e = |t| format!("{prefix}{t}.json", prefix = prefix, t = t); - std::fs::create_dir_all(&prefix)?; - write_json(mkname_e("experiment"), self)?; - write_json(mkname_e("config"), cli)?; - write_json(mkname_e("stats"), &stats)?; + let prefix = start_experiment(&self, cli, stats)?; plotall(cli, &prefix, &domain, &sensor, &kernel, &spread, &μ_hat, &op𝒟, &opA, &b_hat, &b, kernel_plot_width)?; - // Run the algorithm(s) - for named @ Named { name : alg_name, data : alg } in algorithms.iter() { - let this_prefix = format!("{}{}/", prefix, alg_name); + let plotgrid = lingrid(&domain, &[if N==1 { 1000 } else { 100 }; N]); + + let save_extra = |_, ()| Ok(()); - let running = || if !cli.quiet { - println!("{}\n{}\n{}", - format!("Running {} on experiment {}…", alg_name, experiment_name).cyan(), - format!("{:?}", iterator_options).bright_black(), - format!("{:?}", alg).bright_black()); - }; - let not_implemented = || { - let msg = format!("Algorithm “{alg_name}” not implemented for \ - dataterm {dataterm:?} and regularisation {regularisation:?}. \ - Skipping.").red(); - eprintln!("{}", msg); - }; - // Create Logger and IteratorFactory - let mut logger = Logger::new(); - let reg : Box<dyn WeightOptim<_, _, _, N>> = match regularisation { - Regularisation::Radon(α) => Box::new(RadonRegTerm(α)), - Regularisation::NonnegRadon(α) => Box::new(NonnegRadonRegTerm(α)), - }; - let findim_data = reg.prepare_optimise_weights(&opA, &b); - let inner_config : InnerSettings<F> = Default::default(); - let inner_it = inner_config.iterator_options; - let logmap = |iter, Timed { cpu_time, data }| { - let IterInfo { - value, - n_spikes, - inner_iters, - merged, - pruned, - postprocessing, - this_iters, - .. - } = data; - let post_value = match (postprocessing, dataterm) { - (Some(mut μ), DataTerm::L2Squared) => { - // Comparison postprocessing is only implemented for the case handled - // by the FW variants. - reg.optimise_weights( - &mut μ, &opA, &b, &findim_data, &inner_config, - inner_it - ); - dataterm.value_at_residual(opA.apply(&μ) - &b) - + regularisation.apply(&μ) - }, - _ => value, - }; - CSVLog { - iter, - value, - post_value, - n_spikes, - cpu_time : cpu_time.as_secs_f64(), - inner_iters, - merged, - pruned, - this_iters - } - }; - let iterator = iterator_options.instantiate() - .timed() - .mapped(logmap) - .into_log(&mut logger); - let plotgrid = lingrid(&domain, &[if N==1 { 1000 } else { 100 }; N]); - - // Create plotter and directory if needed. - let plot_count = if cli.plot >= PlotLevel::Iter { 2000 } else { 0 }; - let plotter = SeqPlotter::new(this_prefix, plot_count, plotgrid); - - // Run the algorithm - let start = Instant::now(); - let start_cpu = ProcessTime::now(); + do_runall(experiment_name, &prefix, cli, algorithms, plotgrid, save_extra, + |alg, iterator, plotter, running| + { let μ = match alg { AlgorithmConfig::FB(ref algconfig) => { match (regularisation, dataterm) { - (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => { - running(); + (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); pointsource_fb_reg( &opA, &b, NonnegRadonRegTerm(α), &op𝒟, algconfig, iterator, plotter ) - }, - (Regularisation::Radon(α), DataTerm::L2Squared) => { - running(); + }), + (Regularisation::Radon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); pointsource_fb_reg( &opA, &b, RadonRegTerm(α), &op𝒟, algconfig, iterator, plotter ) - }, - _ => { - not_implemented(); - continue - } + }), + _ => Err(NotImplemented) } }, AlgorithmConfig::FISTA(ref algconfig) => { match (regularisation, dataterm) { - (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => { - running(); + (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); pointsource_fista_reg( &opA, &b, NonnegRadonRegTerm(α), &op𝒟, algconfig, iterator, plotter ) - }, - (Regularisation::Radon(α), DataTerm::L2Squared) => { - running(); + }), + (Regularisation::Radon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); pointsource_fista_reg( &opA, &b, RadonRegTerm(α), &op𝒟, algconfig, iterator, plotter ) - }, - _ => { - not_implemented(); - continue - } + }), + _ => Err(NotImplemented), } }, AlgorithmConfig::RadonFB(ref algconfig) => { match (regularisation, dataterm) { - (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => { - running(); + (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); pointsource_radon_fb_reg( &opA, &b, NonnegRadonRegTerm(α), algconfig, iterator, plotter ) - }, - (Regularisation::Radon(α), DataTerm::L2Squared) => { - running(); + }), + (Regularisation::Radon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); pointsource_radon_fb_reg( &opA, &b, RadonRegTerm(α), algconfig, iterator, plotter ) - }, - _ => { - not_implemented(); - continue - } + }), + _ => Err(NotImplemented), } }, AlgorithmConfig::RadonFISTA(ref algconfig) => { match (regularisation, dataterm) { - (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => { - running(); + (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); pointsource_radon_fista_reg( &opA, &b, NonnegRadonRegTerm(α), algconfig, iterator, plotter ) - }, - (Regularisation::Radon(α), DataTerm::L2Squared) => { - running(); + }), + (Regularisation::Radon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); pointsource_radon_fista_reg( &opA, &b, RadonRegTerm(α), algconfig, iterator, plotter ) - }, - _ => { - not_implemented(); - continue - } + }), + _ => Err(NotImplemented), } }, AlgorithmConfig::SlidingFB(ref algconfig) => { match (regularisation, dataterm) { - (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => { - running(); + (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); pointsource_sliding_fb_reg( &opA, &b, NonnegRadonRegTerm(α), &op𝒟, algconfig, iterator, plotter ) - }, - (Regularisation::Radon(α), DataTerm::L2Squared) => { - running(); + }), + (Regularisation::Radon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); pointsource_sliding_fb_reg( &opA, &b, RadonRegTerm(α), &op𝒟, algconfig, iterator, plotter ) - }, - _ => { - not_implemented(); - continue - } + }), + _ => Err(NotImplemented), } }, AlgorithmConfig::PDPS(ref algconfig) => { - running(); + print!("{running}"); match (regularisation, dataterm) { - (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => { + (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => Ok({ pointsource_pdps_reg( &opA, &b, NonnegRadonRegTerm(α), &op𝒟, algconfig, iterator, plotter, L2Squared ) - }, - (Regularisation::Radon(α),DataTerm::L2Squared) => { + }), + (Regularisation::Radon(α),DataTerm::L2Squared) => Ok({ pointsource_pdps_reg( &opA, &b, RadonRegTerm(α), &op𝒟, algconfig, iterator, plotter, L2Squared ) - }, - (Regularisation::NonnegRadon(α), DataTerm::L1) => { + }), + (Regularisation::NonnegRadon(α), DataTerm::L1) => Ok({ pointsource_pdps_reg( &opA, &b, NonnegRadonRegTerm(α), &op𝒟, algconfig, iterator, plotter, L1 ) - }, - (Regularisation::Radon(α), DataTerm::L1) => { + }), + (Regularisation::Radon(α), DataTerm::L1) => Ok({ pointsource_pdps_reg( &opA, &b, RadonRegTerm(α), &op𝒟, algconfig, iterator, plotter, L1 ) - }, + }), } }, AlgorithmConfig::FW(ref algconfig) => { match (regularisation, dataterm) { - (Regularisation::Radon(α), DataTerm::L2Squared) => { - running(); + (Regularisation::Radon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); pointsource_fw_reg(&opA, &b, RadonRegTerm(α), algconfig, iterator, plotter) - }, - (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => { - running(); + }), + (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); pointsource_fw_reg(&opA, &b, NonnegRadonRegTerm(α), algconfig, iterator, plotter) - }, - _ => { - not_implemented(); - continue - } + }), + _ => Err(NotImplemented), } - } - }; - - let elapsed = start.elapsed().as_secs_f64(); - let cpu_time = start_cpu.elapsed().as_secs_f64(); - - println!("{}", format!("Elapsed {elapsed}s (CPU time {cpu_time}s)… ").yellow()); - - // Save results - println!("{}", "Saving results…".green()); - - let mkname = |t| format!