From 3279288783f64e8a8e8fb6394d66a23f49899869 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Fri, 8 Jan 2021 18:04:16 +0100
Subject: Fixed some bugs, and made the simulation catch errors correctly.

---
 langevin.cpp | 29 ++++++++++++++++++++---------
 p-spin.hpp   | 19 ++++++++++++++++++-
 2 files changed, 38 insertions(+), 10 deletions(-)

diff --git a/langevin.cpp b/langevin.cpp
index f494809..cf61b85 100644
--- a/langevin.cpp
+++ b/langevin.cpp
@@ -26,6 +26,12 @@ Vector randomVector(unsigned N, Distribution d, Generator& r) {
   return z;
 }
 
+class gradientDescentStallException: public std::exception {
+  virtual const char* what() const throw() {
+    return "Gradient descent stalled.";
+  }
+} gradientDescentStall;
+
 std::tuple<double, Vector> gradientDescent(const Tensor& J, const Vector& z0, double ε, double γ0 = 1, double δγ = 2) {
   Vector z = z0;
   double γ = γ0;
@@ -46,9 +52,8 @@ std::tuple<double, Vector> gradientDescent(const Tensor& J, const Vector& z0, do
       γ /= δγ;
     }
 
-    if (γ < 1e-15) {
-      std::cerr << "Gradient descent stalled." << std::endl;
-      exit(1);
+    if (γ < 1e-50) {
+      throw gradientDescentStall;
     }
   }
 
@@ -182,13 +187,19 @@ int main(int argc, char* argv[]) {
   Vector z = zSaddle;
   for (unsigned i = 0; i < n; i++) {
     std::tie(W, z) = langevin(J, z, T, γ, M, r);
-    Vector zNewSaddle = findSaddle(J, z, ε);
-    Scalar H;
-    Matrix ddH;
-    std::tie(H, std::ignore, ddH) = hamGradHess(J, zNewSaddle);
-    Eigen::SelfAdjointEigenSolver<Matrix> es(ddH.adjoint() * ddH);
-    std::cout << (zNewSaddle - zSaddle).norm() << " " << real(H) << " " << imag(H) << " " << es.eigenvalues().transpose() << std::endl;
+    try {
+      Vector zNewSaddle = findSaddle(J, z, ε);
+      Scalar H;
+      Matrix ddH;
+      std::tie(H, std::ignore, ddH) = hamGradHess(J, zNewSaddle);
+      Eigen::SelfAdjointEigenSolver<Matrix> es(ddH.adjoint() * ddH);
+      std::cout << N << "\t" << M * (i+1) << "\t" << H << "\t"
+        << zNewSaddle.transpose() << "\t" << es.eigenvalues().transpose()
+        << std::endl;
     std::cerr << M * (i+1) << " steps taken to move " << (zNewSaddle - zSaddle).norm() << ", saddle information saved." << std::endl;
+    } catch (std::exception& e) {
+      std::cerr << "Could not find a saddle: " << e.what() << std::endl;
+    }
   }
 
   return 0;
diff --git a/p-spin.hpp b/p-spin.hpp
index 83e4e39..3532556 100644
--- a/p-spin.hpp
+++ b/p-spin.hpp
@@ -27,6 +27,7 @@ std::tuple<Scalar, Vector, Matrix> hamGradHess(const Tensor& J, const Vector& z)
 }
 
 std::tuple<double, Vector> WdW(const Tensor& J, const Vector& z) {
+  /*
   Vector gradient;
   Matrix hessian;
   std::tie(std::ignore, gradient, hessian) = hamGradHess(J, z);
@@ -40,7 +41,23 @@ std::tuple<double, Vector> WdW(const Tensor& J, const Vector& z) {
   Scalar zProjGrad = z.transpose() * projGradConj;
 
   double W = projGrad.norm();
-  Vector dW = hessian * (projGradConj - (zProjGrad / N) * z) - (zGrad * projGradConj + zProjGrad * gradient) / N;
+  Vector dW = hessian * projGradConj - (zGrad * projGradConj + (z.transpose() * projGradConj) * (gradient + hessian * z)) / N;
+  */
+
+  Vector dH;
+  Matrix ddH;
+  std::tie(std::ignore, dH, ddH) = hamGradHess(J, z);
+
+  double N = z.size();
+  Scalar dHz = (Scalar)(dH.transpose() * z) / N;
+
+  Vector pdH = dH - dHz * z;
+  Vector pdHc = pdH.conjugate();
+
+  Scalar pdHcz = pdH.dot(z) / N;
+
+  double W = pdH.squaredNorm();
+  Vector dW = ddH * (pdHc - pdHcz * z) - (dHz * pdHc + pdHcz * dH);
 
   return {W, dW};
 }
-- 
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