seems almost perfect, why do they tend to seem translated to the right?

Cargo.toml

@@ -17,4 +17,5 @@ python = ["dep:numpy", "dep:pyo3"]
 numpy = {version = "0.19", optional = true}
 pyo3 = {version = "0.19", features = ["extension-module"], optional = true}
 rand = "0.8.5"
+rand_distr = "0.4.3"
 

src/physics/single_chain/efjc/thermodynamics/isometric/mod.rs

@@ -6,6 +6,9 @@ mod test;
 /// The extensible freely-jointed chain (EFJC) model thermodynamics in the isometric ensemble approximated using an asymptotic approach.
 pub mod asymptotic;
 
+/// The extensible freely-jointed chain (EFJC) model thermodynamics in the isometric ensemble calculated using Monte Carlo methods.
+pub mod monte_carlo;
+
 /// The structure of the thermodynamics of the EFJC model in the isometric ensemble.
 pub struct EFJC
 {

src/physics/single_chain/efjc/thermodynamics/isometric/monte_carlo/mod.rs

@@ -0,0 +1,63 @@
+mod test;
+
+use rand::prelude::*;
+
+use rand_distr::{Normal, Distribution};
+
+use std::f64::consts::TAU as TWO_PI;
+
+pub fn random_configuration<const NUMBER_OF_LINKS: usize>(dist: Normal<f64>, rng: &mut ThreadRng) -> [[f64; 3]; NUMBER_OF_LINKS]
+{
+    let mut lambda: f64 = 0.0;
+    let mut phi: f64 = 0.0;
+    let mut theta: f64 = 0.0;
+    let mut position = [0.0; 3];
+    let mut configuration = [[0.0; 3]; NUMBER_OF_LINKS];
+    configuration.iter_mut().for_each(|coordinate|{
+        lambda = dist.sample(rng);
+        phi = TWO_PI * rng.gen::<f64>();
+        theta = (1.0 - 2.0 * rng.gen::<f64>()).acos();
+        position[0] += lambda * (theta.sin() * phi.cos());
+        position[1] += lambda * (theta.sin() * phi.sin());
+        position[2] += lambda * theta.cos();
+        coordinate.iter_mut().zip(position.iter()).for_each(|(coordinate_i, position_i)|
+            *coordinate_i = *position_i
+        );
+    });
+    configuration
+}
+
+pub fn random_nondimensional_end_to_end_length<const NUMBER_OF_LINKS: usize>(dist: Normal<f64>, rng: &mut ThreadRng) -> f64
+{
+    random_configuration::<NUMBER_OF_LINKS>(dist, rng)[NUMBER_OF_LINKS - 1].iter().map(|entry| entry * entry).sum::<f64>().sqrt()
+}
+
+pub fn nondimensional_equilibrium_radial_distribution<const NUMBER_OF_BINS: usize, const NUMBER_OF_LINKS: usize>(gamma_max: &f64, kappa: &f64, number_of_samples: usize) -> ([f64; NUMBER_OF_BINS], [f64; NUMBER_OF_BINS])
+{
+    let mut rng = rand::thread_rng();
+    let dist = Normal::new(1.0, 1.0/kappa.sqrt()).unwrap();
+    let number_of_links_f64 = NUMBER_OF_LINKS as f64;
+    let mut bin_centers = [0.0_f64; NUMBER_OF_BINS];
+    bin_centers.iter_mut().enumerate().for_each(|(bin_index, bin_center)|
+        *bin_center = gamma_max * ((bin_index as f64) + 0.5)/(NUMBER_OF_BINS as f64)
+    );
+    let mut bin_counts = [0_u128; NUMBER_OF_BINS];
+    let mut gamma: f64 = 0.0;
+    (0..number_of_samples).for_each(|_|{
+        gamma = random_nondimensional_end_to_end_length::<NUMBER_OF_LINKS>(dist, &mut rng)/number_of_links_f64;
+        for (bin_center, bin_count) in bin_centers.iter().zip(bin_counts.iter_mut())
+        {
+            if &gamma < bin_center
+            {
+                *bin_count += 1;
+                break
+            }
+        }
+    });
+    let normalization = gamma_max * (number_of_samples as f64)/(NUMBER_OF_BINS as f64);
+    let mut bin_probabilities = [0.0_f64; NUMBER_OF_BINS];
+    bin_probabilities.iter_mut().zip(bin_counts.iter()).for_each(|(bin_probability, bin_count)|
+        *bin_probability = (*bin_count as f64)/normalization
+    );
+    (bin_centers, bin_probabilities)
+}