("{prefix}{alg_name}_{t}"); - - write_json(mkname("config.json"), &named)?; - write_json(mkname("stats.json"), &AlgorithmStats { cpu_time, elapsed })?; - μ.write_csv(mkname("reco.txt"))?; - logger.write_csv(mkname("log.txt"))?; - } - - Ok(()) + }, + _ => Err(NotImplemented), + }?; + Ok((μ, ())) + }) } } -// *** macro end boiler plate *** -}} -// *** actual code *** + + +#[replace_float_literals(F::cast_from(literal))] +impl<F, NoiseDistr, S, K, P, B, const N : usize> RunnableExperiment<F> for +Named<ExperimentBiased<F, NoiseDistr, S, K, P, B, N>> +where + F : ClapFloat + nalgebra::RealField + ToNalgebraRealField<MixedType=F>, + [usize; N] : Serialize, + S : Sensor<F, N> + Copy + Serialize + std::fmt::Debug, + P : Spread<F, N> + Copy + Serialize + std::fmt::Debug, + Convolution<S, P>: Spread<F, N> + Bounded<F> + LocalAnalysis<F, Bounds<F>, N> + Copy + // TODO: shold not have differentiability as a requirement, but + // decide availability of sliding based on it. + //+ for<'b> Differentiable<&'b Loc<F, N>, Output = Loc<F, N>>, + // TODO: very weird that rust only compiles with Differentiable + // instead of the above one on references, which is required by + // poitsource_sliding_fb_reg. + + DifferentiableRealMapping<F, N> + + Lipschitz<L2, FloatType=F>, + for<'b> <Convolution<S, P> as DifferentiableMapping<Loc<F,N>>>::Differential<'b> : Lipschitz<L2, FloatType=F>, // TODO: should not be required generally, only for sliding_fb. + AutoConvolution<P> : BoundedBy<F, K>, + K : SimpleConvolutionKernel<F, N> + + LocalAnalysis<F, Bounds<F>, N> + + Copy + Serialize + std::fmt::Debug, + Cube<F, N>: P2Minimise<Loc<F, N>, F> + SetOrd, + PlotLookup : Plotting<N>, + DefaultBT<F, N> : SensorGridBT<F, S, P, N, Depth=DynamicDepth> + BTSearch<F, N>, + BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, + RNDM<F, N> : SpikeMerging<F>, + NoiseDistr : Distribution<F> + Serialize + std::fmt::Debug, + B : Mapping<Loc<F, N>, Codomain = F> + Serialize + std::fmt::Debug, +{ + + fn algorithm_defaults(&self, alg : DefaultAlgorithm) -> Option<AlgorithmConfig<F>> { + self.data.base.algorithm_defaults.get(&alg).cloned() + } + + fn runall(&self, cli : &CommandLineArgs, + algs : Option<Vec<Named<AlgorithmConfig<F>>>>) -> DynError { + // Get experiment configuration + let &Named { + name : ref experiment_name, + data : ExperimentBiased { + λ, + ref bias, + base : ExperimentV2 { + domain, sensor_count, ref noise_distr, sensor, spread, kernel, + ref μ_hat, regularisation, kernel_plot_width, dataterm, noise_seed, + .. + } + } + } = self; + + // Set up algorithms + let algorithms = match (algs, dataterm) { + (Some(algs), _) => algs, + _ => vec![DefaultAlgorithm::SlidingPDPS.get_named()], + }; + + // Set up operators + let depth = DynamicDepth(8); + let opA = DefaultSG::new(domain, sensor_count, sensor, spread, depth); + let op𝒟 = DefaultSeminormOp::new(depth, domain, kernel); + let opAext = RowOp(opA.clone(), IdOp::new()); + let fnR = Zero::new(); + let h = map3(domain.span_start(), domain.span_end(), sensor_count, + |a, b, n| (b-a)/F::cast_from(n)) + .into_iter() + .reduce(NumTraitsFloat::max) + .unwrap(); + let z = DVector::zeros(sensor_count.iter().product()); + let opKz = Grad::new_for(&z, h, sensor_count, ForwardNeumann).unwrap(); + let y = opKz.apply(&z); + let fnH = Weighted{ base_fn : L1.as_mapping(), weight : λ}; // TODO: L_{2,1} + // let zero_y = y.clone(); + // let zeroBTFN = opA.preadjoint().apply(&zero_y); + // let opKμ = ZeroOp::new(&zero_y, zeroBTFN); + + // Set up random number generator. + let mut rng = StdRng::seed_from_u64(noise_seed); + + // Generate the data and calculate SSNR statistic + let bias_vec = DVector::from_vec(opA.grid() + .into_iter() + .map(|v| bias.apply(v)) + .collect::<Vec<F>>()); + let b_hat : DVector<_> = opA.apply(μ_hat) + &bias_vec; + let noise = DVector::from_distribution(b_hat.len(), &noise_distr, &mut rng); + let b = &b_hat + &noise; + // Need to wrap calc_ssnr into a function to hide ultra-lame nalgebra::RealField + // overloading log10 and conflicting with standard NumTraits one. + let stats = ExperimentStats::new(&b, &noise); + + let prefix = start_experiment(&self, cli, stats)?; + + plotall(cli, &prefix, &domain, &sensor, &kernel, &spread, + &μ_hat, &op𝒟, &opA, &b_hat, &b, kernel_plot_width)?; + + opA.write_observable(&bias_vec, format!("{prefix}bias"))?; + + let plotgrid = lingrid(&domain, &[if N==1 { 1000 } else { 100 }; N]); + + let save_extra = |prefix, z| opA.write_observable(&z, format!("{prefix}z")); -impl_experiment!(ExperimentV2, regularisation, std::convert::identity); + // Run the algorithms + do_runall(experiment_name, &prefix, cli, algorithms, plotgrid, save_extra, + |alg, iterator, plotter, running| + { + let Pair(μ, z) = match alg { + AlgorithmConfig::ForwardPDPS(ref algconfig) => { + match (regularisation, dataterm) { + (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); + pointsource_forward_pdps_pair( + &opAext, &b, NonnegRadonRegTerm(α), &op𝒟, algconfig, + iterator, plotter, + /* opKμ, */ &opKz, &fnR, &fnH, z.clone(), y.clone(), + ) + }), + (Regularisation::Radon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); + pointsource_forward_pdps_pair( + &opAext, &b, RadonRegTerm(α), &op𝒟, algconfig, + iterator, plotter, + /* opKμ, */ &opKz, &fnR, &fnH, z.clone(), y.clone(), + ) + }), + _ => Err(NotImplemented) + } + }, + AlgorithmConfig::SlidingPDPS(ref algconfig) => { + match (regularisation, dataterm) { + (Regularisation::NonnegRadon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); + pointsource_sliding_pdps_pair( + &opAext, &b, NonnegRadonRegTerm(α), &op𝒟, algconfig, + iterator, plotter, + /* opKμ, */ &opKz, &fnR, &fnH, z.clone(), y.clone(), + ) + }), + (Regularisation::Radon(α), DataTerm::L2Squared) => Ok({ + print!("{running}"); + pointsource_sliding_pdps_pair( + &opAext, &b, RadonRegTerm(α), &op𝒟, algconfig, + iterator, plotter, + /* opKμ, */ &opKz, &fnR, &fnH, z.clone(), y.clone(), + ) + }), + _ => Err(NotImplemented) + } + }, + _ => Err(NotImplemented) + }?; + Ok((μ, z)) + }) + } +} + + +/// Calculative minimum and maximum values of all the `logs`, and save them into +/// corresponding file names given as the first elements of the tuples in the vectors. +fn save_logs<F : Float, const N : usize>( + logs : Vec<(String, Logger<Timed<IterInfo<F, N>>>)> +) -> DynError { + // Process logs for relative values + println!("{}", "Processing logs…"); + + + // Find minimum value and initial value within a single log + let proc_single_log = |log : &Logger<Timed<IterInfo<F, N>>>| { + let d = log.data(); + let mi = d.iter() + .map(|i| i.data.value) + .reduce(NumTraitsFloat::min); + d.first() + .map(|i| i.data.value) + .zip(mi) + }; + + // Find minimum and maximum value over all logs + let (v_ini, v_min) = logs.iter() + .filter_map(|&(_, ref log)| proc_single_log(log)) + .reduce(|(i1, m1), (i2, m2)| (i1.max(i2), m1.min(m2))) + .ok_or(anyhow!("No algorithms found"))?; + + let logmap = |Timed { cpu_time, iter, data }| { + let IterInfo { + value, + n_spikes, + inner_iters, + merged, + pruned, + //postprocessing, + this_iters, + .. + } = data; + // let post_value = match (postprocessing, dataterm) { + // (Some(mut μ), DataTerm::L2Squared) => { + // // Comparison postprocessing is only implemented for the case handled + // // by the FW variants. + // reg.optimise_weights( + // &mut μ, &opA, &b, &findim_data, &inner_config, + // inner_it + // ); + // dataterm.value_at_residual(opA.apply(&μ) - &b) + // + regularisation.apply(&μ) + // }, + // _ => value, + // }; + let relative_value = (value - v_min)/(v_ini - v_min); + CSVLog { + iter, + value, + relative_value, + //post_value, + n_spikes, + cpu_time : cpu_time.as_secs_f64(), + inner_iters, + merged, + pruned, + this_iters + } + }; + + println!("{}", "Saving logs …".green()); + + for (name, logger) in logs { + logger.map(logmap).write_csv(name)?; + } + + Ok(()) +} + /// Plot experiment setup #[replace_float_literals(F::cast_from(literal))] @@ -749,7 +1071,7 @@ sensor : &Sensor, kernel : &Kernel, spread : &Spread, - μ_hat : &DiscreteMeasure<Loc<F, N>, F>, + μ_hat : &RNDM<F, N>, op𝒟 : &𝒟, opA : &A, b_hat : &A::Observable, @@ -761,10 +1083,10 @@ Spread : RealMapping<F, N> + Support<F, N> + Clone, Kernel : RealMapping<F, N> + Support<F, N>, Convolution<Sensor, Spread> : DifferentiableRealMapping<F, N> + Support<F, N>, - //Differential<Loc<F, N>, Convolution<Sensor, Spread>> : RealVectorField<F, N, N>, 𝒟 : DiscreteMeasureOp<Loc<F, N>, F>, 𝒟::Codomain : RealMapping<F, N>, - A : ForwardModel<Loc<F, N>, F>, + A : ForwardModel<RNDM<F, N>, F>, + for<'a> &'a A::Observable : Instance<A::Observable>, A::PreadjointCodomain : DifferentiableRealMapping<F, N> + Bounded<F>, PlotLookup : Plotting<N>, Cube<F, N> : SetOrd { @@ -776,38 +1098,35 @@ let base = Convolution(sensor.clone(), spread.clone()); let resolution = if N==1 { 100 } else { 40 }; - let pfx = |n| format!("{}{}", prefix, n); + let pfx = |n| format!