Made log-Fourier padding symmetric, and began writing regular integrator

2 files changed, 227 insertions, 0 deletions

diff --git a/log-fourier.cpp b/log-fourier.cpp
index 9ae70be..9d1f2cb 100644
--- a/log-fourier.cpp
+++ b/log-fourier.cpp
@@ -64,6 +64,8 @@ std::vector<Complex> LogarithmicFourierTransform::fourier(const std::vector<Real
     for (unsigned n = 0; n < pad*N; n++) {
       if (n < N) {
         a[n] = c[n] * exp((1 - k) * τ(n));
+      } else if (n >= (pad - 1) * N) {
+        a[n] = c[pad*N-n-1] * exp((1 - k) * τ(pad*N-n-1));
       } else {
         a[n] = 0;
       }
@@ -92,6 +94,12 @@ std::vector<Real> LogarithmicFourierTransform::inverse(const std::vector<Complex
         } else {
           a[n] = ĉ[n] * std::exp((1 - k) * ω(n));
         }
+      } else if (n >= (pad - 1) * N) {
+        if (σ < 0) {
+          a[n] = ĉ[pad*N-n-1] * std::exp((1 - k) * ω(pad*N-n-1));
+        } else {
+          a[n] = std::conj(ĉ[pad*N-n-1]) * std::exp((1 - k) * ω(pad*N-n-1));
+        }
       } else {
         a[n] = 0;
       }
diff --git a/log_integrator.cpp b/log_integrator.cpp
new file mode 100644
index 0000000..a8d9778
--- /dev/null
+++ b/log_integrator.cpp
@@ -0,0 +1,219 @@
+#include "log-fourier.hpp"
+#include "p-spin.hpp"
+#include <getopt.h>
+#include <iostream>
+
+int main(int argc, char* argv[]) {
+  /* Model parameters */
+  unsigned p = 2;
+  unsigned s = 2;
+  Real λ = 0.5;
+  Real τ₀ = 0;
+
+  /* Log-Fourier parameters */
+  unsigned log2n = 8;
+  Real Δτ = 0.1;
+  Real k = 0.1;
+
+  /* Iteration parameters */
+  Real ε = 1e-14;
+  Real γ₀ = 1;
+  Real x = 0.5;
+  Real β₀ = 0;
+  Real βₘₐₓ = 0.7;
+  Real Δβ = 0.01;
+  bool loadData = false;
+  unsigned stepsToRespond = 1000;
+  unsigned pad = 4;
+
+  int opt;
+
+  while ((opt = getopt(argc, argv, "p:s:2:T:t:b:d:g:k:D:e:0:lS:x:P:")) != -1) {
+    switch (opt) {
+    case 'p':
+      p = atoi(optarg);
+      break;
+    case 's':
+      s = atoi(optarg);
+      break;
+    case '2':
+      log2n = atoi(optarg);
+      break;
+    case 't':
+      τ₀ = atof(optarg);
+      break;
+    case 'b':
+      βₘₐₓ = atof(optarg);
+      break;
+    case 'd':
+      Δβ = atof(optarg);
+      break;
+    case 'g':
+      γ₀ = atof(optarg);
+      break;
+    case 'k':
+      k = atof(optarg);
+      break;
+    case 'D':
+      Δτ = atof(optarg);
+      break;
+    case 'e':
+      ε = atof(optarg);
+      break;
+    case '0':
+      β₀ = atof(optarg);
+      break;
+    case 'x':
+      x = atof(optarg);
+      break;
+    case 'P':
+      pad = atoi(optarg);
+      break;
+    case 'l':
+      loadData = true;
+      break;
+    case 'S':
+      stepsToRespond = atoi(optarg);
+      break;
+    default:
+      exit(1);
+    }
+  }
+
+  unsigned N = pow(2, log2n);
+
+  LogarithmicFourierTransform fft(N, k, Δτ, pad);
+
+  Real Γ₀ = 1;
+  Real μₜ₋₁ = Γ₀;
+  if (τ₀ > 0) {
+    μₜ₋₁ = (sqrt(1+4*Γ₀*τ₀)-1)/(2*τ₀);
+  }
+
+  std::vector<Real> Cₜ₋₁(N);
+  std::vector<Real> Rₜ₋₁(N);
+  std::vector<Complex> Ĉₜ₋₁(N);
+  std::vector<Complex> Ȓₜ₋₁(N);
+
+  if (!loadData) {
