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-rw-r--r--log-fourier_integrator.cpp196
1 files changed, 111 insertions, 85 deletions
diff --git a/log-fourier_integrator.cpp b/log-fourier_integrator.cpp
index 51f5326..a032401 100644
--- a/log-fourier_integrator.cpp
+++ b/log-fourier_integrator.cpp
@@ -2,6 +2,31 @@
#include "p-spin.hpp"
#include <getopt.h>
#include <iostream>
+#include <fstream>
+
+std::string logFourierFile(std::string prefix, unsigned p, unsigned s, Real λ, Real τ₀, Real β, unsigned log2n, Real Δτ, Real k) {
+ return prefix + "_" + std::to_string(p) + "_" + std::to_string(s) + "_" + std::to_string(λ) + "_" + std::to_string(τ₀) + "_" + std::to_string(β) + "_" + std::to_string(log2n) + "_" + std::to_string(Δτ) + "_" + std::to_string(k) + ".dat";
+}
+
+std::tuple<std::vector<Complex>, std::vector<Complex>> RddfCtdfCt(LogarithmicFourierTransform& fft, const std::vector<Real>& C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ) {
+ std::vector<Real> dfC(C.size());
+ std::vector<Real> RddfC(C.size());
+ for (unsigned n = 0; n < C.size(); n++) {
+ RddfC[n] = R[n] * ddf(λ, p, s, C[n]);
+ dfC[n] = df(λ, p, s, C[n]);
+ }
+ std::vector<Complex> RddfCt = fft.fourier(RddfC, false);
+ std::vector<Complex> dfCt = fft.fourier(dfC, true);
+
+ return {RddfCt, dfCt};
+}
+
+Real estimateZ(LogarithmicFourierTransform& fft, const std::vector<Real>& C, const std::vector<Complex>& Ct, const std::vector<Real>& R, const std::vector<Complex>& Rt, unsigned p, unsigned s, Real λ, Real τ₀, Real β) {
+ auto [RddfCt, dfCt] = RddfCtdfCt(fft, C, R, p, s, λ);
+ Real Γ₀ = 1 + τ₀ / 2;
+
+ return ((2 * Γ₀ * std::conj(Rt[0]) + pow(β, 2) * (RddfCt[0] * Ct[0] + dfCt[0] * std::conj(Rt[0]))) / Ct[0]).real();
+}
int main(int argc, char* argv[]) {
/* Model parameters */
@@ -16,14 +41,16 @@ int main(int argc, char* argv[]) {
Real k = 0.1;
/* Iteration parameters */
- Real ε = 1e-13;
+ Real ε = 1e-14;
Real γ = 1;
+ Real β₀ = 0;
Real βₘₐₓ = 0.7;
Real Δβ = 0.01;
+ bool loadData = false;
int opt;
- while ((opt = getopt(argc, argv, "p:s:2:T:t:b:d:g:k:D:")) != -1) {
+ while ((opt = getopt(argc, argv, "p:s:2:T:t:b:d:g:k:D:e:0:l")) != -1) {
switch (opt) {
case 'p':
p = atoi(optarg);
@@ -52,6 +79,15 @@ int main(int argc, char* argv[]) {
case 'D':
Δτ = atof(optarg);
break;
+ case 'e':
+ ε = atof(optarg);
+ break;
+ case '0':
+ β₀ = atof(optarg);
+ break;
+ case 'l':
+ loadData = true;
+ break;
default:
exit(1);
}
@@ -62,71 +98,62 @@ int main(int argc, char* argv[]) {
LogarithmicFourierTransform fft(N, k, Δτ, 4);
Real Γ₀ = 1.0 + τ₀;
- Real μ = 1.0;
-/* Real μ = Γ₀;
- if (τ₀ > 0) {
- μ = (sqrt(1+4*Γ₀*τ₀)-1)/(2*τ₀);
- }
-*/
+ Real μₜ₋₁ = 1.0;
std::vector<Real> Cₜ₋₁(N);
std::vector<Real> Rₜ₋₁(N);
