Working multithreaded version backup

bachelorarbeit/plotter.py

@@ -0,0 +1,125 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import scienceplots
+
+i = 1
+
+names = [
+    "omnes_integrand",
+    "omnes_integrand_zoom",
+    "omnes_integrand_tan",
+    "phi0_integrand",
+    "phi0_integrand_zoom",
+    "phi0_integrand_tan",
+    "delta",
+    "omnes",
+    "phi0",
+    "phi0_delta_rel_diff",
+]
+
+files = [open("exports/" + n + ".txt") for n in names]
+
+export_filenames = ["figures/" + n + ".png" for n in names]
+
+titles = [
+    r"$\frac{\delta_1^1(s') - \delta_1^1(s)}{s'(s'-s)}$, $\sqrt{s}=1$ GeV",
+    r"$\frac{\delta_1^1(s') - \delta_1^1(s)}{s'(s'-s)}$, $\sqrt{s}=1$ GeV",
+    r"$\frac{1}{\cos^2(u)}\frac{\delta_1^1(\tan{u}) - \delta_1^1(s)}{\tan{u}(\tan{u}-s)}$, $\sqrt{s}=1$ GeV",
+    r"$\frac{\ln{|\frac{F(s')}{F(s)}|^2}}{(x^2+s_0)(x^2+s_0-s)}$, $\sqrt{s}=1$ GeV",
+    r"$\frac{\ln{|\frac{F(s')}{F(s)}|^2}}{(x^2+s_0)(x^2+s_0-s)}$, $\sqrt{s}=1$ GeV",
+    r"$\frac{1}{\cos^2(u)}\frac{\ln{|\frac{F(\tan^2{u}+s_0)}{F(s)}|^2}}{(\tan^2{u}+s_0)(\tan^2{u}+s_0-s)}$, $\sqrt{s}=1$ GeV",
+    "",
+    "",
+    "",
+    "",
+]
+
+xlabels = [
+    r"$\sqrt{s}$ [GeV]",
+    r"$\sqrt{s}$ [GeV]",
+    r"$u$",
+    r"$x$",
+    r"$x$",
+    r"$u$",
+    r"$\sqrt{s}$ [GeV]",
+    r"$\sqrt{s}$ [GeV]",
+    r"$\sqrt{s}$ [GeV]",
+    r"$\sqrt{s}$ [GeV]",
+]
+
+ylabels = [
+    r"integrand",
+    r"integrand",
+    r"integrand",
+    r"integrand",
+    r"integrand",
+    r"integrand",
+    r"$\delta_1^1(s)$",
+    r"$|\Omega(s)|^2$",
+    r"$\phi_0(s)$",
+    r"$\frac{\phi_0(s)}{\delta_1^1(s)}$",
+]
+
+y_logarithmic = [
+    False,
+    False,
+    False,
+    False,
+    False,
+    False,
+    False,
+    True,
+    False,
+    False,
+]
+
+x_sqrt = [
+    True,
+    True,
+    False,
+    False,
+    False,
+    False,
+    True,
+    True,
+    True,
+    True,
+]
+
+for i in range(len(names)):
+    print(i)
+    plt.figure()
+    filecont = []
+    for line in files[i]:
+        filecont.append(line.split(','))
+
+    data = []
+    for curve in filecont:
+        curve_numbers = []
+        for val in curve:
+            try:
+                curve_numbers.append(float(val))
+            except ValueError:
+                continue
+        if x_sqrt[i]:
+            curve_numbers_paired = np.array([[x**0.5 for x in curve_numbers[0::2]], curve_numbers[1::2]])
+        else:
+            curve_numbers_paired = np.array([curve_numbers[0::2], curve_numbers[1::2]])
+        data.append(curve_numbers_paired)
+
+    # Plotting
+
+    plt.style.use(['science'])
+
+    plt.figure(figsize=(4,3))
+    plt.title(titles[i], fontsize = 15)
+    if y_logarithmic[i]:
+        plt.yscale('log')
+    for j in range(len(data)):
+        plt.plot(data[j][0], data[j][1])
+    plt.xlabel(xlabels[i], fontsize = 12)
+    plt.ylabel(ylabels[i], fontsize = 12)
+    plt.grid(which='major', color='#000000', linestyle='-', alpha = 0.3)
+    plt.grid(which='minor', color='#000000', linestyle='-', alpha=0.1)
+    plt.savefig(export_filenames[i], dpi=400)
+    plt.close()