src/physics/single_chain/efjc/thermodynamics/isometric/monte_carlo/test.rs

@@ -0,0 +1,40 @@
+#![cfg(test)]
+
+use super::*;
+
+const GAMMA_MAX: f64 = 1.5;
+const KAPPA: f64 = 50.0;
+const NUMBER_OF_BINS: usize = 100;
+const NUMBER_OF_LINKS: usize = 3;
+const NUMBER_OF_SAMPLES: usize = 100000;
+
+#[test]
+fn monte_carlo_random_configuration()
+{
+    let mut rng = rand::thread_rng();
+    let dist = Normal::new(1.0, 1.0/KAPPA.sqrt()).unwrap();
+    let configuration = random_configuration::<NUMBER_OF_LINKS>(dist, &mut rng);
+    assert_eq!(configuration.len(), NUMBER_OF_LINKS);
+    assert_eq!(configuration[0].len(), 3);
+}
+
+#[test]
+fn monte_carlo_random_nondimensional_end_to_end_length()
+{
+    let mut rng = rand::thread_rng();
+    let dist = Normal::new(1.0, 1.0/KAPPA.sqrt()).unwrap();
+    let gamma = random_nondimensional_end_to_end_length::<NUMBER_OF_LINKS>(dist, &mut rng)/(NUMBER_OF_LINKS as f64);
+    assert!(gamma >= 0.0);
+}
+
+#[test]
+fn monte_carlo_nondimensional_equilibrium_radial_distribution()
+{
+    let (gamma, g_eq) = nondimensional_equilibrium_radial_distribution::<NUMBER_OF_BINS, NUMBER_OF_LINKS>(&GAMMA_MAX, &KAPPA, NUMBER_OF_SAMPLES);
+    assert_eq!(gamma.len(), NUMBER_OF_BINS);
+    assert_eq!(g_eq.len(), NUMBER_OF_BINS);
+    gamma.iter().zip(g_eq.iter()).for_each(|(gamma_i, g_eq_i)|{
+        assert!(gamma_i > &0.0);
+        assert!(g_eq_i >= &0.0);
+    });
+}

src/physics/single_chain/frc/thermodynamics/isometric/monte_carlo/mod.rs

@@ -60,7 +60,7 @@ pub fn nondimensional_equilibrium_radial_distribution<const NUMBER_OF_BINS: usiz
     let gamma_max = (2.0 - 2.0*(PI - theta).cos()).sqrt()/2.0;
     let mut bin_centers = [0.0_f64; NUMBER_OF_BINS];
     bin_centers.iter_mut().enumerate().for_each(|(bin_index, bin_center)|
-        *bin_center = gamma_max*((bin_index as f64) + 0.5)/(NUMBER_OF_BINS as f64)
+        *bin_center = gamma_max * ((bin_index as f64) + 0.5)/(NUMBER_OF_BINS as f64)
     );
     let mut bin_counts = [0_u128; NUMBER_OF_BINS];
     let mut gamma: f64 = 0.0;
@@ -75,7 +75,7 @@ pub fn nondimensional_equilibrium_radial_distribution<const NUMBER_OF_BINS: usiz
             }
         }
     });
-    let normalization = (number_of_samples as f64)/(NUMBER_OF_BINS as f64);
+    let normalization = gamma_max * (number_of_samples as f64)/(NUMBER_OF_BINS as f64);
     let mut bin_probabilities = [0.0_f64; NUMBER_OF_BINS];
     bin_probabilities.iter_mut().zip(bin_counts.iter()).for_each(|(bin_probability, bin_count)|
         *bin_probability = (*bin_count as f64)/normalization

tests/efjc.rs

@@ -0,0 +1,16 @@
+use polymers::physics::single_chain::efjc::thermodynamics::isometric::monte_carlo::nondimensional_equilibrium_radial_distribution;
+
+const GAMMA_MAX: f64 = 1.5;
+const KAPPA: f64 = 50.0;
+const NUMBER_OF_BINS: usize = 1000;
+const NUMBER_OF_LINKS: usize = 3;
+const NUMBER_OF_SAMPLES: usize = 10000000;
+
+#[test]
+fn monte_carlo_nondimensional_equilibrium_radial_distribution()
+{
+    let (gamma, g_eq) = nondimensional_equilibrium_radial_distribution::<NUMBER_OF_BINS, NUMBER_OF_LINKS>(&GAMMA_MAX, &KAPPA, NUMBER_OF_SAMPLES);
+    gamma.iter().zip(g_eq.iter()).for_each(|output|{
+        println!("{:?}", output)
+    });
+}

tests/frc.rs

@@ -8,7 +8,7 @@ const KAPPA: f64 = 5.0/11.0;
 const NUMBER_OF_BINS: usize = 1000;
 const NUMBER_OF_LINKS: usize = 256;
 const NUMBER_OF_SAMPLES: usize = 10000000;
-const TOL: f64 = 5e-2;
+const TOL: f64 = 8e-2;
 
 #[test]
 fn monte_carlo_nondimensional_equilibrium_radial_distribution_wlc_limit()