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zrSG@nxos;QCy(d0t#m9op4+z4=MDY(M}1r95d`+#c{QH5fnZYqH^A7%30$TF>9D53d~dpI75JXA-?m_D zq{#JV&DM;XDucO(sV(bfq55?5TMe=~mjo`uD#x3=Wfpn}!JuIzJ1t6f;R#jPV z+D3DElOn5CkGfr!!NN<^E8RUhs2-s{N(c__ZY~KjX@)$h)oiFqqpMjIq+>Pi3%M1t z)ht$dlt~4PX zt8!n^x{+*8!C~`LdTsd+4XQ`)i&`->#FoqFg4ee ziY3=Hqnp~GdaMQ>hCOR)cK7eh)v8CMS(lYc1-hw4UNXxZ%uqd6_;twnJ_Lg)*jaYh uj>p?G{r@PAe60i#$2Hpc)WMDa5Jqk61HKV9is-v0p-r?oZ! literal 0 HcmV?d00001 diff --git a/bachelorarbeit/src/calc.rs b/bachelorarbeit/src/calc.rs new file mode 100644 index 0000000..9ad9825 --- /dev/null +++ b/bachelorarbeit/src/calc.rs @@ -0,0 +1,221 @@ +use core::f64::consts::PI; +use gauss_quad::GaussLegendre; +use std::collections::HashMap; +use std::io; +use std::rc::Rc; + +use crate::gq_storage; // This should be moved to main.rs after new archtitecture (see main.rs TODO) + +pub type Complex = num::complex::Complex; + +const M_ROH: f64 = 0.7736; +const M_PI: f64 = 0.13957; +pub const S0: f64 = 4.0 * M_PI * M_PI; +const M_K: f64 = 0.496; +const B0: f64 = 1.055; +const B1: f64 = 0.15; +const LAMBDA1: f64 = 1.57; +const LAMBDA2: f64 = -1.96; +const LAMBDA_HIGH: f64 = 10.0; +pub const EPSILON: f64 = 1e-15; +const S_MID_CUTOFF: f64 = 1.42 * 1.42; +const INF: f64 = 1e5; + +#[derive(Default)] +pub struct Cache { + pub gauss_quad_lut: HashMap, Rc<[f64]>), nohash_hasher::BuildNoHashHasher>, + pub delta_lut: HashMap>, + pub omnes_lut: HashMap>, nohash_hasher::BuildNoHashHasher> // First key is n, second is s +} + +impl Cache { + pub fn from_file(filepath: &str) -> io::Result { + let me = Cache{ + gauss_quad_lut: gq_storage::deserialize(filepath, |_| true)?.into_iter() + .map(|(roots, weights)| (u32::try_from(roots.len()).unwrap(), (Rc::from(roots), Rc::from(weights)))).collect(), + delta_lut: HashMap::with_hasher(Default::default()), + omnes_lut: HashMap::with_hasher(Default::default()) + }; + Ok(me) + } +} + +// derivated values + +fn lambda_0() -> f64 { + delta((2.0*M_K).powi(2)) +} + +fn delta_mid_cutoff() -> f64 { + delta(S_MID_CUTOFF) +} + +fn atan_shift(x: f64) -> f64 { + let atan_std: f64 = x.atan(); + if atan_std < 0.0 { + atan_std + PI + } else { + atan_std + } +} + +fn integrate f64>(roots: &[f64], weights: &[f64], a:f64, b:f64, mut f: G) -> f64 { + let mut sum: f64 = 0.0; + let mut i: usize = 0; + if roots.len() != weights.len() { + panic!("Error: roots and weights are of different length"); + } + + while i < roots.len() { + sum += weights[i] * f(roots[i]*(b-a)/2.0 + (a+b)/2.0); + i += 1; + } + sum * (b-a)/2.0 +} + +fn integrate_complex Complex>(roots: &[f64], weights: &[f64], a:f64, b:f64, mut f: G) -> Complex { + let mut sum: Complex = Complex::new(0.0,0.0); + let mut i: usize = 0; + if roots.len() != weights.len() { + panic!("Error: roots and weights are of different length"); + } + while i < roots.len() { + sum += weights[i] * f(roots[i]*(b-a)/2.0 + (a+b)/2.0); + i += 1; + } + sum * (b-a)/2.0 +} + +fn omega(s: f64) -> f64 { + let a = s.sqrt(); + let b = (1.05f64.powi(2) - s).sqrt(); + (a - b) / (a + b) +} + +fn k(s: f64) -> f64 { + (s/4.0 - M_PI.powi(2)).sqrt() +} + +pub fn delta_with_lut(cache:&mut Cache, s: f64) -> f64 { + match cache.delta_lut.get(&s.to_bits()) { + Some(val) => { + *val + } + None => { + let val = delta(s); + cache.delta_lut.insert(s.to_bits(), val); + val + } + } +} + +pub fn delta(s: f64) -> f64 { + if s <= 2.0 * M_K { + atan_shift( + (s.sqrt() / (2.0*k(s).powi(3)) + * (M_ROH.powi(2) - s) + * ( (2.0*M_PI.powi(3)) / (M_ROH.powi(2) * s.sqrt()) + B0 + B1 * omega(s)) + ).powi(-1) + ) + } else if s <= S_MID_CUTOFF { + let par = 0.5 * s.sqrt() / M_K - 1.0; + lambda_0() + LAMBDA1 * par + LAMBDA2 * par.powi(2) + } else { + PI + + (delta_mid_cutoff() - PI) + * (LAMBDA_HIGH * LAMBDA_HIGH + S_MID_CUTOFF) + / (LAMBDA_HIGH * LAMBDA_HIGH + s) + } +} + +pub fn omnes_integrand_tan(cache:&mut Cache, s_tick:f64, s:f64) -> Complex { + let sub = s_tick.tan(); + (delta_with_lut(cache, sub) - delta_with_lut(cache, s)) + / ( + sub + * (sub - s + Complex::new(0.0, EPSILON)) + * s_tick.cos().powi(2) + ) +} + +pub fn omnes_integrand(cache:&mut Cache, s_tick:f64, s:f64) -> Complex { + (delta_with_lut(cache, s_tick) - delta_with_lut(cache, s)) + / (s_tick * (s_tick - s + Complex::new(0.0, EPSILON))) +} + +pub fn omnes(cache:&mut Cache, s:f64, n:u32, use_tan: bool) -> Complex { + let roots: Rc<[f64]>; + let weights: Rc<[f64]>; + + if let Some(inner_lut) = cache.omnes_lut.get(&n) { + if let Some(res) = inner_lut.get(&s.to_bits()) { + return *res + } + } + + if !cache.omnes_lut.contains_key(&n) { + cache.omnes_lut.insert(n, HashMap::with_hasher(Default::default())); + } + + match cache.gauss_quad_lut.get_mut(&n) { + Some(gq_values) => { + roots = Rc::clone(&gq_values.0); + weights = Rc::clone(&gq_values.1); + } + None => { + let gq_values = GaussLegendre::nodes_and_weights(n.try_into().unwrap()); + roots = Rc::from(gq_values.0.as_slice()); + weights = Rc::from(gq_values.1.as_slice()); + } + } + + if !cache.gauss_quad_lut.contains_key(&n) { + let gq_values = GaussLegendre::nodes_and_weights(n.try_into().unwrap()); + cache.gauss_quad_lut.insert(n, (Rc::from(gq_values.0), Rc::from(gq_values.1))); + println!("n_omnes={} is not included in the lookup file. Consider generating a new lookup file via the appropriate function in gq_storage.rs", n); + } + + let intgrl = if use_tan { + integrate_complex(&roots, &weights, S0.atan(), PI / 2.0, |s_tick| omnes_integrand_tan(cache, s_tick, s)) + } else { + integrate_complex(&roots, &weights, S0, INF, |s_tick| omnes_integrand(cache, s_tick, s)) + }; + let omnes_res = (s/PI*(intgrl)).exp() * (S0 / Complex::new(S0 - s, -EPSILON)).powf(delta_with_lut(cache, s) / PI); + //cache.omnes_lut.get_mut(&n).unwrap().insert(s.to_bits(), omnes_res); + println!("{:?}", omnes_res); + omnes_res +} + +pub fn phi0_integrand(cache:&mut Cache, x: f64, s: f64, n_omnes:u32, use_tan_omnes: bool) -> f64 { + let x_sub = x.tan().powi(2) + S0; + let omnes_s = omnes(cache, s, n_omnes, use_tan_omnes); + let omnes_x = omnes(cache, x_sub, n_omnes, use_tan_omnes); + (omnes_x / omnes_s).norm_sqr().ln() + / ( (x_sub)* (x_sub-s) ) + / x.cos().powi(2) // Don't use x_sub here, since this term is from tan substitution itself +} + +pub fn phi0(cache:&mut Cache, s: f64, n_omnes: u32, n_phi0: u32, use_tan_omnes: bool, use_tan_phi0: bool, use_xsub: bool) -> f64 { + if !cache.gauss_quad_lut.contains_key(&n_phi0) { + let gq_values = GaussLegendre::nodes_and_weights(n_phi0.try_into().unwrap()); + cache.gauss_quad_lut.insert(n_phi0, (Rc::from(gq_values.0), Rc::from(gq_values.1))); + println!("n_omnes={} is not included in the lookup file. Consider generating a new lookup file via the appropriate function in gq_storage.rs", n_phi0); + } + let (ref roots, ref weights) = cache.gauss_quad_lut.get(&n_phi0).unwrap(); + let (roots, weights) = (Rc::clone(roots), Rc::clone(weights)); + + let analyt = omnes(cache, s, n_omnes, use_tan_omnes).norm_sqr().ln() / S0.sqrt() / 2.0; + let intgrl = s / PI * integrate(&*roots, &*weights, 0.0, PI / 2.0, |x| phi0_integrand(cache,x,s,n_omnes, use_tan_omnes)); + -(s-S0).sqrt() * (intgrl - analyt) +} + +#[allow(unused)] +pub fn bit_pattern_randomness_tester(a:f64, b:f64, n_points: u64) -> Vec{ + let mut modulos = vec![0.0; n_points as usize]; + let x_values: Vec = (0..modulos.len() as u32).map(|x| (f64::from(x) * ((b - a) / f64::from(modulos.len() as u32)) + a).to_bits()).collect(); + for i in 0..x_values.len() { + let val = (x_values[i] % n_points) as usize; + modulos[val] += 1.0; + } + modulos +} diff --git