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-rw-r--r--log-fourier.cpp29
-rw-r--r--log-fourier.hpp7
-rw-r--r--log-fourier_integrator.cpp39
-rw-r--r--log_get_energy.cpp12
4 files changed, 46 insertions, 41 deletions
diff --git a/log-fourier.cpp b/log-fourier.cpp
index e60439a..d5ac17d 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, Real shift) : N(N), pad(pad), k(k), Δτ(Δτ) {
- τₛ = -shift * N;
- ωₛ = -(1-shift) * N;
+LogarithmicFourierTransform::LogarithmicFourierTransform(unsigned N, Real k, Real Δτ, unsigned pad, Real shift) : N(N), pad(pad), k(k), Δτ(Δτ), 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));
@@ -37,11 +37,11 @@ Real LogarithmicFourierTransform::s(unsigned n) const {
}
Real LogarithmicFourierTransform::t(unsigned n) const {
- return exp(τ(n));
+ return std::exp(τ(n)) / shift;
}
Real LogarithmicFourierTransform::ν(unsigned n) const {
- return exp(ω(n));
+ return std::exp(ω(n)) * shift;
}
Complex Γ(Complex z) {
@@ -50,7 +50,7 @@ Complex Γ(Complex z) {
gsl_sf_lngamma_complex_e((double)z.real(), (double)z.imag(), &logΓ, &argΓ);
- return exp((Real)logΓ.val + II * (Real)argΓ.val);
+ return std::exp((Real)logΓ.val + II * (Real)argΓ.val);
}
std::vector<Complex> LogarithmicFourierTransform::fourier(const std::vector<Real>& c, bool symmetric) {
@@ -63,16 +63,16 @@ std::vector<Complex> LogarithmicFourierTransform::fourier(const std::vector<Real
for (Real σ : σs) {
for (unsigned n = 0; n < pad*N; n++) {
if (n < N) {
- a[n] = c[n] * exp((1 - k) * τ(n));
+ a[n] = c[n] * std::exp((1 - k) * τ(n));
} else if (n >= (pad - 1) * N) {
- a[n] = c[pad*N-n-1] * exp((1 - k) * τ(pad*N-n-1));
+ a[n] = c[pad*N-n-1] * std::exp((1 - k) * τ(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::exp(II*(0.5 * N + τₛ) * s(n) / Δτ) * std::pow(II * σ, II * s(n) - k) * Γ(k - II * s(n));
+ â[(pad*N / 2 + n) % (pad*N)] *= 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++) {
@@ -82,6 +82,8 @@ std::vector<Complex> LogarithmicFourierTransform::fourier(const std::vector<Real
for (unsigned n = 0; n < N; n++) {
ĉ[n] -= ĉ[N - 1];
+ if (symmetric) ĉ[n] = ĉ[n].real();
+ ĉ[n] /= shift;
}
return ĉ;
@@ -95,14 +97,14 @@ std::vector<Real> LogarithmicFourierTransform::inverse(const std::vector<Complex
if (n < N) {
a[n] = (ĉ[n].real() + II * σ * ĉ[n].imag()) * std::exp((1 - k) * ω(n));
} else if (n >= (pad - 1) * N) {
- a[n] = (ĉ[pad*N-n-1].real() + II * σ * ĉ[pad*N-n-1].imag()) * std::exp((1 - k) * ω(pad*N-n-1));
+ a[n] = (ĉ[pad*N-n-1].real() - II * σ * ĉ[pad*N-n-1].imag()) * std::exp((1 - k) * ω(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::exp(-II*(0.5 * N + τₛ) * s(n) / Δτ) * std::pow(-II * σ, II * s(n) - k) * Γ(k - II * s(n));
+ â[(pad*N / 2 + n) % (pad*N)] *= 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++) {
@@ -112,6 +114,7 @@ std::vector<Real> LogarithmicFourierTransform::inverse(const std::vector<Complex
for (unsigned n = 0; n < N; n++) {
