From 73f4eaba3a08a5e1b85512868c3916c7fd4e4571 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 8 May 2025 18:11:35 -0300
Subject: Updated to work with shift

---
 log-fourier.cpp | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

(limited to 'log-fourier.cpp')

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);
-- 
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