a/bachelorarbeit/src/gq_storage.rs b/bachelorarbeit/src/gq_storage.rs new file mode 100644 index 0000000..77c916c --- /dev/null +++ b/bachelorarbeit/src/gq_storage.rs @@ -0,0 +1,84 @@ +//! This module writes and reads roots and weights of gauss-quad into files, using a dedicated file format. +//! The format works as follows: One u64 is written, indicating the n of the roots and weights that follow +//! (thereby hinting at the number of floats that are following before the next u64, which is 2*n). This is repeated for +//! arbitrary n. + +#![allow(dead_code)] + +use std::{ + fs::File, + io::{self, BufReader, BufWriter, Read, Write, Seek, SeekFrom}, +}; + +use gauss_quad::GaussLegendre; + +/// Writes roots and weights of gauss-quad into a file at `filepath`. params contains roots and weights for multiple n. +pub fn serialize(filepath: &str, params: Vec<(Vec, Vec)>) -> io::Result<()> { + let file = File::create(filepath)?; + let mut file = BufWriter::new(file); + for (roots, weights) in params.iter() { + file.write_all(&u64::try_from(roots.len()).unwrap().to_le_bytes())?; + for root in roots { + file.write_all(&root.to_bits().to_le_bytes())?; + } + for weight in weights { + file.write_all(&weight.to_bits().to_le_bytes())?; + } + } + Ok(()) +} + +pub fn deserialize(filepath: &str, filter: impl Fn(u64) -> bool) -> io::Result, Vec)>> { + let file = File::open(filepath)?; + let mut file = BufReader::new(file); + let mut buf = [0u8; 8]; + + let mut values = Vec::new(); + + 'outer: loop { + let res = file.read(&mut buf)?; + if res < 8 { + break; + } + let n = u64::from_le_bytes(buf); + + // skips stored floats for n that should not be stored + if !filter(n) { + file.seek(SeekFrom::Current(i64::try_from(2*n*8).unwrap())).unwrap(); + continue; + } + + // Stores roots and weights into values Vec + + let mut roots = Vec::new(); + for _ in 0..n { + let res = file.read(&mut buf)?; + if res < 8 { + break 'outer; + } + roots.push(f64::from_bits(u64::from_le_bytes(buf))); + } + + let mut weights = Vec::new(); + for _ in 0..n { + let res = file.read(&mut buf)?; + if res < 8 { + break 'outer; + } + weights.push(f64::from_bits(u64::from_le_bytes(buf))); + } + values.push((roots, weights)); + } + Ok(values) +} + +pub fn fill_with_gauss_quad(n_values: Vec) { + let mut params = Vec::new(); + for i in n_values { + let gq = GaussLegendre::init(usize::try_from(i).unwrap()); + params.push((gq.nodes, gq.weights)); + } + serialize("./gauss_quad_lut.morello", params).unwrap(); + let res = deserialize("./gauss_quad_lut.morello", |_| true); + println!("{:?}", res); +} \ No newline at end of file diff --git a/bachelorarbeit/src/main.rs b/bachelorarbeit/src/main.rs new file mode 100644 index 0000000..dd07f2d --- /dev/null +++ b/bachelorarbeit/src/main.rs @@ -0,0 +1,247 @@ + +// TODO +// - Lookup Table implementieren -> Weights, roots schon früher rausziehen? +// -> Warum macht delta_lut alles langsamer? +// - Omnes auch komplex integrieren (geht nicht mit Integralmethode von gauss-quad) +// - Textfelder und "Berechnen"-Button in UI, um z.B. Wertebereich zu setzen +// - Neue Architketur: struct calculator, das lookups speichert -> In die nötigen Funktionen übergeben. Dadurch kann man omnes auch als single calc machen und trotzdem die Punkte nur einmal berechnen +// - AutoImport ausschalten + + +use egui_plot::{log_grid_spacer, AxisHints, GridInput, GridMark, Legend, Line, Plot}; +use num::complex::ComplexFloat; +use std::time::Instant; + +mod gq_storage; +mod calc; + +struct App { + plot_data: Vec, + plots_available: [String; 6], + calc_cache: calc::Cache, + scaling_type: ScalingType, + a: f64, + b: f64, + n_points: u32, + n_omnes: u32, + n_phi0: u32, + use_tan_omnes: bool, + use_tan_phi0: bool, + use_xsub_phi0: bool +} + +#[derive(Clone)] +struct