+    /* Start from the exact solution for β = 0 */
+    for (unsigned n = 0; n < N; n++) {
+      if (τ₀ > 0) {
+        if (τ₀ == 2) {
+          Cₜ₋₁[n] = Γ₀ * exp(-fft.t(n) / 2) * (1 + fft.t(n) / 2);
+        } else {
+          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(-μₜ₋₁ * fft.t(n)) / μₜ₋₁;
+      }
+      Rₜ₋₁[n] = exp(-μₜ₋₁ * fft.t(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] = (Real)1.0 / (μₜ₋₁ + II * fft.ν(n));
+    }
+  } else {
+    logFourierLoad(Cₜ₋₁, Rₜ₋₁, Ĉₜ₋₁, Ȓₜ₋₁, p, s, λ, τ₀, β₀, log2n, Δτ, k);
+    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 β = β₀ + Δβ;
+  while (β < βₘₐₓ) {
+    Real γ = γ₀;
+    Real ΔCmin = 1000;
+    Real ΔCₜ = 100;
+    unsigned stepsUp = 0;
+    while (ΔCₜ > ε) {
+      std::vector<Real> RddfC(N);
+      std::vector<Real> dfC(N);
+      for (unsigned i = 0; i < N; i++) {
+        RddfC[i] = Rₜ[i] * ddf(λ, p, s, Cₜ[i]);
+        dfC[i] = df(λ, p, s, Cₜ[i]);
+      }
+
+      std::vector<Real> dC(N);
+      std::vector<Real> dR(N);
+
+      for (unsigned i = 0; i < N; i++) {
+        dC[i] += -μₜ * Cₜ[i];
+        Real ΓR;
+        for (unsigned j = 0; j < N; j++) {
+          
+        }
+      }
+
+
+      std::vector<Complex> Ĉₜ₊₁(N);
+      std::vector<Complex> Ȓₜ₊₁(N);
+      for (unsigned n = 0; n < N; n++) {
+        Ȓₜ₊₁[n] = ((Real)1.0 + std::pow(β, 2) * RddfCt[n] * Ȓₜ[n]) / (μₜ + II * fft.ν(n));
+        Ĉₜ₊₁[n] = (2 * Γ₀ * std::conj(Ȓₜ[n]) / (1 + std::pow(τ₀ * fft.ν(n), 2)) + std::pow(β, 2) * (RddfCt[n] * Ĉₜ[n] + dfCt[n] * std::conj(Ȓₜ[n]))) / (μₜ + II * fft.ν(n));
+      }
+      std::vector<Real> Rₜ₊₁ = fft.inverse(Ȓₜ₊₁);
+      std::vector<Real> Cₜ₊₁ = fft.inverse(Ĉₜ₊₁);
+
+      μₜ *= pow(tanh(Cₜ₊₁[0]-1)+1, x);
+
+      ΔCₜ = 0;
+      for (unsigned i = 0; i < N; i++) {
+        ΔCₜ += std::norm(Cₜ[i] - Cₜ₊₁[i]);
+        ΔCₜ += std::norm(Rₜ[i] - Rₜ₊₁[i]);
+      }
+      ΔCₜ = sqrt(ΔCₜ) / (2*N);
+
+      if (ΔCₜ < 0.9 * ΔCmin) {
+        ΔCmin = ΔCₜ;
+        stepsUp = 0;
+      } else {
+        stepsUp++;
+      }
+
+      if (stepsUp > stepsToRespond) {
+        γ = std::max(γ/2, (Real)1e-4);
+        stepsUp = 0;
+        ΔCmin = ΔCₜ;
+      }
+
+      for (unsigned i = 0; i < N; i++) {
+        Cₜ[i] += γ * (Cₜ₊₁[i] - Cₜ[i]);
+        Rₜ[i] += γ * (Rₜ₊₁[i] - Rₜ[i]);
+        Ĉₜ[i] += γ * (Ĉₜ₊₁[i] - Ĉₜ[i]);
+        Ȓₜ[i] += γ * (Ȓₜ₊₁[i] - Ȓₜ[i]);
+      }
+
+      std::cerr << "\x1b[2K" << "\r";
+      std::cerr << β << " " << μₜ << " " << ΔCₜ << " " << γ << " " << Cₜ[0];
+    }
+
+    if (std::isnan(Cₜ[0])) {
+      γ₀ /= 2;
+      Cₜ = Cₜ₋₁;
+      Rₜ = Rₜ₋₁;
+      Ĉₜ = Ĉₜ₋₁;
+      Ȓₜ = Ȓₜ₋₁;
+      μₜ = μₜ₋₁;
+    } else {
+      Real E = energy(fft, Cₜ, Rₜ, p, s, λ, β);
+
+      std::cerr << "\x1b[2K" << "\r";
+      std::cerr << β << " " << μₜ << " " << Ĉₜ[0].real() << " " << E << " " << γ << std::endl;
+
+      logFourierSave(Cₜ, Rₜ, Ĉₜ, Ȓₜ, p, s, λ, τ₀, β, log2n, Δτ, k);
+
+      β += Δβ;
+      Cₜ₋₁ = Cₜ;
+      Rₜ₋₁ = Rₜ;
+      Ĉₜ₋₁ = Ĉₜ;
+      Ȓₜ₋₁ = Ȓₜ;
+      μₜ₋₁ = μₜ;
+    }
+  }
+
+  return 0;
+}