1 files changed, 278 insertions, 0 deletions
diff --git a/log-fourier.cpp b/log-fourier.cpp
new file mode 100644
index 0000000..16a7f3f
--- /dev/null
+++ b/log-fourier.cpp
@@ -0,0 +1,278 @@
+#include "log-fourier.hpp"
+#include "p-spin.hpp"
+
+#include <fstream>
+
+Complex Γ(Complex z) {
+  gsl_sf_result logΓ;
+  gsl_sf_result argΓ;
+
+  gsl_sf_lngamma_complex_e((double)z.real(), (double)z.imag(), &logΓ, &argΓ);
+
+  return std::exp((Real)logΓ.val + II * (Real)argΓ.val);
+}
+
+LogarithmicFourierTransform::LogarithmicFourierTransform(unsigned N, Real k, Real Δτ, unsigned pad, Real shift) : N(N), pad(pad), k(k), Δτ(Δτ), ts(N), νs(N), Γs(pad * N), exp1kω(N), exp1kτ(N), expkω(N), expkτ(N), shift(shift) {
+  τₛ = -0.5 * N;
+  ωₛ = -0.5 * N;
+  sₛ = -0.5 * pad * N;
+  a = reinterpret_cast<Complex*>(FFTW_ALLOC_COMPLEX(pad*N));
+  â = reinterpret_cast<Complex*>(FFTW_ALLOC_COMPLEX(pad*N));
+  FFTW_IMPORT_WISDOM("fftw.wisdom");
+  a_to_â = FFTW_PLAN_DFT_1D(pad*N, reinterpret_cast<FFTW_COMPLEX*>(a), reinterpret_cast<FFTW_COMPLEX*>(â), FFTW_BACKWARD, 0);
+  â_to_a = FFTW_PLAN_DFT_1D(pad*N, reinterpret_cast<FFTW_COMPLEX*>(â), reinterpret_cast<FFTW_COMPLEX*>(a), FFTW_BACKWARD, 0);
+  FFTW_EXPORT_WISDOM("fftw.wisdom");
+  for (unsigned n = 0; n < N; n++) {
+    ts[n] = std::exp(τ(n)) / shift;
+    νs[n] = std::exp(ω(n)) * shift;
+    exp1kτ[n] = std::exp((1 - k) * τ(n));
+    exp1kω[n] = std::exp((1 - k) * ω(n));
+    expkτ[n] = std::exp(-k * τ(n));
+    expkω[n] = std::exp(-k * ω(n));
+  }
+  for (unsigned n = 0; n < pad * N; n++) {
+    Γs[n] = Γ(k - II * s(n));
+  }
+}
+
+LogarithmicFourierTransform::~LogarithmicFourierTransform() {
+  FFTW_DESTROY_PLAN(a_to_â);
+  FFTW_DESTROY_PLAN(â_to_a);
+  FFTW_FREE(a);
+  FFTW_FREE(â);
+  FFTW_CLEANUP();
+}
+
+Real LogarithmicFourierTransform::τ(unsigned n) const {
+  return Δτ * (n + τₛ);
+}
+
+Real LogarithmicFourierTransform::ω(unsigned n) const {
+  return Δτ * (n + ωₛ);
+}
+
+Real LogarithmicFourierTransform::s(unsigned n) const {
+  return (n + sₛ) * 2*M_PI / (pad * N * Δτ);
+}
+
+Real LogarithmicFourierTransform::t(unsigned n) const {
+  return ts[n];
+}
+
+Real LogarithmicFourierTransform::ν(unsigned n) const {
+  return νs[n];
+}
+
+std::vector<Complex> LogarithmicFourierTransform::fourier(const std::vector<Real>& c, bool symmetric) {
+  std::vector<Complex> ĉ(N);
+  std::vector<Real> σs = {1};
+  /* c is either even or zero for negative arguments */
+  if (symmetric){
+    σs.push_back(-1);
+  }
+  for (Real σ : σs) {
+    for (unsigned n = 0; n < pad*N; n++) {
+      if (n < N) {
+        a[n] = c[n] * exp1kτ[n];
+      } else if (n >= (pad - 1) * N) {
+        a[n] = c[pad*N-n-1] * exp1kτ[pad*N-n-1];
+      } else {
+        a[n] = 0;
+      }
+    }
+    FFTW_EXECUTE(a_to_â);
+    for (unsigned n = 0; n < pad*N; n++) {
+      â[(pad*N / 2 + n) % (pad*N)] *= std::pow(II * σ, II * s(n) - k) * Γs[n];
+    }
+    FFTW_EXECUTE(â_to_a);
+    for (unsigned n = 0; n < N; n++) {
+      ĉ[n] += expkω[n] * a[(pad - 1)*N+n] / (Real)(pad*N);
+    }
+  }
+
+  for (unsigned n = 0; n < N; n++) {
+    ĉ[n] -= ĉ[N - 1];
+    if (symmetric) ĉ[n] = ĉ[n].real();
