Restored cubic model class and refactored somewhat.

1 files changed, 130 insertions, 46 deletions

diff --git a/least_squares.cpp b/least_squares.cpp
index f69f117..51c79c6 100644
--- a/least_squares.cpp
+++ b/least_squares.cpp
@@ -26,6 +26,10 @@ public:
     const Eigen::Tensor<Real, 2> JxT = contract(xT, ip20);
     return Eigen::Map<const Matrix>(JxT.data(), dimension(0), dimension(1));
   }
+
+  Tensor operator+(const Eigen::Tensor<Real, 3>& J) const {
+    return Eigen::Tensor<Real, 3>::operator+(J);
+  }
 };
 
 Matrix operator*(const Eigen::Matrix<Real, 1, Eigen::Dynamic>& x, const Tensor& J) {
@@ -35,6 +39,17 @@ Matrix operator*(const Eigen::Matrix<Real, 1, Eigen::Dynamic>& x, const Tensor&
   return Eigen::Map<const Matrix>(JxT.data(), J.dimension(1), J.dimension(2));
 }
 
+class Tensor4 : public Eigen::Tensor<Real, 4> {
+  using Eigen::Tensor<Real, 4>::Tensor;
+
+public:
+  Eigen::Tensor<Real, 3> operator*(const Vector& x) const {
+    const std::array<Eigen::IndexPair<int>, 1> ip30 = {Eigen::IndexPair<int>(3, 0)};
+    const Eigen::Tensor<Real, 1> xT = Eigen::TensorMap<const Eigen::Tensor<Real, 1>>(x.data(), x.size());
+    return contract(xT, ip30);
+  }
+};
+
 Vector normalize(const Vector& x) {
   return x * sqrt((Real)x.size() / x.squaredNorm());
 }
@@ -55,16 +70,70 @@ Vector VFromABJ(const Vector& b, const Matrix& A, const Matrix& Jx, const Vector
   return b + (A + 0.5 * Jx) * x;
 }
 
-class QuadraticModel {
+class Model {
+public:
+  unsigned N;
+  unsigned M;
+
+  Model(unsigned N, unsigned M) : N(N), M(M) {}
+
+  virtual std::tuple<Vector, Matrix, Tensor> VdVddV(const Vector& x) const {
+    std::cerr << "VdVddV needs to be defined in your specialization of this class!" << std::endl;
+    return {Vector::Zero(M), Matrix::Zero(M, N), Tensor(M, N, N)};
+  }
+
+  std::tuple<Real, Vector, Matrix> HdHddH(const Vector& x) const {
+    auto [V, dV, ddV] = VdVddV(x);
+
+    Real H = HFromV(V);
+    Vector dH = dHFromVdV(V, dV);
+    Matrix ddH = V.transpose() * ddV + dV.transpose() * dV;
+
+    return {H, dH, ddH};
+  }
+
+  std::tuple<Real, Vector> getHamGrad(const Vector& x) const {
+    Vector V;
+    Matrix dV;
+    std::tie(V, dV, std::ignore) = VdVddV(x);
+
+    Real H = HFromV(V);
+    Vector dH = makeTangent(dHFromVdV(V, dV), x);
+
+    return {H, dH};
+  }
+
+  std::tuple<Real, Vector, Matrix> hamGradHess(const Vector& x) const {
+    auto [H, dH, ddH] = HdHddH(x);
+
+    Vector gradH = dH - dH.dot(x) * x / (Real)N;
+    Matrix hessH = ddH - (dH * x.transpose() + x.dot(dH) * Matrix::Identity(N, N) + (ddH * x) * x.transpose()) / (Real)N  + 2.0 * x * x.transpose();
+
+    return {H, gradH, hessH};
+  }
+
+  virtual Real getHamiltonian(const Vector& x) const {
+    Real H;
+    std::tie(H, std::ignore, std::ignore) = HdHddH(x);
+    return H;
+  }
+
+  Vector spectrum(const Vector& x) const {
+    Matrix hessH;
+    std::tie(std::ignore, std::ignore, hessH) = hamGradHess(x);
+    Eigen::EigenSolver<Matrix> eigenS(hessH);
+    return eigenS.eigenvalues().real();
+  }
+};
+
+class QuadraticModel : public Model{
 private:
   Tensor J;
   Matrix A;
   Vector b;
 