bachelorarbeit/src/calc.rs

@@ -13,18 +13,18 @@ use crate::gq_storage;
 
 pub type Complex = num::complex::Complex<f64>;
 
-const M_ROH: f64 = 0.7736;
+pub const M_ROH: f64 = 0.7736;
-const M_PI: f64 = 0.13957;
+pub const M_PI: f64 = 0.13957;
 pub const S0: f64 = 4.0 * M_PI * M_PI;
-const M_K: f64 = 0.496;
+pub const M_K: f64 = 0.496;
-const B0: f64 = 1.055;
+pub const B0: f64 = 1.055;
-const B1: f64 = 0.15;
+pub const B1: f64 = 0.15;
-const LAMBDA1: f64 = 1.57;
+pub const LAMBDA1: f64 = 1.57;
-const LAMBDA2: f64 = -1.96;
+pub const LAMBDA2: f64 = -1.96;
-const LAMBDA_HIGH: f64 = 10.0;
+pub const LAMBDA_HIGH: f64 = 10.0;
 pub const EPSILON: f64 = 1e-15;
-const S_MID_CUTOFF: f64 = 1.42 * 1.42;
+pub const S_MID_CUTOFF: f64 = 1.42;
-const INF: f64 = 1e6;
+pub const INF: f64 = 1e6;
 
 #[derive(Default)]
 pub struct Cache {
@@ -105,12 +105,8 @@ impl Cache {
 
 // derivated values
 
-fn lambda_0() -> f64 {
+fn lambda_0(cache: &Cache) -> f64 {
-    delta((2.0 * M_K).powi(2))
+    delta_with_lut(cache, (2.0 * M_K).powi(2))
-}
-
-fn delta_mid_cutoff() -> f64 {
-    delta(S_MID_CUTOFF)
 }
 
 fn atan_shift(x: f64) -> f64 {
@@ -133,7 +129,6 @@ fn integrate<G: Fn(f64) -> f64 + Send + Sync>(
     if roots.len() != weights.len() {
         panic!("Error: roots and weights are of different length");
     }
-    println!("Calculating single integration: ");
     let prog = indicatif::ProgressBar::new(roots.len() as u64);
     let prog_ = prog.clone();
     let sum:f64 = (weights.par_iter(), roots.par_iter()).into_par_iter().map(move |(weight,root)| {
@@ -183,30 +178,69 @@ fn k(s: f64) -> f64 {
 }
 
 pub fn delta_with_lut(cache: &Cache, s: f64) -> f64 {
-    // println!("delta_with_lut");
     match cache.delta_lut.get(&s.to_bits()) {
         Some(val) => *val,
         None => {
-            let val = delta(s);
+            let val = delta(cache, s);
             let _ = cache.delta_lut.insert(s.to_bits(), val);
             val
         }
     }
 }
 
