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#include <getopt.h>
#include <stereographic.hpp>
#include <unordered_map>
#include <list>
#include "complex_normal.hpp"
#include "p-spin.hpp"
#include "dynamics.hpp"
#include "stokes.hpp"
#include "pcg-cpp/include/pcg_random.hpp"
#include "randutils/randutils.hpp"
#include "unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h"
#define PSPIN_P 3
const int p = PSPIN_P; // polynomial degree of Hamiltonian
using Complex = std::complex<Real>;
using ComplexVector = Vector<Complex>;
using ComplexMatrix = Matrix<Complex>;
using ComplexTensor = Tensor<Complex, p>;
using Rng = randutils::random_generator<pcg32>;
std::list<std::array<ComplexVector, 2>> saddlesCloserThan(const std::unordered_map<uint64_t, ComplexVector>& saddles, Real δ) {
std::list<std::array<ComplexVector, 2>> pairs;
for (auto it1 = saddles.begin(); it1 != saddles.end(); it1++) {
for (auto it2 = std::next(it1); it2 != saddles.end(); it2++) {
if ((it1->second - it2->second).norm() < δ) {
pairs.push_back({it1->second, it2->second});
}
}
}
return pairs;
}
template <class Generator>
std::tuple<ComplexTensor, ComplexVector, ComplexVector> matchImaginaryEnergies(const ComplexTensor& J0, const ComplexVector& z10, const ComplexVector& z20, Real ε, Real Δ, Generator& r) {
Real σ = sqrt(factorial(p) / (Real(2) * pow(z10.size(), p - 1)));
complex_normal_distribution<Real> dJ(0, σ, 0);
ComplexTensor J = J0;
Complex H1, H2;
ComplexVector z1, z2;
std::tie(H1, std::ignore, std::ignore) = hamGradHess(J, z10);
std::tie(H2, std::ignore, std::ignore) = hamGradHess(J, z20);
Real prevdist = abs(imag(H1-H2));
Real γ = prevdist / 10;
std::function<void(ComplexTensor&, std::array<unsigned, p>)> perturbJ =
[&γ, &dJ, &r] (ComplexTensor& JJ, std::array<unsigned, p> ind) {
Complex Ji = getJ<Complex, p>(JJ, ind);
setJ<Complex, p>(JJ, ind, Ji + γ * dJ(r.engine()));
};
while (true) {
ComplexTensor Jp = J;
iterateOver<Complex, p>(Jp, perturbJ);
try {
z1 = findSaddle(Jp, z10, Δ);
z2 = findSaddle(Jp, z20, Δ);
Real dist = (z1 - z2).norm();
std::tie(H1, std::ignore, std::ignore) = hamGradHess(Jp, z1);
std::tie(H2, std::ignore, std::ignore) = hamGradHess(Jp, z2);
if (abs(imag(H1 - H2)) < prevdist && dist > Real(1) / 100) {
J = Jp;
prevdist = abs(imag(H1 - H2));
γ = prevdist / 10;
if (abs(imag(H1 - H2)) < ε && dist > Real(1) / 100) {
break;
}
}
} catch (std::exception& e) {}
}
return {J, z1, z2};
}
int main(int argc, char* argv[]) {
// model parameters
unsigned N = 10; // number of spins
Real T = 1; // temperature
Real Rκ = 1; // real part of distribution parameter
Real Iκ = 0; // imaginary part of distribution parameter
// simulation parameters
Real ε = 1e-12;
Real εJ = 1e-5;
Real δ = 1e-2; // threshold for determining saddle
Real Δ = 1e-3;
Real γ = 1e-2; // step size
unsigned t = 1000; // number of Langevin steps
unsigned M = 100;
unsigned n = 100;
int opt;
while ((opt = getopt(argc, argv, "N:M: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;
case 'n':
n = (unsigned)atof(optarg);
break;
case 'M':
M = (unsigned)atof(optarg);
break;
default:
exit(1);
}
}
Complex κ(Rκ, Iκ);
Real σ = sqrt(factorial(p) / ((Real)2 * pow(N, p - 1)));
Rng r;
complex_normal_distribution<Real> d(0, 1, 0);
ComplexTensor J = generateCouplings<Complex, PSPIN_P>(N, complex_normal_distribution<Real>(0, σ, κ), r.engine());
ComplexVector z = normalize(randomVector<Complex>(N, d, r.engine()));
std::function<Real(const ComplexTensor&, const ComplexVector&)> energyNormGrad = []
(const ComplexTensor& J, const ComplexVector& z) {
Real W;
std::tie(W, std::ignore) = WdW(J, z);
return W;
};
std::unordered_map<uint64_t, ComplexVector> saddles;
std::list<std::array<ComplexVector, 2>> nearbySaddles;
while (true) { // Until we find two saddles sufficiently close...
std::tie(std::ignore, z) = metropolis(J, z, energyNormGrad, T, γ, M, d, r.engine());
try {
ComplexVector zSaddleNext = findSaddle(J, z, ε);
uint64_t saddleKey = round(1e2 * real(zSaddleNext(0)));
auto got = saddles.find(saddleKey);
if (got == saddles.end()) {
saddles[saddleKey] = zSaddleNext;
nearbySaddles = saddlesCloserThan(saddles, δ);
if (nearbySaddles.size() > 0) {
break;
}
std::cerr << "Found " << saddles.size() << " distinct saddles." << std::endl;
}
} catch (std::exception& e) {
// std::cerr << "Could not find a saddle: " << e.what() << std::endl;
}
}
std::cerr << "Found sufficiently nearby saddles, perturbing J to equalize Im H." << std::endl;
ComplexVector z1 = nearbySaddles.front()[0];
ComplexVector z2 = nearbySaddles.front()[1];
std::tie(J, z1, z2) = matchImaginaryEnergies(J, z1, z2, 1e-15, ε, r);
std::cerr << "Im H is now sufficently close, starting to relax rope." << std::endl;
Rope stokes(10, z1, z2, J);
for (unsigned i = 0; i < 9; i++) {
stokes.relaxDiscreteGradient(J, 1e6, 0.1, 0);
std::cout << stokes.n() << " " << stokes.cost(J) << std::endl;
stokes = stokes.interpolate();
}
return 0;
}
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