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#include "stokes.hpp"
#include "complex_normal.hpp"
#include <fstream>
using Complex = std::complex<Real>;
template<int p>
Tensor<Real, p> makeSpikeHelper(const Vector<Real>& x) {
Eigen::array<Eigen::IndexPair<int>, 0> ei = {};
Tensor<Real, 1> xT = Eigen::TensorMap<Tensor<const Real, 1>>(x.data(), {x.size()});
return xT.contract(makeSpikeHelper<p - 1>(x), ei);
}
template <>
Tensor<Real, 1> makeSpikeHelper(const Vector<Real>& x) {
Tensor<Real, 1> xT = Eigen::TensorMap<Tensor<const Real, 1>>(x.data(), {x.size()});
return xT;
}
template<int p, int ...ps>
Tensor<Real, p> makeSpike(const Vector<Real>& x) {
return makeSpikeHelper<p>(x);
}
template <int p, int ...ps>
int getFirstP() {
return p;
}
template<int ...ps, class Generator, typename... T>
void collectStokesData(std::string tag, unsigned N, Generator& r, Real ε, Real δz₀, bool minimum, bool spike, T... μs) {
unsigned nIts = 5;
unsigned nGs = 4;
unsigned coDim = 16;
Real newSaddleThres = 1e-4;
pSpinModel<Real, ps...> ReM(N, r, μs...);
std::normal_distribution<Real> Red(0, 1);
Vector<Real> xMin(N);
if (minimum) {
xMin = randomMinimum<Real>(ReM, Red, r, ε);
} else {
xMin = randomSaddle<Real, Real>(ReM, Red, r, ε);
}
Real Hx;
std::tie(Hx, std::ignore, std::ignore, std::ignore) = ReM.hamGradHess(xMin);
if (spike) {
const unsigned p = getFirstP<ps...>();
Real εgs = sqrt((p - 1) * log(p - 1) / (p - 2));
Real εth = sqrt((p - 1) * 2.0 / p);
Real εTarget = std::uniform_real_distribution<Real>(εth, εgs)(r);
std::get<0>(ReM.Js) -= factorial(p) * (εTarget * N + Hx) * makeSpike<ps...>(xMin) / pow(N, p);
}
Vector<Real> dHx;
Matrix<Real> ddHx;
std::tie(Hx, dHx, ddHx, std::ignore) = ReM.hamGradHess(xMin);
Matrix<Real> xHess = ddHx - xMin.dot(dHx) * Matrix<Real>::Identity(xMin.size(), xMin.size()) / (Real)N;
xHess -= (xHess * xMin) * xMin.transpose() / (Real)N;
Eigen::EigenSolver<Matrix<Real>> eigenS(xHess);
complex_normal_distribution<Real> d(0, 1, 0);
pSpinModel M = ReM.template cast<Complex>();;
Vector<Complex> zMin = xMin.cast<Complex>();
Vector<Complex> zSaddle = zMin;
Real δz = δz₀;
while ((zSaddle - zMin).norm() < newSaddleThres * N || abs(imag(M.getHamiltonian(zSaddle))) < 1e-10) {
Vector<Complex> z0 = normalize(zSaddle + δz * randomVector<Complex>(N, d, r));
zSaddle = findSaddle(M, z0, ε);
δz *= 1.01;
}
Complex Hz;
Vector<Complex> dHz;
Matrix<Complex> ddHz;
std::tie(Hz, dHz, ddHz, std::ignore) = M.hamGradHess(zSaddle);
Matrix<Complex> zHess = ddHz - (zSaddle.transpose() * dHz) * Matrix<Complex>::Identity(N, N) / (Real)N;
zHess -= (zHess * zSaddle) * zSaddle.adjoint() / zSaddle.squaredNorm();
Eigen::ComplexEigenSolver<Matrix<Complex>> eigenSz(zHess);
Real φ = atan2(Hz.imag(), Hx - Hz.real());
M *= exp(Complex(0, φ));
std::ofstream file("stokes_info_" + tag + ".dat");
file.precision(15);
file << N << std::endl;
((file << ps << " "), ...) << std::endl;;
((file << μs << " "), ...) << std::endl;;
std::ofstream tensorFile("stokes_tensor_" + tag + ".dat", std::ios::out | std::ios::binary | std::ios::trunc);
std::apply([&tensorFile](const Tensor<Real, ps>&... Js) -> void {
(tensorFile.write((char*)Js.data(), Js.size() * sizeof(Real)), ...);
} , ReM.Js);
file << xMin.transpose() << std::endl;
file << Hx << std::endl;
file << eigenS.eigenvalues().real().transpose() << std::endl;
file << zSaddle.transpose() << std::endl;
file << Hz << " " << zSaddle.squaredNorm() << std::endl;
file << eigenSz.eigenvalues().transpose() << std::endl;
file << φ << " " << (xMin - zSaddle).norm() << std::endl;
unsigned nTest = 1000;
file << nIts << " " << nGs << " " << coDim << " " << nTest << std::endl;
std::vector<Vector<Complex>> oldGs;
for (int j = 0; j < nIts; j++) {
Cord c(M, zMin, zSaddle, nGs + pow(2, j));
for (unsigned i = 0; i < oldGs.size(); i++) {
c.gs[i] = oldGs[i];
}
c.relaxNewton(c.gs.size() * 2, 1, 1e-10, 1e4);
oldGs = c.gs;
Real reConstraintError = 0;
Real imConstraintError = 0;
Real imEnergyError = 0;
Real ell = 0;
for (unsigned i = 0; i < nTest; i++) {
Real t = (i + 1.0) / (nTest + 1.0);
Vector<Complex> zi = c.f(t);
imEnergyError += pow(std::imag(M.getHamiltonian(zi) - M.getHamiltonian(zMin)), 2);
Complex constraintError = (Complex)(zi.transpose() * zi) - (Complex)N;
reConstraintError += pow(real(constraintError), 2);
imConstraintError += pow(imag(constraintError), 2);
ell += c.df(t).norm();
}
file << oldGs.size() << " " << ell / nTest << " " << c.totalCost(nTest) / (nTest) << " " << sqrt(imEnergyError / (Real)(nTest)) << " " << sqrt(reConstraintError / (Real)(nTest)) << " " << sqrt(imConstraintError / (Real)(nTest)) << std::endl;
for (const Vector<Complex>& gi : c.gs) {
file << gi.transpose() << std::endl;
}
}
}
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