def test_delete_col5(setup): s1 = setup.s1 nc = s1.shape[1] s1[1, [1, 2, 3]] = 1 assert s1.nnz == 3 s1.delete_columns(2) assert s1.nnz == 2 assert s1.shape[1] == nc - 1 assert np.all(s1.col[array_arange(s1.ptr, n=s1.ncol)] < 3) s1.delete_columns(2, True) assert s1.nnz == 1 assert s1.shape[1] == nc - 1 assert np.all(s1.col[array_arange(s1.ptr, n=s1.ncol)] < 2) # Delete a non-existing column s1.delete_columns(100000, True) assert s1.nnz == 1 assert s1.shape[1] == nc - 1 s1.empty()
def real_space_coupling(self, ret_indices=False): """ Return the real-space coupling parent where they fold into the parent real-space unit cell The resulting parent object only contains the inner-cell couplings for the elements that couple out of the real-space matrix. Parameters ---------- ret_indices : bool, optional if true, also return the atomic indices (corresponding to `real_space_parent`) that encompass the coupling matrix Returns ------- parent : parent object only retaining the elements of the atoms that couple out of the primary unit cell atom_index : indices for the atoms that couple out of the geometry (`ret_indices`) """ opt = self._options s_ax = opt['semi_axis'] k_ax = opt['k_axis'] PC = self.parent.tile(max(1, self._unfold[s_ax]), s_ax).tile(self._unfold[k_ax], k_ax) # Geometry short-hand g = PC.geometry # Remove all inner-cell couplings (0, 0, 0) to figure out the # elements that couple out of the real-space region n = PC.shape[0] idx = g.sc.sc_index([0, 0, 0]) cols = _a.arangei(n) + idx * n csr = PC._csr.copy([0]) # we just want the sparse pattern, so forget about the other elements csr.delete_columns(cols, keep_shape=True) # Now PC only contains couplings along the k and semi-inf directions # Extract the connecting orbitals and reduce them to unique atomic indices orbs = g.osc2uc(csr.col[array_arange(csr.ptr[:-1], n=csr.ncol)], True) atom_idx = g.o2a(orbs, True) # Only retain coupling atoms PC = PC.sub(atom_idx) # Remove all out-of-cell couplings such that we only have inner-cell couplings. nsc = PC.nsc.copy() nsc[s_ax] = 1 nsc[k_ax] = 1 PC.set_nsc(nsc) if ret_indices: return PC, atom_idx return PC
def _mulliken(self): # Calculate the Mulliken elements # First we re-create the sparse matrix as required for csr_matrix ptr = self._csr.ptr ncol = self._csr.ncol # Indices of non-zero elements idx = array_arange(ptr[:-1], n=ncol) # Create the new pointer array new_ptr = _a.emptyi(len(ptr)) new_ptr[0] = 0 col = self._csr.col[idx] _a.cumsumi(ncol, out=new_ptr[1:]) # The shape of the matrices shape = self.shape[:2] # Create list of charges to be returned Q = list() if self.orthogonal: # We only need the diagonal elements S = csr_matrix(shape, dtype=self.dtype) S.setdiag(1.) for i in range(self.shape[2]): DM = csr_matrix((self._csr._D[idx, i], col, new_ptr), shape=shape) Q.append(DM.multiply(S)) Q[-1].eliminate_zeros() else: # We now what S is and do it element-wise. q = self._csr._D[idx, :-1] * self._csr._D[idx, self.S_idx].reshape( -1, 1) for i in range(q.shape[1]): Q.append(csr_matrix((q[:, i], col, new_ptr), shape=shape)) Q[-1].eliminate_zeros() return Q
