Split functions into library to deduplicate code

5 files changed, 161 insertions, 192 deletions

diff --git a/Makefile b/Makefile
index c013825..d4c15bf 100644
--- a/Makefile
+++ b/Makefile
@@ -1,6 +1,6 @@
 all: walk correlations integrator fourier_integrator get_energy
 
-CC := clang++ -std=c++17 -Wno-mathematical-notation-identifier-extension -O3 -march=native -mtune=native -fopenmp -lfftw3 -g
+CC := clang++ -std=c++17 -flto -Wno-mathematical-notation-identifier-extension -O3 -march=native -mtune=native -fopenmp
 
 walk: walk.cpp
 	$(CC) walk.cpp -o walk
@@ -11,8 +11,11 @@ correlations: correlations.cpp
 integrator: integrator.cpp
 	$(CC) integrator.cpp -o integrator
 
-fourier_integrator: fourier_integrator.cpp
-	$(CC) fourier_integrator.cpp -o fourier_integrator
+fourier.o: fourier.cpp fourier.hpp
+	$(CC) fourier.cpp -c -o fourier.o
 
-get_energy: get_energy.cpp
-	$(CC) get_energy.cpp -o get_energy
+fourier_integrator: fourier_integrator.cpp fourier.hpp fourier.o
+	$(CC) fourier_integrator.cpp fourier.o -lfftw3 -o fourier_integrator
+
+get_energy: get_energy.cpp fourier.hpp fourier.o
+	$(CC) get_energy.cpp fourier.o -lfftw3 -o get_energy
diff --git a/fourier.cpp b/fourier.cpp
new file mode 100644
index 0000000..7808989
--- /dev/null
+++ b/fourier.cpp
@@ -0,0 +1,86 @@
+#include "fourier.hpp"
+
+inline Real fP(unsigned p, Real q) {
+  return 0.5 * pow(q, p);
+}
+
+inline Real dfP(unsigned p, Real q) {
+  return 0.5 * p * pow(q, p - 1);
+}
+
+inline Real ddfP(unsigned p, Real q) {
+  return 0.5 * p * (p - 1) * pow(q, p - 2);
+}
+
+Real f(Real λ, unsigned p, unsigned s, Real q) {
+  return (1 - λ) * fP(p, q) + λ * fP(s, q);
+}
+
+Real df(Real λ, unsigned p, unsigned s, Real q) {
+  return (1 - λ) * dfP(p, q) + λ * dfP(s, q);
+}
+
+Real ddf(Real λ, unsigned p, unsigned s, Real q) {
+  return (1 - λ) * ddfP(p, q) + λ * ddfP(s, q);
+}
+
+FourierTransform::FourierTransform(unsigned n, Real Δω, Real Δτ, unsigned flags) : a(2 * n), â(n + 1), Δω(Δω), Δτ(Δτ) {
+  plan_r2c = fftw_plan_dft_r2c_1d(2 * n, a.data(), reinterpret_cast<fftw_complex*>(â.data()), flags);
+  plan_c2r = fftw_plan_dft_c2r_1d(2 * n, reinterpret_cast<fftw_complex*>(â.data()), a.data(), flags);
+}
+
+FourierTransform::~FourierTransform() {
+  fftw_destroy_plan(plan_r2c);
+  fftw_destroy_plan(plan_c2r);
+  fftw_cleanup();
+}
+
+std::vector<Complex> FourierTransform::fourier(const std::vector<Real>& c) {
+  a = c;
+  fftw_execute(plan_r2c);
+  std::vector<Complex> ĉ(â.size());
+  for (unsigned i = 0; i < â.size(); i++) {
+    ĉ[i] = â[i] * (Δτ * M_PI);
+  }
+  return ĉ;
+}
+
+std::vector<Real> FourierTransform::inverse(const std::vector<Complex>& ĉ) {
+  â = ĉ;
+  fftw_execute(plan_c2r);
+  std::vector<Real> c(a.size());
+  for (unsigned i = 0; i < a.size(); i++) {
+    c[i] = a[i] * (Δω / (2 * M_PI));
+  }
+  return c;
+}
+
+std::string fourierFile(std::string prefix, unsigned p, unsigned s, Real λ, Real τ₀, Real y, unsigned log2n, Real τₘₐₓ) {
+  return prefix + "_" + std::to_string(p) + "_" + std::to_string(s) + "_" + std::to_string(λ) + "_" + std::to_string(τ₀) + "_" + std::to_string(y) + "_" + std::to_string(log2n) + "_" + std::to_string(τₘₐₓ) + ".dat";
+}
+
+Real energy(const std::vector<Real>& C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ, Real y, Real Δτ) {
+  Real e = 0;
+
+  for (unsigned i = 0; i < C.size() / 2; i++) {
+    e += y * R[i] * df(λ, p, s, C[i]) * M_PI * Δτ;
+  }
+
+  return e;
+}
+
+std::tuple<std::vector<Complex>, std::vector<Complex>> RddfCtdfCt(FourierTransform& fft, const std::vector<Real>& C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ) {
+  std::vector<Real> RddfC(C.size());
+  for (unsigned i = 0; i < C.size(); i++) {
+    RddfC[i] = R[i] * ddf(λ, p, s, C[i]);
+  }
+  std::vector<Complex> RddfCt = fft.fourier(RddfC);
+
+  std::vector<Real> dfC(C.size());
+  for (unsigned i = 0; i < C.size(); i++) {
+    dfC[i] = df(λ, p, s, C[i]);
+  }
+  std::vector<Complex> dfCt = fft.fourier(dfC);
+
+  return {RddfCt, dfCt};
+}
diff --git a/fourier.hpp b/fourier.hpp
new file mode 100644
index 0000000..86335f7
--- /dev/null
+++ b/fourier.hpp
@@ -0,0 +1,32 @@
+#pragma once
+#include <cmath>
+#include <fftw3.h>
+#include <complex>
+#include <vector>
+
+using Real = double;
+using Complex = std::complex<Real>;
+using namespace std::complex_literals;
+
+Real f(Real λ, unsigned p, unsigned s, Real q);
+Real df(Real λ, unsigned p, unsigned s, Real q);
+Real ddf(Real λ, unsigned p, unsigned s, Real q);
+
+class FourierTransform {
+private:
+  std::vector<Real> a;
+  std::vector<Complex> â;
+  fftw_plan plan_r2c;
+  fftw_plan plan_c2r;
+  Real Δω;
+  Real Δτ;
+public:
+  FourierTransform(unsigned n, Real Δω, Real Δτ, unsigned flags = 0);
+  ~FourierTransform();
+  std::vector<Complex> fourier(const std::vector<Real>& c);
+  std::vector<Real> inverse(const std::vector<Complex>& ĉ);
+};
+
+std::string fourierFile(std::string prefix, unsigned p, unsigned s, Real λ, Real τ₀, Real y, unsigned log2n, Real τₘₐₓ);
+Real energy(const std::vector<Real>& C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ, Real y, Real Δτ);
+std::tuple<std::vector<Complex>, std::vector<Complex>> RddfCtdfCt(FourierTransform& fft, const std::vector<Real>& C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ);
diff --git a/fourier_integrator.cpp b/fourier_integrator.cpp
index 22866f2..86c3b24 100644
--- a/fourier_integrator.cpp
+++ b/fourier_integrator.cpp
@@ -1,80 +1,8 @@
+#include "fourier.hpp"
 #include <getopt.h>
-#include <vector>
-#include <cmath>
 #include <iostream>
-#include <fftw3.h>
-#include <complex>
 #include <fstream>
 