PlotCurve { + points: Vec<[f64;2]>, + name: String, +} + +impl Default for App { + fn default() -> Self { + App { + plot_data: Vec::default(), + plots_available: ["Delta".to_string(), "Omnes Integrand".to_string(), "Omnes".to_string(), "Phi0 Integrand".to_string(), "Phi0".to_string(), "Prozentueller Fehler".to_string()], + calc_cache: calc::Cache::default(), + scaling_type: ScalingType::default(), + a: calc::S0, + b: 9.0, + n_points: 5000, + n_omnes:1000, + n_phi0:1000, + use_tan_omnes: true, + use_tan_phi0: true, + use_xsub_phi0: true + } + } +} + +#[derive(Debug, Default, PartialEq, Clone, Copy)] +enum ScalingType { + Logarithmic, + #[default] + Linear +} + +impl eframe::App for App { + fn update(&mut self, ctx: &egui::Context, _frame: &mut eframe::Frame) { + egui::CentralPanel::default().show(ctx, |ui| { + let cur_scaling_type = self.scaling_type; + egui::ComboBox::from_label("pick y-scaling").selected_text(format!("{:?}", self.scaling_type)).show_ui(ui, |ui| { + ui.selectable_value(&mut self.scaling_type, ScalingType::Logarithmic, "log10"); + ui.selectable_value(&mut self.scaling_type, ScalingType::Linear, "linear"); + }); + + float_text_edit_singleline(ui, &mut self.a); + float_text_edit_singleline(ui, &mut self.b); + int_text_edit_singleline(ui, &mut self.n_points); + int_text_edit_singleline(ui, &mut self.n_omnes); + int_text_edit_singleline(ui, &mut self.n_phi0); + + ui.checkbox(&mut self.use_tan_omnes, "Use tan()-subst. for Omnes"); + ui.checkbox(&mut self.use_tan_phi0, "Use tan()-subst. for Phi0"); + ui.checkbox(&mut self.use_xsub_phi0, "Use second subst. for Phi0"); + + let button_clear = ui.button("Clear canvas"); + if button_clear.clicked() { + self.plot_data = Vec::new(); + } + + for i in 0..self.plots_available.len() { + let button = ui.button( format!("Calculate {}", self.plots_available[i].clone())); + if button.clicked() { + let x_values: Vec = (0..self.n_points).map(|x| -> f64 {f64::from(x) * ((self.b - self.a) / f64::from(self.n_points)) + self.a}).collect(); + match i { + 0 => { + let y_values_delta:Vec = x_values.iter().map(|&x| calc::delta_with_lut(&mut self.calc_cache, x)).collect(); + self.plot_data.push(PlotCurve { + points: x_values.iter().zip(y_values_delta.iter()).map(|(&x,&y)| [x.powf(0.5),y]).collect(), + name: "Delta".to_string() + }) + } + 1 => { + let y_values_omnes_integrand: Vec = x_values.iter().map(|&x| calc::omnes_integrand(&mut self.calc_cache, x, 100.0).abs()).collect(); + self.plot_data.push(PlotCurve { + points: x_values.iter().zip(y_values_omnes_integrand.iter()).map(|(&x,&y)| [x.powf(0.5),y]).collect(), + name: "Omnes Integrand".to_string() + }) + } + 2 => { + let y_values_omnes: Vec = x_values.iter().map(|&x| calc::omnes(&mut self.calc_cache, x, self.n_omnes, self.use_tan_omnes).abs().powi(2)).collect(); + self.plot_data.push(PlotCurve { + points: x_values.iter().zip(y_values_omnes.iter()).map(|(&x,&y)| [x.powf(0.5),y]).collect(), + name: "Omnes".to_string() + }) + } + 3 => { + let y_values_phi0_integrand: Vec = x_values.iter().map(|&x| calc::phi0_integrand(&mut self.calc_cache, x, 10000.0, self.n_omnes, self.use_tan_omnes)).collect(); + self.plot_data.push(PlotCurve { + points: x_values.iter().zip(y_values_phi0_integrand.iter()).map(|(&x,&y)| [x.powf(0.5),y]).collect(), + name: "Phi0 Integrand".to_string() + }) + } + 4 => { + let t0 = Instant::now(); + let y_values_phi0: Vec = x_values.iter().map(|&x| calc::phi0(&mut self.calc_cache, x, self.n_omnes, self.n_phi0, self.use_tan_omnes, self.use_tan_phi0, self.use_xsub_phi0)).collect(); + println!("{:?