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#pragma once
#include <eigen3/Eigen/Dense>
#include "tensor.hpp"
#define PSPIN_P 3
const unsigned p = PSPIN_P; // polynomial degree of Hamiltonian
using Scalar = std::complex<double>;
using Vector = Eigen::VectorXcd;
using Matrix = Eigen::MatrixXcd;
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 pBang = factorial(p);
Matrix hessian = ((p - 1) * p / pBang) * Jz;
Vector gradient = (p / pBang) * Jzz;
Scalar hamiltonian = Jzzz / pBang;
return {hamiltonian, gradient, hessian};
}
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);
Vector dzdt = project(z, dH.conjugate());
double a = z.squaredNorm();
Scalar A = (Scalar)(z.transpose() * dzdt) / a;
Scalar B = dH.dot(z) / a;
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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