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#include <getopt.h>
#include <limits>
#include <unordered_map>
#include <list>
#include "Eigen/Dense"
#include "Eigen/src/Eigenvalues/ComplexEigenSolver.h"
#include "Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h"
#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 RealVector = Vector<Real>;
using RealMatrix = Matrix<Real>;
using RealTensor = Tensor<Real, p>;
using ComplexVector = Vector<Complex>;
using ComplexMatrix = Matrix<Complex>;
using ComplexTensor = Tensor<Complex, p>;
using Rng = randutils::random_generator<pcg32>;
int main(int argc, char* argv[]) {
// model parameters
unsigned N = 10; // number of spins
Real T = 1; // temperature
Real Rκ = 0; // real part of distribution parameter
Real Iκ = 0; // imaginary part of distribution parameter
// simulation parameters
Real ε = 1e-15;
Real εJ = 1e-5;
Real δ = 1; // threshold for determining saddle
Real Δ = 1e-3;
Real γ = 1e-1; // 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;
pSpinModel<Real, p> pSpin;
std::get<0>(pSpin.Js) = generateCouplings<Real, p>(N, std::normal_distribution<Real>(0, σ), r.engine());
std::normal_distribution<Real> Red(0, 1);
RealVector zMin = randomMinimum(pSpin, Red, r, ε);
Real Hr;
RealVector dHr;
RealMatrix ddHr;
std::tie(Hr, dHr, ddHr, std::ignore) = pSpin.hamGradHess(zMin);
Eigen::EigenSolver<Matrix<Real>> eigenS(ddHr - (dHr * zMin.transpose() + zMin.dot(dHr) * Matrix<Real>::Identity(zMin.size(), zMin.size()) + (ddHr * zMin) * zMin.transpose()) / (Real)zMin.size() + 2.0 * zMin * zMin.transpose());
std::cout << eigenS.eigenvalues().transpose() << std::endl;
for (unsigned i = 0; i < N; i++) {
RealVector zNew = normalize(zMin + 0.01 * eigenS.eigenvectors().col(i).real());
std::cout << pSpin.getHamiltonian(zNew) - Hr << " " << real(eigenS.eigenvectors().col(i).dot(zMin)) << std::endl;
}
std::cout << std::endl;
getchar();
complex_normal_distribution<Real> d(0, 1, 0);
pSpinModel<Complex, p> complexPSpin = pSpin.cast<Complex>();;
ComplexVector zSaddle = zMin.cast<Complex>();
ComplexVector zSaddleNext;
bool foundSaddle = false;
while (!foundSaddle) {
ComplexVector z0 = normalize(zSaddle + δ * randomVector<Complex>(N, d, r.engine()));
try {
zSaddleNext = findSaddle(complexPSpin, z0, ε);
Real saddleDistance = (zSaddleNext - zSaddle).norm();
if (saddleDistance / N > 1e-2) {
std::cout << saddleDistance << std::endl;
foundSaddle = true;
}
} catch (std::exception& e) {}
}
Complex H1 = complexPSpin.getHamiltonian(zSaddle);
Complex H2 = complexPSpin.getHamiltonian(zSaddleNext);
Real φ = atan2( H2.imag() - H1.imag(), H1.real() - H2.real());
std::cerr << (zSaddle - zSaddleNext).norm() / (Real)N << " " << φ << " " << H1 * exp(Complex(0, φ)) << " " << H2 * exp(Complex(0, φ)) << std::endl;
std::get<0>(complexPSpin.Js) = exp(Complex(0, φ)) * std::get<0>(complexPSpin.Js);
Cord test(complexPSpin, zSaddle, zSaddleNext, 3);
test.relaxNewton(10, 1, 1e4);
std::cout << test.z0.transpose() << std::endl;
std::cout << test.z1.transpose() << std::endl;
for (Vector<Complex>& g : test.gs) {
std::cout << g.transpose() << std::endl;
}
return 0;
}
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