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#include <complex>
#include <cstdlib>
#include <functional>
#include <getopt.h>
#include <random>
#include "pcg-cpp/include/pcg_random.hpp"
#include "randutils/randutils.hpp"
#include "complex_normal.hpp"
#include "p-spin.hpp"
#include "stereographic.hpp"
using Rng = randutils::random_generator<pcg32>;
template <class Distribution, class Generator>
Vector randomVector(unsigned N, Distribution d, Generator& r) {
Vector z(N);
for (unsigned i = 0; i < N; i++) {
z(i) = d(r);
}
return z;
}
Vector findSaddle(const Tensor& J, const Vector& z0, double γ0, double δ, double ε, Rng& r) {
Vector z = z0;
double W;
Vector dW;
std::tie(W, dW) = WdW(J, z);
while (W > δ) {
double γ = pow(r.variate<double, std::normal_distribution>(0, γ0), 2);
Vector zNew = z - γ * dW.conjugate();
zNew *= sqrt(z.size()) / sqrt((Scalar)(zNew.transpose() * zNew));
double WNew;
Vector dWNew;
std::tie(WNew, dWNew) = WdW(J, zNew);
if (WNew < W) {
z = zNew;
W = WNew;
dW = dWNew;
std::cout << W << std::endl;
}
}
Vector ζ = euclideanToStereographic(z);
Vector dH;
Matrix ddH;
std::tie(std::ignore, dH, ddH) = stereographicHamGradHess(J, ζ);
while (W > ε) {
double γ = pow(r.variate<double, std::normal_distribution>(0, γ0), 2);
Vector ζNew = ζ - ddH.ldlt().solve(dH);
double WNew;
Vector dWNew;
std::tie(WNew, dWNew) = WdW(J, stereographicToEuclidean(ζNew));
if (WNew < W) {
ζ = ζNew;
W = WNew;
dW = dWNew;
std::tie(std::ignore, dH, ddH) = stereographicHamGradHess(J, ζ);
std::cout << WNew << std::endl;
}
}
return stereographicToEuclidean(ζ);
}
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, sqrt(T), 0);
while (!quit(W, steps)) {
double γ = pow(r.variate<double, std::normal_distribution>(0, γ0), 2);
Vector η = randomVector(z.size(), d, r.engine());
z -= γ * (dW.conjugate() / pow((double)z.size(), 2) + η);
z *= sqrt(z.size()) / sqrt((Scalar)(z.transpose() * z));
std::tie(W, dW) = WdW(J, z);
}
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 ε = 1e-4;
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:E:")) != -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 'E':
ε = 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;
Tensor J = generateCouplings<Scalar, PSPIN_P>(N, complex_normal_distribution<>(0, σ, κ), r.engine());
Vector z = randomVector(N, complex_normal_distribution<>(0, 1, 0), r.engine());
z *= sqrt(N) / sqrt((Scalar)(z.transpose() * z)); // Normalize.
std::function<bool(double, unsigned)> f = [δ](double W, unsigned) {
std::cout << W << std::endl;
return W < δ;
};
//Vector zm = langevin(J, z, T, γ, f, r);
Vector zm = findSaddle(J, z, γ, δ, ε, 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 << constraint << std::endl;
std::cout << H / (double)N << std::endl;
}
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