1 files changed, 197 insertions, 0 deletions
diff --git a/log-fourier.cpp b/log-fourier.cpp
new file mode 100644
index 0000000..47d5c5c
--- /dev/null
+++ b/log-fourier.cpp
@@ -0,0 +1,197 @@
+#include "log-fourier.hpp"
+#include "p-spin.hpp"
+#include <complex>
+#include <fstream>
+
+LogarithmicFourierTransform::LogarithmicFourierTransform(unsigned N, Real k, Real Δτ, unsigned pad) : N(N), pad(pad), k(k), Δτ(Δτ) {
+  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_from_filename("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_to_filename("fftw.wisdom");
+}
+
+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 exp(τ(n));
+}
+
+Real LogarithmicFourierTransform::ν(unsigned n) const {
+  return exp(ω(n));
+}
+
+Complex Γ(Complex z) {
+  gsl_sf_result logΓ;
+  gsl_sf_result argΓ;
+
+  gsl_sf_lngamma_complex_e(z.real(), z.imag(), &logΓ, &argΓ);
+
+  return exp(logΓ.val + 1i * argΓ.val);
+}
+
+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] * exp((1 - k) * τ(n));
+      } else {
+        a[n] = 0;
+      }
+    }
+    fftw_execute(a_to_â);
+    for (unsigned n = 0; n < pad*N; n++) {
+      â[(pad*N / 2 + n) % (pad*N)] *= pow(1i * σ, 1i * s(n) - k) * Γ(k - 1i * s(n));
+    }
+    fftw_execute(â_to_a);
+    for (unsigned n = 0; n < N; n++) {
+      ĉ[n] += exp(-k * ω(n)) * a[(pad - 1)*N+n] / (Real)(pad*N);
+    }
+  }
+
+  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) {
+        if (σ < 0) {
+          a[n] = std::conj(ĉ[n]) * exp((1 - k) * ω(n));
+        } else {
+          a[n] = ĉ[n] * exp((1 - k) * ω(n));
+        }
+      } else {
+        a[n] = 0;
+      }
+    }
+    fftw_execute(a_to_â);
+    for (unsigned n = 0; n < pad*N; n++) {
+      â[(pad*N / 2 + n) % (pad*N)] *= pow(-1i * σ, 1i * s(n) - k) * Γ(k - 1i * s(n));
+    }
+    fftw_execute(â_to_a);
+    for (unsigned n = 0; n < N; n++) {
+      c[n] += exp(-k * τ(n)) * a[(pad - 1)*N+n].real() / (Real)(pad*N) / (2 * M_PI);
+    }
+  }
+
+  return c;
+}
+
+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";
+}
+
+void logFourierSave(const std::vector<Real>& C, const std::vector<Real>& R, const std::vector<Complex>& Ct, const std::vector<Complex>& Rt, unsigned p, unsigned s, Real λ, Real τ₀, Real β, unsigned log2n, Real Δτ, Real k) {
+    unsigned N = 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*)(Ct.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*)(Rt.data()), N * sizeof(Complex));
+    outfileRt.close();
+}
+
+bool logFourierLoad(std::vector<Real>& C, std::vector<Real>& R, std::vector<Complex>& Ct, std::vector<Complex>& Rt, 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 = 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*)(Ct.data()), N * sizeof(Complex));
+  ctfile.close();
+
+  rtfile.read((char*)(Rt.data()), N * sizeof(Complex));
+  rtfile.close();
+
+  return true;
+}
+
+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 = 1.0;
+
+  return ((2 * Γ₀ * std::conj(Rt[0]) + pow(β, 2) * (RddfCt[0] * Ct[0] + dfCt[0] * std::conj(Rt[0]))) / Ct[0]).real();
+}
+
+Real energy(const LogarithmicFourierTransform& fft, std::vector<Real>&  C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ, Real β) {
+  Real E = 0;
+  for (unsigned n = 0; n < C.size()/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   = R[2*n]   * df(λ, p, s, C[2*n]);
+    Real f₂ₙ₊₁ = R[2*n+1] * df(λ, p, s, C[2*n+1]);
+    Real f₂ₙ₊₂ = R[2*n+2] * df(λ, p, s, C[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
+        );
+  }
+  return  β * E;
+}
+