Wave number and angular frequency

Since the FFTW3 stores the spectra from the zero-th wave number, I need to map the indices to the wave numbers \(k\) as follows:

src/domain.c

// wave numbers
//   0, 1, ..., N/2-1, -N/2, -N/2+1, ..., -2, -1
// e.g. glsize = 8
//   -> +0 +1 +2 +3 -4 -3 -2 -1
for(size_t dim = 0; dim < NDIMS; dim++){
  int * restrict waves = allwaves[dim];
  const int glsize = (int)domain->p_glsizes[dim];
  const int mysize = (int)domain->s_x1_mysizes[dim];
  const int offset = (int)domain->s_x1_offsets[dim];
  for(int n = 0; n < mysize; n++){
    waves[n] = n + offset;
    if(glsize / 2 <= waves[n]){
      // negative wave numbers
      waves[n] -= glsize;
    }
  }
}

Also for convenience, the angular frequency

\[\frac{2 \pi}{L} k\]

are computed and stored:

src/domain.c

for(size_t dim = 0; dim < NDIMS; dim++){
  const double length = domain->lengths[dim];
  const size_t mysize = domain->s_x1_mysizes[dim];
  const int * restrict waves = allwaves[dim];
  double * restrict freqs = allfreqs[dim];
  for(size_t n = 0; n < mysize; n++){
    freqs[n] = 2. * M_PI / length * waves[n];
  }
}