1 files changed, 172 insertions, 0 deletions
diff --git a/fourier_integrator.cpp b/fourier_integrator.cpp
new file mode 100644
index 0000000..86c3b24
--- /dev/null
+++ b/fourier_integrator.cpp
@@ -0,0 +1,172 @@
+#include "fourier.hpp"
+#include <getopt.h>
+#include <iostream>
+#include <fstream>
+
+int main(int argc, char* argv[]) {
+  unsigned p = 2;
+  unsigned s = 2;
+  Real λ = 0.5;
+  Real τ₀ = 0;
+  Real y₀ = 0;
+  Real yₘₐₓ = 0.5;
+  Real Δy = 0.05;
+
+  unsigned log2n = 8;
+  Real τₘₐₓ = 20;
+
+  unsigned maxIterations = 1000;
+  Real ε = 1e-14;
+  Real γ = 0;
+
+  bool loadData = false;
+
+  int opt;
+
+  while ((opt = getopt(argc, argv, "p:s:2:T:t:0:y:d:I:g:l")) != -1) {
+    switch (opt) {
+    case 'p':
+      p = atoi(optarg);
+      break;
+    case 's':
+      s = atoi(optarg);
+      break;
+    case '2':
+      log2n = atoi(optarg);
+      break;
+    case 'T':
+      τₘₐₓ = atof(optarg);
+      break;
+    case 't':
+      τ₀ = atof(optarg);
+      break;
+    case '0':
+      y₀ = atof(optarg);
+      break;
+    case 'y':
+      yₘₐₓ = atof(optarg);
+      break;
+    case 'd':
+      Δy = atof(optarg);
+      break;
+    case 'I':
+      maxIterations = (unsigned)atof(optarg);
+      break;
+    case 'g':
+      γ = atof(optarg);
+      break;
+    case 'l':
+      loadData = true;
+      break;
+    default:
+      exit(1);
+    }
+  }
+
+  unsigned n = pow(2, log2n);
+
+  Real Δτ = τₘₐₓ / M_PI / n;
+  Real Δω = M_PI / τₘₐₓ;
+
+  Real z = (-1+sqrt(1+2*τ₀)) / (2 * τ₀);
+  Real Γ₀ = 1;
+
+  std::vector<Real> C(2 * n);
+  std::vector<Real> R(2 * n);
+
+  FourierTransform fft(n, Δω, Δτ);
+  std::vector<Complex> Ct;
+  std::vector<Complex> Rt;
+
+  Real y = y₀;
+
+  if (!loadData) {
+    // start from the exact solution for τ₀ = 0
+    for (unsigned i = 0; i < n; i++) {
+      Real τ = i * Δτ * M_PI;
+      C[i] = Γ₀ / 2 * (exp(-z * τ) - z * τ₀ * exp(-τ / τ₀)) / (z - pow(z, 3) * pow(τ₀, 2));
+      if (i > 0) {
+        C[2 * n - i] = C[i];
+      }
+      R[i] = exp(-z * τ);
+    }
+    Ct = fft.fourier(C);
+    Rt = fft.fourier(R);
+  } else {
+    std::ifstream cfile(fourierFile("C", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::binary);
+    cfile.read((char*)(C.data()), C.size() * sizeof(Real));
+    cfile.close();
+    std::ifstream rfile(fourierFile("R", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::binary);
+    rfile.read((char*)(R.data()), R.size() * sizeof(Real));
+    rfile.close();
+
+    Ct = fft.fourier(C);
+    Rt = fft.fourier(R);
+
+    auto [RddfCt, dfCt] = RddfCtdfCt(fft, C, R, p, s, λ);
+
+    z = ((Γ₀ * std::conj(Rt[0]) + pow(y, 2) * (RddfCt[0] * Ct[0] + dfCt[0] * std::conj(Rt[0]))) / Ct[0]).real();
+  }
+
+  while (y += Δy, y <= yₘₐₓ) {
+    Real ΔC = 1;;
+    unsigned it = 0;
+    while (sqrt(ΔC / C.size()) > ε) {
+      it++;
+      auto [RddfCt, dfCt] = RddfCtdfCt(fft, C, R, p, s, λ);
+
+      for (unsigned i = 0; i < Rt.size(); i++) {
+        Real ω = i * Δω;
+        Rt[i] = (1.0 + pow(y, 2) * RddfCt[i] * Rt[i]) / (z + 1i * ω);
+      }
+
+      for (unsigned i = 0; i < Ct.size(); i++) {
+        Real ω = i * Δω;
+        Ct[i] = (Γ₀ * std::conj(Rt[i]) / (1 + pow(τ₀ * ω, 2)) + pow(y, 2) * (RddfCt[i] * Ct[i] + dfCt[i] * std::conj(Rt[i]))) / (z + 1i * ω);
+      }
+
+      std::vector<Real> Cnew = fft.inverse(Ct);
+      std::vector<Real> Rnew = fft.inverse(Rt);
+      for (unsigned i = n; i < 2 * n; i++) {
+        Rnew[i] = 0;
+      }
+
+      ΔC = 0;
+      for (unsigned i = 0; i < Cnew.size(); i++) {
+        ΔC += pow(Cnew[i] - C[i], 2);
+        ΔC += pow(Rnew[i] - R[i], 2);
+      }
+
+      for (unsigned i = 0; i < Cnew.size(); i++) {
+        C[i] += γ * (Cnew[i] - C[i]);
+      }
+
+      for (unsigned i = 0; i < Rnew.size(); i++) {
+        R[i] += γ * (Rnew[i] - R[i]);
+      }
+
+      z *= Cnew[0];
+
+      std::cerr << it << " " << p << " " << s << " " << τ₀ << " " << sqrt(ΔC / C.size()) << std::endl;
+
+      if (it > maxIterations) {
+        it = 0;
+        γ /= 2;
+      }
+    }
+
+    Real e = energy(C, R, p, s, λ, y, Δτ);
+
+    std::cerr << "y " << y << " " << e << " " << z << std::endl;
+
+    std::ofstream outfile(fourierFile("C", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::out | std::ios::binary);
+    outfile.write((const char*)(C.data()), C.size() * sizeof(Real));
+    outfile.close();
+
+    std::ofstream outfileR(fourierFile("R", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::out | std::ios::binary);
+    outfileR.write((const char*)(R.data()), R.size() * sizeof(Real));
+    outfileR.close();
+  }
+
+  return 0;
+}