c[n] -= c[N - 1];
+ c[n] *= shift;
}
return c;
@@ -189,11 +192,9 @@ 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) {
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) * df(λ, p, s, 1);
for (unsigned n = n₀; n < C.size()/2-1; n++) {
Real R₂ₙ = R[2*n];
@@ -203,7 +204,7 @@ Real energy(const LogarithmicFourierTransform& fft, std::vector<Real>& C, const
Real C₂ₙ₊₁ = C[2*n+1];
Real C₂ₙ₊₂ = C[2*n+2];
- //if (C₂ₙ₊₂ < 0 || R₂ₙ₊₂ < 0) break;
+ 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);
diff --git a/log-fourier.hpp b/log-fourier.hpp
index b1e4bd1..b5bb4c0 100644
--- a/log-fourier.hpp
+++ b/log-fourier.hpp
@@ -20,6 +20,7 @@ private:
Real τₛ;
Real ωₛ;
Real sₛ;
+ Real shift;
public:
LogarithmicFourierTransform(unsigned N, Real k, Real Δτ, unsigned pad = 4, Real shift = 0.5);
~LogarithmicFourierTransform();
@@ -32,11 +33,11 @@ public:
std::vector<Real> inverse(const std::vector<Complex>& ĉ);
};
-std::string logFourierFile(std::string prefix, unsigned p, unsigned s, Real λ, Real τ₀, Real β, unsigned log2n, Real Δτ, Real k);
+std::string logFourierFile(std::string prefix, unsigned p, unsigned s, Real λ, Real τ₀, Real β, unsigned log2n, Real Δτ, Real shift);
-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);
+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 shift);
-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);
+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 shift);
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);
diff --git a/log-fourier_integrator.cpp b/log-fourier_integrator.cpp
index 7b24a55..9db21f0 100644
--- a/log-fourier_integrator.cpp
+++ b/log-fourier_integrator.cpp
@@ -13,7 +13,7 @@ int main(int argc, char* argv[]) {
unsigned log2n = 8;
Real Δτ = 0.1;
Real k = -0.01;
- Real shift = 0.5;
+ Real logShift = 0;
/* Iteration parameters */
Real ε = 1e-15;
@@ -54,12 +54,12 @@ int main(int argc, char* argv[]) {
case 'k':
k = atof(optarg);
break;
+ case 'h':
+ logShift = atof(optarg);
+ break;
case 'D':
Δτ = atof(optarg);
break;
- case 'h':
- shift = atof(optarg);
- break;
case 'e':
ε = atof(optarg);
break;
@@ -85,13 +85,14 @@ int main(int argc, char* argv[]) {
unsigned N = pow(2, log2n);
- LogarithmicFourierTransform fft(N, k, Δτ, pad, shift);
-
Real Γ₀ = 1;
- Real μₜ₋₁ = Γ₀;
- if (τ₀ > 0) {
- μₜ₋₁ = (sqrt(1+4*Γ₀*τ₀)-1)/(2*τ₀);
- }
+ Real μ₀ = τ₀ > 0 ? (sqrt(1+4*Γ₀*τ₀)-1)/(2*τ₀) : Γ₀;
+
+ LogarithmicFourierTransform fft(N, k, Δτ, pad, μ₀ * pow(10, logShift));
+
+ std::cerr << "Starting, μ₀ = " << μ₀ << ", range " << fft.t(0) << " " << fft.t(N-1) << std::endl;
+
+ Real μₜ₋₁ = μ₀;
std::vector<Real> Cₜ₋₁(N);
std::vector<Real> Rₜ₋₁(N);
@@ -103,20 +104,20 @@ int main(int argc, char* argv[]) {
for (unsigned n = 0; n < N; n++) {
if (τ₀ > 0) {
if (τ₀ == 2) {
- Cₜ₋₁[n] = Γ₀ * exp(-fft.t(n) / 2) * (1 + fft.t(n) / 2);
+ Cₜ₋₁[n] = Γ₀ * std::exp(-fft.t(n) / 2) * (1 + fft.t(n) / 2);
} else {