-using Real = double;
-using Complex = std::complex<Real>;
-using namespace std::complex_literals;
-
-inline Real fP(unsigned p, Real q) {
-  return 0.5 * pow(q, p);
-}
-
-inline Real dfP(unsigned p, Real q) {
-  return 0.5 * p * pow(q, p - 1);
-}
-
-inline Real ddfP(unsigned p, Real q) {
-  return 0.5 * p * (p - 1) * pow(q, p - 2);
-}
-
-inline Real f(Real λ, unsigned p, unsigned s, Real q) {
-  return (1 - λ) * fP(p, q) + λ * fP(s, q);
-}
-
-inline Real df(Real λ, unsigned p, unsigned s, Real q) {
-  return (1 - λ) * dfP(p, q) + λ * dfP(s, q);
-}
-
-inline Real ddf(Real λ, unsigned p, unsigned s, Real q) {
-  return (1 - λ) * ddfP(p, q) + λ * ddfP(s, q);
-}
-
-class FourierTransform {
-private:
-  std::vector<Real> a;
-  std::vector<Complex> â;
-  fftw_plan plan_r2c;
-  fftw_plan plan_c2r;
-  Real Δω;
-  Real Δτ;
-public:
-  FourierTransform(unsigned n, Real Δω, Real Δτ) : a(2 * n), â(n + 1), Δω(Δω), Δτ(Δτ) {
-    plan_r2c = fftw_plan_dft_r2c_1d(2 * n, a.data(), reinterpret_cast<fftw_complex*>(â.data()), 0);
-    plan_c2r = fftw_plan_dft_c2r_1d(2 * n, reinterpret_cast<fftw_complex*>(â.data()), a.data(), 0);
-  }
-
-  ~FourierTransform() {
-    fftw_destroy_plan(plan_r2c);
-    fftw_destroy_plan(plan_c2r);
-    fftw_cleanup();
-  }
-
-  std::vector<Complex> fourier(const std::vector<Real>& c) {
-    a = c;
-    fftw_execute(plan_r2c);
-    std::vector<Complex> ĉ(â.size());
-    for (unsigned i = 0; i < â.size(); i++) {
-      ĉ[i] = â[i] * (Δτ * M_PI);
-    }
-    return ĉ;
-  }
-
-  std::vector<Real> inverse(const std::vector<Complex>& ĉ) {
-    â = ĉ;
-    fftw_execute(plan_c2r);
-    std::vector<Real> c(a.size());
-    for (unsigned i = 0; i < a.size(); i++) {
-      c[i] = a[i] * (Δω / (2 * M_PI));
-    }
-    return c;
-  }
-};
-
 int main(int argc, char* argv[]) {
   unsigned p = 2;
   unsigned s = 2;
@@ -147,6 +75,10 @@ int main(int argc, char* argv[]) {
   std::vector<Real> R(2 * n);
 
   FourierTransform fft(n, Δω, Δτ);
+  std::vector<Complex> Ct;
+  std::vector<Complex> Rt;
+
+  Real y = y₀;
 
   if (!loadData) {
     // start from the exact solution for τ₀ = 0
@@ -158,37 +90,30 @@ int main(int argc, char* argv[]) {
       }
       R[i] = exp(-z * τ);
     }
+    Ct = fft.fourier(C);
+    Rt = fft.fourier(R);
   } else {
-    std::string file_end = std::to_string(p) + "_" + std::to_string(s) + "_" + std::to_string(λ) + "_" + std::to_string(τ₀) + "_" + std::to_string(y₀) + "_" + std::to_string(log2n) + "_" + std::to_string(τₘₐₓ) + ".dat";
-    std::ifstream cfile("C_"+file_end, std::ios::binary);
+    std::ifstream cfile(fourierFile("C", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::binary);
     cfile.read((char*)(C.data()), C.size() * sizeof(Real));
     cfile.close();
-    std::ifstream rfile("R_"+file_end, std::ios::binary);
+    std::ifstream rfile(fourierFile("R", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::binary);
     rfile.read((char*)(R.data()), R.size() * sizeof(Real));
     rfile.close();
-  }
 
-  std::vector<Complex> Ct = fft.fourier(C);
-  std::vector<Complex> Rt = fft.fourier(R);
+    Ct = fft.fourier(C);
+    Rt = fft.fourier(R);
 
