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#include <eigen3/Eigen/Dense>
#include <getopt.h>
#include "pcg-cpp/include/pcg_random.hpp"
#include "randutils/randutils.hpp"
#include "tensor.hpp"
Vector normalize(const Vector& z) {
return z * sqrt((Real)z.size() / (Real)(z.transpose() * z));
}
template <int... ps>
class Model {
private:
std::tuple<Tensor<ps>...> Js;
public:
unsigned N;
unsigned M;
template <class Generator, typename... T>
Model(unsigned N, unsigned M, Generator& r, T... μs) : N(N), M(M) {
Js = std::make_tuple(μs * generateRealPSpinCouplings<ps>(N, M, r)...);
}
unsigned numPs() const {
return std::tuple_size(Js);
}
private:
std::tuple<Vector, Matrix, Tensor<3>> hamGradTensorHelper(const Vector& z, const Tensor<1>& J) const {
Tensor<3> J3(N, N, M);;
J3.setZero();
Matrix Jz = Matrix::Zero(N, M);
Vector Jzz = Eigen::Map<const Vector>(J.data(), M);
return {Jzz, Jz, J3};
}
std::tuple<Vector, Matrix, Tensor<3>> hamGradTensorHelper(const Vector& z, const Tensor<2>& J) const {
Tensor<3> J3(N, N, M);;
J3.setZero();
Matrix Jz = Eigen::Map<const Matrix>(J.data(), N, M);
Vector Jzz = z.transpose() * Jz;
return {Jzz, Jz, J3};
}
template <int p>
std::tuple<Vector, Matrix, Tensor<3>> hamGradTensorHelper(const Vector z, const Tensor<p>& J) const {
Tensor<3> J3 = contractDown(J, z);
Tensor<1> zT = Eigen::TensorMap<constTensor<1>>(z.data(), N);
Tensor<2> J3zT = J3.contract(zT, ip00);
Matrix Jz = Eigen::Map<const Matrix>(J3zT.data(), N, M);
Vector Jzz = z.transpose() * Jz;
return {Jzz, Jz, J3};
}
template <int p, int... qs>
std::tuple<Vector, Matrix, Tensor<3>> hamGradHessHelper(const Vector& z, const Tensor<p>& J, const Tensor<qs>& ...Js) const {
auto [Jzz, Jz, J3] = hamGradTensorHelper(z, J);
Real pBang = factorial(p-1);
Tensor<3> ddH = ((p - 1) * p / pBang) * J3;
Matrix dH = (p / pBang) * Jz;
Vector H = Jzz / pBang;
if constexpr (sizeof...(Js) > 0) {
auto [Hs, dHs, ddHs] = hamGradHessHelper(z, Js...);
H += Hs;
dH += dHs;
ddH += ddHs;
}
return {H, dH, ddH};
}
public:
std::tuple<Vector, Matrix, Tensor<3>> VdVddV(const Vector& z) const {
return std::apply([&z, this](const Tensor<ps>& ...Ks) -> std::tuple<Vector, Matrix, Tensor<3>> { return hamGradHessHelper(z, Ks...); }, Js);
}
std::tuple<Real, Vector, Matrix> HdHddH(const Vector& z) const {
auto [V, dV, ddV] = VdVddV(z);
Real H = 0.5 * V.squaredNorm();
Vector dH = dV * V;
Tensor<1> VT = Eigen::TensorMap<constTensor<1>>(V.data(), M);
Tensor<2> ddVzT = ddV.contract(VT, ip20);
Matrix ddH = Eigen::Map<const Matrix>(ddVzT.data(), N, N) + dV * dV.transpose();
return {H, dH, ddH};
}
std::tuple<Real, Vector, Matrix> hamGradHess(const Vector& x) const {
auto [H, dH, ddH] = HdHddH(x);
Vector gradH = dH - dH.dot(x) * x / N;
Matrix hessH = ddH - (dH * x.transpose() + x.dot(dH) * Matrix::Identity(N, N) + (ddH * x) * x.transpose()) / (Real)N + 2.0 * x * x.transpose();
return {H, gradH, hessH};
}
Vector HessSpectrum(const Vector& x) const {
Matrix hessH;
std::tie(std::ignore, std::ignore, hessH) = hamGradHess(x);
Eigen::EigenSolver<Matrix> eigenS(hessH);
return eigenS.eigenvalues().real();
}
};
template <int ...ps>
Vector findMinimum(const Model<ps...>& M, const Vector& x0, Real ε) {
Vector x = x0;
Real λ = 100;
auto [H, g, m] = M.hamGradHess(x0);
while (g.norm() / x.size() > ε && λ < 1e8) {
Vector dz = (m + λ * (Matrix)abs(m.diagonal().array()).matrix().asDiagonal()).partialPivLu().solve(g);
dz -= x.dot(dz) * x / M.N;
Vector zNew = normalize(x - dz);
auto [HNew, gNew, mNew] = M.hamGradHess(zNew);
if (HNew * 1.0001 <= H) {
x = zNew;
H = HNew;
g = gNew;
m = mNew;
λ /= 2;
} else {
λ *= 1.5;
}
}
return x;
}
using Rng = randutils::random_generator<pcg32>;
using Real = double;
int main(int argc, char* argv[]) {
unsigned N = 10;
Real α = 1;
Real σ = 1;
int opt;
while ((opt = getopt(argc, argv, "N:a:s:")) != -1) {
switch (opt) {
case 'N':
N = (unsigned)atof(optarg);
break;
case 'a':
α = atof(optarg);
break;
case 's':
σ = atof(optarg);
break;
default:
exit(1);
}
}
unsigned M = (unsigned)(α * N);
Rng r;
Model<1, 2> leastSquares(N, M, r.engine(), sqrt(2) * pow(σ, 2), sqrt(2));
Vector x = Vector::Zero(N);
x(0) = sqrt(N);
double energy;
std::tie(energy, std::ignore, std::ignore) = leastSquares.hamGradHess(x);
std::cout << energy / N << std::endl;
Vector xMin = findMinimum(leastSquares, x, 1e-12);
std::tie(energy, std::ignore, std::ignore) = leastSquares.hamGradHess(xMin);
std::cout << energy / N << std::endl;
std::cout << leastSquares.HessSpectrum(xMin)(1) / N << std::endl;
return 0;
}
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