("{prefix}{n}"); let plotgrid = lingrid(&[[-kernel_plot_width, kernel_plot_width]; N].into(), &[resolution; N]); - PlotLookup::plot_into_file(sensor, plotgrid, pfx("sensor"), "sensor".to_string()); - PlotLookup::plot_into_file(kernel, plotgrid, pfx("kernel"), "kernel".to_string()); - PlotLookup::plot_into_file(spread, plotgrid, pfx("spread"), "spread".to_string()); - PlotLookup::plot_into_file_diff(&base, plotgrid, pfx("base_sensor"), "base_sensor".to_string()); + PlotLookup::plot_into_file(sensor, plotgrid, pfx("sensor")); + PlotLookup::plot_into_file(kernel, plotgrid, pfx("kernel")); + PlotLookup::plot_into_file(spread, plotgrid, pfx("spread")); + PlotLookup::plot_into_file(&base, plotgrid, pfx("base_sensor")); let plotgrid2 = lingrid(&domain, &[resolution; N]); let ω_hat = op𝒟.apply(μ_hat); let noise = opA.preadjoint().apply(opA.apply(μ_hat) - b); - PlotLookup::plot_into_file(&ω_hat, plotgrid2, pfx("omega_hat"), "ω̂".to_string()); - PlotLookup::plot_into_file(&noise, plotgrid2, pfx("omega_noise"), - "noise Aᵀ(Aμ̂ - b)".to_string()); + PlotLookup::plot_into_file(&ω_hat, plotgrid2, pfx("omega_hat")); + PlotLookup::plot_into_file(&noise, plotgrid2, pfx("omega_noise")); let preadj_b = opA.preadjoint().apply(b); let preadj_b_hat = opA.preadjoint().apply(b_hat); //let bounds = preadj_b.bounds().common(&preadj_b_hat.bounds()); PlotLookup::plot_into_file_spikes( - "Aᵀb".to_string(), &preadj_b, - "Aᵀb̂".to_string(), Some(&preadj_b_hat), - plotgrid2, None, &μ_hat, + Some(&preadj_b), + Some(&preadj_b_hat), + plotgrid2, + &μ_hat, pfx("omega_b") ); - PlotLookup::plot_into_file_diff(&preadj_b, plotgrid2, pfx("preadj_b"), - "preadj_b".to_string()); - PlotLookup::plot_into_file_diff(&preadj_b_hat, plotgrid2, pfx("preadj_b_hat"), - "preadj_b_hat".to_string()); + PlotLookup::plot_into_file(&preadj_b, plotgrid2, pfx("preadj_b")); + PlotLookup::plot_into_file(&preadj_b_hat, plotgrid2, pfx("preadj_b_hat")); // Save true solution and observables - let pfx = |n| format!("{}{}", prefix, n); μ_hat.write_csv(pfx("orig.txt"))?; opA.write_observable(&b_hat, pfx("b_hat"))?; opA.write_observable(&b, pfx("b_noisy"))
--- a/src/seminorms.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/seminorms.rs Tue Dec 31 09:25:45 2024 -0500 @@ -12,9 +12,11 @@ use alg_tools::bisection_tree::*; use alg_tools::mapping::RealMapping; use alg_tools::iter::{Mappable, FilterMapX}; -use alg_tools::linops::{Apply, Linear, BoundedLinear}; +use alg_tools::linops::{Mapping, Linear, BoundedLinear}; +use alg_tools::instance::Instance; use alg_tools::nalgebra_support::ToNalgebraRealField; -use crate::measures::{DiscreteMeasure, DeltaMeasure, SpikeIter}; +use alg_tools::norms::Linfinity; +use crate::measures::{DiscreteMeasure, DeltaMeasure, SpikeIter, Radon, RNDM}; use nalgebra::DMatrix; use std::marker::PhantomData; use itertools::Itertools; @@ -22,9 +24,12 @@ /// Abstraction for operators $𝒟 ∈ 𝕃(𝒵(Ω); C_c(Ω))$. /// /// Here $𝒵(Ω) ⊂ ℳ(Ω)$ is the space of sums of delta measures, presented by [`DiscreteMeasure`]. -pub trait DiscreteMeasureOp<Domain, F> : BoundedLinear<DiscreteMeasure<Domain, F>, FloatType=F> -where F : Float + ToNalgebraRealField, - Domain : 'static { +pub trait DiscreteMeasureOp<Domain, F> + : BoundedLinear<DiscreteMeasure<Domain, F>, Radon, Linfinity, F> +where + F : Float + ToNalgebraRealField, + Domain : 'static + Clone + PartialEq, +{ /// The output type of [`Self::preapply`]. type PreCodomain; @@ -38,7 +43,7 @@ fn findim_matrix<'a, I>(&self, points : I) -> DMatrix<F::MixedType> where I : ExactSizeIterator<Item=&'a Domain> + Clone; - /// [`Apply::apply`] that typically returns an uninitialised [`PreBTFN`] + /// [`Mapping`] that typically returns an uninitialised [`PreBTFN`] /// instead of a full [`BTFN`]. fn preapply(&self, μ : DiscreteMeasure<Domain, F>) -> Self::PreCodomain; } @@ -73,7 +78,7 @@ pub struct ConvolutionSupportGenerator<F : Float, K, const N : usize> where K : SimpleConvolutionKernel<F, N> { kernel : K, - centres : DiscreteMeasure<Loc<F, N>, F>, + centres : RNDM<F, N>, } impl<F : Float, K, const N : usize> ConvolutionSupportGenerator<F, K, N> @@ -130,9 +135,9 @@ where F : Float + ToNalgebraRealField, BT : BTImpl<F, N, Data=usize>, K : SimpleConvolutionKernel<F, N> { - /// Depth of the [`BT`] bisection tree for the outputs [`Apply::apply`]. + /// Depth of the [`BT`] bisection tree for the outputs [`Mapping::apply`]. depth : BT::Depth, - /// Domain of the [`BT`] bisection tree for the outputs [`Apply::apply`]. + /// Domain of the [`BT`] bisection tree for the outputs [`Mapping::apply`]. domain : Cube<F, N>, /// The convolution kernel kernel : K, @@ -146,7 +151,7 @@ /// Creates a new convolution operator $𝒟$ with `kernel` on `domain`. /// - /// The output of [`Apply::apply`] is a [`BT`] of given `depth`. + /// The output of [`Mapping::apply`] is a [`BT`] of given `depth`. pub fn new(depth : BT::Depth, domain : Cube<F, N>, kernel : K) -> Self { ConvolutionOp { depth : depth, @@ -157,7 +162,7 @@ } /// Returns the support generator for this convolution operator. - fn support_generator(&self, μ : DiscreteMeasure<Loc<F, N>, F>) + fn support_generator(&self, μ : RNDM<F, N>) -> ConvolutionSupportGenerator<F, K, N> { // TODO: can we avoid cloning μ? @@ -173,94 +178,43 @@ } } -impl<F, K, BT, const N : usize> Apply<DiscreteMeasure<Loc<F, N>, F>> +impl<F, K, BT, const N : usize> Mapping<RNDM<F, N>> for ConvolutionOp<F, K, BT, N> -where F : Float + ToNalgebraRealField, - BT : BTImpl<F, N, Data=usize>, - K : SimpleConvolutionKernel<F, N>, - Weighted<Shift<K, F, N>, F> : LocalAnalysis<F, BT::Agg, N> { +where + F : Float + ToNalgebraRealField, + BT : BTImpl<F, N, Data=usize>, + K : SimpleConvolutionKernel<F, N>, + Weighted<Shift<K, F, N>, F> : LocalAnalysis<F, BT::Agg, N> +{ - type Output = BTFN<F, ConvolutionSupportGenerator<F, K, N>, BT, N>; + type Codomain = BTFN<F, ConvolutionSupportGenerator<F, K, N>, BT, N>; - fn apply(&self, μ : DiscreteMeasure<Loc<F, N>, F>) -> Self::Output { - let g = self.support_generator(μ); + fn apply<I>(&self, μ : I) -> Self::Codomain + where I : Instance<RNDM<F, N>> { + let g = self.support_generator(μ.own()); BTFN::construct(self.domain.clone(), self.depth, g) } } -impl<'a, F, K, BT, const N : usize> Apply<&'a DiscreteMeasure<Loc<F, N>, F>> +/// [`ConvolutionOp`]s as linear operators over [`DiscreteMeasure`]s. +impl<F, K, BT, const N : usize> Linear<RNDM<F, N>> +for ConvolutionOp<F, K, BT, N> +where + F : Float + ToNalgebraRealField, + BT : BTImpl<F, N, Data=usize>, + K : SimpleConvolutionKernel<F, N>, + Weighted<Shift<K, F, N>, F> : LocalAnalysis<F, BT::Agg, N> +{ } + +impl<F, K, BT, const N : usize> +BoundedLinear<RNDM<F, N>, Radon, Linfinity, F> for ConvolutionOp<F, K, BT, N> where F : Float + ToNalgebraRealField, BT : BTImpl<F, N, Data=usize>, K : SimpleConvolutionKernel<F, N>, Weighted<Shift<K, F, N>, F> : LocalAnalysis<F, BT::Agg, N> { - type Output = BTFN<F, ConvolutionSupportGenerator<F, K, N>, BT, N>; - - fn apply(&self, μ : &'a DiscreteMeasure<Loc<F, N>, F>) -> Self::Output { - self.apply(μ.clone()) - } -} - -/// [`ConvolutionOp`]s as linear operators over [`DiscreteMeasure`]s. -impl<F, K, BT, const N : usize> Linear<DiscreteMeasure<Loc<F, N>, F>> -for ConvolutionOp<F, K, BT, N> -where F : Float + ToNalgebraRealField, - BT : BTImpl<F, N, Data=usize>, - K : SimpleConvolutionKernel<F, N>, - Weighted<Shift<K, F, N>, F> : LocalAnalysis<F, BT::Agg, N> { - type Codomain = BTFN<F, ConvolutionSupportGenerator<F, K, N>, BT, N>; -} - -impl<F, K, BT, const N : usize> Apply<DeltaMeasure<Loc<F, N>, F>> -for ConvolutionOp<F, K, BT, N> -where F : Float + ToNalgebraRealField, - BT : BTImpl<F, N, Data=usize>, - K : SimpleConvolutionKernel<F, N> { - - type Output = Weighted<Shift<K, F, N>, F>; - - #[inline] - fn apply(&self, δ : DeltaMeasure<Loc<F, N>, F>) -> Self::Output { - self.kernel.clone().shift(δ.x).weigh(δ.α) - } -} - -impl<'a, F, K, BT, const N : usize> Apply<&'a DeltaMeasure<Loc<F, N>, F>> -for ConvolutionOp<F, K, BT, N> -where F : Float + ToNalgebraRealField, - BT : BTImpl<F, N, Data=usize>, - K : SimpleConvolutionKernel<F, N> { - - type Output = Weighted<Shift<K, F, N>, F>; - - #[inline] - fn apply(&self, δ : &'a DeltaMeasure<Loc<F, N>, F>) -> Self::Output { - self.kernel.clone().shift(δ.x).weigh(δ.α) - } -} - -/// [`ConvolutionOp`]s as linear operators over [`DeltaMeasure`]s. -/// -/// The codomain is different from the implementation for [`DiscreteMeasure`]. -impl<F, K, BT, const N : usize> Linear<DeltaMeasure<Loc<F, N>, F>> -for ConvolutionOp<F, K, BT, N> -where F : Float + ToNalgebraRealField, - BT : BTImpl<F, N, Data=usize>, - K : SimpleConvolutionKernel<F, N> { - type Codomain = Weighted<Shift<K, F, N>, F>; -} - -impl<F, K, BT, const N : usize> BoundedLinear<DiscreteMeasure<Loc<F, N>, F>> -for ConvolutionOp<F, K, BT, N> -where F : Float + ToNalgebraRealField, - BT : BTImpl<F, N, Data=usize>, - K : SimpleConvolutionKernel<F, N>, - Weighted<Shift<K, F, N>, F> : LocalAnalysis<F, BT::Agg, N> { - - type FloatType = F; - - fn opnorm_bound(&self) -> F { + fn opnorm_bound(&self, _ : Radon, _ : Linfinity) -> F { // With μ = ∑_i α_i δ_{x_i}, we have // |𝒟μ|_∞ // = sup_z |∑_i α_i φ(z - x_i)| @@ -292,10 +246,10 @@ DMatrix::from_iterator(n, n, values) } - /// A version of [`Apply::apply`] that does not instantiate the [`BTFN`] codomain with + /// A version of [`Mapping::apply`] that does not instantiate the [`BTFN`] codomain with /// a bisection tree, instead returning a [`PreBTFN`]. This can improve performance when /// the output is to be added as the right-hand-side operand to a proper BTFN. - fn preapply(&self, μ : DiscreteMeasure<Loc<F, N>, F>) -> Self::PreCodomain { + fn preapply(&self, μ : RNDM<F, N>) -> Self::PreCodomain { BTFN::new_pre(self.support_generator(μ)) } }