-  Real y = y₀;
+    auto [RddfCt, dfCt] = RddfCtdfCt(fft, C, R, p, s, λ);
+
+    z = ((Γ₀ * std::conj(Rt[0]) + pow(y, 2) * (RddfCt[0] * Ct[0] + dfCt[0] * std::conj(Rt[0]))) / Ct[0]).real();
+  }
 
   while (y += Δy, y <= yₘₐₓ) {
     Real ΔC = 1;;
     unsigned it = 0;
     while (sqrt(ΔC / C.size()) > ε) {
       it++;
-      std::vector<Real> RddfC(C.size());
-      for (unsigned i = 0; i < C.size(); i++) {
-        RddfC[i] = R[i] * ddf(λ, p, s, C[i]);
-      }
-      std::vector<Complex> RddfCt = fft.fourier(RddfC);
-
-      std::vector<Real> dfC(C.size());
-      for (unsigned i = 0; i < C.size(); i++) {
-        dfC[i] = df(λ, p, s, C[i]);
-      }
-      std::vector<Complex> dfCt = fft.fourier(dfC);
+      auto [RddfCt, dfCt] = RddfCtdfCt(fft, C, R, p, s, λ);
 
       for (unsigned i = 0; i < Rt.size(); i++) {
         Real ω = i * Δω;
@@ -230,21 +155,15 @@ int main(int argc, char* argv[]) {
       }
     }
 
-    Real energy = 0;
-
-    for (unsigned i = 0; i < n; i++) {
-      energy += y * R[i] * df(λ, p, s, C[i]) * M_PI * Δτ;
-    }
-
-    std::cerr << "y " << y << " " << energy << std::endl;
+    Real e = energy(C, R, p, s, λ, y, Δτ);
 
-    std::string file_end = std::to_string(p) + "_" + std::to_string(s) + "_" + std::to_string(λ) + "_" + std::to_string(τ₀) + "_" + std::to_string(y) + "_" + std::to_string(log2n) + "_" + std::to_string(τₘₐₓ) + ".dat";
+    std::cerr << "y " << y << " " << e << " " << z << std::endl;
 
-    std::ofstream outfile("C_" + file_end, std::ios::out | std::ios::binary);
+    std::ofstream outfile(fourierFile("C", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::out | std::ios::binary);
     outfile.write((const char*)(C.data()), C.size() * sizeof(Real));
     outfile.close();
 
-    std::ofstream outfileR("R_" + file_end, std::ios::out | std::ios::binary);
+    std::ofstream outfileR(fourierFile("R", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::out | std::ios::binary);
     outfileR.write((const char*)(R.data()), R.size() * sizeof(Real));
     outfileR.close();
   }
diff --git a/get_energy.cpp b/get_energy.cpp
index 6164a6d..a388e0c 100644
--- a/get_energy.cpp
+++ b/get_energy.cpp
@@ -1,80 +1,8 @@
+#include "fourier.hpp"
 #include <getopt.h>
-#include <vector>
-#include <cmath>
 #include <iostream>
-#include <fftw3.h>
-#include <complex>
 #include <fstream>
 