std::vector<Complex> Ĉₜ₋₁(N);
std::vector<Complex> Ȓₜ₋₁(N);
- /* Start from the exact solution for β = 0 */
- for (unsigned n = 0; n < N; n++) {
- if (τ₀ > 0) {
- Cₜ₋₁[n] = Γ₀ * (exp(-μ * fft.t(n)) - μ * τ₀ * exp(-fft.t(n) / τ₀)) / (μ - pow(μ, 3) * pow(τ₀, 2));
- } else {
- Cₜ₋₁[n] = Γ₀ * exp(-μ * fft.t(n)) / μ;
- }
- Rₜ₋₁[n] = exp(-μ * fft.t(n));
+ if (!loadData) {
+ /* Start from the exact solution for β = 0 */
+ for (unsigned n = 0; n < N; n++) {
+ if (τ₀ != 1) {
+ Cₜ₋₁[n] = Γ₀ * (exp(-μₜ₋₁ * fft.t(n)) - μₜ₋₁ * τ₀ * exp(-fft.t(n) / τ₀)) / (μₜ₋₁ - pow(μₜ₋₁, 3) * pow(τ₀, 2));
+ } else {
+ Cₜ₋₁[n] = Γ₀ * exp(-fft.t(n)) * (1 + fft.t(n));
+ }
+ Rₜ₋₁[n] = exp(-μₜ₋₁ * fft.t(n));
- Ĉₜ₋₁[n] = 2 * Γ₀ / (pow(μ, 2) + pow(fft.ν(n), 2)) / (1 + pow(τ₀ * fft.ν(n), 2));
- Ȓₜ₋₁[n] = 1.0 / (μ + 1i * fft.ν(n));
+ Ĉₜ₋₁[n] = 2 * Γ₀ / (pow(μₜ₋₁, 2) + pow(fft.ν(n), 2)) / (1 + pow(τ₀ * fft.ν(n), 2));
+ Ȓₜ₋₁[n] = 1.0 / (μₜ₋₁ + 1i * fft.ν(n));
+ }
+ } else {
+ std::ifstream cfile(logFourierFile("C", p, s, λ, τ₀, β₀, log2n, Δτ, k), std::ios::binary);
+ cfile.read((char*)(Cₜ₋₁.data()), N * sizeof(Real));
+ cfile.close();
+ std::ifstream rfile(logFourierFile("R", p, s, λ, τ₀, β₀, log2n, Δτ, k), std::ios::binary);
+ rfile.read((char*)(Rₜ₋₁.data()), N * sizeof(Real));
+ rfile.close();
+
+ Ĉₜ₋₁ = fft.fourier(Cₜ₋₁, true);
+ Ȓₜ₋₁ = fft.fourier(Rₜ₋₁, false);
+
+ μₜ₋₁ = estimateZ(fft, Cₜ₋₁, Ĉₜ₋₁, Rₜ₋₁, Ȓₜ₋₁, p, s, λ, τ₀, β₀);
}
std::vector<Real> Cₜ = Cₜ₋₁;
std::vector<Real> Rₜ = Rₜ₋₁;
std::vector<Complex> Ĉₜ = Ĉₜ₋₁;
std::vector<Complex> Ȓₜ = Ȓₜ₋₁;
+ Real μₜ = μₜ₋₁;
- Real fac = 1;
- Real β = 0;
+ Real β = β₀ + Δβ;
while (β < βₘₐₓ) {
Real ΔC = 100;
- Real ΔC₀ = 100;
- unsigned it = 0;
while (ΔC > ε) {
- std::vector<Real> dfC(N);
- std::vector<Real> RddfC(N);
- for (unsigned n = 0; n < N; n++) {
- RddfC[n] = Rₜ[n] * ddf(λ, p, s, Cₜ[n]);
- dfC[n] = df(λ, p, s, Cₜ[n]);
- }
- std::vector<Complex> RddfCt = fft.fourier(RddfC, false);
- std::vector<Complex> dfCt = fft.fourier(dfC, true);
+ auto [RddfCt, dfCt] = RddfCtdfCt(fft, Cₜ, Rₜ, p, s, λ);
- std::vector<Complex> Ȓₜ₊₁(N);
std::vector<Complex> Ĉₜ₊₁(N);
-
+ std::vector<Complex> Ȓₜ₊₁(N);
for (unsigned n = 0; n < N; n++) {
- Ȓₜ₊₁[n] = (1.0 + pow(β, 2) * RddfCt[n] * Ȓₜ[n]) / (μ + 1i * fft.ν(n));
+ Ȓₜ₊₁[n] = (1.0 + pow(β, 2) * RddfCt[n] * Ȓₜ[n]) / (μₜ + 1i * fft.ν(n));
+ Ĉₜ₊₁[n] = (2 * Γ₀ * std::conj(Ȓₜ[n]) / (1 + pow(τ₀ * fft.ν(n), 2)) + pow(β, 2) * (RddfCt[n] * Ĉₜ[n] + dfCt[n] * std::conj(Ȓₜ[n]))) / (μₜ + 1i * fft.ν(n));
}
-
std::vector<Real> Rₜ₊₁ = fft.inverse(Ȓₜ₊₁);
-
- for (unsigned n = 0; n < N; n++) {
- RddfC[n] = Rₜ₊₁[n] * ddf(λ, p, s, Cₜ[n]);
- }
- RddfCt = fft.fourier(RddfC, false);
- for (unsigned n = 0; n < N; n++) {