+    ĉ[n] /= shift;
+  }
+
+  return ĉ;
+}
+
+std::vector<Real> LogarithmicFourierTransform::inverse(const std::vector<Complex>& ĉ) {
+  std::vector<Real> c(N);
+  std::vector<Real> σs = {1, -1};
+  for (Real σ : σs) {
+    for (unsigned n = 0; n < pad * N; n++) {
+      if (n < N) {
+        a[n] = (ĉ[n].real() + II * σ * ĉ[n].imag()) * exp1kω[n];
+      } else if (n >= (pad - 1) * N) {
+        a[n] = (ĉ[pad*N-n-1].real() - II * σ * ĉ[pad*N-n-1].imag()) * exp1kω[pad*N-n-1];
+      } else {
+        a[n] = 0;
+      }
+    }
+    FFTW_EXECUTE(a_to_â);
+    for (unsigned n = 0; n < pad*N; n++) {
+      â[(pad*N / 2 + n) % (pad*N)] *= std::pow(-II * σ, II * s(n) - k) * Γs[n];
+    }
+    FFTW_EXECUTE(â_to_a);
+    for (unsigned n = 0; n < N; n++) {
+      c[n] += expkτ[n] * a[(pad - 1)*N+n].real() / (Real)(pad*N) / (2 * M_PI);
+    }
+  }
+
+  for (unsigned n = 0; n < N; n++) {
+    c[n] -= c[N - 1];
+    c[n] *= shift;
+  }
+
+  return c;
+}
+
+std::string logFourierFile(std::string prefix, unsigned p, unsigned s, Real λ, Real τ₀, Real β, unsigned log2n, Real Δτ, Real shift) {
+  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(shift) + ".dat";
+}
+
+void logFourierSave(const std::vector<Real>& C, const std::vector<Real>& R, const std::vector<Complex>& Ĉ, const std::vector<Complex>& Ȓ, unsigned p, unsigned s, Real λ, Real τ₀, Real β, unsigned log2n, Real Δτ, Real k) {
+    unsigned N = std::pow(2, log2n);
+    std::ofstream outfile(logFourierFile("C", p, s, λ, τ₀, β, log2n, Δτ, k), std::ios::out | std::ios::binary);
+    outfile.write((const char*)(C.data()), N * sizeof(Real));
+    outfile.close();
+
+    std::ofstream outfileCt(logFourierFile("Ct", p, s, λ, τ₀, β, log2n, Δτ, k), std::ios::out | std::ios::binary);
+    outfileCt.write((const char*)(Ĉ.data()), N * sizeof(Complex));
+    outfileCt.close();
+
+    std::ofstream outfileR(logFourierFile("R", p, s, λ, τ₀, β, log2n, Δτ, k), std::ios::out | std::ios::binary);
+    outfileR.write((const char*)(R.data()), N * sizeof(Real));
+    outfileR.close();
+
+    std::ofstream outfileRt(logFourierFile("Rt", p, s, λ, τ₀, β, log2n, Δτ, k), std::ios::out | std::ios::binary);
+    outfileRt.write((const char*)(Ȓ.data()), N * sizeof(Complex));
+    outfileRt.close();
+}
+
+bool logFourierLoad(std::vector<Real>& C, std::vector<Real>& R, std::vector<Complex>& Ĉ, std::vector<Complex>& Ȓ, unsigned p, unsigned s, Real λ, Real τ₀, Real β, unsigned log2n, Real Δτ, Real k) {
+  std::ifstream cfile(logFourierFile("C", p, s, λ, τ₀, β, log2n, Δτ, k), std::ios::binary);
+  std::ifstream rfile(logFourierFile("R", p, s, λ, τ₀, β, log2n, Δτ, k), std::ios::binary);
+  std::ifstream ctfile(logFourierFile("Ct", p, s, λ, τ₀, β, log2n, Δτ, k), std::ios::binary);
+  std::ifstream rtfile(logFourierFile("Rt", p, s, λ, τ₀, β, log2n, Δτ, k), std::ios::binary);
+
+  if ((!cfile.is_open() || !rfile.is_open()) || (!ctfile.is_open() || !rtfile.is_open())) {
+    return false;
+  }
+
+  unsigned N = std::pow(2, log2n);
+
+  cfile.read((char*)(C.data()), N * sizeof(Real));
+  cfile.close();
+
+  rfile.read((char*)(R.data()), N * sizeof(Real));
+  rfile.close();
+