-pub fn delta(s: f64) -> f64 {
+
-    if s <= 2.0 * M_K {
+
+const BLEND_RANGE: f64 = 0.1;
+
+#[allow(unused)]
+pub fn delta_low(cache: &Cache, s: f64) -> f64 {
     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 {
+}
+
+#[allow(unused)]
+pub fn delta_mid(cache: &Cache, s: f64) -> f64 {
     let par = 0.5 * s.sqrt() / M_K - 1.0;
-        lambda_0() + LAMBDA1 * par + LAMBDA2 * par.powi(2)
+    lambda_0(cache) + LAMBDA1 * par + LAMBDA2 * par.powi(2)
+}
+
+#[allow(unused)]
+pub fn delta_high(cache: &Cache, s: f64) -> f64 {
+    PI + (delta(cache, S_MID_CUTOFF.powi(2)) - PI) * (LAMBDA_HIGH * LAMBDA_HIGH + S_MID_CUTOFF)
+        / (LAMBDA_HIGH * LAMBDA_HIGH + s)
+}
+
+#[allow(unused)]
+pub fn delta_blend(cache: &Cache, s: f64) -> f64 {
+    if (s - 4.0*M_K.powi(2)).abs() < BLEND_RANGE {
+        let t = (s - 4.0*M_K.powi(2) + BLEND_RANGE) / (2.0*BLEND_RANGE);
+        (1.0 - t) * delta_low(cache, s) + t * delta_mid(cache, s)
+    } else if (s - S_MID_CUTOFF.powi(2)).abs() < BLEND_RANGE {
+        let t = (s - S_MID_CUTOFF.powi(2) + BLEND_RANGE) / (2.0*BLEND_RANGE);
+        (1.0 - t) * delta_mid(cache, s) + t * delta_high(cache, s)
     } else {
-        PI + (delta_mid_cutoff() - PI) * (LAMBDA_HIGH * LAMBDA_HIGH + S_MID_CUTOFF)
+        delta(cache, s)
+    }
+}
+
+fn delta(cache: &Cache, s: f64) -> f64 {
+    let s_sqrt = s.sqrt();
+    if s <= 4.0 * M_K.powi(2) {
+        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.powi(2) {
+        let par = 0.5 * s_sqrt / M_K - 1.0;
+        lambda_0(cache) + LAMBDA1 * par + LAMBDA2 * par.powi(2)
+    } else {
+        PI + (delta_with_lut(cache, S_MID_CUTOFF.powi(2)) - PI) * (LAMBDA_HIGH * LAMBDA_HIGH + S_MID_CUTOFF)
             / (LAMBDA_HIGH * LAMBDA_HIGH + s)
     }
 }
@@ -218,13 +252,11 @@ pub fn omnes_integrand_tan(cache: &Cache, s_tick: f64, s: f64) -> Complex {
 }
 
 pub fn omnes_integrand_notan(cache: &Cache, s_tick: f64, s: f64) -> Complex {
-    // println!("omnes_integrand_notan");
     (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: &Cache, s: f64, n: u32, use_tan: bool) -> Complex {
-    // println!("Omnes");
     if let Some(inner_lut) = cache.omnes_lut.get(&n) {
         if let Some(res) = inner_lut.get(&s.to_bits()) {
             return *res;
@@ -236,24 +268,20 @@ pub fn omnes(cache: &Cache, s: f64, n: u32, use_tan: bool) -> Complex {
             .insert(n, DashMap::with_hasher(Default::default()));
     }
 
-    // println!("Retrieving roots and weights omnes");
     let roots: Arc<[f64]>;
     let weights: Arc<[f64]>;
     match cache.gauss_quad_lut.get(&n) {
         Some(gq_values) => {
-            // println!("Somobomo");
             roots = Arc::clone(&gq_values.0);
             weights = Arc::clone(&gq_values.1);
         }
         None => {
-            // println!("Nononono");
             let gq_values = GaussLegendre::nodes_and_weights(n.try_into().unwrap());
             roots = Arc::from(gq_values.0.as_slice());
             weights = Arc::from(gq_values.1.as_slice());
         }
     }
 
-    // println!("will maybe calc n_omnes");
     if !cache.gauss_quad_lut.contains_key(&n) {
         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 gq_values = GaussLegendre::nodes_and_weights(n.try_into().unwrap());
@@ -262,7 +290,6 @@ pub fn omnes(cache: &Cache, s: f64, n: u32, use_tan: bool) -> Complex {
             .insert(n, (Arc::from(gq_values.0), Arc::from(gq_values.1)));
     }
 