- Ĉₜ₊₁[n] = (2 * Γ₀ * std::conj(Ȓₜ₊₁[n]) / (1 + pow(τ₀ * fft.ν(n), 2)) + pow(β, 2) * (RddfCt[n] * Ĉₜ[n] + dfCt[n] * std::conj(Ȓₜ₊₁[n]))) / (μ + 1i * fft.ν(n));
- }
std::vector<Real> Cₜ₊₁ = fft.inverse(Ĉₜ₊₁);
- μ *= pow(tanh(Cₜ₊₁[0]-1)+1, 0.05);
+ μₜ *= pow(tanh(Cₜ₊₁[0]-1)+1, 0.05);
ΔC = 0;
for (unsigned i = 0; i < N; i++) {
@@ -142,53 +169,52 @@ int main(int argc, char* argv[]) {
Ȓₜ[i] += γ * (Ȓₜ₊₁[i] - Ȓₜ[i]);
}
- /*
- if (ΔC < ΔC₀) {
- ΔC₀ = ΔC;
- it = 0;
- γ = std::min(1.001 * γ, 1.0);
- } else {
- it++;
- }
-
- if (it > 100) {
- γ = std::max(0.5 * γ, 1e-3);
- it = 0;
- ΔC₀ = ΔC;
- }
- */
-
std::cerr << "\x1b[2K" << "\r";
- std::cerr << β << " " << μ << " " << ΔC << " " << γ << " " << Cₜ[0];
+ std::cerr << β << " " << μₜ << " " << ΔC << " " << γ << " " << Cₜ[0];
}
- /* Integrate the energy using Simpson's rule */
- Real E = 0;
- for (unsigned n = 0; n < N/2-1; n++) {
- Real h₂ₙ = fft.t(2*n+1) - fft.t(2*n);
- Real h₂ₙ₊₁ = fft.t(2*n+2) - fft.t(2*n+1);
- Real f₂ₙ = Rₜ[2*n] * df(λ, p, s, Cₜ[2*n]);
- Real f₂ₙ₊₁ = Rₜ[2*n+1] * df(λ, p, s, Cₜ[2*n+1]);
- Real f₂ₙ₊₂ = Rₜ[2*n+2] * df(λ, p, s, Cₜ[2*n+2]);
- E += (h₂ₙ + h₂ₙ₊₁) / 6 * (
- (2 - h₂ₙ₊₁ / h₂ₙ) * f₂ₙ
- + pow(h₂ₙ + h₂ₙ₊₁, 2) / (h₂ₙ * h₂ₙ₊₁) * f₂ₙ₊₁
- + (2 - h₂ₙ / h₂ₙ₊₁) * f₂ₙ₊₂
- );
- }
- E *= β;
+ if (std::isnan(Cₜ[0])) {
+ Cₜ = Cₜ₋₁;
+ Rₜ = Rₜ₋₁;
+ Ĉₜ = Ĉₜ₋₁;
+ Ȓₜ = Ȓₜ₋₁;
+ μₜ = μₜ₋₁;
+ γ /= 2;
+ } else {
+ /* Integrate the energy using Simpson's rule */
+ Real E = 0;
+ for (unsigned n = 0; n < N/2-1; n++) {
+ Real h₂ₙ = fft.t(2*n+1) - fft.t(2*n);
+ Real h₂ₙ₊₁ = fft.t(2*n+2) - fft.t(2*n+1);
+ Real f₂ₙ = Rₜ[2*n] * df(λ, p, s, Cₜ[2*n]);
+ Real f₂ₙ₊₁ = Rₜ[2*n+1] * df(λ, p, s, Cₜ[2*n+1]);
+ Real f₂ₙ₊₂ = Rₜ[2*n+2] * df(λ, p, s, Cₜ[2*n+2]);
+ E += (h₂ₙ + h₂ₙ₊₁) / 6 * (
+ (2 - h₂ₙ₊₁ / h₂ₙ) * f₂ₙ
+ + pow(h₂ₙ + h₂ₙ₊₁, 2) / (h₂ₙ * h₂ₙ₊₁) * f₂ₙ₊₁
+ + (2 - h₂ₙ / h₂ₙ₊₁) * f₂ₙ₊₂
+ );
+ }
+ E *= β;
std::cerr << "\x1b[2K" << "\r";
- std::cerr << β << " " << μ << " " << Ĉₜ[0].real() << " " << E << " " << γ << std::endl;
- β += Δβ;
- Cₜ₋₁ = Cₜ;
- Rₜ₋₁ = Rₜ;
- Ĉₜ₋₁ = Ĉₜ;
- Ȓₜ₋₁ = Ȓₜ;
- }
-
- for (unsigned i = 0; i < N; i++) {
- std::cout << fft.t(i) << " " << Cₜ[i] << std::endl;
+ std::cerr << β << " " << μₜ << " " << Ĉₜ[0].real() << " " << E << " " << γ << std::endl;
+
+ std::ofstream outfile(logFourierFile("C", p, s, λ, τ₀, β, log2n, Δτ, k), std::ios::out | std::ios::binary);
+ outfile.write((const char*)(Cₜ.data()), N * sizeof(Real));
+ outfile.close();
+
+ std::ofstream outfileR(logFourierFile("R", p, s, λ, τ₀, β, log2n, Δτ, k), std::ios::out | std::ios::binary);
+ outfileR.write((const char*)(Rₜ.data()), N * sizeof(Real));
+ outfileR.close();
+
+ β += Δβ;
+ Cₜ₋₁ = Cₜ;
+ Rₜ₋₁ = Rₜ;
+ Ĉₜ₋₁ = Ĉₜ;
+ Ȓₜ₋₁ = Ȓₜ;
+ μₜ₋₁ = μₜ;
+ }
}
return 0;