}", t0.elapsed()); + self.plot_data.push(PlotCurve { + points: x_values.iter().zip(y_values_phi0.iter()).map(|(&x,&y)| [x.powf(0.5),y]).collect(), + name: "Phi0".to_string() + }) + // let y_values_phi0 = calc::bit_pattern_randomness_tester(self.a, self.b, self.n_points as u64); + // self.plot_data.push(PlotCurve { + // points: (0..self.n_points).zip(y_values_phi0.iter()).map(|(x,&y)| [x as f64,y]).collect(), + // name: "Phi0".to_string() + // }) + } + 5 => { + let y_values_phi0: Vec = x_values.iter().map(|&x| { + let t0 = Instant::now(); + let val = calc::phi0(&mut self.calc_cache, x.powi(2), self.n_omnes, self.n_phi0, self.use_tan_omnes, self.use_tan_phi0, self.use_xsub_phi0) / calc::delta_with_lut(&mut self.calc_cache, x.powi(2)) - 1.0; + println!("time for x = {}: {:?}", x, t0.elapsed()); + val + }).collect(); + self.plot_data.push(PlotCurve { + points: x_values.iter().zip(y_values_phi0.iter()).map(|(&x,&y)| [x,y]).collect(), + name: "Phi0".to_string() + }) + } + 6_usize.. => { + panic!("Not all buttons have been assigned data!"); + } + } + } + } + + if self.scaling_type != cur_scaling_type { + for curve in self.plot_data.iter_mut() { + for [_x,y] in curve.points.iter_mut() { + if self.scaling_type == ScalingType::Linear { + *y = 10.0f64.powf(*y); + } else if self.scaling_type == ScalingType::Logarithmic { + *y = y.log10(); + } + } + } + } + + let plot = Plot::new("my_plot") + .grid_spacing(5.0f32..=300.0f32) + .x_axis_label("sqrt(s) [GeV]") + .y_axis_label("|Omega|^2") + .legend(Legend::default()); + + let plot = match self.scaling_type { + ScalingType::Linear => plot.custom_y_axes(vec![AxisHints::new_y().formatter(|mark, _l, _| scientific_notation(mark.value, false))]), + ScalingType::Logarithmic => {plot.y_grid_spacer(|input| { + let input_exp = GridInput {bounds: (inverse_log_map(input.bounds.0), inverse_log_map(input.bounds.1)), base_step_size: input.base_step_size}; + let lin_gridmarks = (log_grid_spacer(10))(input_exp); + let mut log_gridmarks: Vec = Vec::new(); + for v in lin_gridmarks.iter() { + if v.value - v.value.floor() < 0.9 { + log_gridmarks.push(GridMark{value:log_map(v.value), step_size:v.step_size / 1.14}); + } + } + log_gridmarks + }) + .label_formatter(|_,point| format!("x = {:.5}\ny = {:.5}", point.x, 10.0f64.powf(point.y)).to_string()) + .custom_y_axes(vec![AxisHints::new_y().formatter(|mark, _l, _| scientific_notation(mark.value, true))]) + } + }; + + plot.show(ui, |plot_ui| { + for i in 0..self.plot_data.len() { + plot_ui.line(Line::new(self.plot_data[i].points.clone()).name(self.plot_data[i].name.clone())); // is clone necessary? + } + }); + }); + } +} + +fn main() { + let mut app = App::default(); + app.calc_cache = calc::Cache::from_file("./gauss_quad_lut.morello").unwrap(); + // let x_values: Vec = (0..app.n_points).map(|x| -> f64 {f64::from(x) * ((app.b - app.a) / f64::from(app.n_points)) + app.a}).collect(); + // let t0 = Instant::now(); + // let y_values_phi0: Vec = x_values.iter().map(|&x| calc::phi0(&mut app.calc_cache, x, app.n_omnes, app.n_phi0)).collect(); + // std::hint::black_box(&y_values_phi0); + // println!("{:?}", t0.elapsed()); + + eframe::run_native("Morellus", eframe::NativeOptions::default(), Box::new(|_cc| Box::new(app))).unwrap(); +} + +fn log_map(x:f64) -> f64 { + x.floor() + (1.0 + (x - x.floor()) * 10.0).log10() +} + +fn inverse_log_map(x:f64) -> f64 { + x.floor() + (10f64.powf(x - x.floor()) - 1.0) / 10.0 +} + +fn scientific_notation(x:f64, log:bool) -> String { + if log { + format!("{}*10^{}", format!( + "{:.15}", 10f64.powf(x - x.floor())) + .trim_end_matches('0').trim_end_matches('.').to_string(), + x.floor()).to_string() + } else { + format!("{:.9}", x).trim_end_matches('0').trim_end_matches('.').to_string() + } +} + +fn int_text_edit_singleline(ui: &mut egui::Ui, value: &mut u32) -> egui::Response { + let mut tmp_value = format!