From 2316044fd02bf22b5b6c0f414874dada2c7603e4 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 7 Jan 2021 11:23:20 +0100
Subject: Implemented some lazy optimizations and C++17isms.

---
 langevin.cpp      | 19 +++++++------------
 p-spin.hpp        | 21 ++++++++++++++-------
 stereographic.hpp |  6 +-----
 tensor.hpp        |  8 ++++----
 4 files changed, 26 insertions(+), 28 deletions(-)

diff --git a/langevin.cpp b/langevin.cpp
index 1b328b6..b67d358 100644
--- a/langevin.cpp
+++ b/langevin.cpp
@@ -17,7 +17,7 @@
 using Rng = randutils::random_generator<pcg32>;
 
 Vector normalize(const Vector& z) {
-  return z * sqrt(z.size()) / sqrt((Scalar)(z.transpose() * z));
+  return z * sqrt((double)z.size() / (Scalar)(z.transpose() * z));
 }
 
 template <class Distribution, class Generator>
@@ -33,19 +33,14 @@ Vector randomVector(unsigned N, Distribution d, Generator& r) {
 
 std::tuple<double, Vector> gradientDescent(const Tensor& J, const Vector& z0, double ε, double γ0 = 1, double δγ = 2) {
   Vector z = z0;
-
-  double W;
-  Vector dW;
-  std::tie(W, dW) = WdW(J, z);
-
   double γ = γ0;
 
+  auto [W, dW] = WdW(J, z);
+
   while (W > ε) {
     Vector zNew = normalize(z - γ * dW.conjugate());
 
-    double WNew;
-    Vector dWNew;
-    std::tie(WNew, dWNew) = WdW(J, zNew);
+    auto [WNew, dWNew] = WdW(J, zNew);
 
     if (WNew < W) { // If the step lowered the objective, accept it!
       z = zNew;
@@ -66,12 +61,12 @@ std::tuple<double, Vector> gradientDescent(const Tensor& J, const Vector& z0, do
 }
 
 Vector findSaddle(const Tensor& J, const Vector& z0, double ε, double δW = 2, double γ0 = 1, double δγ = 2) {
-  double W;
-  std::tie(W, std::ignore) = WdW(J, z0);
-
   Vector z = z0;
   Vector ζ = euclideanToStereographic(z);
 
+  double W;
+  std::tie(W, std::ignore) = WdW(J, z);
+
   Vector dH;
   Matrix ddH;
   std::tie(std::ignore, dH, ddH) = stereographicHamGradHess(J, ζ, z);
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};
 }
diff --git a/stereographic.hpp b/stereographic.hpp
index 8313f25..61d81c5 100644
--- a/stereographic.hpp
+++ b/stereographic.hpp
@@ -51,11 +51,7 @@ Matrix stereographicJacobian(const Vector& ζ) {
 }
 
 std::tuple<Scalar, Vector, Matrix> stereographicHamGradHess(const Tensor& J, const Vector& ζ, const Vector& z) {
-  Scalar hamiltonian;
-  Vector gradZ;
-  Matrix hessZ;
-  std::tie(hamiltonian, gradZ, hessZ) = hamGradHess(J, z);
-
+  auto [hamiltonian, gradZ, hessZ] = hamGradHess(J, z);
   Matrix jacobian = stereographicJacobian(ζ);
 
   Matrix metric = jacobian * jacobian.adjoint();
diff --git a/tensor.hpp b/tensor.hpp
index 41be3fd..f442f87 100644
--- a/tensor.hpp
+++ b/tensor.hpp
@@ -55,12 +55,12 @@ contractDown(const Eigen::Tensor<Scalar, 2>& J, const Eigen::Matrix<Scalar, Eige
   return Eigen::Map<const Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>>(J.data(), z.size(), z.size());
 }
 
+const std::array<Eigen::IndexPair<int>, 1> ip00 = {Eigen::IndexPair<int>(0, 0)};
+
 template <class Scalar, int r>
 Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>
 contractDown(const Eigen::Tensor<Scalar, r>& J, const Eigen::Matrix<Scalar, Eigen::Dynamic, 1>& z) {
-  Eigen::Tensor<Scalar, 1> zT =
-      Eigen::TensorMap<Eigen::Tensor<const Scalar, 1>>(z.data(), {z.size()});
-  std::array<Eigen::IndexPair<int>, 1> ip = {Eigen::IndexPair<int>(0, 0)};
-  Eigen::Tensor<Scalar, r - 1> Jz = J.contract(zT, ip);
+  Eigen::Tensor<Scalar, 1> zT = Eigen::TensorMap<Eigen::Tensor<const Scalar, 1>>(z.data(), {z.size()});
+  Eigen::Tensor<Scalar, r - 1> Jz = J.contract(zT, ip00);
   return contractDown(Jz, z);
 }
-- 
cgit v1.2.3-70-g09d2