- Cₜ₋₁[n] = Γ₀ * (exp(-μₜ₋₁ * fft.t(n)) - μₜ₋₁ * τ₀ * exp(-fft.t(n) / τ₀)) / (μₜ₋₁ - pow(μₜ₋₁, 3) * pow(τ₀, 2));
+ Cₜ₋₁[n] = Γ₀ * (std::exp(-μ₀ * fft.t(n)) - μ₀ * τ₀ * std::exp(-fft.t(n) / τ₀)) / (μ₀ - pow(μ₀, 3) * pow(τ₀, 2));
}
} else {
- Cₜ₋₁[n] = Γ₀ * exp(-μₜ₋₁ * fft.t(n)) / μₜ₋₁;
+ Cₜ₋₁[n] = Γ₀ * std::exp(-μ₀ * fft.t(n)) / μ₀;
}
- Rₜ₋₁[n] = exp(-μₜ₋₁ * fft.t(n));
+ Rₜ₋₁[n] = std::exp(-μ₀ * fft.t(n));
- Ĉₜ₋₁[n] = 2 * Γ₀ / (pow(μₜ₋₁, 2) + pow(fft.ν(n), 2)) / (1 + pow(τ₀ * fft.ν(n), 2));
- Ȓₜ₋₁[n] = (Real)1.0 / (μₜ₋₁ + II * fft.ν(n));
+ Ĉₜ₋₁[n] = 2 * Γ₀ / (pow(μ₀, 2) + pow(fft.ν(n), 2)) / (1 + pow(τ₀ * fft.ν(n), 2));
+ Ȓₜ₋₁[n] = (Real)1.0 / (μ₀ + II * fft.ν(n));
}
} else {
- logFourierLoad(Cₜ₋₁, Rₜ₋₁, Ĉₜ₋₁, Ȓₜ₋₁, p, s, λ, τ₀, β₀, log2n, Δτ, shift);
+ logFourierLoad(Cₜ₋₁, Rₜ₋₁, Ĉₜ₋₁, Ȓₜ₋₁, p, s, λ, τ₀, β₀, log2n, Δτ, logShift);
μₜ₋₁ = estimateZ(fft, Cₜ₋₁, Ĉₜ₋₁, Rₜ₋₁, Ȓₜ₋₁, p, s, λ, τ₀, β₀);
}
@@ -139,7 +140,7 @@ int main(int argc, char* argv[]) {
std::vector<Complex> Ȓₜ₊₁(N);
for (unsigned n = 0; n < N; n++) {
Ȓₜ₊₁[n] = ((Real)1.0 + std::pow(β, 2) * RddfCt[n] * Ȓₜ[n]) / (μₜ + II * fft.ν(n));
- Ĉₜ₊₁[n] = (2 * Γ₀ * std::conj(Ȓₜ[n]) / (1 + std::pow(τ₀ * fft.ν(n), 2)) + std::pow(β, 2) * (RddfCt[n] * Ĉₜ[n] + dfCt[n] * std::conj(Ȓₜ[n]))) / (μₜ + II * fft.ν(n));
+ Ĉₜ₊₁[n] = ((2 * Γ₀ * std::conj(Ȓₜ[n]) / (1 + std::pow(τ₀ * fft.ν(n), 2)) + std::pow(β, 2) * (RddfCt[n] * Ĉₜ[n] + dfCt[n] * std::conj(Ȓₜ[n]))) / (μₜ + II * fft.ν(n))).real();
}
std::vector<Real> Rₜ₊₁ = fft.inverse(Ȓₜ₊₁);
std::vector<Real> Cₜ₊₁ = fft.inverse(Ĉₜ₊₁);
@@ -190,7 +191,7 @@ 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, shift);
+ logFourierSave(Cₜ, Rₜ, Ĉₜ, Ȓₜ, p, s, λ, τ₀, β, log2n, Δτ, logShift);
β += Δβ;
Cₜ₋₁ = Cₜ;
diff --git a/log_get_energy.cpp b/log_get_energy.cpp
index b01034c..a183861 100644
--- a/log_get_energy.cpp
+++ b/log_get_energy.cpp
@@ -16,7 +16,7 @@ int main(int argc, char* argv[]) {
Real Δτ = 0.1;
Real k = 0.1;
unsigned pad = 2;
- Real shift = 0.5;
+ Real logShift = 0;
/* Iteration parameters */
Real β₀ = 0;
@@ -25,7 +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:h:")) != -1) {
+ while ((opt = getopt(argc, argv, "p:s:2:T:t:b:d:k:h:D:0:")) != -1) {
switch (opt) {
case 'p':
p = atoi(optarg);
@@ -49,7 +49,7 @@ int main(int argc, char* argv[]) {
k = atof(optarg);
break;
case 'h':
- shift = atof(optarg);
+ logShift = atof(optarg);
break;
case 'D':
Δτ = atof(optarg);
@@ -63,8 +63,10 @@ int main(int argc, char* argv[]) {
}
unsigned N = pow(2, log2n);
+ Real Γ₀ = 1;
+ Real μ₀ = τ₀ > 0 ? (sqrt(1+4*Γ₀*τ₀)-1)/(2*τ₀) : Γ₀;
- LogarithmicFourierTransform fft(N, k, Δτ, pad, shift);
+ LogarithmicFourierTransform fft(N, k, Δτ, pad, μ₀ * pow(10, logShift));
std::vector<Real> C(N);
std::vector<Real> R(N);
@@ -76,7 +78,7 @@ 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, shift)) {
+ if (logFourierLoad(C, R, Ct, Rt, p, s, λ, τ₀, β, log2n, Δτ, logShift)) {
Real e = energy(fft, C, R, p, s, λ, β);