-    // println!("Will calculate integrate complex");
     let intgrl = if use_tan {
         integrate_complex(&roots, &weights, S0.atan(), PI / 2.0, |s_tick| {
             omnes_integrand_tan(cache, s_tick, s)
@@ -297,21 +324,14 @@ pub fn phi0_integrand(
     cutoff_s: f64,
     cutoff_factor: Complex,
 ) -> f64 {
-    // println!("phi0_integrand");
     let sub = match (use_tan_phi0, use_xsub) {
         (true, true) => s_tick.tan().powi(2) + S0,
         (true, false) => s_tick.tan(),
         (false, true) => s_tick.powi(2) + S0,
         (false, false) => s_tick,
     };
-    // let omnes_s = if use_cutoff && s >= cutoff_s {
-    //     cutoff_factor * s.powf(cutoff_power)
-    // } else {
-    //     omnes(cache, s, n_omnes, use_tan_omnes)
-    // };
     let omnes_sub = if use_cutoff && sub >= cutoff_s {
         cutoff_factor * sub.powf(cutoff_power)
-        // Complex::new((0.00002f64).powf(cutoff_power), 0.0)
     } else {
         omnes(cache, sub, n_omnes, use_tan_omnes)
     };
@@ -340,7 +360,6 @@ pub fn phi0(
     cutoff_power: f64,
     cutoff_s: f64
 ) -> f64 {
-    // println!("phi0");
     if !cache.gauss_quad_lut.contains_key(&n_phi0) {
         let gq_values = GaussLegendre::nodes_and_weights(n_phi0.try_into().unwrap());
         let _ = cache
@@ -353,14 +372,13 @@ pub fn phi0(
         (Arc::clone(&ent.0), Arc::clone(&ent.1))
     };
 
-    // println!("Will run omnes");
     let analyt = if use_reduced_integrand {
-        omnes(cache, s, n_omnes, use_tan_omnes).norm().ln() / S0.sqrt()
-    } else {
         (omnes(cache, s, n_omnes, use_tan_omnes) / omnes(cache, S0, n_omnes, use_tan_omnes))
             .norm()
             .ln()
             / (s * (s - S0).powf(1.5))
+    } else {
+        omnes(cache, s, n_omnes, use_tan_omnes).norm().ln() / S0.sqrt()
     };
 
     let cutoff_factor = omnes(cache, cutoff_s, n_omnes, use_tan_omnes) * cutoff_s.powf(-cutoff_power);

bachelorarbeit/src/main.rs

@@ -4,10 +4,12 @@
 
 use indicatif;
 use std::time::Instant;
+use std::fs;
+use core::f64::consts::PI;
 
 use egui_plot::{log_grid_spacer, AxisHints, GridInput, GridMark, Legend, Line, Plot};
 use num::{complex::ComplexFloat, Float};
-
+use eframe::Theme;
 // use scc::HashMap;
 
 mod calc;
@@ -15,7 +17,7 @@ mod gq_storage;
 
 struct App {
     plot_data: Vec<PlotCurve>,
-    plots_available: [String; 7],
+    plots_available: [String; 9],
     calc_cache: calc::Cache,
     scaling_type: ScalingType,
     a: f64,
@@ -30,6 +32,7 @@ struct App {
     use_cutoff: bool,
     cutoff_power: f64,
     cutoff_s: f64,
+    export_filename: String,
 }
 
 #[derive(Clone)]
@@ -48,27 +51,31 @@ impl Default for App {
                 "Phi0".to_string(),
                 "Phi0 / delta".to_string(),
                 "s^cutoff_power".to_string(),
+                "Omnes integrand".to_string(),
                 "phi0 integrand".to_string(),
                 "Phi0_cut / Phi0".to_string(),
+                "Phi0 / delta".to_string(),
             ],
             calc_cache: calc::Cache::default(),
             scaling_type: ScalingType::default(),
             a: calc::S0,
             b: 9.0,
-            n_points: 500,
+            n_points:2500,
-            n_omnes: 500,
+            n_omnes:2500,
-            n_phi0: 500,
+            n_phi0:2500,
             
             // Substitutions params
             use_tan_omnes: true,
             use_tan_phi0: true,
             use_xsub_phi0: true,
-            use_reduced_integrand: true,
+            use_reduced_integrand: false,
 