def density(self, grid, spinor=None, tol=1e-7, eta=False): r""" Expand the density matrix to the charge density on a grid This routine calculates the real-space density components on a specified grid. This is an *in-place* operation that *adds* to the current values in the grid. Note: To calculate :math:`\rho(\mathbf r)` in a unit-cell different from the originating geometry, simply pass a grid with a unit-cell different than the originating supercell. The real-space density is calculated as: .. math:: \rho(\mathbf r) = \sum_{\nu\mu}\phi_\nu(\mathbf r)\phi_\mu(\mathbf r) D_{\nu\mu} While for non-collinear/spin-orbit calculations the density is determined from the spinor component (`spinor`) by .. math:: \rho_{\boldsymbol\sigma}(\mathbf r) = \sum_{\nu\mu}\phi_\nu(\mathbf r)\phi_\mu(\mathbf r) \sum_\alpha [\boldsymbol\sigma \mathbf \rho_{\nu\mu}]_{\alpha\alpha} Here :math:`\boldsymbol\sigma` corresponds to a spinor operator to extract relevant quantities. By passing the identity matrix the total charge is added. By using the Pauli matrix :math:`\boldsymbol\sigma_x` only the :math:`x` component of the density is added to the grid (see `Spin.X`). Parameters ---------- grid : Grid the grid on which to add the density (the density is in ``e/Ang^3``) spinor : (2,) or (2, 2), optional the spinor matrix to obtain the diagonal components of the density. For un-polarized density matrices this keyword has no influence. For spin-polarized it *has* to be either 1 integer or a vector of length 2 (defaults to total density). For non-collinear/spin-orbit density matrices it has to be a 2x2 matrix (defaults to total density). tol : float, optional DM tolerance for accepted values. For all density matrix elements with absolute values below the tolerance, they will be treated as strictly zeros. eta: bool, optional show a progressbar on stdout """ try: # Once unique has the axis keyword, we know we can safely # use it in this routine # Otherwise we raise an ImportError unique([[0, 1], [2, 3]], axis=0) except: raise NotImplementedError( self.__class__.__name__ + '.density requires numpy >= 1.13, either update ' 'numpy or do not use this function!') geometry = self.geometry # Check that the atomic coordinates, really are all within the intrinsic supercell. # If not, it may mean that the DM does not conform to the primary unit-cell paradigm # of matrix elements. It complicates things. fxyz = geometry.fxyz f_min = fxyz.min() f_max = fxyz.max() if f_min < 0 or 1. < f_max: warn( self.__class__.__name__ + '.density has been passed a geometry where some coordinates are ' 'outside the primary unit-cell. This may potentially lead to problems! ' 'Double check the charge density!') del fxyz, f_min, f_max # Extract sub variables used throughout the loop shape = _a.asarrayi(grid.shape) dcell = grid.dcell # Sparse matrix data csr = self._csr # In the following we don't care about division # So 1) save error state, 2) turn off divide by 0, 3) calculate, 4) turn on old error state old_err = np.seterr(divide='ignore', invalid='ignore') # Placeholder for the resulting coefficients DM = None if self.spin.kind > Spin.POLARIZED: if spinor is None: # Default to the total density spinor = np.identity(2, dtype=np.complex128) else: spinor = _a.arrayz(spinor) if spinor.size != 4 or spinor.ndim != 2: raise ValueError( self.