From adfceb56d987dbbcfcf8daded405cc687a82b272 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Tue, 1 Apr 2025 10:05:23 -0300
Subject: Incorporated interative scheme for treating the active case.

---
 Makefile       |  2 +-
 integrator.cpp | 95 +++++++++++++++++++++++++++++++++++++++++++++++++++-------
 2 files changed, 86 insertions(+), 11 deletions(-)

diff --git a/Makefile b/Makefile
index 25e23dd..3519e50 100644
--- a/Makefile
+++ b/Makefile
@@ -1,6 +1,6 @@
 all: walk correlations integrator
 
-CC := clang++ -std=c++17 -Wno-mathematical-notation-identifier-extension -O3 -march=native -mtune=native -fopenmp
+CC := clang++ -std=c++17 -Wno-mathematical-notation-identifier-extension -O3 -march=native -mtune=native -fopenmp -g
 
 walk: walk.cpp
 	$(CC) walk.cpp -o walk
diff --git a/integrator.cpp b/integrator.cpp
index e184de6..349e2ff 100644
--- a/integrator.cpp
+++ b/integrator.cpp
@@ -19,23 +19,66 @@ Real ddf(Real q) {
   return 0.5 * p * (p - 1) * pow(q, p - 2);
 }
 
-Real integrate(const std::vector<Real>& C, Real Δτ, Real τ₀) {
+Real integrate(const std::vector<Real>& C) {
   Real I = 0;
 #pragma omp parallel for reduction(+:I)
   for (unsigned σ = 0; σ < C.size() - 1; σ++) {
     unsigned τ_σ = C.size() - 1 - σ;
     Real Cτ_σ = (C[τ_σ] + C[τ_σ - 1]) / 2;
-    Real dCσ = (C[σ + 1] - C[σ]) / Δτ;
+    Real dCσ = C[σ + 1] - C[σ];
 
-    Real dddC = 0;
-    if (σ > 3 && σ < C.size() && C.size() > 3) {
-      dddC += (C[τ_σ] - 3 * C[τ_σ+1] + 3 * C[τ_σ+2] - C[τ_σ+3]) / pow(Δτ, 3);
+    I += df(Cτ_σ) * dCσ;
+  }
+  return I;
+}
+
+Real integratePast(const std::vector<Real>& C, signed τ) {
+  Real I = 0;
+#pragma omp parallel for reduction(+:I)
+  for (signed σ = -C.size() + τ + 3; σ < τ - 2; σ++) {
+    signed τ_σ = τ - σ;
+
+    Real Cτ_σ = (C[abs(τ_σ)] + C[abs(τ_σ) - 1]) / 2;
+    Real Cσ = (C[abs(σ) + 1] + C[abs(σ)]) / 2;
+    Real dddC;
+    if (τ_σ != 0) {
+      dddC = (τ_σ / abs(τ_σ)) * (C[abs(τ_σ)+2] - 2 * C[abs(τ_σ)+1] + 2 * C[abs(τ_σ)-1] - C[abs(τ_σ)-2]) / 2;
+    } else {
+      dddC = 0;
     }
-    I += Δτ * df(Cτ_σ) * (dCσ - pow(τ₀, 2) * dddC);
+
+    I += dddC * ddf(Cτ_σ) * Cσ;
+  }
+#pragma omp parallel for reduction(+:I)
+  for (signed σ = -C.size() + τ + 3; σ < -1; σ++) {
+    signed τ_σ = τ - σ;
+
+    Real Cτ_σ = (C[abs(τ_σ)] + C[abs(τ_σ) - 1]) / 2;
+    Real dddC;
+    if (σ != 0) {
+      dddC = -(σ / abs(σ)) * (C[abs(σ)+2] - 2 * C[abs(σ)+1] + 2 * C[abs(σ)-1] - C[abs(σ)-2]) / 2;
+    } else {
+      dddC = 0;
+    }
+
+    I += dddC * df(Cτ_σ);
   }
   return I;
 }
 
+Real integrateDelay(const std::vector<Real>& C, unsigned τ, Real Δτ, Real τ₀) {
+  Real I = 0;
+#pragma omp parallel for reduction(+:I)
+  for (signed σ = 2; σ < C.size() - τ - 2; σ++) {
+    unsigned τ_σ = τ + σ;
+    Real dC = -(C[σ+1] - C[σ-1]) / 2;
+    Real dddC = -(C[σ+2] - 2 * C[σ+1] + 2 * C[σ-1] - C[σ-2]) / 2;
+
+    I += (dC - pow(τ₀ / Δτ, 2) * dddC) * exp(-(τ_σ * Δτ / τ₀));
+  }
+  return I  / τ₀;
+}
+
 Real energy(const std::vector<Real>& C, Real Δτ, Real τ₀) {
   Real I = 0;
   for (unsigned σ = 0; σ < C.size() - 1; σ++) {
@@ -78,8 +121,10 @@ int main(int argc, char* argv[]) {
     }
   }
 
-  Real z = 0.5;
-  Real Γ₀ = 0.5 * (2 * τ₀) / (sqrt(1 + 2 * τ₀) - 1);
+//  Real z = (sqrt(1 + 2 * τ₀) - 1) / (2 * τ₀);
+//  Real z = 0.4833773593561142778087;
+  Real z = 0.4794707565634420155347 - 2 * pow(y, 2);
+  Real Γ₀ = 1.0;
 
   Real τ = 0;
   std::vector<Real> C;
@@ -87,12 +132,42 @@ int main(int argc, char* argv[]) {
 
   C.push_back(1);
 
-  while (std::cout << τ << " " << C.back() << std::endl, τ < τₘₐₓ) {
+//  while (std::cout << τ << " " << C.back() << std::endl, τ < τₘₐₓ) {
+  while (τ < τₘₐₓ) {
     τ += Δτ;
-    Real dC = -z * C.back() - 2 / Γ₀ * pow(y, 2) * integrate(C, Δτ, τ₀);
+    Real dC = -z * C.back() - 2 / Γ₀ * pow(y, 2) * integrate(C);
     C.push_back(C.back() + Δτ * dC);
   }
 
+
+  for (unsigned it = 0; it < 20; it++) {
+    τ = 0;
+    std::vector<Real> C2;
+    C2.reserve(τₘₐₓ / Δτ + 1);
+    C2.push_back(1);
+    while (τ < τₘₐₓ) {
+      τ += Δτ;
+      Real dC = -z * C2.back() + integrateDelay(C, C2.size() - 1, Δτ, τ₀) - 2 / Γ₀ * pow(y, 2) * (integrate(C2) - pow(τ₀ / Δτ, 2) * integratePast(C, C2.size()-1));
+      C2.push_back(C2.back() + Δτ * dC);
+    }
+
+    Real error = 0;
+
+    for (unsigned i = 0; i < std::min(C.size(), C2.size()); i++) {
+      error += pow(C[i] - C2[i], 2);
+    }
+
+    std::cerr << "Iteration " << it << ": " << sqrt(error / C.size()) << std::endl;
+
+    C = C2;
+  }
+
+  τ = 0;
+  for (Real Ci : C) {
+    std::cout << τ << " " << Ci << std::endl;
+    τ += Δτ;
+  }
+
   std::cerr << - 2 * y / Γ₀ * energy(C, Δτ, τ₀) << std::endl;
 
   return 0;
-- 
cgit v1.2.3-70-g09d2