 public:
-  unsigned N;
-  unsigned M;
-  QuadraticModel(unsigned N, unsigned M, Rng& r, double μ1, double μ2, double μ3) : N(N), M(M), J(M, N, N), A(M, N), b(M) {
+  QuadraticModel(unsigned N, unsigned M, Rng& r, double μ1, double μ2, double μ3) : Model(N, M), J(M, N, N), A(M, N), b(M) {
     Eigen::StaticSGroup<Eigen::Symmetry<1,2>> ssym1;
     for (unsigned k = 0; k < N; k++) {
       for (unsigned j = k; j < N; j++) {
@@ -83,7 +152,7 @@ public:
     }
   }
 
-  std::tuple<Vector, Matrix, const Tensor&> VdVddV(const Vector& x) const {
+  std::tuple<Vector, Matrix, Tensor> VdVddV(const Vector& x) const override {
     Matrix Jx = J * x;
     Vector V = VFromABJ(b, A, Jx, x);
     Matrix dV = A + Jx;
@@ -91,55 +160,69 @@ public:
     return {V, dV, J};
   }
 
-  std::tuple<Real, Vector, Matrix> HdHddH(const Vector& x) const {
-    auto [V, dV, ddV] = VdVddV(x);
-
-    Real H = HFromV(V);
-    Vector dH = dHFromVdV(V, dV);
-    Matrix ddH = V.transpose() * ddV + dV.transpose() * dV;
-
-    return {H, dH, ddH};
-  }
-
   /* Unfortunately benchmarking indicates that ignorning entries of a returned tuple doesn't result
    * in those execution paths getting optimized out. It is much more efficient to compute the
    * energy alone when only the energy is needed.
    */
-  Real getHamiltonian(const Vector& x) const {
+  Real getHamiltonian(const Vector& x) const override {
     return HFromV(VFromABJ(b, A, J * x, x));
   }
+};
 
-  std::tuple<Real, Vector> getHamGrad(const Vector& x) const {
-    Vector V;
-    Matrix dV;
-    std::tie(V, dV, std::ignore) = VdVddV(x);
+class CubicModel : public Model {
+private:
+  Tensor4 J3;
+  Tensor J2;
+  Matrix A;
+  Vector b;
 
-    Real H = HFromV(V);
-    Vector dH = makeTangent(dHFromVdV(V, dV), x);
+public:
+  CubicModel(unsigned N, unsigned M, Rng& r, double μ1, double μ2, double μ3, double μ4) : Model(N, M), J3(M, N, N, N), J2(M, N, N), A(M, N), b(M) {
+    Eigen::StaticSGroup<Eigen::Symmetry<1,2>, Eigen::Symmetry<2,3>> ssym2;
+    for (unsigned i = 0; i < M; i++) {
+      for (unsigned j = 0; j < N; j++) {
+        for (unsigned k = j; k < N; k++) {
+          for (unsigned l = k; l < N; l++) {
+            ssym2(J3, i, j, k, l) = (sqrt(6) * μ4 / pow(N, 1.5)) * r.variate<Real, std::normal_distribution>();
+          }
+        }
+      }
+    }
 
-    return {H, dH};
-  }
+    Eigen::StaticSGroup<Eigen::Symmetry<1,2>> ssym1;
+    for (unsigned k = 0; k < N; k++) {
+      for (unsigned j = k; j < N; j++) {
+        for (unsigned i = 0; i < M; i++) {
+          ssym1(J2, i, j, k) = r.variate<Real, std::normal_distribution>(0, sqrt(2) * μ3 / N);
+        }
+      }
+    }
 
-  std::tuple<Real, Vector, Matrix> hamGradHess(const Vector& x) const {
-    auto [H, dH, ddH] = HdHddH(x);
+    for (Real& Aij : A.reshaped()) {
+      Aij = r.variate<Real, std::normal_distribution>(0, μ2 / sqrt(N));
+    }
 
