# Speed

### From FEFF

Generally, fms matrix inversion takes most of the computation time. In real space, for every
energy point feff does one matrix inversion of order nclus*(lmax+1)^{2}*nsp. In reciprocal space, for every energy point feff does nkp matrix inversions of order nu*(lmax+1)^{2}*nsp. Here, nu is the number of atoms in the unit cell, nkp the number of k-vectors in the mesh, nclus the number of atoms in the real space cluster, lmax the angular momentum cutoff, nsp the number of spins (1 or 2). So, the relative speed is something like (nu=nclus)^{a} *nkp , where a is the scaling of matrix inversion. In general, unit cells with more atoms (nu) are larger and therefore require less k-vectors (nkp). However, I don't have a general rule for speed. Obviously, for very small systems (1-5 atoms in the unit cell), RECIPROCAL is faster. For larger systems, more study is needed. Also, it's worth noting that pot sometimes can get slow in reciprocal space.