("{}", value); + let res = ui.text_edit_singleline(&mut tmp_value); + if let Ok(result) = tmp_value.parse::() { + *value = result; + } + res +} + +fn float_text_edit_singleline(ui: &mut egui::Ui, value: &mut f64) -> egui::Response { + let mut tmp_value = format!("{}", value); + let res = ui.text_edit_singleline(&mut tmp_value); + if let Ok(result) = tmp_value.parse::() { + *value = result; + } + res +} \ No newline at end of file diff --git a/bachelorarbeit/text.txt b/bachelorarbeit/text.txt new file mode 100644 index 0000000..d2f608a --- /dev/null +++ b/bachelorarbeit/text.txt @@ -0,0 +1,19 @@ +BTreeMap: 1.2234s + phi0_integrand: + omnes: 29.30% + get: 22.87% + integrate_complex: 5.01% + delta_with_lut + get: 2.50% + omnes_integrand: 37.98% + delta_with_lut -> get: 22.20% + +HashMap: 1.0767s + phi0_integrand: + omnes: 35.22% + get: 30.40% + integrate_complex: 3.95% + delta_with_lut + get: 1.88% + omnes_integrand: 27.21% + delta_with_lut -> get: 14.03% diff --git a/calc.py b/calc.py new file mode 100644 index 0000000..c445eff --- /dev/null +++ b/calc.py @@ -0,0 +1,34 @@ +import math + +m_e = 9.10938e-31 +e = 1.602e-19 +pi = 3.141592 +epsilon_0 = 8.854e-12 +h_bar = 1.05457e-34 +h=6.626e-34 +c=299792458 +my_B=9.274e-24 +k_B=1.381e-23 +avog=6.022e26 +m_Kalium=39.0983/avog + +def E(n): + return -m_e*e**4 / (2*(4*pi*epsilon_0*h_bar*n)**2) + +def dE(n1,n2): + return -m_e*e**4 / (2*(4*pi*epsilon_0*h_bar)**2) * (1/n2**2 - 1/n1**2) + +def lamb(E1,E2): + return c*h*(E1-E2)**-1 + +# print(E(3)) +# print(E(2)) +# print(lamb(E(3),E(2)-2*my_B*2)*10**9) +Ekin = 3/2*k_B*600 +v_x = math.sqrt(2*Ekin/m_Kalium) +t_acc = 0.2 / v_x +F = my_B * 2 +d = 1/2*F/m_Kalium*t_acc**2 +v_z_end = F/m_Kalium*t_acc +print(v_z_end/v_x) +print(1.492+0.1492) \ No newline at end of file diff --git a/ersterTest.py b/ersterTest.py new file mode 100644 index 0000000..269cc1a --- /dev/null +++ b/ersterTest.py @@ -0,0 +1,280 @@ +import numpy as np +import matplotlib.pyplot as plt +from scipy.special import roots_legendre +import cmath +from time import time + +# constant values (GeV) + +M_roh = 0.7736 +M_pi = 0.13957 +s_0 = 4*M_pi**2 +M_K = 0.496 +B_0 = 1.055 +B_1 = 0.15 +lambda_1 = 1.57 +lambda_2 = -1.96 +lambda_high = 10 +epsilon = 0.000000001 +s_mid_high = 1.42**2 # this is the s value, so it is in GeV^2 + +# derivative values +lambda_0 = 0 # this is fixed by the low energy parametrization: lambda_0 = delta1_low(4M_K**2) (sqrt(s)=2M_K) +delta1_mid_high = 0 # again, this is fixed by the value of delta1_mid at 1.42 GeV (see later in the code) + +# Numerical constants +gl_n_omnes = 100 # number of points used in the Gauss Legendre Integration +gl_n_phi0 = 100 + +gl_lookup = {} +omnes_lookup = {} +delta_lookup = {} + +# Print iterations progress +def printProgressBar (iteration, total, prefix = '', suffix = '', decimals = 1, length = 100, fill = '█', printEnd = "\r"): + """ + Call in a loop to create terminal progress bar + @params: + iteration - Required : current iteration (Int) + total - Required : total iterations (Int) + prefix - Optional : prefix string (Str) + suffix - Optional : suffix string (Str) + decimals - Optional : positive number of decimals in percent complete (Int) + length - Optional : character length of bar (Int) + fill - Optional : bar fill character (Str) + printEnd - Optional : end character (e.g. "\r", "\r\n") (Str) + """ + percent = ("{0:." + str(decimals) + "f}").format(100 * (iteration / float(total))) + filledLength = int(length * iteration // total) + bar = fill * filledLength + '-' * (length - filledLength) + print(f'\r{prefix} |{bar}| {percent}% {suffix}', end = printEnd) + # Print New Line on Complete + if iteration == total: + print() + +''' the standard implementation of arctan gives angles in (-pi/2, pi/2). This gives angles in (0, pi). Note: This doesn't imply a simple shift of all values by pi, but a transposition of the results