1 files changed, 14 insertions, 24 deletions

diff --git a/langevin.cpp b/langevin.cpp
index 49efab4..e5ed0b8 100644
--- a/langevin.cpp
+++ b/langevin.cpp
@@ -69,41 +69,36 @@ Vector findSaddle(const Tensor& J, const Vector& z0, double ε, double δW, doub
   double W;
   std::tie(W, std::ignore) = WdW(J, z0);
 
-  Vector ζ = euclideanToStereographic(z0);
+  Vector z = z0;
+  Vector ζ = euclideanToStereographic(z);
+
   Vector dH;
   Matrix ddH;
-  std::tie(std::ignore, dH, ddH) = stereographicHamGradHess(J, ζ);
-
-  unsigned steps = 0;
-  unsigned gradSteps = 0;
+  std::tie(std::ignore, dH, ddH) = stereographicHamGradHess(J, ζ, z);
 
   while (W > ε) {
-    // ddH is complex symmetric, which is (almost always) invertible
+    // ddH is complex symmetric, which is (almost always) invertible, so a
+    // partial pivot LU decomposition can be used.
     Vector dζ = ddH.partialPivLu().solve(dH);
     Vector ζNew = ζ - dζ;
+    Vector zNew = stereographicToEuclidean(ζNew);
 
     double WNew;
-    std::tie(WNew, std::ignore) = WdW(J, stereographicToEuclidean(ζNew));
+    std::tie(WNew, std::ignore) = WdW(J, zNew);
 
     if (WNew < W) { // If Newton's step lowered the objective, accept it!
       ζ = ζNew;
+      z = zNew;
       W = WNew;
     } else { // Otherwise, do gradient descent until W is a factor δW smaller.
-      Vector z;
-      std::tie(W, z) = gradientDescent(J, stereographicToEuclidean(ζ), γ0, W / δW);
+      std::tie(W, z) = gradientDescent(J, z, γ0, W / δW);
       ζ = euclideanToStereographic(z);
-      gradSteps++;
     }
 
-    std::tie(std::ignore, dH, ddH) = stereographicHamGradHess(J, ζ);
-    steps++;
-
-    if (steps % 100 == 0) {
-      std::cerr << steps << " minimization steps, W is " << W << " " << gradSteps << "." << std::endl;
-    }
+    std::tie(std::ignore, dH, ddH) = stereographicHamGradHess(J, ζ, z);
   }
 
-  return stereographicToEuclidean(ζ);
+  return z;
 }
 
 std::tuple<double, Vector> langevin(const Tensor& J, const Vector& z0, double T, double γ, unsigned N, Rng& r) {
@@ -189,13 +184,7 @@ int main(int argc, char* argv[]) {
   Rng r;
 
   Tensor J = generateCouplings<Scalar, PSPIN_P>(N, complex_normal_distribution<>(0, σ, κ), r.engine());
-  Vector z0 = randomVector(N, complex_normal_distribution<>(0, 1, 0), r.engine());
-  z0 *= sqrt(N) / sqrt((Scalar)(z0.transpose() * z0)); // Normalize.
-
-  std::function<bool(double, unsigned)> f = [δ](double W, unsigned) {
-    std::cout << W << std::endl;
-    return W < δ;
-  };
+  Vector z0 = normalize(randomVector(N, complex_normal_distribution<>(0, 1, 0), r.engine()));
 
   Vector zSaddle = findSaddle(J, z0, ε, δ, γ);
 
@@ -209,6 +198,7 @@ int main(int argc, char* argv[]) {
     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;
+    std::cerr << M * (i+1) << " steps taken to move " << (zNewSaddle - zSaddle).norm() << ", saddle information saved." << std::endl;
   }
 
   return 0;