             // Cutoff params
             use_cutoff: false,
             cutoff_power: -1.0,
             cutoff_s: 100.0, 
+
+            export_filename: "plot_data".to_string(),
         }
     }
 }
@@ -83,6 +90,7 @@ enum ScalingType {
 impl eframe::App for App {
     fn update(&mut self, ctx: &egui::Context, _frame: &mut eframe::Frame) {
         egui::CentralPanel::default().show(ctx, |ui| {
+            ui.set_min_width(ui.available_width());
             let cur_scaling_type = self.scaling_type;
 
             ui.vertical(|ui| {
@@ -97,12 +105,20 @@ impl eframe::App for App {
                                     "the lower bound of the interval that functions are calculated in",
                                 );
                                 float_text_edit_singleline(ui, &mut self.a, true);
+                                let seta_pi2 = ui.button("S0");
+                                if seta_pi2.clicked() {
+                                    self.a = calc::S0;
+                                }
                                 ui.end_row();
 
                                 ui.label("calc interval end:").on_hover_text(
                                     "the upper bound of the interval that functions are calculated in",
                                 );
                                 float_text_edit_singleline(ui, &mut self.b, true);
+                                let setb_pi2 = ui.button("pi/2");
+                                if setb_pi2.clicked() {
+                                    self.b = 1.5707963268;
+                                }
                                 ui.end_row();
 
                                 ui.label("N for omnes:").on_hover_text(
@@ -180,6 +196,25 @@ impl eframe::App for App {
                             float_text_edit_singleline(ui, &mut self.cutoff_s, true);
                             ui.end_row();
                         });
+                        let textedit = egui::TextEdit::singleline(&mut self.export_filename);
+                        ui.add(textedit);
+                        let button_export = ui.button("Export data");
+                        if button_export.clicked() {
+                            let mut plot_data_str = String::new();
+                            for curve in &mut self.plot_data {
+                                for point in &mut curve.points {
+                                    plot_data_str.push_str(&point[0].to_string());
+                                    plot_data_str.push_str(",");
+                                    plot_data_str.push_str(&point[1].to_string());
+                                    plot_data_str.push_str(",");
+                                }
+                                plot_data_str.push_str("\n");
+                            }
+                            let mut filename = "./exports/".to_owned();
+                            filename.push_str(&self.export_filename);
+                            filename.push_str(".txt");
+                            fs::write(filename, plot_data_str).expect("Unable to write file");
+                        }
                     })
                 });
 
@@ -199,76 +234,52 @@ impl eframe::App for App {
                                 .collect();
                             match i {
                                 0 => {
-                                    let y_values_delta: Vec<f64> = if self.scaling_type
+                                    let y_values: Vec<f64> = x_values.iter().map(|&x| {
-                                        == ScalingType::Linear
+                                        let val = calc::delta_with_lut(&mut self.calc_cache, x);
-                                    {
+                                        match self.scaling_type {
-                                        x_values
+                                            ScalingType::Linear => {
-                                            .iter()
+                                                val
-                                            .map(|&x| calc::delta_with_lut(&mut self.calc_cache, x))
+                                            }
-                                            .collect()
+                                            ScalingType::Logarithmic => {
-                                    } else {
+                                                val.log10()
-                                        x_values
+                                            }
-                                            .iter()
+                                        }
-                                            .map(|&x| {
+                                    }).collect();
-                                                calc::delta_with_lut(&mut self.calc_cache, x)
-                                                    .log10()
-                                            })
-                                            .collect()
-                                    };
 