from (-pi/2, 0) to (pi/2, pi).''' +def arctan_shift(x): + atan_std = np.arctan(x) + if atan_std < 0: + return atan_std + np.pi + return atan_std + +def log_shift(x): + log_std = cmath.log(x) + if log_std.imag < 0: + return 2*np.pi*1j + log_std + else: + return log_std + +def omega(s): + # in this instance, Elena uses s_0**(1/2) = 1.05 GeV, but later she uses s_0 = 4*M_pi**2 + a = np.sqrt(s) + b = np.sqrt(1.05**2 - s) + return (a - b) / (a + b) + + +# ---------------- +# Delta function section +# ---------------- + +def k(s): + return np.sqrt(s/4-M_pi**2) + +def delta1_low(s): + #a = np.sqrt(s) / (2*k(s)**3) * (M_roh**2 - s) * ( (2*M_pi**3) / (M_roh**2*np.sqrt(s)) + B_0 + B_1*omega(s) ) + return arctan_shift((np.sqrt(s) / (2*k(s)**3) * (M_roh**2 - s) * ( (2*M_pi**3)/(M_roh**2*np.sqrt(s)) + B_0 + B_1*omega(s)))**-1) + +def delta1_mid(s): + return lambda_0 + lambda_1 * (0.5*np.sqrt(s) / M_K - 1) + lambda_2 * (0.5*np.sqrt(s) / M_K - 1)**2 + +def delta1_high(s): + return np.pi + (delta1_mid_high - np.pi) * (lambda_high**2 + s_mid_high) / (lambda_high**2 + s) + + +def delta(s): + # if s in delta_lookup: + # return delta_lookup[s] + # if s < (2*M_K)**2: + # delta_lookup[s] = delta1_low(s) + # elif s < s_mid_high: + # delta_lookup[s] = delta1_mid(s) + # else: + # delta_lookup[s] = delta1_high(s) + # return delta_lookup[s] + if s < (2*M_K)**2: + return delta1_low(s) + elif s < s_mid_high: + return delta1_mid(s) + else: + return delta1_high(s) + + +# set cutoff values +lambda_0 = delta1_low((2*M_K)**2) +delta1_mid_high = delta1_mid(s_mid_high) + + +# ---------------- +# Omnes Integral section +# ---------------- + +delta_time = 0 + +def omnes_integrand(s_tick,s): + global delta_time + delta_s_tick = delta(s_tick) + delta_s = delta(s) + return (delta_s_tick - delta_s)/(s_tick*(s_tick-s+epsilon*1j)) + + +def integral_gl(f,s,a,b,n, prog=False): + if n not in gl_lookup: + # print("now calculating roots, weights") + t0 = time() + gl_lookup[n] = roots_legendre(n) + #print("time to calculate roots and weights with n={}: {} seconds".format(n,time() - t0)) + roots, weights = gl_lookup[n] + sum = 0 + for i in range(n): + if prog: + printProgressBar(i,n) + sum += weights[i]*f(roots[i]*(b-a)/2 + (a+b)/2,s) + sum *= (b-a)/2 + return sum + +def subst(f, phi, phi_deriv): + return lambda x,s : f(phi(x),s)*phi_deriv(x) + +def integral_gl_tan_reparam(f,s,a,b,n, prog=False): + return integral_gl(subst(f,np.tan,lambda x : (1 / np.cos(x)**2)),s,np.arctan(a),np.pi / 2,n,prog) + +def omnes(s, a=s_0, inf = 10000000000, optimized = True, n = gl_n_omnes): + if s in omnes_lookup: + return omnes_lookup[s] + elif optimized: + analyt = delta(s) / s * cmath.log(((inf-s-epsilon*1j)*a) / ((a-s-epsilon*1j)*inf)) + res = cmath.exp(s/np.pi*(integral_gl_tan_reparam(omnes_integrand,s,a,inf,n) + analyt)) + #omnes_lookup[s] = res + return res + else: + res = cmath.exp(s/np.pi*(integral_gl(omnes_integrand,s,a,inf,n)+delta(s) / s * cmath.log(((inf-s-epsilon*1j)*a) / ((a-s-epsilon*1j)*inf)))) + #omnes_lookup[s] = res + return res + # A more easily readible version of the formula + # if optimized == True: + # m = integral_gl_tan_reparam(omnes_integrand,s,a,inf,n)- + # else: + # m = integral_gl(omnes_integrand,s,a,inf,n) + # n = ((inf-s-epsilon*1j)*a) / ((a-s-epsilon*1j)*inf) + # p = delta(s) / s * cmath.log(n) + # omnes_lookup[s] = cmath.exp(s/np.pi*(m+p)) + # if s > 0.74**2 and s < 0.76**2: + # print(s, m, n, p, cmath.exp(s/np.pi*(m+p))) + # return cmath.exp(s/np.pi*(m+p)) + +# ---------------- +# Phase reconstruction section +# ---------------- + +def phi0_integrand_bad(s_tick, s): + omnes_s = omnes(s) + omnes_s_tick = omnes(s_tick) + #a = np.log(cmath.polar(omnes_s_tick / omnes_s)[0]**2) + #b = np.sqrt(s_tick - s_0) * s_tick * (s_tick - s) + return