MCMC FJC

.github/workflows/rust.yml

@@ -52,7 +52,7 @@ jobs:
       - name: checkout
         uses: actions/checkout@v4
       - name: tree
-        run: $([[ $(cargo tree --color always --edges normal | wc -l) -eq 1 ]])
+        run: cargo tree --color always --edges normal
       - name: build
         run: cargo build --color always --release --verbose
       - name: clippy

Cargo.toml

@@ -16,7 +16,5 @@ python = ["dep:numpy", "dep:pyo3"]
 [dependencies]
 numpy = {version = "0.19", optional = true}
 pyo3 = {version = "0.19", features = ["extension-module"], optional = true}
-
-[dev-dependencies]
 rand = "0.8.5"
 

conftest.py

@@ -20,6 +20,10 @@ def pytest_collection_finish(session):
     run(
         ['sed', '-i', 's@: test@@', '__pycache__/cargo.tests']
     )
+    # remove monte carlo tests
+    run(
+        ['sed', '-i', '-r', '/monte/d', '__pycache__/cargo.tests']
+    )
     f = open("__pycache__/julia.tests", "w")
     run(
         ['grep', '-r', '@testset', 'src/'],

src/math/mod.rs

@@ -52,7 +52,7 @@ pub fn integrate_1d(f: &dyn Fn(&f64) -> f64, x_min: &f64, x_max: &f64, num_point
 
 pub fn integrate_1d_grid(f: &dyn Fn(&f64) -> f64, grid: &[f64], dx: &f64) -> f64
 {
-    grid.iter().map(|x| f(x)).sum::<f64>()*dx
+    grid.iter().map(f).sum::<f64>()*dx
 }
 
 pub fn integrate_2d(f: &dyn Fn(&f64, &f64) -> f64, x_min: &f64, x_max: &f64, y_min: &f64, y_max: &f64, num_points: &u128) -> f64

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

@@ -9,6 +9,9 @@ mod test;
 /// The freely-jointed chain (FJC) model thermodynamics in the isometric ensemble approximated using a Legendre transformation.
 pub mod legendre;
 
+/// The freely-jointed chain (FJC) model thermodynamics in the isometric ensemble calculated using Monte Carlo methods.
+pub mod monte_carlo;
+
 use super::
 {
     treloar_sums,

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

@@ -0,0 +1,58 @@
+mod test;
+
+use rand::prelude::*;
+
+use std::f64::consts::TAU as TWO_PI;
+
+pub fn random_configuration<const NUMBER_OF_LINKS: usize>(rng: &mut ThreadRng) -> [[f64; 3]; NUMBER_OF_LINKS]
+{
+    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|{
+        phi = TWO_PI * rng.gen::<f64>();
+        theta = (1.0 - 2.0 * rng.gen::<f64>()).acos();
+        position[0] += theta.sin() * phi.cos();
+        position[1] += theta.sin() * phi.sin();
+        position[2] += 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>(rng: &mut ThreadRng) -> f64
+{
+    random_configuration::<NUMBER_OF_LINKS>(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>(number_of_samples: usize) -> ([f64; NUMBER_OF_BINS], [f64; NUMBER_OF_BINS])
+{
+    let mut rng = rand::thread_rng();
+    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 = ((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>(&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 = (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/fjc/thermodynamics/isometric/monte_carlo/test.rs

@@ -0,0 +1,38 @@
+#![cfg(test)]
+
+use super::*;
+
+const NUMBER_OF_BINS: usize = 100;
+const NUMBER_OF_LINKS: usize = 8;
+const NUMBER_OF_SAMPLES: usize = 100000;
+
+#[test]
+fn monte_carlo_random_configuration()
+{
+    let mut rng = rand::thread_rng();
+    let configuration = random_configuration::<NUMBER_OF_LINKS>(&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 gamma = random_nondimensional_end_to_end_length::<NUMBER_OF_LINKS>(&mut rng)/(NUMBER_OF_LINKS as f64);
+    assert!(gamma >= 0.0);
+    assert!(gamma <= 1.0);
+}
+
+#[test]
+fn monte_carlo_nondimensional_equilibrium_radial_distribution()
+{
+    let (gamma, g_eq) = nondimensional_equilibrium_radial_distribution::<NUMBER_OF_BINS, NUMBER_OF_LINKS>(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!(gamma_i < &1.0);
+        assert!(g_eq_i >= &0.0);
+    });
+}

tests/fjc.rs

@@ -0,0 +1,23 @@
+use polymers::physics::single_chain::fjc::thermodynamics::isometric::
+{
+    nondimensional_equilibrium_radial_distribution as check_geq,
+    monte_carlo::nondimensional_equilibrium_radial_distribution
+};
+
+const NUMBER_OF_BINS: usize = 1000;
+const NUMBER_OF_LINKS: usize = 8;
+const NUMBER_OF_SAMPLES: usize = 10000000;
+const TOL: f64 = 5e-2;
+
+#[test]
+fn monte_carlo_nondimensional_equilibrium_radial_distribution()
+{
+    let (gamma, g_eq) = nondimensional_equilibrium_radial_distribution::<NUMBER_OF_BINS, NUMBER_OF_LINKS>(NUMBER_OF_SAMPLES);
+    let mut check = 0.0;
+    let mut residual = 0.0;
+    gamma.iter().zip(g_eq.iter()).for_each(|(gamma_i, g_eq_i)|{
+        check = check_geq(&(NUMBER_OF_LINKS as u8), &gamma_i);
+        residual = (g_eq_i - &check).abs();
+        assert!(residual < TOL || residual/check < TOL || g_eq_i < &TOL);
+    });
+}