The charge-flipping algorithm in crystallography

The charge-flipping algorithm (CFA) is a member of the diverse family of dual-space iterative phasing algorithms. These algorithms use alternating modifications in direct and reciprocal space to find a solution to the phase problem. The current state-of-the-art CFA is reviewed and it is put in the context of related dual-space algorithms with relevance for crystallography. The CFA has found applications in many crystallographic problems. The principal applications in various fields are described with sections devoted to routine structure solution, the solution of complex structures from powder diffraction data, the solution of incommensurately modulated crystals and quasicrystals, macromolecular crystallography and single-particle imaging.