--- a/src/sliding_fb.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/sliding_fb.rs Tue Dec 31 09:25:45 2024 -0500 @@ -10,15 +10,12 @@ use itertools::izip; use std::iter::Iterator; -use alg_tools::iterate::{ - AlgIteratorFactory, - AlgIteratorState -}; +use alg_tools::iterate::AlgIteratorFactory; use alg_tools::euclidean::Euclidean; use alg_tools::sets::Cube; use alg_tools::loc::Loc; -use alg_tools::mapping::{Apply, Differentiable}; -use alg_tools::norms::{Norm, L2}; +use alg_tools::mapping::{Mapping, DifferentiableMapping, Instance}; +use alg_tools::norms::Norm; use alg_tools::bisection_tree::{ BTFN, PreBTFN, @@ -33,14 +30,19 @@ }; use alg_tools::mapping::RealMapping; use alg_tools::nalgebra_support::ToNalgebraRealField; +use alg_tools::norms::{L2, Linfinity}; use crate::types::*; -use crate::measures::{DeltaMeasure, DiscreteMeasure, Radon}; +use crate::measures::{DiscreteMeasure, Radon, RNDM}; use crate::measures::merging::{ - //SpikeMergingMethod, + SpikeMergingMethod, SpikeMerging, }; -use crate::forward_model::ForwardModel; +use crate::forward_model::{ + ForwardModel, + AdjointProductBoundedBy, + LipschitzValues, +}; use crate::seminorms::DiscreteMeasureOp; //use crate::tolerance::Tolerance; use crate::plot::{ @@ -56,7 +58,44 @@ calculate_residual, calculate_residual2, }; -use crate::transport::TransportLipschitz; +//use crate::transport::TransportLipschitz; + +/// Transport settings for [`pointsource_sliding_fb_reg`]. +#[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)] +#[serde(default)] +pub struct TransportConfig<F : Float> { + /// Transport step length $θ$ normalised to $(0, 1)$. + pub θ0 : F, + /// Factor in $(0, 1)$ for decreasing transport to adapt to tolerance. + pub adaptation : F, + /// Transport tolerance wrt. ω + pub tolerance_ω : F, + /// Transport tolerance wrt. ∇v + pub tolerance_dv : F, +} + +#[replace_float_literals(F::cast_from(literal))] +impl <F : Float> TransportConfig<F> { + /// Check that the parameters are ok. Panics if not. + pub fn check(&self) { + assert!(self.θ0 > 0.0); + assert!(0.0 < self.adaptation && self.adaptation < 1.0); + assert!(self.tolerance_dv > 0.0); + assert!(self.tolerance_ω > 0.0); + } +} + +#[replace_float_literals(F::cast_from(literal))] +impl<F : Float> Default for TransportConfig<F> { + fn default() -> Self { + TransportConfig { + θ0 : 0.01, + adaptation : 0.9, + tolerance_ω : 1000.0, // TODO: no idea what this should be + tolerance_dv : 1000.0, // TODO: no idea what this should be + } + } +} /// Settings for [`pointsource_sliding_fb_reg`]. #[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)] @@ -64,15 +103,8 @@ pub struct SlidingFBConfig<F : Float> { /// Step length scaling pub τ0 : F, - /// Transport step length $θ$ normalised to $(0, 1)$. - pub θ0 : F, - /// Maximum transport mass scaling. - // /// The maximum transported mass is this factor times $\norm{b}^2/(2α)$. - // pub max_transport_scale : F, - /// Transport tolerance wrt. ω - pub transport_tolerance_ω : F, - /// Transport tolerance wrt. ∇v - pub transport_tolerance_dv : F, + /// Transport parameters + pub transport : TransportConfig<F>, /// Generic parameters pub insertion : FBGenericConfig<F>, } @@ -82,38 +114,243 @@ fn default() -> Self { SlidingFBConfig { τ0 : 0.99, - θ0 : 0.99, - //max_transport_scale : 10.0, - transport_tolerance_ω : 1.0, // TODO: no idea what this should be - transport_tolerance_dv : 1.0, // TODO: no idea what this should be + transport : Default::default(), insertion : Default::default() } } } -/// Scale each |γ|_i ≠ 0 by q_i=q̄/g(γ_i) +/// Internal type of adaptive transport step length calculation +pub(crate) enum TransportStepLength<F : Float, G : Fn(F, F) -> F> { + /// Fixed, known step length + Fixed(F), + /// Adaptive step length, only wrt. maximum transport. + /// Content of `l` depends on use case, while `g` calculates the step length from `l`. + AdaptiveMax{ l : F, max_transport : F, g : G }, + /// Adaptive step length. + /// Content of `l` depends on use case, while `g` calculates the step length from `l`. + FullyAdaptive{ l : F, max_transport : F, g : G }, +} + +/// Constrution and a priori transport adaptation. #[replace_float_literals(F::cast_from(literal))] -fn scale_down<'a, I, F, G, const N : usize>( - iter : I, - q̄ : F, - mut g : G -) where F : Float, - I : Iterator<Item = &'a mut DeltaMeasure<Loc<F,N>, F>>, - G : FnMut(&DeltaMeasure<Loc<F,N>, F>) -> F { - iter.for_each(|δ| { - if δ.α != 0.0 { - let b = g(δ); - if b * δ.α > 0.0 { - δ.α *= q̄/b; +pub(crate) fn initial_transport<F, G, D, Observable, const N : usize>( + γ1 : &mut RNDM<F, N>, + μ : &mut RNDM<F, N>, + opAapply : impl Fn(&RNDM<F, N>) -> Observable, + ε : F, + τ : F, + θ_or_adaptive : &mut TransportStepLength<F, G>, + opAnorm : F, + v : D, + tconfig : &TransportConfig<F> +) -> (Vec<F>, RNDM<F, N>) +where + F : Float + ToNalgebraRealField, + G : Fn(F, F) -> F, + Observable : Euclidean<F, Output=Observable>, + for<'a> &'a Observable : Instance<Observable>, + //for<'b> A::Preadjoint<'b> : LipschitzValues<FloatType=F>, + D : DifferentiableMapping<Loc<F, N>, DerivativeDomain=Loc<F, N>>, +{ + + use TransportStepLength::*; + + // Save current base point and shift μ to new positions. Idea is that + // μ_base(_masses) = μ^k (vector of masses) + // μ_base_minus_γ0 = μ^k - π_♯^0γ^{k+1} + // γ1 = π_♯^1γ^{k+1} + // μ = μ^{k+1} + let μ_base_masses : Vec<F> = μ.iter_masses().collect(); + let mut μ_base_minus_γ0 = μ.clone(); // Weights will be set in the loop below. + // Construct μ^{k+1} and π_♯^1γ^{k+1} initial candidates + //let mut sum_norm_dv = 0.0; + let γ_prev_len = γ1.len(); + assert!(μ.len() >= γ_prev_len); + γ1.extend(μ[γ_prev_len..].iter().cloned()); + + // Calculate initial transport and step length. + // First calculate initial transported weights + for (δ, ρ) in izip!(μ.iter_spikes(), γ1.iter_spikes_mut()) { + // If old transport has opposing sign, the new transport will be none. + ρ.α = if (ρ.α > 0.0 && δ.α < 0.0) || (ρ.α < 0.0 && δ.α > 0.0) { + 0.0 + } else { + δ.α + }; + }; + + // A priori transport adaptation based on bounding 2 ‖A‖ ‖A(γ₁-γ₀)‖‖γ‖ by scaling γ. + // 1. Calculate transport rays. + // If the Lipschitz factor of the values v=∇F(μ) are not known, estimate it. + match *θ_or_adaptive { + Fixed(θ) => { + let θτ = τ * θ; + for (δ, ρ) in izip!(μ.iter_spikes(), γ1.iter_spikes_mut()) { + ρ.x = δ.x - v.differential(&δ.x) * (ρ.α.signum() * θτ); + } + }, + AdaptiveMax{ l : ℓ_v, ref mut max_transport, g : ref calculate_θ } => { + *max_transport = max_transport.max(γ1.norm(Radon)); + let θτ = τ * calculate_θ(ℓ_v, *max_transport); + for (δ, ρ) in izip!(μ.iter_spikes(), γ1.iter_spikes_mut()) { + ρ.x = δ.x - v.differential(&δ.x) * (ρ.α.signum() * θτ); + } + }, + FullyAdaptive{ l : ref mut adaptive_ℓ_v, ref mut max_transport, g : ref calculate_θ } => { + *max_transport = max_transport.max(γ1.norm(Radon)); + let mut θ = calculate_θ(*adaptive_ℓ_v, *max_transport); + loop { + let θτ = τ * θ; + for (δ, ρ) in izip!(μ.iter_spikes(), γ1.iter_spikes_mut()) { + let dv_x = v.differential(&δ.x); + ρ.x = δ.x - &dv_x * (ρ.α.signum() * θτ); + // Estimate Lipschitz factor of ∇v + let this_ℓ_v = (dv_x - v.differential(&ρ.x)).norm2(); + *adaptive_ℓ_v = adaptive_ℓ_v.max(this_ℓ_v); + } + let new_θ = calculate_θ(*adaptive_ℓ_v / tconfig.adaptation, *max_transport); + if new_θ <= θ { + break + } + θ = new_θ; } } - }); + } + + // 2. Adjust transport mass, if needed. + // This tries to remove the smallest transport masses first. + if true { + // Alternative 1 : subtract same amount from all transport rays until reaching zero + loop { + let nr =γ1.norm(Radon); + let n = τ * 2.0 * opAnorm * (opAapply(&*γ1)-opAapply(&*μ)).norm2(); + if n <= 0.0 || nr <= 0.0 { + break + } + let reduction_needed = nr - (ε * tconfig.tolerance_dv / n); + if reduction_needed <= 0.0 { + break + } + let (min_nonzero, n_nonzero) = γ1.iter_masses() + .map(|α| α.abs()) + .filter(|α| *α > F::EPSILON) + .fold((F::INFINITY, 0), |(a, n), b| (a.min(b), n+1)); + assert!