__class__.__name__ + '.density with NC/SO spin, requires a 2x2 matrix.') DM = _a.emptyz([self.nnz, 2, 2]) idx = array_arange(csr.ptr[:-1], n=csr.ncol) if self.spin.kind == Spin.NONCOLINEAR: # non-collinear DM[:, 0, 0] = csr._D[idx, 0] DM[:, 1, 1] = csr._D[idx, 1] DM[:, 1, 0] = csr._D[idx, 2] - 1j * csr._D[idx, 3] #TODO check sign here! DM[:, 0, 1] = np.conj(DM[:, 1, 0]) else: # spin-orbit DM[:, 0, 0] = csr._D[idx, 0] + 1j * csr._D[idx, 4] DM[:, 1, 1] = csr._D[idx, 1] + 1j * csr._D[idx, 5] DM[:, 1, 0] = csr._D[idx, 2] - 1j * csr._D[idx, 3] #TODO check sign here! DM[:, 0, 1] = csr._D[idx, 6] + 1j * csr._D[idx, 7] # Perform dot-product with spinor, and take out the diagonal real part DM = dot(DM, spinor.T)[:, [0, 1], [0, 1]].sum(1).real elif self.spin.kind == Spin.POLARIZED: if spinor is None: spinor = _a.onesd(2) elif isinstance(spinor, Integral): # extract the provided spin-polarization s = _a.zerosd(2) s[spinor] = 1. spinor = s else: spinor = _a.arrayd(spinor) if spinor.size != 2 or spinor.ndim != 1: raise ValueError( self.__class__.__name__ + '.density with polarized spin, requires spinor ' 'argument as an integer, or a vector of length 2') idx = array_arange(csr.ptr[:-1], n=csr.ncol) DM = csr._D[idx, 0] * spinor[0] + csr._D[idx, 1] * spinor[1] else: idx = array_arange(csr.ptr[:-1], n=csr.ncol) DM = csr._D[idx, 0] # Create the DM csr matrix. csrDM = csr_matrix( (DM, csr.col[idx], np.insert(np.cumsum(csr.ncol), 0, 0)), shape=(self.shape[:2]), dtype=DM.dtype) # Clean-up del idx, DM # To heavily speed up the construction of the density we can recreate # the sparse csrDM matrix by summing the lower and upper triangular part. # This means we only traverse the sparse UPPER part of the DM matrix # I.e.: # psi_i * DM_{ij} * psi_j + psi_j * DM_{ji} * psi_i # is equal to: # psi_i * (DM_{ij} + DM_{ji}) * psi_j # Secondly, to ease the loops we extract the main diagonal (on-site terms) # and store this for separate usage csr_sum = [None] * geometry.n_s no = geometry.no primary_i_s = geometry.sc_index([0, 0, 0]) for i_s in range(geometry.n_s): # Extract the csr matrix o_start, o_end = i_s * no, (i_s + 1) * no csr = csrDM[:, o_start:o_end] if i_s == primary_i_s: csr_sum[i_s] = triu(csr) + tril(csr, -1).transpose() else: csr_sum[i_s] = csr # Recreate the column-stacked csr matrix csrDM = ss_hstack(csr_sum, format='csr') del csr, csr_sum # Remove all zero elements (note we use the tolerance here!) csrDM.data = np.where(np.fabs(csrDM.data) > tol, csrDM.data, 0.) # Eliminate zeros and sort indices etc. csrDM.eliminate_zeros() csrDM.sort_indices() csrDM.prune() # 1. Ensure the grid has a geometry associated with it sc = grid.sc.copy() if grid.geometry is None: # Create the actual geometry that encompass the grid ia, xyz, _ = geometry.within_inf(sc) if len(ia) > 0: grid.set_geometry(Geometry(xyz, geometry.atom[ia], sc=sc)) # Instead of looping all atoms in the supercell we find the exact atoms # and their supercell indices. add_R = _a.zerosd(3) + geometry.maxR() # Calculate the required additional vectors required to increase the fictitious # supercell by add_R in each direction. # For extremely skewed lattices this will be way too much, hence we make # them square. o = sc.toCuboid(True) sc = SuperCell(o._v, origo=o.origo) + np.diag(2 * add_R) sc.origo -= add_R # Retrieve all atoms within the grid supercell # (and the neighbours that connect into the cell) IA, XYZ, ISC = geometry.within_inf(sc) # Retrieve progressbar eta = tqdm_eta(len(IA), self.