1 files changed, 86 insertions, 0 deletions
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};
+}