From bdf7b97b2e2d5efc4c2b5fee2868dfc33c891d16 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Sat, 29 Mar 2025 12:23:08 -0300
Subject: Fixed several bugs.
---
integrator.cpp | 34 ++++++++++++++++++++++++----------
1 file changed, 24 insertions(+), 10 deletions(-)
diff --git a/integrator.cpp b/integrator.cpp
index bb22a36..ea5c477 100644
--- a/integrator.cpp
+++ b/integrator.cpp
@@ -16,29 +16,43 @@ public:
}
};
+unsigned p = 3;
+
Real f(Real q) {
- return 0.5 * pow(q, 2);
+ return 0.5 * pow(q, p);
}
Real df(Real q) {
- return q;
+ return 0.5 * p * pow(q, p - 1);
}
Real ddf(Real q) {
- return 1;
+ return 0.5 * p * (p - 1) * pow(q, p - 2);
}
Real integrate(const std::vector<Point>& Cₜ) {
Real I = 0;
for (unsigned i = 0; i < Cₜ.size() - 1; i++) {
+ unsigned j = Cₜ.size() - 1 - i;
Real Δτ = Cₜ[i + 1].τ() - Cₜ[i].τ();
- Real C = (Cₜ[i + 1].C() + Cₜ[i].C()) / 2;
+ Real C = (Cₜ[j].C() + Cₜ[j - 1].C()) / 2;
Real dC = (Cₜ[i + 1].C() - Cₜ[i].C()) / Δτ;
I += Δτ * df(C) * dC;
}
return I;
}
+Real energy(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].C() + Ct[i + 1].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;
@@ -66,20 +80,20 @@ int main(int argc, char* argv[]) {
}
}
+ Real z = 0.5 + 0.0 * pow(y, 2);
+
std::vector<Point> Cₜ;
- Cₜ.reserve(τₘₐₓ / Δτ);
+ Cₜ.reserve(τₘₐₓ / Δτ + 1);
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);
+ Real dC = -z * Cₜ.back().C() - 2 * pow(y, 2) * integrate(Cₜ);
Cₜ.push_back({Cₜ.back().τ() + Δτ, Cₜ.back().C() + Δτ * dC});
+ std::cout << Cₜ.back().τ() << " " << Cₜ.back().C() << std::endl;
}
- for (const Point& p : Cₜ) {
- std::cout << p.τ() << " " << p.C() << std::endl;
- }
+ std::cerr << - 2 * y * energy(Cₜ) << std::endl;
return 0;
}
--
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