__class__.__name__ + '.density', 'atom', eta) cell = geometry.cell atom = geometry.atom axyz = geometry.axyz a2o = geometry.a2o def xyz2spherical(xyz, offset): """ Calculate the spherical coordinates from indices """ rx = xyz[:, 0] - offset[0] ry = xyz[:, 1] - offset[1] rz = xyz[:, 2] - offset[2] # Calculate radius ** 2 xyz_to_spherical_cos_phi(rx, ry, rz) return rx, ry, rz def xyz2sphericalR(xyz, offset, R): """ Calculate the spherical coordinates from indices """ rx = xyz[:, 0] - offset[0] idx = indices_fabs_le(rx, R) ry = xyz[idx, 1] - offset[1] ix = indices_fabs_le(ry, R) ry = ry[ix] idx = idx[ix] rz = xyz[idx, 2] - offset[2] ix = indices_fabs_le(rz, R) ry = ry[ix] rz = rz[ix] idx = idx[ix] if len(idx) == 0: return [], [], [], [] rx = rx[idx] # Calculate radius ** 2 ix = indices_le(rx**2 + ry**2 + rz**2, R**2) idx = idx[ix] if len(idx) == 0: return [], [], [], [] rx = rx[ix] ry = ry[ix] rz = rz[ix] xyz_to_spherical_cos_phi(rx, ry, rz) return idx, rx, ry, rz # Looping atoms in the sparse pattern is better since we can pre-calculate # the radial parts and then add them. # First create a SparseOrbital matrix, then convert to SparseAtom spO = SparseOrbital(geometry, dtype=np.int16) spO._csr = SparseCSR(csrDM) spA = spO.toSparseAtom(dtype=np.int16) del spO na = geometry.na # Remove the diagonal part of the sparse atom matrix off = na * primary_i_s for ia in range(na): del spA[ia, off + ia] # Get pointers and delete the atomic sparse pattern # The below complexity is because we are not finalizing spA csr = spA._csr a_ptr = np.insert(_a.cumsumi(csr.ncol), 0, 0) a_col = csr.col[array_arange(csr.ptr, n=csr.ncol)] del spA, csr # Get offset in supercell in orbitals off = geometry.no * primary_i_s origo = grid.origo # TODO sum the non-origo atoms to the csrDM matrix # this would further decrease the loops required. # Loop over all atoms in the grid-cell for ia, ia_xyz, isc in zip(IA, XYZ - origo.reshape(1, 3), ISC): # Get current atom ia_atom = atom[ia] IO = a2o(ia) IO_range = range(ia_atom.no) cell_offset = (cell * isc.reshape(3, 1)).sum(0) - origo # Extract maximum R R = ia_atom.maxR() if R <= 0.: warn("Atom '{}' does not have a wave-function, skipping atom.". format(ia_atom)) eta.update() continue # Retrieve indices of the grid for the atomic shape idx = grid.index(ia_atom.toSphere(ia_xyz)) # Now we have the indices for the largest orbital on the atom # Subsequently we have to loop the orbitals and the # connecting orbitals # Then we find the indices that overlap with these indices # First reduce indices to inside the grid-cell idx[idx[:, 0] < 0, 0] = 0 idx[shape[0] <= idx[:, 0], 0] = shape[0] - 1 idx[idx[:, 1] < 0, 1] = 0 idx[shape[1] <= idx[:, 1], 1] = shape[1] - 1 idx[idx[:, 2] < 0, 2] = 0 idx[shape[2] <= idx[:, 2], 2] = shape[2] - 1 # Remove duplicates, requires numpy >= 1.13 idx = unique(idx, axis=0) if len(idx) == 0: eta.update() continue # Get real-space