                                     self.plot_data.push(PlotCurve {
                                         points: x_values
                                             .iter()
-                                            .zip(y_values_delta.iter())
+                                            .zip(y_values.iter())
-                                            .map(|(&x, &y)| [x.powf(0.5), y])
+                                            .map(|(&x, &y)| [x, y])
                                             .collect(),
                                         name: format!("(#{}) Delta", self.plot_data.len() + 1),
-                                    })
+                                    });
                                 }
                                 1 => {
-                                    let y_values_omnes: Vec<f64> = if self.scaling_type
+                                    let cutoff_factor = calc::omnes(&mut self.calc_cache, self.cutoff_s, self.n_omnes, self.use_tan_omnes) * self.cutoff_s;
-                                        == ScalingType::Linear
+
-                                    {
+                                    let y_values: Vec<f64> = x_values.iter().map(|&x| {
-                                        print!("Calculating all plot points: ");
+                                       let val = calc::omnes(
-                                        let bar =
-                                            indicatif::ProgressBar::new(u64::from(self.n_points));
-                                        let res = x_values
-                                            .iter()
-                                            .map(|&x| {
-                                                bar.inc(1);
-                                                calc::omnes(
                                             &mut self.calc_cache,
                                             x,
                                             self.n_omnes,
                                             self.use_tan_omnes,
-                                                )
+                                        ).abs().powi(2);
-                                                .abs()
+                                        match self.scaling_type {
-                                                .powi(2)
+                                            ScalingType::Linear => {
-                                            })
+                                                val
-                                            .collect();
+                                            }
-                                        bar.finish();
+                                            ScalingType::Logarithmic => {
-                                        res
+                                                val.log10()
-                                    } else {
+                                            }
-                                        x_values
+                                        }
-                                            .iter()
+                                    }).collect();
-                                            .map(|&x| {
+
-                                                calc::omnes(
-                                                    &mut self.calc_cache,
-                                                    x,
-                                                    self.n_omnes,
-                                                    self.use_tan_omnes,
-                                                )
-                                                .abs()
-                                                .powi(2)
-                                                .log10()
-                                            })
-                                            .collect()
-                                    };
                                     self.plot_data.push(PlotCurve {
                                         points: x_values
                                             .iter()
-                                            .zip(y_values_omnes.iter())
+                                            .zip(y_values.iter())
-                                            .map(|(&x, &y)| [x.powf(0.5), y])
+                                            .map(|(&x, &y)| [x, y])
                                             .collect(),
                                         name: format!(
                                             "(#{}) Omnes, {} ot, n_o={}",
@@ -318,7 +329,7 @@ impl eframe::App for App {
                                         points: x_values
                                             .iter()
                                             .zip(y_values_phi0.iter())
-                                            .map(|(&x, &y)| [x.powf(0.5), y])
+                                            .map(|(&x, &y)| [x, y])
                                             .collect(),
                                         name: format!(
                                             "(#{}) phi0, {} ot, {} pt, {} ss, n_o={}, n_p={}",
@@ -333,6 +344,9 @@ impl eframe::App for App {
                                 }
                                 3 => {
                                     let y_values_phi0: Vec<f64> = {
+                                        let bar =
+                                            indicatif::ProgressBar::new(u64::from(self.n_points));
+                                        let t0 = Instant::now();
                                         x_values
                                             .iter()
                                             .map(|&x| {
@@ -352,7 +366,7 @@ impl eframe::App for App {
                                                 ) / calc::delta_with_lut(
                                                     &mut self.calc_cache,
                                                     x,
-                                                );
+                                                ) - 1.0;
                                                 match self.scaling_type {
                                                     ScalingType::Linear => {
                                                         val
@@ -368,7 +382,7 @@ impl eframe::App for App {
                                         points: x_values
                                             .iter()
                                             .zip(y_values_phi0.iter())
-                                            .map(|(&x, &y)| [x.powf(0.5), y])
+                                            .map(|(&x, &y)| [x, y])
                                             .collect(),
                                         name: format!(
                                             "(#{}) phi0 / delta, {} ot, {} pt, {} ss, n_o={}, n_p={}",
@@ -400,21 +414,52 @@ impl eframe::App for App {
                                         points: x_values
                                             .iter()
                                             .zip(y_values_func.iter())
-                                            .map(|(&x, &y)| [x.powf(0.5), y])
+                                            .map(|(&x, &y)| [x, y])
