def base_multipole_fields(self, options): mol = cache.molecule["pna"] cppe_state = CppeState(options, mol, lambda s: None) cppe_state.calculate_static_energies_and_fields() multipole_fields = cppe_state.multipole_fields potentials = cppe_state.potentials polsites = get_polarizable_sites(potentials) ref = np.zeros((len(potentials), 3)) for i, p1 in enumerate(polsites): for j, p2 in enumerate(polsites): if not p1.is_polarizable: continue if p1.index == p2.index: continue if p1.excludes_site(p2.index): continue diff = p1.position - p2.position for m in p2.multipoles: M_full = symmetry.unfold_tensor(m.values, m.k) if options.get("damp_multipole", False): a_i = p1.polarizability.isotropic_value a_j = p2.polarizability.isotropic_value damp = cppe_state.options["damping_factor_multipole"] a = 1/(a_i*a_j)**(1/6) * damp ref[p1.index, :] += polfields.thole_exp_field( diff, m.k, M_full, 1, a) else: ref[p1.index, :] += polfields.field( diff, m.k, M_full, 1) np.testing.assert_allclose(ref.flatten(), multipole_fields, atol=1e-14)
def test_solver_by_inversion(self): mol = cache.molecule["pna"] options = {"potfile": self.potfile_path, "induced_thresh": 1e-12} cppe_state = CppeState(options, mol, print_callback) cppe_state.calculate_static_energies_and_fields() static_fields = cppe_state.static_fields zeros = np.zeros_like(static_fields) cppe_state.update_induced_moments(zeros, False) potentials = cppe_state.potentials polsites = get_polarizable_sites(potentials) npolsites = cppe_state.get_polarizable_site_number() bmat = np.zeros((3 * npolsites, 3 * npolsites)) for s1, pot1 in enumerate(polsites): pol = pot1.polarizability inv_alpha = triangle_to_mat(pol.values) bmat[block(s1, s1)] = np.linalg.inv(inv_alpha) for s2, pot2 in enumerate(polsites): if pot1.excludes_site(pot2.index) or s1 == s2: continue diff = pot2.position - pot1.position T12 = T_recursive(2, diff) if s1 > s2: bmat[block(s1, s2)] = -triangle_to_mat(T12) bmat[block(s2, s1)] = -triangle_to_mat(T12) # Test the matrix apply bmatrix_cpp = BMatrix(polsites, options) ret = bmatrix_cpp.compute_apply(static_fields) ret_ref = bmat @ static_fields np.testing.assert_allclose(ret, ret_ref, atol=1e-12) ret1 = bmatrix_cpp.compute_apply_slice(static_fields, 0, 8) ret2 = bmatrix_cpp.compute_apply_slice(static_fields, 8, npolsites) ret_all = ret1 + ret2 np.testing.assert_allclose(ret_all, ret_ref, atol=1e-12) # build the Bmatrix from C++ A = LinearOperator(2 * (static_fields.size,), matvec=bmatrix_cpp.compute_apply) Afull = A @ np.eye(static_fields.size) np.testing.assert_allclose(Afull, bmat, atol=1e-20) induced_moments_direct = np.linalg.inv(bmat) @ static_fields induced_moments_solver = cppe_state.get_induced_moments() np.testing.assert_almost_equal(induced_moments_solver, induced_moments_direct, decimal=9) ind_mom = InducedMoments(potentials, options) res_cg = ind_mom.compute_cg(static_fields) np.testing.assert_allclose(res_cg, induced_moments_direct, atol=1e-10) binv = bmatrix_cpp.direct_inverse() np.testing.assert_allclose(binv @ static_fields, induced_moments_direct, atol=1e-15)
def grad_nuclear_field_fdiff(atoms, coords, potentials, step_au=1e-3): """ Computes the finite difference gradient with a 5-point stencil """ natoms = len(atoms) polsites = cppe.get_polarizable_sites(potentials) grad = np.zeros((natoms, 3, len(polsites), 3)) for i in range(natoms): for c in range(3): print("Computing dE/d{} for atom {}.".format(coords_label[c], i)) for f, p in zip(*stencils["5p"]): coords_p = coords.copy() coords_p[i, c] += f * step_au mol_p = cppe.Molecule() for z, coord in zip(atoms, coords_p): mol_p.append(cppe.Atom(z, *coord)) nf = NuclearFields(mol_p, potentials) en_pert = nf.compute().reshape(len(polsites), 3) grad[i, c] += p * en_pert / step_au return grad
def test_compute_nuclear_interaction_energy_gradient(self): mol = cache.molecule["pna"] options = {"potfile": self.potfile_path} p = PotfileReader(self.potfile_path) potentials = p.read() atoms = [a.atomic_number for a in mol] coords = np.array([a.position for a in mol]) grad_nuc = MultipoleExpansion(mol, potentials).nuclear_gradient() grad_nuc_fd = grad_nuclear_interaction_energy_fdiff( atoms, coords, potentials) np.testing.assert_allclose(grad_nuc_fd, grad_nuc, atol=1e-10) grad_field_fd = grad_nuclear_field_fdiff(atoms, coords, potentials) natoms = len(atoms) polsites = cppe.get_polarizable_sites(potentials) grad_field = NuclearFields(mol, potentials).nuclear_gradient().reshape( (natoms, 3, len(polsites), 3)) np.testing.assert_allclose(grad_field_fd, grad_field, atol=1e-10)
def test_solver_by_inversion(self): f = h5py.File(self.pna_path, 'r') mol = Molecule() options = PeOptions() options.potfile = self.potfile_path options.induced_thresh = 12 for z, coord in zip(f['atom_charges'], f['atom_coords']): mol.append(Atom(z, *coord)) cppe_state = CppeState(options, mol) cppe_state.calculate_static_energies_and_fields() static_fields = np.array(cppe_state.get_static_fields()) zeros = np.zeros_like(static_fields) cppe_state.update_induced_moments(zeros, False) potentials = cppe_state.get_potentials() polsites = get_polarizable_sites(potentials) npolsites = cppe_state.get_polarizable_site_number() bmat = np.zeros((3 * npolsites, 3 * npolsites)) coeffs = Tk_coefficients(5) for s1, pot1 in enumerate(polsites): for pol in pot1.get_polarizabilities(): inv_alpha = triangle_to_mat(pol.get_values()) bmat[block(s1, s1)] = np.linalg.inv(inv_alpha) for s2, pot2 in enumerate(polsites): if pot1.excludes_site(pot2.index) or s1 == s2: continue diff = pot2.get_site_position() - pot1.get_site_position() T12 = Tk_tensor(2, diff, coeffs) if s1 > s2: bmat[block(s1, s2)] = -triangle_to_mat(T12) bmat[block(s2, s1)] = -triangle_to_mat(T12) induced_moments_direct = np.linalg.inv(bmat) @ static_fields induced_moments_solver = cppe_state.get_induced_moments() np.testing.assert_almost_equal(induced_moments_solver, induced_moments_direct, decimal=10)