coordinates for the current atom # as well as the radial parts grid_xyz = dot(idx, dcell) # Perform loop on connection atoms # Allocate the DM_pj arrays # This will have a size equal to number of elements times number of # orbitals on this atom # In this way we do not have to calculate the psi_j multiple times DM_io = csrDM[IO:IO + ia_atom.no, :].tolil() DM_pj = _a.zerosd([ia_atom.no, grid_xyz.shape[0]]) # Now we perform the loop on the connections for this atom # Remark that we have removed the diagonal atom (it-self) # As that will be calculated in the end for ja in a_col[a_ptr[ia]:a_ptr[ia + 1]]: # Retrieve atom (which contains the orbitals) ja_atom = atom[ja % na] JO = a2o(ja) jR = ja_atom.maxR() # Get actual coordinate of the atom ja_xyz = axyz(ja) + cell_offset # Reduce the ia'th grid points to those that connects to the ja'th atom ja_idx, ja_r, ja_theta, ja_cos_phi = xyz2sphericalR( grid_xyz, ja_xyz, jR) if len(ja_idx) == 0: # Quick step continue # Loop on orbitals on this atom for jo in range(ja_atom.no): o = ja_atom.orbital[jo] oR = o.R # Downsize to the correct indices if jR - oR < 1e-6: ja_idx1 = ja_idx.view() ja_r1 = ja_r.view() ja_theta1 = ja_theta.view() ja_cos_phi1 = ja_cos_phi.view() else: ja_idx1 = indices_le(ja_r, oR) if len(ja_idx1) == 0: # Quick step continue # Reduce arrays ja_r1 = ja_r[ja_idx1] ja_theta1 = ja_theta[ja_idx1] ja_cos_phi1 = ja_cos_phi[ja_idx1] ja_idx1 = ja_idx[ja_idx1] # Calculate the psi_j component psi = o.psi_spher(ja_r1, ja_theta1, ja_cos_phi1, cos_phi=True) # Now add this orbital to all components for io in IO_range: DM_pj[io, ja_idx1] += DM_io[io, JO + jo] * psi # Temporary clean up del ja_idx, ja_r, ja_theta, ja_cos_phi del ja_idx1, ja_r1, ja_theta1, ja_cos_phi1, psi # Now we have all components for all orbitals connection to all orbitals on atom # ia. We simply need to add the diagonal components # Loop on the orbitals on this atom ia_r, ia_theta, ia_cos_phi = xyz2spherical(grid_xyz, ia_xyz) del grid_xyz for io in IO_range: # Only loop halve the range. # This is because: triu + tril(-1).transpose() # removes the lower half of the on-site matrix. for jo in range(io + 1, ia_atom.no): DM = DM_io[io, off + IO + jo] oj = ia_atom.orbital[jo] ojR = oj.R # Downsize to the correct indices if R - ojR < 1e-6: ja_idx1 = slice(None) ja_r1 = ia_r.view() ja_theta1 = ia_theta.view() ja_cos_phi1 = ia_cos_phi.view() else: ja_idx1 = indices_le(ia_r, ojR) if len(ja_idx1) == 0: # Quick step continue # Reduce arrays ja_r1 = ia_r[ja_idx1] ja_theta1 = ia_theta[ja_idx1] ja_cos_phi1 = ia_cos_phi[ja_idx1] # Calculate the psi_j component DM_pj[io, ja_idx1] += DM * oj.psi_spher( ja_r1, ja_theta1, ja_cos_phi1, cos_phi=True) # Calculate the psi_i component # Note that this one *also* zeroes points outside the shell # I.e. this step is important because it "nullifies" all but points where # orbital io is defined. psi = ia_atom.orbital[io].psi_spher(ia_r, ia_theta, ia_cos_phi, cos_phi=True) DM_pj[io, :] += DM_io[io, off + IO + io] * psi DM_pj[io, :] *= psi # Temporary clean up ja_idx1 = ja_r1 = ja_theta1 = ja_cos_phi1 = None del ia_r, ia_theta, ia_cos_phi, psi, DM_io # Now add the density grid.grid[idx[:, 0], idx[:, 1], idx[:, 2]] += DM_pj.sum(0) # Clean-up del DM_pj, idx eta.update() eta.close() # Reset the error code for division np.seterr(**old_err)