-using Real = double;
-using Complex = std::complex<Real>;
-using namespace std::complex_literals;
-
-inline Real fP(unsigned p, Real q) {
-  return 0.5 * pow(q, p);
-}
-
-inline Real dfP(unsigned p, Real q) {
-  return 0.5 * p * pow(q, p - 1);
-}
-
-inline Real ddfP(unsigned p, Real q) {
-  return 0.5 * p * (p - 1) * pow(q, p - 2);
-}
-
-inline Real f(Real λ, unsigned p, unsigned s, Real q) {
-  return (1 - λ) * fP(p, q) + λ * fP(s, q);
-}
-
-inline Real df(Real λ, unsigned p, unsigned s, Real q) {
-  return (1 - λ) * dfP(p, q) + λ * dfP(s, q);
-}
-
-inline Real ddf(Real λ, unsigned p, unsigned s, Real q) {
-  return (1 - λ) * ddfP(p, q) + λ * ddfP(s, q);
-}
-
-class FourierTransform {
-private:
-  std::vector<Real> a;
-  std::vector<Complex> â;
-  fftw_plan plan_r2c;
-  fftw_plan plan_c2r;
-  Real Δω;
-  Real Δτ;
-public:
-  FourierTransform(unsigned n, Real Δω, Real Δτ, unsigned flags = 0) : a(2 * n), â(n + 1), Δω(Δω), Δτ(Δτ) {
-    plan_r2c = fftw_plan_dft_r2c_1d(2 * n, a.data(), reinterpret_cast<fftw_complex*>(â.data()), flags);
-    plan_c2r = fftw_plan_dft_c2r_1d(2 * n, reinterpret_cast<fftw_complex*>(â.data()), a.data(), flags);
-  }
-
-  ~FourierTransform() {
-    fftw_destroy_plan(plan_r2c);
-    fftw_destroy_plan(plan_c2r);
-    fftw_cleanup();
-  }
-
-  std::vector<Complex> fourier(const std::vector<Real>& c) {
-    a = c;
-    fftw_execute(plan_r2c);
-    std::vector<Complex> ĉ(â.size());
-    for (unsigned i = 0; i < â.size(); i++) {
-      ĉ[i] = â[i] * (Δτ * M_PI);
-    }
-    return ĉ;
-  }
-
-  std::vector<Real> inverse(const std::vector<Complex>& ĉ) {
-    â = ĉ;
-    fftw_execute(plan_c2r);
-    std::vector<Real> c(a.size());
-    for (unsigned i = 0; i < a.size(); i++) {
-      c[i] = a[i] * (Δω / (2 * M_PI));
-    }
-    return c;
-  }
-};
-
 int main(int argc, char* argv[]) {
   unsigned p = 2;
   unsigned s = 2;
@@ -133,24 +61,25 @@ int main(int argc, char* argv[]) {
     std::vector<Real> C(2 * n);
     std::vector<Real> R(2 * n);
 
-    std::string file_end = std::to_string(p) + "_" + std::to_string(s) + "_" + std::to_string(λ) + "_" + std::to_string(τ₀) + "_" + std::to_string(y) + "_" + std::to_string(log2n) + "_" + std::to_string(τₘₐₓ) + ".dat";
-    std::ifstream cfile("C_"+file_end, std::ios::binary);
+    std::ifstream cfile(fourierFile("C", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::binary);
     if (cfile.is_open()) {
-    cfile.read((char*)(C.data()), C.size() * sizeof(Real));
-    cfile.close();
-    std::ifstream rfile("R_"+file_end, std::ios::binary);
-    rfile.read((char*)(R.data()), R.size() * sizeof(Real));
-    rfile.close();
+      cfile.read((char*)(C.data()), C.size() * sizeof(Real));
+      cfile.close();
 
-    Real energy = 0;
+      std::ifstream rfile(fourierFile("R", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::binary);
+      rfile.read((char*)(R.data()), R.size() * sizeof(Real));
+      rfile.close();
 
-    for (unsigned i = 0; i < n; i++) {
-      energy += y * R[i] * df(λ, p, s, C[i]) * M_PI * Δτ;
-    }
+      Real e = energy(C, R, p, s, λ, y, Δτ);
+
+      std::vector<Complex> Ct = fft.fourier(C);
+      std::vector<Complex> Rt = fft.fourier(R);
+
+      auto [RddfCt, dfCt] = RddfCtdfCt(fft, C, R, p, s, λ);
 
-    std::vector<Complex> Ct = fft.fourier(C);
+      Real z = ((std::conj(Rt[0]) + pow(y, 2) * (RddfCt[0] * Ct[0] + dfCt[0] * std::conj(Rt[0]))) / Ct[0]).real();
 
-    std::cout << y << " " << energy << " " << Ct[0].real() << std::endl;
+      std::cout << y << " " << e << " " << Ct[0].real() << " " << z << std::endl;
     }
   }