                                             .collect(),
                                         name:"cont. polynomial".to_string()
                                     });
                                 }
                                 5 => {
-                                    let cutoff_factor = calc::omnes(&mut self.calc_cache, self.cutoff_s, self.n_omnes, self.use_tan_omnes) * self.cutoff_s;
-                                    println!("{:?}", cutoff_factor);
                                     let y_values_func: Vec<f64> = x_values
                                         .iter()
                                         .map(|&x| { 
+                                            let val = if self.use_tan_omnes {
+                                                calc::omnes_integrand_tan(&self.calc_cache, x, 1.2).abs()
+                                            } else {
+                                                calc::omnes_integrand_notan(&self.calc_cache, x, 1.2).abs()
+                                            };
+                                            match self.scaling_type {
+                                                ScalingType::Linear => {
+                                                    val
+                                                }
+                                                ScalingType::Logarithmic => {
+                                                    val.log10()
+                                                }
+                                            }
+                                        }).collect();
+                                    self.plot_data.push(PlotCurve {
+                                        points: x_values
+                                            .iter()
+                                            .zip(y_values_func.iter())
+                                            .map(|(&x, &y)| [x, y])
+                                            .collect(),
+                                        name: format!(
+                                            "(#{}) omnes integrand",
+                                            self.plot_data.len() + 1,
+                                        ),
+                                    })
+                                }
+                                6 => {
+                                    let bar = indicatif::ProgressBar::new(u64::from(self.n_points));
+                                    let cutoff_factor = calc::omnes(&mut self.calc_cache, self.cutoff_s, self.n_omnes, self.use_tan_omnes) * self.cutoff_s;
+                                    let y_values_func: Vec<f64> = x_values
+                                        .iter()
+                                        .map(|&x| { 
+                                            bar.inc(1);
                                             let val = calc::phi0_integrand(
                                                 &mut self.calc_cache, 
                                                 x, 
-                                                2.0, 
+                                                1.0, 
                                                 self.n_omnes, 
                                                 self.use_tan_omnes, 
                                                 self.use_tan_phi0, 
@@ -438,7 +483,7 @@ impl eframe::App for App {
                                         points: x_values
                                             .iter()
                                             .zip(y_values_func.iter())
-                                            .map(|(&x, &y)| [x.powf(0.5), y])
+                                            .map(|(&x, &y)| [x, y])
                                             .collect(),
                                         name: format!(
                                             "(#{}) phi0 integrand",
@@ -446,7 +491,7 @@ impl eframe::App for App {
                                         ),
                                     })
                                 }
-                                6 => {
+                                7 => {
                                     let bar = indicatif::ProgressBar::new(u64::from(self.n_points));
                                     let y_values: Vec<f64> =
                                         x_values.iter().map(|&x| {
@@ -492,7 +537,7 @@ impl eframe::App for App {
                                         points: x_values
                                             .iter()
                                             .zip(y_values.iter())
-                                            .map(|(&x, &y)| [x.powf(0.5), y])
+                                            .map(|(&x, &y)| [x, y])
                                             .collect(),
                                         name: format!(
                                             "(#{}) phi0_cut / phi0, cutoff power: {}",
@@ -501,7 +546,43 @@ impl eframe::App for App {
                                         ),
                                     });
                                 }
-                                7_usize.. => {
+                                8 => {
+                                    let bar = indicatif::ProgressBar::new(u64::from(self.n_points));
+                                    let y_values_func: Vec<f64> = x_values.iter().map(|&x| {
+                                        bar.inc(1);
+                                        let val = 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,
+                                            self.use_reduced_integrand,
+                                            x == self.a,
+                                            self.use_cutoff, 
+                                            self.cutoff_power,
+                                            self.cutoff_s
+                                        ) / calc::delta_with_lut(&mut self.calc_cache, x);
+                                        match self.scaling_type {
+                                            ScalingType::Linear => {
+                                                val
+                                            }
+                                            ScalingType::Logarithmic => {
+                                                val.log10()
+                                            }
+                                        }
+                                    }).collect();
+                                    self.plot_data.push(PlotCurve {
+                                        points: x_values
+                                            .iter()
+                                            .zip(y_values_func.iter())
+                                            .map(|(&x, &y)| [x, y])
+                                            .collect(),
+                                        name:"cont. polynomial".to_string()
+                                    });
+                                }
+                                9_usize.. => {
                                     panic!("This button has no assigned purpose!");
                                 }
                             }
@@ -524,7 +605,7 @@ impl eframe::App for App {
 