def orbital_momentum(self, projection='orbital', method='onsite'): r""" Calculate orbital angular momentum on either atoms or orbitals Currently this implementation equals the Siesta implementation in that the on-site approximation is enforced thus limiting the calculated quantities to obey the following conditions: 1. Same atom 2. :math:`l>0` 3. :math:`l_\nu \equiv l_\mu` 4. :math:`m_\nu \neq m_\mu` 5. :math:`\zeta_\nu \equiv \zeta_\mu` This allows one to sum the orbital angular moments on a per atom site. Parameters ---------- projection : {'orbital', 'atom'} whether the angular momentum is resolved per atom, or per orbital method : {'onsite'} method used to calculate the angular momentum Returns ------- numpy.ndarray orbital angular momentum with the last dimension equalling the :math:`L_x`, :math:`L_y` and :math:`L_z` components """ # Check that the spin configuration is correct if not self.spin.is_spinorbit: raise ValueError( f"{self.__class__.__name__}.orbital_momentum requires a spin-orbit matrix" ) # First we calculate orb_lmZ = _a.emptyi([self.no, 3]) for atom, idx in self.geometry.atoms.iter(True): # convert to FIRST orbital index per atom oidx = self.geometry.a2o(idx) # loop orbitals for io, orb in enumerate(atom): orb_lmZ[oidx + io, :] = orb.l, orb.m, orb.Z # Now we need to calculate the stuff DM = self.copy() # The Siesta convention *only* calculates contributions # in the primary unit-cell. DM.set_nsc([1] * 3) geom = DM.geometry csr = DM._csr # The siesta moments are only *on-site* per atom. # 1. create a logical index for the matrix elements # that is true for ia-ia interaction and false # otherwise idx = repeat(_a.arangei(geom.no), csr.ncol) aidx = geom.o2a(idx) # Sparse matrix indices for data sidx = array_arange(csr.ptr[:-1], n=csr.ncol, dtype=np.int32) jdx = csr.col[sidx] ajdx = geom.o2a(jdx) # Now only take the elements that are *on-site* and which are *not* # having the same m quantum numbers (if the orbital index is the same # it means they have the same m quantum number) # # 1. on the same atom # 2. l > 0 # 3. same quantum number l # 4. different quantum number m # 5. same zeta onsite_idx = ((aidx == ajdx) & \ (orb_lmZ[idx, 0] > 0) & \ (orb_lmZ[idx, 0] == orb_lmZ[jdx, 0]) & \ (orb_lmZ[idx, 1] != orb_lmZ[jdx, 1]) & \ (orb_lmZ[idx, 2] == orb_lmZ[jdx, 2])).nonzero()[0] # clean variables we don't need del aidx, ajdx # Now reduce arrays to the orbital connections that obey the # above criteria idx = idx[onsite_idx] idx_l = orb_lmZ[idx, 0] idx_m = orb_lmZ[idx, 1] jdx = jdx[onsite_idx] jdx_m = orb_lmZ[jdx, 1] sidx = sidx[onsite_idx] # Sum the spin-box diagonal imaginary parts DM = csr._D[sidx][:, [4, 5]].sum(1) # Define functions to calculate L projections def La(idx_l, DM, sub): if len(sub) == 0: return [] return (idx_l[sub] * (idx_l[sub] + 1) * 0.5)**0.5 * DM[sub] def Lb(idx_l, DM, sub): if len(sub) == 0: return return (idx_l[sub] * (idx_l[sub] + 1) - 2)**0.5 * 0.5 * DM[sub] def Lc(idx, idx_l, DM, sub): if len(sub) == 0: return [], [] sub = sub[idx_l[sub] >= 3] if len(sub) == 0: return [], [] return