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#include <complex>
#include <cstdlib>
#include <functional>
#include <getopt.h>
#include <random>
#include <eigen3/Eigen/Core>
#include <eigen3/unsupported/Eigen/CXX11/Tensor>
#include "pcg-cpp/include/pcg_random.hpp"
#include "randutils/randutils.hpp"
#include "complex_normal.hpp"
#include "tensor.hpp"
#define P_SPIN_P 3
const unsigned p = P_SPIN_P;
using Scalar = std::complex<double>;
using Vector = Eigen::VectorXcd;
using Matrix = Eigen::MatrixXcd;
using Tensor = Eigen::Tensor<Scalar, p>;
using Rng = randutils::random_generator<pcg32>;
Vector initializeVector(unsigned N, Rng& r) {
Vector z(N);
complex_normal_distribution<> dist(0, 1, 0);
for (unsigned i = 0; i < N; i++) {
z(i) = dist(r.engine());
}
z *= sqrt(N) / sqrt(z.dot(z));
return z;
}
std::tuple<Scalar, Vector, Matrix> hamGradHess(const Tensor& J, const Vector& z) {
Matrix Jz = contractDown(J, z);
Vector Jzz = Jz * z;
Matrix hessian = ((p - 1) * (double)p / factorial(p)) * Jz;
Vector gradient = ((double)p / factorial(p)) * Jzz;
Scalar hamiltonian = (1.0 / factorial(p)) * Jzz.dot(z);
return {hamiltonian, gradient, hessian};
}
std::tuple<double, Vector> WdW(const Tensor& J, const Vector& z) {
Vector gradient;
Matrix hessian;
std::tie(std::ignore, gradient, hessian) = hamGradHess(J, z);
Vector projectedGradient = gradient - (gradient.dot(z) / (double)z.size()) * z;
double W = projectedGradient.cwiseAbs2().sum();
Vector dW = hessian.conjugate() * projectedGradient;
return {W, dW};
}
Vector langevin(const Tensor& J, const Vector& z0, double T, double γ0,
std::function<bool(double, unsigned)> quit, Rng& r) {
Vector z = z0;
double W;
Vector dW;
std::tie(W, dW) = WdW(J, z);
unsigned steps = 0;
complex_normal_distribution<> d(0, T, 0);
while (!quit(W, steps)) {
double γ = pow(r.variate<double, std::normal_distribution>(0, γ0), 2);
Vector η(z.size());
for (unsigned i = 0; i < z.size(); i++) {
η(i) = d(r.engine());
}
Vector zNext = z - γ * dW + η;
zNext *= sqrt(zNext.size()) / sqrt(zNext.dot(zNext));
double WNext;
Vector dWNext;
std::tie(WNext, dWNext) = WdW(J, zNext);
if (exp((W - WNext) / T) > r.uniform(0.0, 1.0)) {
z = zNext;
W = WNext;
dW = dWNext;
}
}
return z;
}
int main(int argc, char* argv[]) {
// model parameters
unsigned N = 10; // number of spins
double T = 1; // temperature
double Rκ = 1; // real part of distribution parameter
double Iκ = 0; // imaginary part of distribution parameter
// simulation parameters
double δ = 1e-2; // threshold for determining saddle
double γ = 1e-2; // step size
unsigned t = 1000; // number of Langevin steps
int opt;
while ((opt = getopt(argc, argv, "N:T:e:r:i:g:t:")) != -1) {
switch (opt) {
case 'N':
N = (unsigned)atof(optarg);
break;
case 't':
t = (unsigned)atof(optarg);
break;
case 'T':
T = atof(optarg);
break;
case 'e':
δ = atof(optarg);
break;
case 'g':
γ = atof(optarg);
case 'r':
Rκ = atof(optarg);
break;
case 'i':
Iκ = atof(optarg);
break;
default:
exit(1);
}
}
Scalar κ(Rκ, Iκ);
double σ = sqrt(factorial(p) / (2.0 * pow(N, p - 1)));
Rng r;
complex_normal_distribution<> d(0, σ, κ);
Tensor J = generateCouplings<Scalar, p>(N, d, r.engine());
Vector z = initializeVector(N, r);
std::function<bool(double, unsigned)> findSaddle = [δ](double W, unsigned) {
std::cout << W << std::endl;
return W < δ;
};
Vector zm = langevin(J, z, T, γ, findSaddle, r);
Scalar H;
Vector dH;
std::tie(H, dH, std::ignore) = hamGradHess(J, zm);
Vector constraint = dH - ((double)p * H / (double)N) * zm;
std::cout << std::endl << zm.dot(zm) << std::endl;
std::cout << constraint.cwiseAbs2().sum() << std::endl;
}
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