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#pragma once
#include <exception>
#include <eigen3/Eigen/LU>
#include <random>
#include <iostream>
#include "p-spin.hpp"
#include "stereographic.hpp"
class gradientDescentStallException: public std::exception {
virtual const char* what() const throw() {
return "Gradient descent stalled.";
}
};
template <class Real, class Scalar, int p>
std::tuple<Real, Vector<Scalar>> gradientDescent(const Tensor<Scalar, p>& J, const Vector<Scalar>& z0, Real ε, Real γ0 = 1, Real δγ = 2) {
Vector<Scalar> z = z0;
Real γ = γ0;
auto [W, dW] = WdW(J, z);
while (W > ε) {
Vector<Scalar> zNew = normalize(z - γ * dW.conjugate());
auto [WNew, dWNew] = WdW(J, zNew);
if (WNew < W) { // If the step lowered the objective, accept it!
z = zNew;
W = WNew;
dW = dWNew;
γ = γ0;
} else { // Otherwise, shrink the step and try again.
γ /= δγ;
}
if (γ < 1e-50) {
throw gradientDescentStallException();
}
}
return {W, z};
}
template <class Real, class Scalar, int p>
Vector<Scalar> findSaddle(const Tensor<Scalar, p>& J, const Vector<Scalar>& z0, Real ε, Real δW = 2, Real γ0 = 1, Real δγ = 2) {
Vector<Scalar> z = z0;
Vector<Scalar> dH;
Matrix<Scalar> ddH;
std::tie(std::ignore, dH, ddH) = hamGradHess(J, z);
Scalar zz = z.transpose() * z;
Vector<Scalar> ż = zDot(z, dH) + z * (zz - (Real)z.size());
Matrix<Scalar> dż = dzDot(z, dH) + Matrix<Scalar>::Identity(z.size(), z.size()) * (zz - (Real)z.size()) + 2.0 * z * z.transpose();
Matrix<Scalar> dżc = dzDotConjugate(z, dH, ddH);
Vector<Scalar> b(2 * z.size());
Matrix<Scalar> M(2 * z.size(), 2 * z.size());
b << ż.conjugate(), ż;
M << dż.conjugate(), dżc, dżc.conjugate(), dż;
while (ż.norm() > ε) {
Vector<Scalar> dz = M.partialPivLu().solve(b).tail(z.size());
dz -= z.conjugate().dot(dz) / z.squaredNorm() * z.conjugate();
z = normalize(z - dz);
std::cout << "error : " << z.transpose() * z << " "<< ż.norm() << " " << dz.norm() << std::endl;
getchar();
std::tie(std::ignore, dH, ddH) = hamGradHess(J, z);
zz = z.transpose() * z;
ż = zDot(z, dH) + z * (zz - (Real)z.size());
dż = dzDot(z, dH) + Matrix<Scalar>::Identity(z.size(), z.size()) * (zz - (Real)z.size()) + 2.0 * z * z.transpose();
dżc = dzDotConjugate(z, dH, ddH);
b << ż.conjugate(), ż;
M << dż.conjugate(), dżc, dżc.conjugate(), dż;
}
return z;
}
template <class Scalar, class Distribution, class Generator>
Vector<Scalar> randomVector(unsigned N, Distribution d, Generator& r) {
Vector<Scalar> z(N);
for (unsigned i = 0; i < N; i++) {
z(i) = d(r);
}
return z;
}
template <class Real, class Scalar, int p, class Distribution, class Generator>
std::tuple<Real, Vector<Scalar>> metropolis(const Tensor<Scalar, p>& J, const Vector<Scalar>& z0,
std::function<Real(const Tensor<Scalar, p>&, const Vector<Scalar>&)>& energy,
Real T, Real γ, unsigned N, Distribution d, Generator& r) {
Vector<Scalar> z = z0;
Real E = energy(J, z);
std::uniform_real_distribution<Real> D(0, 1);
for (unsigned i = 0; i < N; i++) {
Vector<Scalar> zNew = normalize(z + γ * randomVector<Scalar>(z.size(), d, r));
Real ENew = energy(J, zNew);
if (E - ENew > T * log(D(r))) {
z = zNew;
E = ENew;
}
}
return {E, z};
}
template <class Real, class Scalar, int p, class Distribution, class Generator>
Vector<Scalar> randomSaddle(const Tensor<Scalar, p>& J, Distribution d, Generator& r, Real ε) {
Vector<Scalar> zSaddle;
bool foundSaddle = false;
while (!foundSaddle) {
Vector<Scalar> z0 = normalize(randomVector<Scalar>(J.dimension(0), d, r.engine()));
try {
zSaddle = findSaddle(J, z0, ε);
foundSaddle = true;
} catch (std::exception& e) {}
}
return zSaddle;
}
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