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author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2021-01-05 18:11:21 +0100 |
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committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2021-01-05 18:11:21 +0100 |
commit | 5ee6815f0734b2089c5b4c068cc21f2983bdba24 (patch) | |
tree | 179e2ec28f57662ce91491d79799270f2727b144 /langevin.cpp | |
parent | 7c3e71970b6f2d48530bc2ab4fc0f2932522b98b (diff) | |
download | code-5ee6815f0734b2089c5b4c068cc21f2983bdba24.tar.gz code-5ee6815f0734b2089c5b4c068cc21f2983bdba24.tar.bz2 code-5ee6815f0734b2089c5b4c068cc21f2983bdba24.zip |
A lot of work, and fixed a huge bug regarding the meaning of .dot in the Eigen library for complex vectors.
Diffstat (limited to 'langevin.cpp')
-rw-r--r-- | langevin.cpp | 82 |
1 files changed, 66 insertions, 16 deletions
diff --git a/langevin.cpp b/langevin.cpp index 9da4ef6..3bc12ed 100644 --- a/langevin.cpp +++ b/langevin.cpp @@ -9,6 +9,7 @@ #include "complex_normal.hpp" #include "p-spin.hpp" +#include "stereographic.hpp" using Rng = randutils::random_generator<pcg32>; @@ -23,6 +24,57 @@ Vector randomVector(unsigned N, Distribution d, Generator& 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; @@ -32,24 +84,16 @@ Vector langevin(const Tensor& J, const Vector& z0, double T, double γ0, std::tie(W, dW) = WdW(J, z); unsigned steps = 0; - complex_normal_distribution<> d(0, T, 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()); - Vector zNext = z - γ * dW + η; - zNext *= sqrt(zNext.size()) / sqrt(zNext.dot(zNext)); + z -= γ * (dW.conjugate() / pow((double)z.size(), 2) + η); + z *= sqrt(z.size()) / sqrt((Scalar)(z.transpose() * z)); - double WNext; - Vector dWNext; - std::tie(WNext, dWNext) = WdW(J, zNext); - - if (exp((W - WNext) / T) > r.uniform(0.0, 1.0)) { - z = zNext; - W = WNext; - dW = dWNext; - } + std::tie(W, dW) = WdW(J, z); } return z; @@ -63,13 +107,14 @@ int main(int argc, char* argv[]) { 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:")) != -1) { + while ((opt = getopt(argc, argv, "N:T:e:r:i:g:t:E:")) != -1) { switch (opt) { case 'N': N = (unsigned)atof(optarg); @@ -83,6 +128,9 @@ int main(int argc, char* argv[]) { case 'e': δ = atof(optarg); break; + case 'E': + ε = atof(optarg); + break; case 'g': γ = atof(optarg); case 'r': @@ -103,14 +151,15 @@ int main(int argc, char* argv[]) { 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(z.dot(z)); // Normalize. + z *= sqrt(N) / sqrt((Scalar)(z.transpose() * z)); // Normalize. - std::function<bool(double, unsigned)> findSaddle = [δ](double W, unsigned) { + 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, findSaddle, r); + //Vector zm = langevin(J, z, T, γ, f, r); + Vector zm = findSaddle(J, z, γ, δ, ε, r); Scalar H; Vector dH; @@ -119,5 +168,6 @@ int main(int argc, char* argv[]) { Vector constraint = dH - ((double)p * H / (double)N) * zm; + std::cout << constraint << std::endl; std::cout << H / (double)N << std::endl; } |