From 5bf9d56ab096878498eee9a8b91a093a494910f0 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Sat, 29 Mar 2025 07:34:24 -0300
Subject: Started writing code for integrating mean-field equations

---
 Makefile       |  4 ++-
 integrator.cpp | 85 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 88 insertions(+), 1 deletion(-)
 create mode 100644 integrator.cpp

diff --git a/Makefile b/Makefile
index 2b5214f..6b77cca 100644
--- a/Makefile
+++ b/Makefile
@@ -1,4 +1,4 @@
-all: walk correlations
+all: walk correlations integrator
 
 CC := clang++ -std=c++17 -Wno-mathematical-notation-identifier-extension -O3 -march=native -mtune=native
 
@@ -8,3 +8,5 @@ walk: walk.cpp
 correlations: correlations.cpp
 	$(CC) correlations.cpp -o correlations
 
+integrator: integrator.cpp
+	$(CC) integrator.cpp -o integrator
diff --git a/integrator.cpp b/integrator.cpp
new file mode 100644
index 0000000..bb22a36
--- /dev/null
+++ b/integrator.cpp
@@ -0,0 +1,85 @@
+#include <getopt.h>
+#include <vector>
+#include <array>
+#include <cmath>
+#include <iostream>
+
+using Real = double;
+
+class Point : public std::array<Real, 2> {
+public:
+  Real τ() const {
+    return front();
+  }
+  Real C() const {
+    return back();
+  }
+};
+
+Real f(Real q) {
+  return 0.5 * pow(q, 2);
+}
+
+Real df(Real q) {
+  return q;
+}
+
+Real ddf(Real q) {
+  return 1;
+}
+
+Real integrate(const std::vector<Point>& Cₜ) {
+  Real I = 0;
+  for (unsigned i = 0; i < Cₜ.size() - 1; i++) {
+    Real Δτ = Cₜ[i + 1].τ() - Cₜ[i].τ();
+    Real C = (Cₜ[i + 1].C() + Cₜ[i].C()) / 2;
+    Real dC = (Cₜ[i + 1].C() - Cₜ[i].C()) / Δτ;
+    I += Δτ * df(C) * dC;
+  }
+  return I;
+}
+
+int main(int argc, char* argv[]) {
+  Real Δτ = 1e-3;
+  Real τₘₐₓ = 1e3;
+  Real τ₀ = 0;
+  Real y = 0.5;
+
+  int opt;
+
+  while ((opt = getopt(argc, argv, "d:T:t:y:")) != -1) {
+    switch (opt) {
+    case 'd':
+      Δτ = atof(optarg);
+      break;
+    case 'T':
+      τₘₐₓ = atof(optarg);
+      break;
+    case 't':
+      τ₀ = atof(optarg);
+      break;
+    case 'y':
+      y = atof(optarg);
+      break;
+    default:
+      exit(1);
+    }
+  }
+
+  std::vector<Point> Cₜ;
+  Cₜ.reserve(τₘₐₓ / Δτ);
+
+  Cₜ.push_back({0, 1});
+  Cₜ.push_back({Δτ, 1 - Δτ});
+
+  while (Cₜ.back().τ() < τₘₐₓ) {
+    Real dC = -Cₜ.back().C() - 2 * pow(y, 2) * integrate(Cₜ);
+    Cₜ.push_back({Cₜ.back().τ() + Δτ, Cₜ.back().C() + Δτ * dC});
+  }
+
+  for (const Point& p : Cₜ) {
+    std::cout << p.τ() << " " << p.C() << std::endl;
+  }
+
+  return 0;
+}
-- 
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