Formula: f_psp(r) = r * (r * V_loc(r) + Z_val) Example input: r=2.0 bohr, V_loc=-1.0 Ha, Z_val=3.0 Example output: f_psp(r)=2.0

Formula: dV_sph = 4*pi*r^2 Example input: r=2.0 bohr Example output: dV_sph=50.2654824574

Generate random wave functions.

Formula: rho_spin = ratio * rho_total Example input: ratio=0.3, rho_total=2.0 Example output: rho_spin=0.6

Formula: ratio = n_spin_target / n_total, fallback=0.5 when n_total~0 Example input: n_spin_target=3, n_total=10 Example output: ratio=0.3

Formula: n_target = n_occ - 0.5 * int rho_aug(r) dr Example input: n_occ=5.4, rho_aug_integral=0.8 Example output: n_target=5.0

Formula: N_occ = sum_{k,b} f_{k,b} Example input: [[2.0, 1.0], [2.0, 0.5]] Example output: N_occ=5.5

Map a types identifier to a list with a type id for each atom. types can be a single str, or a dictionary mapping chemical symbols and/or ato

Formula: occ_up(k) = occ_combined(k) occ_dn(k) = occ_combined(k + n_k) Example input: occ_combined=[[0.9],[0.8],[0.7],[0.6]], n_k=2 Example output: oc

Complex-rotate coefficients compensating discontinuous phase shift. This changes the coefficients to counteract the phase discontinuity of ov

Wrap to [0, 1)

Construct density-mixer object. Parameters: beta: float Mixing parameter between zero and one (one is most a