torchref.base.fourier.fft module
FFT operations for crystallographic calculations.
Functions for forward and inverse Fourier transforms following crystallographic sign conventions.
- torchref.base.fourier.fft.fft(reciprocal_grid, volume=None)[source]
Perform FFT to obtain real space electron density.
Uses fftn with norm=”forward” to match crystallographic sign convention directly, avoiding expensive flip/roll operations.
Crystallographic convention: ρ(r) = (1/V) Σ F(h) exp(-2πi h·r)
- PyTorch fftn with norm=”forward” gives:
fftn(x)[n] = (1/N) Σ_k x[k] exp(-2πi k·n/N)
When input structure factors F are correctly scaled (with V/N factor from ifft), we need to multiply by N/V to recover the original electron density:
ρ = fftn(F) * (N / V)
- Parameters:
reciprocal_grid (torch.Tensor) – Reciprocal space grid of shape (Nx, Ny, Nz) or (B, Nx, Ny, Nz). Expected to contain correctly scaled structure factors (from ifft with volume).
volume (float, optional) – Unit cell volume in ų. If provided, result is scaled by N/V to give correctly normalized electron density.
- Returns:
Real-valued tensor of electron density with same shape as input.
- Return type:
- torchref.base.fourier.fft.ifft(real_space_map, volume=None)[source]
Perform inverse FFT to obtain reciprocal space structure factors.
Crystallographic convention: F(h) = Σ ρ(r) exp(+2πi h·r) * ΔV where ΔV = V_cell / N is the voxel volume.
- PyTorch ifftn with norm=”forward” gives unnormalized DFT:
DFT[k] = Σ x[n] exp(+2πi k·n/N)
- To obtain correctly scaled structure factors, we multiply by voxel volume:
F(h) = DFT(ρ) * (V_cell / N)
- Parameters:
real_space_map (torch.Tensor) – Real space electron density map of shape (Nx, Ny, Nz) or (B, Nx, Ny, Nz).
volume (float, optional) – Unit cell volume in ų. If provided, result is scaled by voxel volume (V_cell / N_total) to give correctly normalized structure factors.
- Returns:
Complex-valued tensor of structure factors with same shape as input.
- Return type: