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#pragma once
#include <eigen3/Eigen/Dense>
#include "tensor.hpp"
#include "factorial.hpp"
template <class Scalar>
using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
template <class Scalar>
using Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>;
template <class Scalar, int p>
using Tensor = Eigen::Tensor<Scalar, p>;
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.
Vector<Scalar> Jzz = Jz * z;
Scalar Jzzz = Jzz.transpose() * z;
double pBang = factorial(p);
Matrix<Scalar> hessian = ((p - 1) * p / pBang) * Jz;
Vector<Scalar> gradient = (p / pBang) * Jzz;
Scalar hamiltonian = Jzzz / pBang;
return {hamiltonian, gradient, hessian};
}
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();
}
template <class Scalar, int p>
std::tuple<double, Vector<Scalar>> WdW(const Tensor<Scalar, p>& J, const Vector<Scalar>& z) {
Vector<Scalar> dH;
Matrix<Scalar> ddH;
std::tie(std::ignore, dH, ddH) = hamGradHess(J, z);
Vector<Scalar> dzdt = project(z, dH.conjugate().eval());
double a = z.squaredNorm();
Scalar A = (Scalar)(z.transpose() * dzdt) / a;
Scalar B = dH.dot(z) / a;
double W = dzdt.squaredNorm();
Vector<Scalar> dW = ddH * (dzdt - A * z.conjugate())
+ 2 * (conj(A) * B * z).real()
- conj(B) * dzdt - conj(A) * dH.conjugate();
return {W, dW};
}
template <class Scalar>
Vector<Scalar> normalize(const Vector<Scalar>& z) {
return z * sqrt((double)z.size() / (Scalar)(z.transpose() * z));
}
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