(n_nonzero > 0); + // Reduction that can be done in all nonzero spikes simultaneously + let h = (reduction_needed / F::cast_from(n_nonzero)).min(min_nonzero); + for (δ, ρ) in izip!(μ.iter_spikes_mut(), γ1.iter_spikes_mut()) { + ρ.α = ρ.α.signum() * (ρ.α.abs() - h).max(0.0); + δ.α = ρ.α; + } + if min_nonzero * F::cast_from(n_nonzero) >= reduction_needed { + break + } + } + } else { + // Alternative 2: first reduce transport rays with greater effect based on differential. + // This is a an inefficient quick-and-dirty implementation. + loop { + let nr = γ1.norm(Radon); + let a = opAapply(&*γ1)-opAapply(&*μ); + let na = a.norm2(); + let n = τ * 2.0 * opAnorm * na; + if n <= 0.0 || nr <= 0.0 { + break + } + let reduction_needed = nr - (ε * tconfig.tolerance_dv / n); + if reduction_needed <= 0.0 { + break + } + let mut max_d = 0.0; + let mut max_d_ind = 0; + for (δ, ρ, i) in izip!(μ.iter_spikes_mut(), γ1.iter_spikes(), 0..) { + // Calculate differential of ‖A(γ₁-γ₀)‖‖γ‖ wrt. each spike + let s = δ.α.signum(); + // TODO: this is very inefficient implementation due to the limitations + // of the closure parameters. + let δ1 = DiscreteMeasure::from([(ρ.x, s)]); + let δ2 = DiscreteMeasure::from([(δ.x, s)]); + let a_part = opAapply(&δ1)-opAapply(&δ2); + let d = a.dot(&a_part)/na * nr + 2.0 * na; + if d > max_d { + max_d = d; + max_d_ind = i; + } + } + // Just set mass to zero for transport ray with greater differential + assert!(max_d > 0.0); + γ1[max_d_ind].α = 0.0; + μ[max_d_ind].α = 0.0; + } + } + + // Set initial guess for μ=μ^{k+1}. + for (δ, ρ, &β) in izip!(μ.iter_spikes_mut(), γ1.iter_spikes(), μ_base_masses.iter()) { + if ρ.α.abs() > F::EPSILON { + δ.x = ρ.x; + //δ.α = ρ.α; // already set above + } else { + δ.α = β; + } + } + // Calculate μ^k-π_♯^0γ^{k+1} and v̆ = A_*(A[μ_transported + μ_transported_base]-b) + μ_base_minus_γ0.set_masses(μ_base_masses.iter().zip(γ1.iter_masses()) + .map(|(&a,b)| a - b)); + (μ_base_masses, μ_base_minus_γ0) +} + +/// A posteriori transport adaptation. +#[replace_float_literals(F::cast_from(literal))] +pub(crate) fn aposteriori_transport<F, const N : usize>( + γ1 : &mut RNDM<F, N>, + μ : &mut RNDM<F, N>, + μ_base_minus_γ0 : &mut RNDM<F, N>, + μ_base_masses : &Vec<F>, + ε : F, + tconfig : &TransportConfig<F> +) -> bool +where F : Float + ToNalgebraRealField { + + // 1. If π_♯^1γ^{k+1} = γ1 has non-zero mass at some point y, but μ = μ^{k+1} does not, + // then the ansatz ∇w̃_x(y) = w^{k+1}(y) may not be satisfied. So set the mass of γ1 + // at that point to zero, and retry. + let mut all_ok = true; + for (α_μ, α_γ1) in izip!(μ.iter_masses(), γ1.iter_masses_mut()) { + if α_μ == 0.0 && *α_γ1 != 0.0 { + all_ok = false; + *α_γ1 = 0.0; + } + } + + // 2. Through bounding ∫ B_ω(y, z) dλ(x, y, z). + // through the estimate ≤ C ‖Δ‖‖γ^{k+1}‖ for Δ := μ^{k+1}-μ^k-(π_♯^1-π_♯^0)γ^{k+1}, + // which holds for some some C if the convolution kernel in 𝒟 has Lipschitz gradient. + let nγ = γ1.norm(Radon); + let nΔ = μ_base_minus_γ0.norm(Radon) + μ.dist_matching(&γ1); + let t = ε * tconfig.tolerance_ω; + if nγ*nΔ > t { + // Since t/(nγ*nΔ)<1, and the constant tconfig.adaptation < 1, + // this will guarantee that eventually ‖γ‖ decreases sufficiently that we + // will not enter here. + *γ1 *= tconfig.adaptation * t / ( nγ * nΔ ); + all_ok = false + } + + if !all_ok { + // Update weights for μ_base_minus_γ0 = μ^k - π_♯^0γ^{k+1} + μ_base_minus_γ0.set_masses(μ_base_masses.iter().zip(γ1.iter_masses()) + .map(|(&a,b)| a - b)); + + } + + all_ok } /// Iteratively solve the pointsource localisation problem using sliding forward-backward /// splitting /// -/// The parametrisatio is as for [`pointsource_fb_reg`]. +/// The parametrisation is as for [`pointsource_fb_reg`]. /// Inertia is currently not supported. #[replace_float_literals(F::cast_from(literal))] pub fn pointsource_sliding_fb_reg<'a, F, I, A, GA, 𝒟, BTA, BT𝒟, G𝒟, S, K, Reg, const N : usize>( @@ -121,203 +358,113 @@ b : &A::Observable, reg : Reg, op𝒟 : &'a 𝒟, - sfbconfig : &SlidingFBConfig<F>, + config : &SlidingFBConfig<F>, iterator : I, mut plotter : SeqPlotter<F, N>, -) -> DiscreteMeasure<Loc<F, N>, F> +) -> RNDM<F, N> where F : Float + ToNalgebraRealField, I : AlgIteratorFactory<IterInfo<F, N>>, - for<'b> &'b A::Observable : std::ops::Neg<Output=A::Observable>, - //+ std::ops::Mul<F, Output=A::Observable>, <-- FIXME: compiler overflow - A::Observable : std::ops::MulAssign<F>, - A::PreadjointCodomain : for<'b> Differentiable<&'b Loc<F, N>, Output=Loc<F, N>>, + for<'b> &'b A::Observable : std::ops::Neg<Output=A::Observable> + Instance<A::Observable>, + for<'b> A::Preadjoint<'b> : LipschitzValues<FloatType=F>, + A::PreadjointCodomain : DifferentiableMapping< + Loc<F, N>, DerivativeDomain=Loc<F, N>, Codomain=F + >, GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, - A : ForwardModel<Loc<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>> - + Lipschitz<&'a 𝒟, FloatType=F> + TransportLipschitz<L2Squared, FloatType=F>, + A : ForwardModel<RNDM<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>> + + AdjointProductBoundedBy<RNDM<F, N>, 𝒟, FloatType=F>, + //+ TransportLipschitz<L2Squared, FloatType=F>, BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, G𝒟 : SupportGenerator<F, N, SupportType = K, Id = usize> + Clone, 𝒟 : DiscreteMeasureOp<Loc<F, N>, F, PreCodomain = PreBTFN<F, G𝒟, N>, Codomain = BTFN<F, G𝒟, BT𝒟, N>>, BT𝒟 : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N> - + Differentiable<Loc<F, N>, Output=Loc<F,N>>, + + DifferentiableMapping<Loc<F, N>, DerivativeDomain=Loc<F,N>>, K: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, - //+ Differentiable<Loc<F, N>, Output=Loc<F,N>>, + //+ Differentiable<Loc<F, N>, Derivative=Loc<F,N>>, BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, Cube<F, N>: P2Minimise<Loc<F, N>, F>, PlotLookup : Plotting<N>, - DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F>, + RNDM<F, N> : SpikeMerging<F>, Reg : SlidingRegTerm<F, N> { - assert!(sfbconfig.τ0 > 0.0 && - sfbconfig.θ0 > 0.0); - - // Set up parameters - let config = &sfbconfig.insertion; - let op𝒟norm = op𝒟.opnorm_bound(); - //let max_transport = sfbconfig.max_transport_scale - // * reg.radon_norm_bound(b.norm2_squared() / 2.0); - //let tlip = opA.transport_lipschitz_factor(L2Squared) * max_transport; - //let ℓ = 0.0; - let θ = sfbconfig.θ0; // (ℓ + tlip); - let τ = sfbconfig.τ0/opA.lipschitz_factor(&op𝒟).unwrap(); - // We multiply tolerance by τ for FB since our subproblems depending on tolerances are scaled - // by τ compared to the conditional gradient approach. - let tolerance = config.tolerance * τ * reg.tolerance_scaling(); - let mut ε = tolerance.initial(); + // Check parameters + assert!(config.τ0 > 0.0, "Invalid step length parameter"); + config.transport.check(); // Initialise iterates let mut μ = DiscreteMeasure::new(); let mut γ1 = DiscreteMeasure::new(); - let mut residual = -b; + let mut residual = -b; // Has to equal $Aμ-b$. + + // Set up parameters + let op𝒟norm = op𝒟.opnorm_bound(Radon, Linfinity); + let opAnorm = opA.opnorm_bound(Radon, L2); + //let max_transport = config.max_transport.scale + // * reg.radon_norm_bound(b.norm2_squared() / 2.0); + //let ℓ = opA.transport.lipschitz_factor(L2Squared) * max_transport; + let ℓ = 0.0; + let τ = config.τ0 / opA.adjoint_product_bound(&op𝒟).unwrap(); + let calculate_θ = |ℓ_v, _| config.transport.