Updated to work with shift

4 files changed, 30 insertions, 21 deletions

diff --git a/log-fourier.cpp b/log-fourier.cpp
index 2e93e87..5b5955a 100644
--- a/log-fourier.cpp
+++ b/log-fourier.cpp
@@ -4,9 +4,9 @@
 #include <fstream>
 #include <types.hpp>
 
-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;
+LogarithmicFourierTransform::LogarithmicFourierTransform(unsigned N, Real k, Real Δτ, unsigned pad, Real shift) : N(N), pad(pad), k(k), Δτ(Δτ) {
+  τₛ = -shift * N;
+  ωₛ = -(1-shift) * N;
   sₛ = -0.5 * pad * N;
   a = reinterpret_cast<Complex*>(FFTW_ALLOC_COMPLEX(pad*N));
   â = reinterpret_cast<Complex*>(FFTW_ALLOC_COMPLEX(pad*N));
@@ -70,7 +70,7 @@ std::vector<Complex> LogarithmicFourierTransform::fourier(const std::vector<Real
     }
     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) * Γ(k - II * s(n));
+      â[(pad*N / 2 + n) % (pad*N)] *= std::exp(II*(0.5 * N + τₛ) * s(n) / Δτ) * std::pow(II * σ, II * s(n) - k) * Γ(k - II * s(n));
     }
     FFTW_EXECUTE(â_to_a);
     for (unsigned n = 0; n < N; n++) {
@@ -98,7 +98,7 @@ std::vector<Real> LogarithmicFourierTransform::inverse(const std::vector<Complex
     }
     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) * Γ(k - II * s(n));
+      â[(pad*N / 2 + n) % (pad*N)] *= std::exp(-II*(0.5 * N + τₛ) * s(n) / Δτ) * std::pow(-II * σ, II * s(n) - k) * Γ(k - II * s(n));
     }
     FFTW_EXECUTE(â_to_a);
     for (unsigned n = 0; n < N; n++) {
@@ -113,8 +113,8 @@ std::vector<Real> LogarithmicFourierTransform::inverse(const std::vector<Complex
   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";
+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>& Ct, const std::vector<Complex>& Rt, unsigned p, unsigned s, Real λ, Real τ₀, Real β, unsigned log2n, Real Δτ, Real k) {
@@ -184,7 +184,7 @@ Real estimateZ(LogarithmicFourierTransform& fft, const std::vector<Real>& C, con
 }
 
 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;
+  Real E = fft.t(0) * (df(λ, p, s, 1) + R[0] * df(λ, p, s, C[0])) / 2;
   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);
diff --git a/log-fourier.hpp b/log-fourier.hpp
index f0b53ef..b1e4bd1 100644
--- a/log-fourier.hpp
+++ b/log-fourier.hpp
@@ -21,7 +21,7 @@ private:
   Real ωₛ;
   Real sₛ;
 public:
-  LogarithmicFourierTransform(unsigned N, Real k, Real Δτ, unsigned pad = 4);
+  LogarithmicFourierTransform(unsigned N, Real k, Real Δτ, unsigned pad = 4, Real shift = 0.5);
   ~LogarithmicFourierTransform();
   Real τ(unsigned n) const;
   Real ω(unsigned n) const;
diff --git a/log-fourier_integrator.cpp b/log-fourier_integrator.cpp
index 55f358a..44ccce1 100644
--- a/log-fourier_integrator.cpp
+++ b/log-fourier_integrator.cpp
@@ -12,22 +12,23 @@ int main(int argc, char* argv[]) {
   /* Log-Fourier parameters */
   unsigned log2n = 8;
   Real Δτ = 0.1;
-  Real k = 0.1;
+  Real k = -0.01;
+  Real shift = 0.4;
 
   /* Iteration parameters */
-  Real ε = 1e-14;
+  Real ε = 1e-15;
   Real γ₀ = 1;
-  Real x = 0.5;
+  Real x = 1;
   Real β₀ = 0;
-  Real βₘₐₓ = 0.7;
+  Real βₘₐₓ = 20;
   Real Δβ = 0.01;
   bool loadData = false;
-  unsigned stepsToRespond = 1000;
-  unsigned pad = 4;
+  unsigned stepsToRespond = 1e7;
+  unsigned pad = 2;
 
   int opt;
 
-  while ((opt = getopt(argc, argv, "p:s:2:T:t:b:d:g:k:D:e:0:lS:x:P:")) != -1) {
+  while ((opt = getopt(argc, argv, "p:s:2:T:t:b:d:g:k:D:e:0:lS:x:P:h:")) != -1) {
     switch (opt) {
     case 'p':
       p = atoi(optarg);
@@ -56,6 +57,9 @@ int main(int argc, char* argv[]) {
     case 'D':
       Δτ = atof(optarg);
       break;
+    case 'h':
+      shift = atof(optarg);
+      break;
     case 'e':
       ε = atof(optarg);
       break;
@@ -81,7 +85,7 @@ int main(int argc, char* argv[]) {
 
   unsigned N = pow(2, log2n);
 
-  LogarithmicFourierTransform fft(N, k, Δτ, pad);
+  LogarithmicFourierTransform fft(N, k, Δτ, pad, shift);
 
   Real Γ₀ = 1;
   Real μₜ₋₁ = Γ₀;
@@ -186,7 +190,7 @@ int main(int argc, char* argv[]) {
       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);
+      logFourierSave(Cₜ, Rₜ, Ĉₜ, Ȓₜ, p, s, λ, τ₀, β, log2n, Δτ, shift);
 
       β += Δβ;
       Cₜ₋₁ = Cₜ;
diff --git a/log_get_energy.cpp b/log_get_energy.cpp
index ae17f6f..b01034c 100644
--- a/log_get_energy.cpp
+++ b/log_get_energy.cpp
@@ -15,6 +15,8 @@ int main(int argc, char* argv[]) {
   unsigned log2n = 8;
   Real Δτ = 0.1;
   Real k = 0.1;
+  unsigned pad = 2;
+  Real shift = 0.5;
 
   /* Iteration parameters */
   Real β₀ = 0;
@@ -23,7 +25,7 @@ int main(int argc, char* argv[]) {
 
   int opt;
 
-  while ((opt = getopt(argc, argv, "p:s:2:T:t:b:d:k:D:0:")) != -1) {
+  while ((opt = getopt(argc, argv, "p:s:2:T:t:b:d:k:D:0:h:")) != -1) {
     switch (opt) {
     case 'p':
       p = atoi(optarg);
@@ -46,6 +48,9 @@ int main(int argc, char* argv[]) {
     case 'k':
       k = atof(optarg);
       break;
+    case 'h':
+      shift = atof(optarg);
+      break;
     case 'D':
       Δτ = atof(optarg);
       break;
@@ -59,7 +64,7 @@ int main(int argc, char* argv[]) {
 
   unsigned N = pow(2, log2n);
 
-  LogarithmicFourierTransform fft(N, k, Δτ, 4);
+  LogarithmicFourierTransform fft(N, k, Δτ, pad, shift);
 
   std::vector<Real> C(N);
   std::vector<Real> R(N);
@@ -71,7 +76,7 @@ int main(int argc, char* argv[]) {
   std::cout << std::setprecision(16);
 
   while (β += Δβ, β <= βₘₐₓ) {
-    if (logFourierLoad(C, R, Ct, Rt, p, s, λ, τ₀, β, log2n, Δτ, k)) {
+    if (logFourierLoad(C, R, Ct, Rt, p, s, λ, τ₀, β, log2n, Δτ, shift)) {
 
       Real e = energy(fft, C, R, p, s, λ, β);