From 12f15f49cd8cc4ab9c809700e8cb88a0efe198d8 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Wed, 17 Feb 2021 16:14:33 +0100
Subject: Rearranged some functions among files, and wrote the normalize
 function to take generic Eigen expressions.

---
 dynamics.hpp |  6 ++----
 p-spin.hpp   | 17 ++++++++---------
 stokes.hpp   | 16 ++++------------
 3 files changed, 14 insertions(+), 25 deletions(-)

diff --git a/dynamics.hpp b/dynamics.hpp
index 22d590a..d421d13 100644
--- a/dynamics.hpp
+++ b/dynamics.hpp
@@ -21,8 +21,7 @@ std::tuple<double, Vector<Scalar>> gradientDescent(const Tensor<Scalar, p>& J, c
   auto [W, dW] = WdW(J, z);
 
   while (W > ε) {
-    Vector<Scalar> zNewTmp = z - γ * dW.conjugate();
-    Vector<Scalar> zNew = normalize(zNewTmp);
+    Vector<Scalar> zNew = normalize(z - γ * dW.conjugate());
 
     auto [WNew, dWNew] = WdW(J, zNew);
 
@@ -102,8 +101,7 @@ std::tuple<double, Vector<Scalar>> metropolis(const Tensor<Scalar, p>& J, const
   std::uniform_real_distribution<double> D(0, 1);
 
   for (unsigned i = 0; i < N; i++) {
-    Vector<Scalar> zNewTmp = z + γ * randomVector<Scalar>(z.size(), d, r);
-    Vector<Scalar> zNew = normalize(zNewTmp);
+    Vector<Scalar> zNew = normalize(z + γ * randomVector<Scalar>(z.size(), d, r));
 
     double ENew = energy(J, zNew);
 
diff --git a/p-spin.hpp b/p-spin.hpp
index 480b3ca..bd3cacc 100644
--- a/p-spin.hpp
+++ b/p-spin.hpp
@@ -5,6 +5,11 @@
 #include "tensor.hpp"
 #include "factorial.hpp"
 
+template <typename Derived>
+Vector<typename Derived::Scalar> normalize(const Eigen::MatrixBase<Derived>& z) {
+  return z * sqrt((double)z.size() / (typename Derived::Scalar)(z.transpose() * z));
+}
+
 template <class Scalar, int p>
 std::tuple<Scalar, Vector<Scalar>, Matrix<Scalar>> hamGradHess(const Tensor<Scalar, p>& J, const Vector<Scalar>& z) {
   Matrix<Scalar> Jz = contractDown(J, z); // Contracts J into p - 2 copies of z.
@@ -21,14 +26,8 @@ std::tuple<Scalar, Vector<Scalar>, Matrix<Scalar>> hamGradHess(const Tensor<Scal
 }
 
 template <class Scalar>
-Vector<Scalar> normalize(const Vector<Scalar>& z) {
-  return z * sqrt((double)z.size() / (Scalar)(z.transpose() * z));
-}
-
-template <class Scalar>
-Vector<Scalar> project(const Vector<Scalar>& z, const Vector<Scalar>& x) {
-  Scalar xz = x.transpose() * z;
-  return x - (xz / z.squaredNorm()) * z.conjugate();
+Vector<Scalar> zDot(const Vector<Scalar>& z, const Vector<Scalar>& dH) {
+  return -dH.conjugate() + (dH.dot(z) / z.squaredNorm()) * z.conjugate();
 }
 
 template <class Scalar, int p>
@@ -37,7 +36,7 @@ std::tuple<double, Vector<Scalar>> WdW(const Tensor<Scalar, p>& J, const Vector<
   Matrix<Scalar> ddH;
   std::tie(std::ignore, dH, ddH) = hamGradHess(J, z);
 
-  Vector<Scalar> dzdt = project(z, dH.conjugate().eval());
+  Vector<Scalar> dzdt = zDot(z, dH);
 
   double a = z.squaredNorm();
   Scalar A = (Scalar)(z.transpose() * dzdt) / a;
diff --git a/stokes.hpp b/stokes.hpp
index 95bb9c4..117f4de 100644
--- a/stokes.hpp
+++ b/stokes.hpp
@@ -1,10 +1,5 @@
 #include "p-spin.hpp"
 
-template <class Scalar>
-Vector<Scalar> zDot(const Vector<Scalar>& z, const Vector<Scalar>& dH) {
-  return -dH.conjugate() + (dH.dot(z) / z.squaredNorm()) * z.conjugate();
-}
-
 template <class Scalar>
 double segmentCost(const Vector<Scalar>& z, const Vector<Scalar>& dz, const Vector<Scalar>& dH) {
   Vector<Scalar> zD = zDot(z, dH);
@@ -68,8 +63,7 @@ class Rope {
 
     Rope(unsigned N, const Vector<Scalar>& z1, const Vector<Scalar>& z2) : z(N + 2) {
       for (unsigned i = 0; i < N + 2; i++) {
-        z[i] = z1 + (z2 - z1) * ((double)i / (N + 1.0));
-        z[i] = normalize(z[i]);
+        z[i] = normalize(z1 + (z2 - z1) * ((double)i / (N + 1.0)));
       }
     }
 
@@ -106,8 +100,7 @@ class Rope {
 
       while (rNew.cost(J) >= this->cost(J)) {
         for (unsigned i = 1; i < z.size() - 1; i++) {
-          rNew.z[i] = z[i] - δ * Δz[i].conjugate();
-          rNew.z[i] = normalize(rNew.z[i]);
+          rNew.z[i] = normalize(z[i] - δ * Δz[i].conjugate());
         }
 
         δ /= 2;
@@ -144,8 +137,7 @@ class Rope {
 
         Vector<Scalar> δz = z[pos] - z[pos - 1];
 
-        zNew[i] = z[pos] - (a - b) / δz.norm() * δz;
-        zNew[i] = normalize(zNew[i]);
+        zNew[i] = normalize(z[pos] - (a - b) / δz.norm() * δz);
       }
 
       z = zNew;
@@ -192,7 +184,7 @@ class Rope {
       }
 
       for (unsigned i = 0; i < z.size() - 1; i++) {
-        r.z[2 * i + 1] = normalize(((z[i] + z[i + 1]) / 2.0).eval());
+        r.z[2 * i + 1] = normalize(((z[i] + z[i + 1]) / 2.0));
       }
 
       return r;
-- 
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