θ0 / (τ*(ℓ + ℓ_v)); + let mut θ_or_adaptive = match opA.preadjoint().value_diff_unit_lipschitz_factor() { + // We only estimate w (the uniform Lipschitz for of v), if we also estimate ℓ_v + // (the uniform Lipschitz factor of ∇v). + // We assume that the residual is decreasing. + Some(ℓ_v0) => TransportStepLength::Fixed(calculate_θ(ℓ_v0 * residual.norm2(), 0.0)), + None => TransportStepLength::FullyAdaptive { + l : 0.0, + max_transport : 0.0, + g : calculate_θ + }, + }; + // We multiply tolerance by τ for FB since our subproblems depending on tolerances are scaled + // by τ compared to the conditional gradient approach. + let tolerance = config.insertion.tolerance * τ * reg.tolerance_scaling(); + let mut ε = tolerance.initial(); + + // Statistics + let full_stats = |residual : &A::Observable, + μ : &RNDM<F, N>, + ε, stats| IterInfo { + value : residual.norm2_squared_div2() + reg.apply(μ), + n_spikes : μ.len(), + ε, + // postprocessing: config.insertion.postprocessing.then(|| μ.clone()), + .. stats + }; let mut stats = IterInfo::new(); // Run the algorithm - iterator.iterate(|state| { - // Calculate smooth part of surrogate model. - // Using `std::mem::replace` here is not ideal, and expects that `empty_observable` - // has no significant overhead. For some reosn Rust doesn't allow us simply moving - // the residual and replacing it below before the end of this closure. - let r = std::mem::replace(&mut residual, opA.empty_observable()); - let v = opA.preadjoint().apply(r); - - // Save current base point and shift μ to new positions. Idea is that - // μ_base(_masses) = μ^k (vector of masses) - // μ_base_minus_γ0 = μ^k - π_♯^0γ^{k+1} - // γ1 = π_♯^1γ^{k+1} - // μ = μ^{k+1} - let μ_base_masses : Vec<F> = μ.iter_masses().collect(); - let mut μ_base_minus_γ0 = μ.clone(); // Weights will be set in the loop below. - // Construct μ^{k+1} and π_♯^1γ^{k+1} initial candidates - let mut sum_norm_dv_times_γinit = 0.0; - let mut sum_abs_γinit = 0.0; - //let mut sum_norm_dv = 0.0; - let γ_prev_len = γ1.len(); - assert!(μ.len() >= γ_prev_len); - γ1.extend(μ[γ_prev_len..].iter().cloned()); - for (δ, ρ) in izip!(μ.iter_spikes_mut(), γ1.iter_spikes_mut()) { - let d_v_x = v.differential(&δ.x); - // If old transport has opposing sign, the new transport will be none. - ρ.α = if (ρ.α > 0.0 && δ.α < 0.0) || (ρ.α < 0.0 && δ.α > 0.0) { - 0.0 - } else { - δ.α - }; - δ.x -= d_v_x * (θ * δ.α.signum()); // This is δ.α.signum() when δ.α ≠ 0. - ρ.x = δ.x; - let nrm = d_v_x.norm(L2); - let a = ρ.α.abs(); - let v = nrm * a; - if v > 0.0 { - sum_norm_dv_times_γinit += v; - sum_abs_γinit += a; - } - } - - // A priori transport adaptation based on bounding ∫ ⟨∇v(x), z-y⟩ dλ(x, y, z). - // This is just one option, there are many. - let t = ε * sfbconfig.transport_tolerance_dv; - if sum_norm_dv_times_γinit > t { - // Scale each |γ|_i by q_i=q̄/‖vx‖_i such that ∑_i |γ|_i q_i ‖vx‖_i = t - // TODO: store the closure values above? - scale_down(γ1.iter_spikes_mut(), - t / sum_abs_γinit, - |δ| v.differential(&δ.x).norm(L2)); - } - //println!("|γ| = {}, |μ| = {}", γ1.norm(crate::measures::Radon), μ.norm(crate::measures::Radon)); + for state in iterator.iter_init(|| full_stats(&residual, &μ, ε, stats.clone())) { + // Calculate initial transport + let v = opA.preadjoint().apply(residual); + let (μ_base_masses, mut μ_base_minus_γ0) = initial_transport( + &mut γ1, &mut μ, |ν| opA.apply(ν), + ε, τ, &mut θ_or_adaptive, opAnorm, + v, &config.transport, + ); // Solve finite-dimensional subproblem several times until the dual variable for the // regularisation term conforms to the assumptions made for the transport above. - let (d, within_tolerances) = 'adapt_transport: loop { - // Update weights for μ_base_minus_γ0 = μ^k - π_♯^0γ^{k+1} - for (δ_γ1, δ_μ_base_minus_γ0, &α_μ_base) in izip!(γ1.iter_spikes(), - μ_base_minus_γ0.iter_spikes_mut(), - μ_base_masses.iter()) { - δ_μ_base_minus_γ0.set_mass(α_μ_base - δ_γ1.get_mass()); - } - - // Calculate transported_minus_τv = -τA_*(A[μ_transported + μ_transported_base]-b) + let (d, _within_tolerances, τv̆) = 'adapt_transport: loop { + // Calculate τv̆ = τA_*(A[μ_transported + μ_transported_base]-b) let residual_μ̆ = calculate_residual2(&γ1, &μ_base_minus_γ0, opA, b); - let transported_minus_τv̆ = opA.preadjoint().apply(residual_μ̆ * (-τ)); + let τv̆ = opA.preadjoint().apply(residual_μ̆ * τ); // Construct μ^{k+1} by solving finite-dimensional subproblems and insert new spikes. let (d, within_tolerances) = insert_and_reweigh( - &mut μ, &transported_minus_τv̆, &γ1, Some(&μ_base_minus_γ0), + &mut μ, &τv̆, &γ1, Some(&μ_base_minus_γ0), op𝒟, op𝒟norm, - τ, ε, - config, - ®, state, &mut stats, + τ, ε, &config.insertion, + ®, &state, &mut stats, ); - // A posteriori transport adaptation based on bounding (1/τ)∫ ω(z) - ω(y) dλ(x, y, z). - let all_ok = if false { // Basic check - // If π_♯^1γ^{k+1} = γ1 has non-zero mass at some point y, but μ = μ^{k+1} does not, - // then the ansatz ∇w̃_x(y) = w^{k+1}(y) may not be satisfied. So set the mass of γ1 - // at that point to zero, and retry. - let mut all_ok = true; - for (α_μ, α_γ1) in izip!(μ.iter_masses(), γ1.iter_masses_mut()) { - if α_μ == 0.0 && *α_γ1 != 0.0 { - all_ok = false; - *α_γ1 = 0.0; - } - } - all_ok - } else { - // TODO: Could maybe optimise, as this is also formed in insert_and_reweigh above. - let mut minus_ω = op𝒟.apply(γ1.sub_matching(&μ) + &μ_base_minus_γ0); - - // let vpos = γ1.iter_spikes() - // .filter(|δ| δ.α > 0.0) - // .map(|δ| minus_ω.apply(&δ.x)) - // .reduce(F::max) - // .and_then(|threshold| { - // minus_ω.minimise_below(threshold, - // ε * config.refinement.tolerance_mult, - // config.refinement.max_steps) - // .map(|(_z, minus_ω_z)| minus_ω_z) - // }); - - // let vneg = γ1.iter_spikes() - // .filter(|δ| δ.α < 0.0) - // .map(|δ| minus_ω.apply(&δ.x)) - // .reduce(F::min) - // .and_then(|threshold| { - // minus_ω.maximise_above(threshold, - // ε * config.refinement.tolerance_mult, - // config.refinement.max_steps) - // .map(|(_z, minus_ω_z)| minus_ω_z) - // }); - let (_, vpos) = minus_ω.minimise(ε * config.refinement.tolerance_mult, - config.refinement.max_steps); - let (_, vneg) = minus_ω.maximise(ε * config.refinement.tolerance_mult, - config.refinement.max_steps); - - let t = τ * ε * sfbconfig.transport_tolerance_ω; - let val = |δ : &DeltaMeasure<Loc<F, N>, F>| { - δ.α * (minus_ω.apply(&δ.x) - if δ.α >= 0.0 { vpos } else { vneg }) - // match if δ.α >= 0.0 { vpos } else { vneg } { - // None => 0.0, - // Some(v) => δ.α * (minus_ω.apply(&δ.x) - v) - // } - }; - // Calculate positive/bad (rp) values under the integral. - // Also store sum of masses for the positive entries. - let (rp, w) = γ1.iter_spikes().fold((0.0, 0.0), |(p, w), δ| { - let v = val(δ); - if v <= 0.0 { (p, w) } else { (p + v, w + δ.α.abs()) } - }); - - if rp > t { - // TODO: store v above? - scale_down(γ1.iter_spikes_mut(), t / w, val); - false - } else { - true - } - }; - - if all_ok { - break 'adapt_transport (d, within_tolerances) + // A posteriori transport adaptation. + if aposteriori_transport( + &mut γ1, &mut μ, &mut μ_base_minus_γ0, &μ_base_masses, + ε, &config.transport + ) { + break 'adapt_transport (d, within_tolerances, τv̆) } }; @@ -330,10 +477,24 @@ stats.transport_error = Some({ assert_eq!(μ_base_masses.len(), γ1.len()); let (a, b) = stats.transport_error.unwrap_or((0.0, 0.0)); - let err = izip!(μ.iter_masses(), γ1.iter_masses()).map(|(v,w)| (v-w).abs()).sum(); - (a + err, b + γ1.norm(Radon)) + (a + μ.dist_matching(&γ1), b + γ1.norm(Radon)) }); + // Merge spikes. + // This expects the prune below to prune γ. + // TODO: This may not work correctly in all cases. + let ins = &config.insertion; + if ins.merge_now(&state) { + if let SpikeMergingMethod::None = ins.merging { + } else { + stats.merged += μ.merge_spikes(ins.merging, |μ_candidate| { + let ν = μ_candidate.sub_matching(&γ1)-&μ_base_minus_γ0; + let mut d = &τv̆ + op𝒟.preapply(ν); + reg.verify_merge_candidate(&mut d, μ_candidate, τ, ε, ins) + }); + } + } + // Prune spikes with zero weight. To maintain correct ordering between μ and γ1, also the // latter needs to be pruned when μ is. // TODO: This could do with a two-vector Vec::retain to avoid copies. @@ -341,40 +502,25 @@ if μ_new.len() != μ.len() { let mut μ_iter = μ.iter_spikes(); γ1.prune_by(|_| μ_iter.next().unwrap().α != F::ZERO); + stats.pruned += μ.len() - μ_new.len(); μ = μ_new; } - // TODO: how to merge? - // Update residual residual = calculate_residual(&μ, opA, b); - // Update main tolerance for next iteration - let ε_prev = ε; - ε = tolerance.update(ε, state.iteration()); + let iter = state.iteration(); stats.this_iters += 1; - // Give function value if needed + // Give statistics if requested state.if_verbose(|| { - // Plot if so requested - plotter.plot_spikes( - format!("iter {} end; {}", state.iteration(), within_tolerances), &d, - "start".to_string(), None::<&A::PreadjointCodomain>, // TODO: Should be Some(&((-τ) * v)), but not implemented - reg.target_bounds(τ, ε_prev), &μ, - ); - // Calculate mean inner iterations and reset relevant counters. - // Return the statistics - let res = IterInfo { - value : residual.norm2_squared_div2() + reg.apply(&μ), - n_spikes : μ.len(), - ε : ε_prev, - postprocessing: config.postprocessing.then(|| μ.clone()), - .. stats - }; - stats = IterInfo::new(); - res - }) - }); + plotter.plot_spikes(iter, Some(&d), Some(&τv̆), &μ); + full_stats(&residual, &μ, ε, std::mem::replace(&mut stats, IterInfo::new())) + }); - postprocess(μ, config, L2Squared, opA, b) + // Update main tolerance for next iteration + ε = tolerance.update(ε, iter); + } + + postprocess(μ, &config.insertion, L2Squared, opA, b) }