np.log(cmath.polar(omnes_s_tick / omnes_s)[0]**2) / (np.sqrt(s_tick - s_0) * s_tick * (s_tick - s)) + +def phi0_integrand(x, s): + omnes_s = omnes(s) + omnes_x = omnes(x**2 + s_0) + + #a = np.log(cmath.polar(omnes_s_tick / omnes_s)[0]**2) + #b = np.sqrt(s_tick - s_0) * s_tick * (s_tick - s) + return 2*np.log(cmath.polar(omnes_x / omnes_s)[0]**2) / ((s_0 + x**2) * (s_0 + x**2 - s)) + +def phi0(s, a=0, inf = 100000, optimized = True, n = gl_n_phi0): + c = np.pi / (s * np.sqrt(s_0)) * np.log(cmath.polar(omnes(s))[0]**2) + + if optimized == True: + integral = integral_gl_tan_reparam(phi0_integrand, s, a, inf, n, False) + else: + integral = integral_gl(phi0_integrand, s, a, inf, n) + return -s * np.sqrt(s-s_0) / (2*np.pi) * (integral - c) + +# ---------------- +# Plotting section +# ---------------- + + +fig, ax = plt.subplots() + +# these are sqrt(s) values, not s +x = np.linspace(s_0**0.5+0.001,3,500) +#x = np.linspace(0.7, 0.85, 500) +x_to_pi2 = np.linspace(np.arctan(s_0)**0.5+0.001,(np.pi/2)**0.5,5000) + +y_delta = [delta(i**2) for i in x] +#y1 = [cmath.polar(omnes_integrand(i**2,0.73))[0]**2 for i in x] +#y2 = [cmath.polar(omnes_integrand(i**2,0.73965))[0]**2 for i in x] +#y3 = [cmath.polar(omnes_integrand(i**2,0.75))[0]**2 for i in x] +#y_omnes_integrand_tan = [cmath.polar(omnes_integrand(np.tan(i**2),2) / np.cos(i**2)**2)[0]**2 for i in x_to_pi)] +#y_omnes_acc = [cmath.polar(omnes(i**2, optimized=True))[0]**2 for i in x] +#y_omnes_best = [cmath.polar(omnes(i**2, inf=10000, n = 10000))[0]**2 for i in x] +#y_phi0_integrand = [phi0_integrand(i**2, 2) for i in x] +#y_phi0_integrand_tan = [phi0_integrand(np.tan(i**2), 0.8)*1/np.cos(i**2)**2 for i in x_to_pi2] +#y_phi0_integrand_tan2 = [phi0_integrand(np.tan(i**2), 10000)*1/np.cos(i**2)**2 for i in x_to_pi2] +#y_phi0_integrand2 = [phi0_integrand(i**2, 0.8035457451490298) for i in x_phi0] + +''' +for n in [10,100,1000,10000]: + print("Phi0 for n_omnes={}, n_phi0={}: {}".format(gl_n_omnes, n, phi0(100**2, n=n))) +''' + +''' +n_values = [10,100,1000,10000,100000] +y_phi0 = [[] for _ in n_values] +for (i_n,n) in enumerate(n_values): + +# for (i,val) in enumerate(x): +# y_phi0[i_n].append(phi0(val**2, n = n)) +# printProgressBar(i,len(x)) + print("Ready with {}".format(n)) + print() +''' +# Test sensitivity of phi0 to n compared to omnes +''' +n_values = np.arange(5, 4000, 25) +y_omnes_n_cmp = [cmath.polar(omnes(0.8**2, n=i))[0]**2 for i in n_values] +y_phi0_n_cmp = [phi0(0.8**2, n=i) for i in n_values] +ax.plot(n_values, y_omnes_n_cmp, label = "omnes") +ax.plot(n_values, y_phi0_n_cmp, label = "phi0") +''' + +ax.plot(x, y_delta, label = r"$\delta$") +#ax.plot(x, y2, label = "delta") +#ax.plot(x, y3, label = "delta") +#ax.plot(x_to_pi2, y_omnes_integrand_tan, label = r"$\Omega$ integrand w/ tan-param.") +#ax.plot(x, y_omnes, label = r'${|\Omega (s)|}^2$') +#ax.plot(x, y_omnes_acc, label = r'${|\Omega (s)|}^2$, reparam') +#ax.plot(x, y_omnes_best, label = r'${|\Omega (s)|}^2$, but best') +#ax.plot(x, y_phi0_integrand, label = r'$\phi_0$ Integrand') +#ax.plot(x_to_pi2, y_phi0_integrand_tan, label = r'$\phi_0$ integrand w/ tan-param.') +#ax.plot(x_to_pi2, y_phi0_integrand_tan2, label = r'$\phi_0$ integrand w/ tan-param, s=10000.') +#ax.plot(x_phi0, y_phi0_integrand2, label = r'$\phi_0$ Integrand2') +#for (i,y) in enumerate(y_phi0): + #ax.plot(x, y, label = r'$\phi_0, n={}$'.format(i)) + +# t0 = time() +# y_phi0 = [phi0(i**2) for i in x] +# ax.plot(x, y_phi0) +# print(time() - t0) + +t0 = time() +print(phi0(10000, n=100)) +print(time() - t0) + +# ax.legend() +# #plt.yscale('log') +# ax.grid(which='major', color='#A4A4A4', linewidth=1) +# ax.grid(which='minor', color='#B5B5B5', linestyle=':', linewidth=0.5) +# ax.minorticks_on() +# plt.show() \ No newline at end of file