From dedcfe0c9aa1ae79dc4d26c559f239571bb26394 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 14 Jan 2021 15:44:26 +0100
Subject: Updated W and dW to use correct constrained gradient.

---
 p-spin.hpp | 38 +++++++++++++-------------------------
 1 file changed, 13 insertions(+), 25 deletions(-)

diff --git a/p-spin.hpp b/p-spin.hpp
index 3532556..91e0152 100644
--- a/p-spin.hpp
+++ b/p-spin.hpp
@@ -26,38 +26,26 @@ std::tuple<Scalar, Vector, Matrix> hamGradHess(const Tensor& J, const Vector& z)
   return {hamiltonian, gradient, hessian};
 }
 
-std::tuple<double, Vector> WdW(const Tensor& J, const Vector& z) {
-  /*
-  Vector gradient;
-  Matrix hessian;
-  std::tie(std::ignore, gradient, hessian) = hamGradHess(J, z);
-
-  Scalar zGrad = gradient.transpose() * z;
-  double N = 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 - (zGrad * projGradConj + (z.transpose() * projGradConj) * (gradient + hessian * z)) / N;
-  */
+Vector project(const Vector& z, const Vector& x) {
+  Scalar xz = x.transpose() * z;
+  return x - (xz / z.squaredNorm()) * z.conjugate();
+}
 
+std::tuple<double, Vector> WdW(const Tensor& J, const Vector& z) {
   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();
+  double a = z.squaredNorm();
+  Vector dzdt = project(z, dH.conjugate());
 
-  Scalar pdHcz = pdH.dot(z) / N;
+  Scalar A = (Scalar)(z.transpose() * dzdt) / a;
+  Scalar B = dH.dot(z) / a;
 
-  double W = pdH.squaredNorm();
-  Vector dW = ddH * (pdHc - pdHcz * z) - (dHz * pdHc + pdHcz * dH);
+  double W = dzdt.squaredNorm();
+  Vector dW = ddH * (dzdt - A * z.conjugate())
+    + 2 * (conj(A) * B * z).real()
+    - conj(B) * dzdt - conj(A) * dH.conjugate();
 
   return {W, dW};
 }
-- 
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