idx[sub], (idx_l[sub] * (idx_l[sub] + 1) - 6)**0.5 * 0.5 * DM[sub] # construct for different m # in Siesta the spin orbital angular momentum # is calculated by swapping i and j indices. # This is somewhat confusing to me, so I reversed everything. # This will probably add to the confusion when comparing the two # Additionally Siesta calculates L for <i|L|j> and then does: # L(:) = [L(3), -L(2), -L(1)] # Here we *directly* store the quantities used. # Pre-allocate the L_xyz quantity per orbital. L = np.zeros([geom.no, 3]) L0 = L[:, 0] L1 = L[:, 1] L2 = L[:, 2] # Pre-calculate all those which have m_i + m_j == 0 b = (idx_m + jdx_m == 0).nonzero()[0] subtract.at(L2, idx[b], idx_m[b] * DM[b]) del b # mi == 0 i_m = idx_m == 0 # mj == -1 sub = logical_and(i_m, jdx_m == -1).nonzero()[0] subtract.at(L0, idx[sub], La(idx_l, DM, sub)) # mj == 1 sub = logical_and(i_m, jdx_m == 1).nonzero()[0] add.at(L1, idx[sub], La(idx_l, DM, sub)) # mi == 1 i_m = idx_m == 1 # mj == -2 sub = logical_and(i_m, jdx_m == -2).nonzero()[0] subtract.at(L0, idx[sub], Lb(idx_l, DM, sub)) # mj == 0 sub = logical_and(i_m, jdx_m == 0).nonzero()[0] subtract.at(L1, idx[sub], La(idx_l, DM, sub)) # mj == 2 sub = logical_and(i_m, jdx_m == 2).nonzero()[0] add.at(L1, idx[sub], Lb(idx_l, DM, sub)) # mi == -1 i_m = idx_m == -1 # mj == -2 sub = logical_and(i_m, jdx_m == -2).nonzero()[0] add.at(L1, idx[sub], Lb(idx_l, DM, sub)) # mj == 0 sub = logical_and(i_m, jdx_m == 0).nonzero()[0] add.at(L0, idx[sub], La(idx_l, DM, sub)) # mj == 2 sub = logical_and(i_m, jdx_m == 2).nonzero()[0] add.at(L0, idx[sub], Lb(idx_l, DM, sub)) # mi == 2 i_m = idx_m == 2 # mj == -3 sub = logical_and(i_m, jdx_m == -3).nonzero()[0] subtract.at(L0, *Lc(idx, idx_l, DM, sub)) # mj == -1 sub = logical_and(i_m, jdx_m == -1).nonzero()[0] subtract.at(L0, idx[sub], Lb(idx_l, DM, sub)) # mj == 1 sub = logical_and(i_m, jdx_m == 1).nonzero()[0] subtract.at(L1, idx[sub], Lb(idx_l, DM, sub)) # mj == 3 sub = logical_and(i_m, jdx_m == 3).nonzero()[0] add.at(L1, *Lc(idx, idx_l, DM, sub)) # mi == -2 i_m = idx_m == -2 # mj == -3 sub = logical_and(i_m, jdx_m == -3).nonzero()[0] add.at(L1, *Lc(idx, idx_l, DM, sub)) # mj == -1 sub = logical_and(i_m, jdx_m == -1).nonzero()[0] subtract.at(L1, idx[sub], Lb(idx_l, DM, sub)) # mj == 1 sub = logical_and(i_m, jdx_m == 1).nonzero()[0] add.at(L0, idx[sub], Lb(idx_l, DM, sub)) # mj == 3 sub = logical_and(i_m, jdx_m == 3).nonzero()[0] add.at(L0, *Lc(idx, idx_l, DM, sub)) # mi == -3 i_m = idx_m == -3 # mj == -2 sub = logical_and(i_m, jdx_m == -2).nonzero()[0] subtract.at(L1, *Lc(idx, idx_l, DM, sub)) # mj == 2 sub = logical_and(i_m, jdx_m == 2).nonzero()[0] add.at(L0, *Lc(idx, idx_l, DM, sub)) # mi == 3 i_m = idx_m == 3 # mj == -2 sub = logical_and(i_m, jdx_m == -2).nonzero()[0] subtract.at(L0, *Lc(idx, idx_l, DM, sub)) # mj == 2 sub = logical_and(i_m, jdx_m == 2).nonzero()[0] subtract.at(L1, *Lc(idx, idx_l, DM, sub)) if "orbital" == projection: return L elif "atom" == projection: # Now perform summation per atom l = np.zeros([geom.na, 3], dtype=L.dtype) add.at(l, geom.o2a(np.arange(geom.no)), L) return l raise ValueError( f"{self.__class__.__name__}.orbital_momentum must define projection to be 'orbital' or 'atom'." )