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/sliding_pdps.rs Tue Dec 31 09:25:45 2024 -0500 @@ -0,0 +1,384 @@ +/*! +Solver for the point source localisation problem using a sliding +primal-dual proximal splitting method. +*/ + +use numeric_literals::replace_float_literals; +use serde::{Serialize, Deserialize}; +//use colored::Colorize; +//use nalgebra::{DVector, DMatrix}; +use std::iter::Iterator; + +use alg_tools::iterate::AlgIteratorFactory; +use alg_tools::euclidean::Euclidean; +use alg_tools::sets::Cube; +use alg_tools::loc::Loc; +use alg_tools::mapping::{Mapping, DifferentiableRealMapping, Instance}; +use alg_tools::norms::Norm; +use alg_tools::direct_product::Pair; +use alg_tools::bisection_tree::{ + BTFN, + PreBTFN, + Bounds, + BTNodeLookup, + BTNode, + BTSearch, + P2Minimise, + SupportGenerator, + LocalAnalysis, + //Bounded, +}; +use alg_tools::mapping::RealMapping; +use alg_tools::nalgebra_support::ToNalgebraRealField; +use alg_tools::linops::{ + BoundedLinear, AXPY, GEMV, Adjointable, IdOp, +}; +use alg_tools::convex::{Conjugable, Prox}; +use alg_tools::norms::{L2, Linfinity, PairNorm}; + +use crate::types::*; +use crate::measures::{DiscreteMeasure, Radon, RNDM}; +use crate::measures::merging::SpikeMerging; +use crate::forward_model::{ + ForwardModel, + AdjointProductPairBoundedBy, + LipschitzValues, +}; +// use crate::transport::TransportLipschitz; +use crate::seminorms::DiscreteMeasureOp; +//use crate::tolerance::Tolerance; +use crate::plot::{ + SeqPlotter, + Plotting, + PlotLookup +}; +use crate::fb::*; +use crate::regularisation::SlidingRegTerm; +// use crate::dataterm::L2Squared; +use crate::sliding_fb::{ + TransportConfig, + TransportStepLength, + initial_transport, + aposteriori_transport, +}; +use crate::dataterm::{calculate_residual, calculate_residual2}; + +/// Settings for [`pointsource_sliding_pdps_pair`]. +#[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)] +#[serde(default)] +pub struct SlidingPDPSConfig<F : Float> { + /// Primal step length scaling. + pub τ0 : F, + /// Primal step length scaling. + pub σp0 : F, + /// Dual step length scaling. + pub σd0 : F, + /// Transport parameters + pub transport : TransportConfig<F>, + /// Generic parameters + pub insertion : FBGenericConfig<F>, +} + +#[replace_float_literals(F::cast_from(literal))] +impl<F : Float> Default for SlidingPDPSConfig<F> { + fn default() -> Self { + let τ0 = 0.99; + SlidingPDPSConfig { + τ0, + σd0 : 0.1, + σp0 : 0.99, + transport : Default::default(), + insertion : Default::default() + } + } +} + +type MeasureZ<F, Z, const N : usize> = Pair<RNDM<F, N>, Z>; + +/// Iteratively solve the pointsource localisation with an additional variable +/// using sliding primal-dual proximal splitting +/// +/// The parametrisation is as for [`crate::forward_pdps::pointsource_forward_pdps_pair`]. +#[replace_float_literals(F::cast_from(literal))] +pub fn pointsource_sliding_pdps_pair< + 'a, F, I, A, GA, 𝒟, BTA, BT𝒟, G𝒟, S, K, Reg, Z, R, Y, /*KOpM, */ KOpZ, H, const N : usize +>( + opA : &'a A, + b : &A::Observable, + reg : Reg, + op𝒟 : &'a 𝒟, + config : &SlidingPDPSConfig<F>, + iterator : I, + mut plotter : SeqPlotter<F, N>, + //opKμ : KOpM, + opKz : &KOpZ, + fnR : &R, + fnH : &H, + mut z : Z, + mut y : Y, +) -> MeasureZ<F, Z, N> +where + F : Float + ToNalgebraRealField, + I : AlgIteratorFactory<IterInfo<F, N>>, + for<'b> &'b A::Observable : std::ops::Neg<Output=A::Observable> + Instance<A::Observable>, + for<'b> A::Preadjoint<'b> : LipschitzValues<FloatType=F>, + BTFN<F, GA, BTA, N> : DifferentiableRealMapping<F, N>, + GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone, + A : ForwardModel< + MeasureZ<F, Z, N>, + F, + PairNorm<Radon, L2, L2>, + PreadjointCodomain = Pair<BTFN<F, GA, BTA, N>, Z>, + > + + AdjointProductPairBoundedBy<MeasureZ<F, Z, N>, 𝒟, IdOp<Z>, FloatType=F>, + BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, + G𝒟 : SupportGenerator<F, N, SupportType = K, Id = usize> + Clone, + 𝒟 : DiscreteMeasureOp<Loc<F, N>, F, PreCodomain = PreBTFN<F, G𝒟, N>, + Codomain = BTFN<F, G𝒟, BT𝒟, N>>, + BT𝒟 : BTSearch<F, N, Data=usize, Agg=Bounds<F>>, + S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N> + + DifferentiableRealMapping<F, N>, + K: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>, + //+ Differentiable<Loc<F, N>, Derivative=Loc<F,N>>, + BTNodeLookup: BTNode<F, usize, Bounds<F>, N>, + Cube<F, N>: P2Minimise<Loc<F, N>, F>, + PlotLookup : Plotting<N>, + RNDM<F, N> : SpikeMerging<F>, + Reg : SlidingRegTerm<F, N>, + // KOpM : Linear<RNDM<F, N>, Codomain=Y> + // + GEMV<F, RNDM<F, N>> + // + Preadjointable< + // RNDM<F, N>, Y, + // PreadjointCodomain = BTFN<F, GA, BTA, N>, + // > + // + TransportLipschitz<L2Squared, FloatType=F> + // + AdjointProductBoundedBy<RNDM<F, N>, 𝒟, FloatType=F>, + // for<'b> KOpM::Preadjoint<'b> : GEMV<F, Y>, + // Since Z is Hilbert, we may just as well use adjoints for K_z. + KOpZ : BoundedLinear<Z, L2, L2, F, Codomain=Y> + + GEMV<F, Z> + + Adjointable<Z, Y, AdjointCodomain = Z>, + for<'b> KOpZ::Adjoint<'b> : GEMV<F, Y>, + Y : AXPY<F> + Euclidean<F, Output=Y> + Clone + ClosedAdd, + for<'b> &'b Y : Instance<Y>, + Z : AXPY<F, Owned=Z> + Euclidean<F, Output=Z> + Clone + Norm<F, L2>, + for<'b> &'b Z : Instance<Z>, + R : Prox<Z, Codomain=F>, + H : Conjugable<Y, F, Codomain=F>, + for<'b> H::Conjugate<'b> : Prox<Y>, +{ + + // Check parameters + assert!(config.τ0 > 0.0 && + config.τ0 < 1.0 && + config.σp0 > 0.0 && + config.σp0 < 1.0 && + config.σd0 > 0.0 && + config.σp0 * config.σd0 <= 1.0, + "Invalid step length parameters"); + config.transport.check(); + + // Initialise iterates + let mut μ = DiscreteMeasure::new(); + let mut γ1 = DiscreteMeasure::new(); + let mut residual = calculate_residual(Pair(&μ, &z), opA, b); + let zero_z = z.similar_origin(); + + // Set up parameters + let op𝒟norm = op𝒟.opnorm_bound(Radon, Linfinity); + // TODO: maybe this PairNorm doesn't make sense here? + let opAnorm = opA.opnorm_bound(PairNorm(Radon, L2, L2), L2); + let bigθ = 0.0; //opKμ.transport_lipschitz_factor(L2Squared); + let bigM = 0.0; //opKμ.adjoint_product_bound(&op𝒟).unwrap().sqrt(); + let nKz = opKz.opnorm_bound(L2, L2); + let ℓ = 0.0; + let opIdZ = IdOp::new(); + let (l, l_z) = opA.adjoint_product_pair_bound(&op𝒟, &opIdZ).unwrap(); + // We need to satisfy + // + // τσ_dM(1-σ_p L_z)/(1 - τ L) + [σ_p L_z + σ_pσ_d‖K_z‖^2] < 1 + // ^^^^^^^^^^^^^^^^^^^^^^^^^ + // with 1 > σ_p L_z and 1 > τ L. + // + // To do so, we first solve σ_p and σ_d from standard PDPS step length condition + // ^^^^^ < 1. then we solve τ from the rest. + let σ_d = config.σd0 / nKz; + let σ_p = config.σp0 / (l_z + config.σd0 * nKz); + // Observe that = 1 - ^^^^^^^^^^^^^^^^^^^^^ = 1 - σ_{p,0} + // We get the condition τσ_d M (1-σ_p L_z) < (1-σ_{p,0})*(1-τ L) + // ⟺ τ [ σ_d M (1-σ_p L_z) + (1-σ_{p,0}) L ] < (1-σ_{p,0}) + let φ = 1.0 - config.σp0; + let a = 1.0 - σ_p * l_z; + let τ = config.τ0 * φ / ( σ_d * bigM * a + φ * l ); + let ψ = 1.0 - τ * l; + let β = σ_p * config.σd0 * nKz / a; // σ_p * σ_d * (nKz * nK_z) / a; + assert!(β < 1.0); + // Now we need κ‖K_μ(π_♯^1 - π_♯^0)γ‖^2 ≤ (1/θ - τ[ℓ_v + ℓ]) ∫ c_2 dγ for κ defined as: + let κ = σ_d * ψ / ((1.0 - β) * ψ - τ * σ_d * bigM); + // The factor two in the manuscript disappears due to the definition of 𝚹 being + // for ‖x-y‖₂² instead of c_2(x, y)=‖x-y‖₂²/2. + let calculate_θ = |ℓ_v, max_transport| { + config.transport.