+  ctfile.read((char*)(Ĉ.data()), N * sizeof(Complex));
+  ctfile.close();
+
+  rtfile.read((char*)(Ȓ.data()), N * sizeof(Complex));
+  rtfile.close();
+
+  return true;
+}
+
+std::tuple<std::vector<Complex>, std::vector<Complex>> ΣD(LogarithmicFourierTransform& fft, const std::vector<Real>& C, const std::vector<Real>& R, Real β, unsigned p, unsigned s, Real λ) {
+  std::vector<Real> D(C.size());
+  std::vector<Real> Σ(C.size());
+  Real β² = std::pow(β, 2);
+  for (unsigned n = 0; n < C.size(); n++) {
+    D[n] = β² * ∂f(λ, p, s, C[n]);
+    Σ[n] = β² * R[n] * ∂∂f(λ, p, s, C[n]);
+  }
+  std::vector<Complex> Σhat = fft.fourier(Σ, false);
+  std::vector<Complex> Dhat = fft.fourier(D, true);
+
+  return {Σhat, Dhat};
+}
+
+Real estimateZ(LogarithmicFourierTransform& fft, const std::vector<Real>& C, const std::vector<Complex>& Ĉ, const std::vector<Real>& R, const std::vector<Complex>& Ȓ, unsigned p, unsigned s, Real λ, Real τ₀, Real β) {
+  auto [Σhat, Dhat] = ΣD(fft, C, R, β, p, s, λ);
+  Real Γ₀ = 1.0;
+
+  return (((2 * Γ₀ + Dhat[0]) * std::conj(Ȓ[0]) + Σhat[0] * Ĉ[0]) / Ĉ[0]).real();
+}
+
+Real energy(const LogarithmicFourierTransform& fft, const std::vector<Real>&  C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ, Real β) {
+  unsigned n₀ = 0;
+  for (unsigned n = 0; n < C.size(); n++) {
+    if (C[n] > 1 || R[n] > 1) n₀ = n % 2 == 0 ? n / 2 : (n + 1) / 2;
+  }
+  Real E = fft.t(2*n₀) * ∂f(λ, p, s, 1);
+  for (unsigned n = n₀; n < C.size()/2-1; n++) {
+    Real R₂ₙ   = R[2*n];
+    Real R₂ₙ₊₁ = R[2*n+1];
+    Real R₂ₙ₊₂ = R[2*n+2];
+    Real C₂ₙ   = C[2*n];
+    Real C₂ₙ₊₁ = C[2*n+1];
+    Real C₂ₙ₊₂ = C[2*n+2];
+
+    if (C₂ₙ₊₂ < 0 || R₂ₙ₊₂ < 0) break;
+
+    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   = R₂ₙ   * ∂f(λ, p, s, C₂ₙ);
+    Real f₂ₙ₊₁ = R₂ₙ₊₁ * ∂f(λ, p, s, C₂ₙ₊₁);
+    Real f₂ₙ₊₂ = R₂ₙ₊₂ * ∂f(λ, p, s, C₂ₙ₊₂);
+
+    E += (h₂ₙ + h₂ₙ₊₁) / 6 * (
+          (2 - h₂ₙ₊₁ / h₂ₙ) * f₂ₙ
+          + std::pow(h₂ₙ + h₂ₙ₊₁, 2) / (h₂ₙ * h₂ₙ₊₁) * f₂ₙ₊₁
+          + (2 - h₂ₙ / h₂ₙ₊₁) * f₂ₙ₊₂
+        );
+  }
+  return  β * E;
+}
+
+Real C0(const LogarithmicFourierTransform& fft, const std::vector<Complex>& Ĉ) {
+  Real C = 0;
+  for (unsigned n = 0; n < Ĉ.size()/2-1; n++) {
+    Real Ĉ₂ₙ   = Ĉ[2*n].real();
+    Real Ĉ₂ₙ₊₁ = Ĉ[2*n+1].real();
+    Real Ĉ₂ₙ₊₂ = Ĉ[2*n+2].real();
+
+    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   = Ĉ₂ₙ;
+    Real f₂ₙ₊₁ = Ĉ₂ₙ₊₁;
+    Real f₂ₙ₊₂ = Ĉ₂ₙ₊₂;
+
+    C += (h₂ₙ + h₂ₙ₊₁) / 6 * (
+          (2 - h₂ₙ₊₁ / h₂ₙ) * f₂ₙ
+          + std::pow(h₂ₙ + h₂ₙ₊₁, 2) / (h₂ₙ * h₂ₙ₊₁) * f₂ₙ₊₁
+          + (2 - h₂ₙ / h₂ₙ₊₁) * f₂ₙ₊₂
+        );
+  }
+  return C * pow(fft.shift, 2) / M_PI;
+}
+
+void smooth(std::vector<Real>& C, Real ε) {
+  unsigned N = C.size();
+  bool trigger0 = false;
+  bool trigger1 = false;
+  for (unsigned i = 0; i < N; i++) {
+    if (C[i] < ε || trigger0) {
+      C[i] = 0;
+      trigger0 = true;
+    }
+    if (C[N-1-i] > 1 - ε || trigger1) {
+      C[N-1-i] = 1;
+      trigger1 = true;
+    }
+  }
+
+  Real Cmax = 0;
+  for (unsigned i = 0; i < N; i++) {
+    if (C[N-1-i] > Cmax) Cmax = C[N-1-i];
+    C[N-1-i] = Cmax;
+  }
+}
+