-    Real dHx = dH.dot(x) / N;
+    for (Real& bi : b) {
+      bi = r.variate<Real, std::normal_distribution>(0, μ1);
+    }
+  }
 
-    Vector gradH = dH - dHx * x;
-    Matrix hessH = ddH - dHx * Matrix::Identity(N, N) - ((dH + ddH * x) / N - 2 * x) * x.transpose();
+  std::tuple<Vector, Matrix, Tensor> VdVddV(const Vector& x) const override {
+    Tensor J3x = J3 * x;
+    Matrix J3xx = J3x * x;
+    Matrix J2x = J2 * x;
+    Vector V1 = (A + 0.5 * J2x + J3xx / 6.0) * x;
+    Matrix dV = A + J2x + 0.5 * J3xx;
 
-    return {H, gradH, hessH};
+    return {b + V1, dV, J2 + J3x};
   }
 
-  Vector spectrum(const Vector& x) const {
-    Matrix hessH;
-    std::tie(std::ignore, std::ignore, hessH) = hamGradHess(x);
-    Eigen::EigenSolver<Matrix> eigenS(hessH);
-    return eigenS.eigenvalues().real();
+  Real getHamiltonian(const Vector& x) const override {
+    return HFromV(VFromABJ(b, A, J2 * x + ((Tensor)(J3 * x) * x) / 3.0, x));
   }
 };
 
-Vector gradientDescent(const QuadraticModel& M, const Vector& x0, Real ε = 1e-7) {
+Vector gradientDescent(const Model& M, const Vector& x0, Real ε = 1e-7) {
   Vector x = x0;
   Real λ = 10;
 
@@ -167,7 +250,7 @@ Vector gradientDescent(const QuadraticModel& M, const Vector& x0, Real ε = 1e-7
   return x;
 }
 
-Vector findMinimum(const QuadraticModel& M, const Vector& x0, Real ε = 1e-5) {
+Vector findMinimum(const Model& M, const Vector& x0, Real ε = 1e-5) {
   Vector x = x0;
   Real λ = 100;
 
@@ -191,21 +274,22 @@ Vector findMinimum(const QuadraticModel& M, const Vector& x0, Real ε = 1e-5) {
   return x;
 }
 
-Vector findSaddle(const QuadraticModel& M, const Vector& x0, Real ε = 1e-12) {
+Vector findSaddle(const Model& M, const Vector& x0, Real ε = 1e-12) {
   Vector x = x0;
-  Vector g;
+  Vector dx, g;
   Matrix m;
 
-  while (std::tie(std::ignore, g, m) = M.hamGradHess(x), g.norm() / M.N > ε) {
-    Vector dx = m.partialPivLu().solve(g);
-    dx -= (x.dot(dx) / M.N) * x;
+  while (
+    std::tie(std::ignore, g, m) = M.hamGradHess(x),
+    dx = makeTangent(m.partialPivLu().solve(g), x),
+    dx.norm() > ε) {
     x = normalize(x - dx);
   }
 
   return x;
 }
 
-Vector metropolisSweep(const QuadraticModel& M, const Vector& x0, Real β, Rng& r, unsigned sweeps = 1, Real ε = 1) {
+Vector metropolisSweep(const Model& M, const Vector& x0, Real β, Rng& r, unsigned sweeps = 1, Real δ = 1) {
   Vector x = x0;
   Real H = M.getHamiltonian(x);
 
@@ -216,7 +300,7 @@ Vector metropolisSweep(const QuadraticModel& M, const Vector& x0, Real β, Rng&
       Vector xNew = x;
 
       for (Real& xNewᵢ : xNew) {
-        xNewᵢ += ε * r.variate<Real, std::normal_distribution>();
+        xNewᵢ += δ * r.variate<Real, std::normal_distribution>();
       }
 
       xNew = normalize(xNew);
@@ -231,9 +315,9 @@ Vector metropolisSweep(const QuadraticModel& M, const Vector& x0, Real β, Rng&
     }
 
     if (rate / M.N < 0.5) {
-      ε /= 1.5;
+      δ /= 1.5;
     } else {
-      ε *= 1.5;
+      δ *= 1.5;
     }
   }