θ0 / (τ*(ℓ + ℓ_v) + κ * bigθ * max_transport) + }; + let mut θ_or_adaptive = match opA.preadjoint().value_diff_unit_lipschitz_factor() { + // We only estimate w (the uniform Lipschitz for of v), if we also estimate ℓ_v + // (the uniform Lipschitz factor of ∇v). + // We assume that the residual is decreasing. + Some(ℓ_v0) => TransportStepLength::AdaptiveMax{ + l: ℓ_v0 * b.norm2(), + max_transport : 0.0, + g : calculate_θ + }, + None => TransportStepLength::FullyAdaptive{ + l : 0.0, + max_transport : 0.0, + g : calculate_θ + }, + }; + // Acceleration is not currently supported + // let γ = dataterm.factor_of_strong_convexity(); + let ω = 1.0; + + // We multiply tolerance by τ for FB since our subproblems depending on tolerances are scaled + // by τ compared to the conditional gradient approach. + let tolerance = config.insertion.tolerance * τ * reg.tolerance_scaling(); + let mut ε = tolerance.initial(); + + let starH = fnH.conjugate(); + + // Statistics + let full_stats = |residual : &A::Observable, μ : &RNDM<F, N>, z : &Z, ε, stats| IterInfo { + value : residual.norm2_squared_div2() + fnR.apply(z) + + reg.apply(μ) + fnH.apply(/* opKμ.apply(μ) + */ opKz.apply(z)), + n_spikes : μ.len(), + ε, + // postprocessing: config.insertion.postprocessing.then(|| μ.clone()), + .. stats + }; + let mut stats = IterInfo::new(); + + // Run the algorithm + for state in iterator.iter_init(|| full_stats(&residual, &μ, &z, ε, stats.clone())) { + // Calculate initial transport + let Pair(v, _) = opA.preadjoint().apply(&residual); + //opKμ.preadjoint().apply_add(&mut v, y); + let z_base = z.clone(); + // We want to proceed as in Example 4.12 but with v and v̆ as in §5. + // With A(ν, z) = A_μ ν + A_z z, following Example 5.1, we have + // P_ℳ[F'(ν, z) + Ξ(ν, z, y)]= A_ν^*[A_ν ν + A_z z] + K_μ ν = A_ν^*A(ν, z) + K_μ ν, + // where A_ν^* becomes a multiplier. + // This is much easier with K_μ = 0, which is the only reason why are enforcing it. + // TODO: Write a version of initial_transport that can deal with K_μ ≠ 0. + + let (μ_base_masses, mut μ_base_minus_γ0) = initial_transport( + &mut γ1, &mut μ, |ν| opA.apply(Pair(ν, &z)), + ε, τ, &mut θ_or_adaptive, opAnorm, + v, &config.transport, + ); + + // Solve finite-dimensional subproblem several times until the dual variable for the + // regularisation term conforms to the assumptions made for the transport above. + let (d, _within_tolerances, Pair(τv̆, τz̆)) = 'adapt_transport: loop { + // Calculate τv̆ = τA_*(A[μ_transported + μ_transported_base]-b) + let residual_μ̆ = calculate_residual2(Pair(&γ1, &z), + Pair(&μ_base_minus_γ0, &zero_z), + opA, b); + let Pair(τv̆, τz) = opA.preadjoint().apply(residual_μ̆ * τ); + // opKμ.preadjoint().gemv(&mut τv̆, τ, y, 1.0); + + // Construct μ^{k+1} by solving finite-dimensional subproblems and insert new spikes. + let (d, within_tolerances) = insert_and_reweigh( + &mut μ, &τv̆, &γ1, Some(&μ_base_minus_γ0), + op𝒟, op𝒟norm, + τ, ε, &config.insertion, + ®, &state, &mut stats, + ); + + // A posteriori transport adaptation. + // TODO: this does not properly treat v^{k+1} - v̆^k that depends on z^{k+1}! + if aposteriori_transport( + &mut γ1, &mut μ, &mut μ_base_minus_γ0, &μ_base_masses, + ε, &config.transport + ) { + break 'adapt_transport (d, within_tolerances, Pair(τv̆, τz)) + } + }; + + stats.untransported_fraction = Some({ + assert_eq!(μ_base_masses.len(), γ1.len()); + let (a, b) = stats.untransported_fraction.unwrap_or((0.0, 0.0)); + let source = μ_base_masses.iter().map(|v| v.abs()).sum(); + (a + μ_base_minus_γ0.norm(Radon), b + source) + }); + stats.transport_error = Some({ + assert_eq!(μ_base_masses.len(), γ1.len()); + let (a, b) = stats.transport_error.unwrap_or((0.0, 0.0)); + (a + μ.dist_matching(&γ1), b + γ1.norm(Radon)) + }); + + // // Merge spikes. + // // This expects the prune below to prune γ. + // // TODO: This may not work correctly in all cases. + // let ins = &config.insertion; + // if ins.merge_now(&state) { + // if let SpikeMergingMethod::None = ins.merging { + // } else { + // stats.merged += μ.merge_spikes(ins.merging, |μ_candidate| { + // let ν = μ_candidate.sub_matching(&γ1)-&μ_base_minus_γ0; + // let mut d = &τv̆ + op𝒟.preapply(ν); + // reg.verify_merge_candidate(&mut d, μ_candidate, τ, ε, ins) + // }); + // } + // } + + // Prune spikes with zero weight. To maintain correct ordering between μ and γ1, also the + // latter needs to be pruned when μ is. + // TODO: This could do with a two-vector Vec::retain to avoid copies. + let μ_new = DiscreteMeasure::from_iter(μ.iter_spikes().filter(|δ| δ.α != F::ZERO).cloned()); + if μ_new.len() != μ.len() { + let mut μ_iter = μ.iter_spikes(); + γ1.prune_by(|_| μ_iter.next().unwrap().α != F::ZERO); + stats.pruned += μ.len() - μ_new.len(); + μ = μ_new; + } + + // Do z variable primal update + z.axpy(-σ_p/τ, τz̆, 1.0); // TODO: simplify nasty factors + opKz.adjoint().gemv(&mut z, -σ_p, &y, 1.0); + z = fnR.prox(σ_p, z); + // Do dual update + // opKμ.gemv(&mut y, σ_d*(1.0 + ω), &μ, 1.0); // y = y + σ_d K[(1+ω)(μ,z)^{k+1}] + opKz.gemv(&mut y, σ_d*(1.0 + ω), &z, 1.0); + // opKμ.gemv(&mut y, -σ_d*ω, μ_base, 1.0);// y = y + σ_d K[(1+ω)(μ,z)^{k+1} - ω (μ,z)^k]-b + opKz.gemv(&mut y, -σ_d*ω, z_base, 1.0);// y = y + σ_d K[(1+ω)(μ,z)^{k+1} - ω (μ,z)^k]-b + y = starH.prox(σ_d, y); + + // Update residual + residual = calculate_residual(Pair(&μ, &z), opA, b); + + // Update step length parameters + // let ω = pdpsconfig.acceleration.accelerate(&mut τ, &mut σ, γ); + + // Give statistics if requested + let iter = state.iteration(); + stats.this_iters += 1; + + state.if_verbose(|| { + plotter.plot_spikes(iter, Some(&d), Some(&τv̆), &μ); + full_stats(&residual, &μ, &z, ε, std::mem::replace(&mut stats, IterInfo::new())) + }); + + // Update main tolerance for next iteration + ε = tolerance.update(ε, iter); + } + + let fit = |μ̃ : &RNDM<F, N>| { + (opA.apply(Pair(μ̃, &z))-b).norm2_squared_div2() + //+ fnR.apply(z) + reg.apply(μ) + + fnH.apply(/* opKμ.apply(&μ̃) + */ opKz.apply(&z)) + }; + + μ.merge_spikes_fitness(config.insertion.merging, fit, |&v| v); + μ.prune(); + Pair(μ, z) +}
--- a/src/types.rs Thu Aug 29 00:00:00 2024 -0500 +++ b/src/types.rs Tue Dec 31 09:25:45 2024 -0500 @@ -4,7 +4,6 @@ use colored::ColoredString; use serde::{Serialize, Deserialize}; -use clap::ValueEnum; use alg_tools::iterate::LogRepr; use alg_tools::euclidean::Euclidean; use alg_tools::norms::{Norm, L1}; @@ -13,7 +12,7 @@ pub use alg_tools::loc::Loc; pub use alg_tools::sets::Cube; -use crate::measures::DiscreteMeasure; +// use crate::measures::DiscreteMeasure; /// [`Float`] with extra display and string conversion traits such that [`clap`] doesn't choke up. pub trait ClapFloat : Float @@ -31,6 +30,8 @@ pub n_spikes : usize, /// Number of iterations this statistic covers pub this_iters : usize, + /// Number of spikes inserted since last IterInfo statistic + pub inserted : usize, /// Number of spikes removed by merging since last IterInfo statistic pub merged : usize, /// Number of spikes removed by pruning since last IterInfo statistic @@ -43,8 +44,8 @@ pub transport_error : Option<(F, F)>, /// Current tolerance pub ε : F, - /// Solve fin.dim problem for this measure to get the optimal `value`. - pub postprocessing : Option<DiscreteMeasure<Loc<F, N>, F>>, + // /// Solve fin.dim problem for this measure to get the optimal `value`. + // pub postprocessing : Option<RNDM<F, N>>, } impl<F : Float, const N : usize> IterInfo<F, N> { @@ -55,10 +56,11 @@ n_spikes : 0, this_iters : 0, merged : 0, + inserted : 0, pruned : 0, inner_iters : 0, ε : F::NAN, - postprocessing : None, + // postprocessing : None, untransported_fraction : None, transport_error : None, } @@ -68,13 +70,14 @@ #[replace_float_literals(F::cast_from(literal))] impl<F, const N : usize> LogRepr for IterInfo<F, N> where F : LogRepr + Float { fn logrepr(&self) -> ColoredString { - format!("{}\t| N = {}, ε = {:.8}, inner_iters_mean = {}, merged+pruned_mean = {}+{}{}{}", + format!("{}\t| N = {}, ε = {:.8}, 𝔼inner_it = {}, 𝔼ins/mer/pru = {}/{}/{}{}{}", self.value.logrepr(), self.n_spikes, self.ε, - self.inner_iters as float / self.this_iters as float, - self.merged as float / self.this_iters as float, - self.pruned as float / self.this_iters as float, + self.inner_iters as float / self.this_iters.max(1) as float, + self.inserted as float / self.this_iters.max(1) as float, + self.merged as float / self.this_iters.max(1) as float, + self.pruned as float / self.this_iters.max(1) as float, match self.untransported_fraction { None => format!(""), Some((a, b)) => if b > 0.0 { @@ -117,7 +120,7 @@ } /// Data term type -#[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug, ValueEnum)] +#[derive(Clone, Copy, PartialEq, Serialize, Deserialize, Debug)] pub enum DataTerm { /// $\\|z\\|\_2^2/2$ L2Squared, @@ -140,10 +143,18 @@ pub struct L2Squared; /// Trait for indicating that `Self` is Lipschitz with respect to the (semi)norm `D`. -pub trait Lipschitz<D> { +pub trait Lipschitz<M> { /// The type of floats type FloatType : Float; /// Returns the Lipschitz factor of `self` with respect to the (semi)norm `D`. - fn lipschitz_factor(&self, seminorm : D) -> Option<Self::FloatType>; + fn lipschitz_factor(&self, seminorm : M) -> Option<Self::FloatType>; } + +/// Trait for norm-bounded functions. +pub trait NormBounded<M> { + type FloatType : Float; + + /// Returns a bound on the values of this function object in the `M`-norm. + fn norm_bound(&self, m : M) -> Self::FloatType; +}