             let plot = Plot::new("my_plot")
                 .grid_spacing(5.0f32..=300.0f32)
-                .x_axis_label("sqrt(s) [GeV]")
+                .x_axis_label("s [GeV^2]")
                 .legend(Legend::default());
 
             let plot = match self.scaling_type {
@@ -545,7 +626,7 @@ impl eframe::App for App {
                             if v.value - v.value.floor() < 0.9 {
                                 log_gridmarks.push(GridMark {
                                     value: log_map(v.value),
-                                    step_size: v.step_size / 1.14,
+                                    step_size: v.step_size / 1.14, // This value just looks best
                                 });
                             }
                         }
@@ -563,7 +644,7 @@ impl eframe::App for App {
                     plot_ui.line(
                         Line::new(self.plot_data[i].points.clone())
                             .name(self.plot_data[i].name.clone()),
-                    ); // is clone necessary?
+                    );
                 }
             });
         });
@@ -574,6 +655,7 @@ impl eframe::App for App {
 fn main() {
     let mut app = App::default();
     app.calc_cache = calc::Cache::from_file("./gauss_quad_lut.morello").unwrap();
+    println!("{}", (2.0 * calc::M_K).powi(2));
 
     // let x_values: Vec<f64> = (0..app.n_points)
     //     .map(|x| -> f64 { f64::from(x) * ((app.b - app.a) / f64::from(app.n_points)) + app.a })
@@ -603,19 +685,30 @@ fn main() {
     // for (o,n_o) in accuracies.iter().enumerate() {
     //     println!("{:?}", n_o);
     //     for (p,n_p) in accuracies.iter().enumerate() {
-    //         let phi0 = calc::phi0(&mut app.calc_cache, 10000.0, *n_o, *n_p , true, true, true, true, true, false, 0.0, 0.0);
+    //         let phi0 = calc::phi0(&mut app.calc_cache, 10000.0, *n_o, *n_p , true, true, true, false, true, false, 0.0, 0.0);
     //         results[o][p] = phi0 / calc::delta(10000.0) - 1.0;
     //     }
     // }
 
     // println!("{:#?}", results);
     
-    let phi0 = calc::phi0(&mut app.calc_cache, 10000.0, 1000, 1000, true, true, true, true, true, false, 0.0, 0.0);
+    let phi0 = calc::phi0(&mut app.calc_cache, 2.0158, 100, 100, true, true, true, false, true, false, 0.0, 0.0);
-    println!("relative difference: {:e}", phi0 / calc::delta(10000.0) - 1.0);
+    println!("relative difference: {:e}", phi0 / calc::delta_with_lut(&mut app.calc_cache, 2.0158) - 1.0);
+
+    // let A = 1.42;
+    // let numerator = 4.0*A*A*calc::M_K * (calc::delta_with_lut(&mut app.calc_cache, A*A) - PI);
+    // let denominator = calc::LAMBDA1 + 2.0*calc::LAMBDA2 * (0.5*A/calc::M_K - 1.0);
+    // println!("{:?}", - numerator / denominator - A*A);
+
+    let options = eframe::NativeOptions {
+        viewport: egui::ViewportBuilder::default().with_inner_size([1500 as f32, 1000 as f32]),
+        default_theme: Theme::Dark,
+        ..Default::default()
+    };
 
     // eframe::run_native(
     //     "Omnes Calculator",
-    //     eframe::NativeOptions::default(),
+    //     options,
     //     Box::new(|_cc| Box::new(app)),
     // )
     // .unwrap();