1 files changed, 14 insertions, 7 deletions

diff --git a/p-spin.hpp b/p-spin.hpp
index b90d80b..16e0a56 100644
--- a/p-spin.hpp
+++ b/p-spin.hpp
@@ -19,12 +19,13 @@ using Tensor = Eigen::Tensor<Scalar, PSPIN_P>;
 std::tuple<Scalar, Vector, Matrix> hamGradHess(const Tensor& J, const Vector& z) {
   Matrix Jz = contractDown(J, z); // Contracts J into p - 2 copies of z.
   Vector Jzz = Jz * z;
+  Scalar Jzzz = Jzz.transpose() * z;
 
-  double f = factorial(p);
+  double pBang = factorial(p);
 
-  Matrix hessian = ((p - 1) * p / f) * Jz;
-  Vector gradient = (p / f) * Jzz;
-  Scalar hamiltonian = (1 / f) * Jzz.transpose() * z;
+  Matrix hessian = ((p - 1) * p / pBang) * Jz;
+  Vector gradient = (p / pBang) * Jzz;
+  Scalar hamiltonian = Jzzz / pBang;
 
   return {hamiltonian, gradient, hessian};
 }
@@ -34,10 +35,16 @@ std::tuple<double, Vector> WdW(const Tensor& J, const Vector& z) {
   Matrix hessian;
   std::tie(std::ignore, gradient, hessian) = hamGradHess(J, z);
 
-  Vector projectedGradient = (gradient - ((gradient.transpose() * z) * z / (double)z.size())).conjugate();
+  Scalar zGrad = gradient.transpose() * z;
+  double N = z.size();
 
-  double W = projectedGradient.cwiseAbs2().sum();
-  Vector dW = hessian * projectedGradient - ((z.transpose() * gradient) * projectedGradient + (z.transpose() * projectedGradient) * (gradient + hessian * z)) / (double)z.size();
+  Vector projGrad = gradient - (zGrad / N) * z;
+  Vector projGradConj = projGrad.conjugate();
+
+  Scalar zProjGrad = z.transpose() * projGradConj;
+
+  double W = projGrad.norm();
+  Vector dW = hessian * (projGradConj - (zProjGrad / N) * z) - (zGrad * projGradConj + zProjGrad * gradient) / N;
 
   return {W, dW};
 }