new casida solver#194
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John-zzh wants to merge 10 commits into
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Can you add a short unit test that validates that this new feature or bugfix works? |
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Thanks for asking, after checking, now I think there is no such bug.... This PR inlcudes: The test examples passed in various setup. |
added 2 commits
May 22, 2026 23:22
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| # def TDDFT_subspace_eigen_solver2(a, b, sigma, pi, nroots): | ||
| # ''' [ a b ] x - [ σ π] x Ω = 0 ''' | ||
| # ''' [ b a ] y [-π -σ] y = 0 ''' | ||
| # original_dtype = a.dtype | ||
| # if original_dtype != np.float64: | ||
| # a = a.astype(np.float64) | ||
| # b = b.astype(np.float64) | ||
| # sigma = sigma.astype(np.float64) | ||
| # pi = pi.astype(np.float64) | ||
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| # d = abs(np.diag(sigma)) | ||
| # d_mh = d**(-0.5) | ||
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| # s_m_p = np.einsum('i,ij,j->ij', d_mh, sigma - pi, d_mh) | ||
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| # '''LU = d^−1/2 (σ − π) d^−1/2''' | ||
| # ''' A = LU ''' | ||
| # L, U = scipy.linalg.lu(s_m_p, permute_l=True) | ||
| # L_inv = np.linalg.inv(L) | ||
| # U_inv = np.linalg.inv(U) | ||
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| # U_invT = U_inv.T | ||
| # '''U^-T d^−1/2 (a−b) d^-1/2 U^-1 = GG^T ''' | ||
| # d_amb_d = np.einsum('i,ij,j->ij', d_mh, a-b, d_mh) | ||
| # GGT = np.dot(U_invT, np.dot(d_amb_d, U_inv)) | ||
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| # G = np.linalg.cholesky(GGT) | ||
| # if np.any(np.isnan(G)): | ||
| # eig, eigv = np.linalg.eigh(GGT) | ||
| # if eig[0] < -1e-4: | ||
| # error_msg = ( | ||
| # "GGT matrix is not positive definite.\n" | ||
| # "SCF not correctly converged is likely to cause this error.\n" | ||
| # "For example, scf converged to the wrong state.\n" | ||
| # ) | ||
| # raise RuntimeError(error_msg) | ||
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| # G_inv = np.linalg.inv(G) | ||
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| # ''' M = G^T L^−1 d^−1/2 (a+b) d^−1/2 L^−T G ''' | ||
| # d_apb_d = np.einsum('i,ij,j->ij', d_mh, a+b, d_mh) | ||
| # M = np.dot(G.T, np.dot(L_inv, np.dot(d_apb_d, np.dot(L_inv.T, G)))) | ||
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| # omega2, Z = np.linalg.eigh(M) | ||
| # if np.any(omega2 <= 0): | ||
| # idx = np.nonzero(omega2 > 0)[0] | ||
| # omega2 = omega2[idx[:nroots]] | ||
| # Z = Z[:,idx[:nroots]] | ||
| # else: | ||
| # omega2 = omega2[:nroots] | ||
| # Z = Z[:,:nroots] | ||
| # omega = omega2**0.5 | ||
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| # ''' It requires Z^T Z = 1/Ω ''' | ||
| # ''' x+y = d^−1/2 L^−T GZ Ω^-0.5 ''' | ||
| # ''' x−y = d^−1/2 U^−1 G^−T Z Ω^0.5 ''' | ||
| # x_p_y = np.einsum('i,ik,k->ik', d_mh, L_inv.T.dot(G.dot(Z)), omega**-0.5) | ||
| # x_m_y = np.einsum('i,ik,k->ik', d_mh, U_inv.dot(G_inv.T.dot(Z)), omega**0.5) | ||
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| # x = (x_p_y + x_m_y)/2 | ||
| # y = x_p_y - x | ||
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| # if original_dtype != np.float64: | ||
| # omega = omega.astype(original_dtype) | ||
| # x = x.astype(original_dtype) | ||
| # y = y.astype(original_dtype) | ||
| # return omega, x, y | ||
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| # def TDDFT_subspace_eigen_solver3(a, b, sigma, pi, k): | ||
| # ''' [ a b ] x - [ σ π] x Ω = 0 | ||
| # [ b a ] y [-π -σ] y = 0 | ||
| # AT=BTΩ | ||
| # B^-1/2 A B^-1/2 B^1/2 T = B^1/2 T Ω | ||
| # MZ = Z Ω | ||
| # M = B^-1/2 A B^-1/2 | ||
| # Z = B^1/2 T | ||
| # ''' | ||
| # half_size = a.shape[0] | ||
| # A = np.empty((2*half_size,2*half_size)) | ||
| # A[:half_size,:half_size] = a[:,:] | ||
| # A[:half_size,half_size:] = b[:,:] | ||
| # A[half_size:,:half_size] = b[:,:] | ||
| # A[half_size:,half_size:] = a[:,:] | ||
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| # B = np.empty_like(A) | ||
| # B[:half_size,:half_size] = sigma[:,:] | ||
| # B[:half_size,half_size:] = pi[:,:] | ||
| # B[half_size:,:half_size] = -pi[:,:] | ||
| # B[half_size:,half_size:] = -sigma[:,:] | ||
| # #B^-1/2 | ||
| # B_neg_tmp = matrix_power(B, -0.5) | ||
| # M = np.dot(B_neg_tmp, A) # B^-1/2 A | ||
| # M = np.dot(M, B_neg_tmp) # B^-1/2 A B^-1/2 | ||
| # omega, Z = np.linalg.eigh(M) | ||
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| # omega = omega[half_size:k] | ||
| # Z = Z[:, half_size:k] | ||
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| # T = np.dot(B_neg_tmp, Z) | ||
| # x = T[:half_size,:] | ||
| # y = T[half_size:,:] | ||
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| # return omega, x, y | ||
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| # def TDDFT_subspace_eigen_solver(a, b, sigma, pi, k): | ||
| # ''' [ a b ] x - [ σ π] x Ω = 0 | ||
| # [ b a ] y [-π -σ] y = 0 | ||
| # AT=BTΩ | ||
| # A^1/2 T = A^-1/2 B A^-1/2 A^1/2 T Ω | ||
| # MZ = Z 1/Ω | ||
| # M = A^-1/2 B A^-1/2 A^1/2 | ||
| # Z = A^1/2 T | ||
| # Z is always returned as normlized vectors, which are not what we wanted | ||
| # because Z^T Z = [x]^T A^1/2 A^1/2 [x] = [x]^T [ a b ] [x] = [x]^T [ σ π] x Ω = Ω | ||
| # [y] [y] [y] [ b a ] [y] [y] [-π -σ] y | ||
| # therefore Z=Z*(Ω**0.5) | ||
| # k: N_states | ||
| # ''' | ||
| # half_size = a.shape[0] | ||
| # A = np.empty((2*half_size,2*half_size)) | ||
| # A[:half_size,:half_size] = a[:,:] | ||
| # A[:half_size,half_size:] = b[:,:] | ||
| # A[half_size:,:half_size] = b[:,:] | ||
| # A[half_size:,half_size:] = a[:,:] | ||
| # B = np.empty_like(A) | ||
| # B[:half_size,:half_size] = sigma[:,:] | ||
| # B[:half_size,half_size:] = pi[:,:] | ||
| # B[half_size:,:half_size] = -pi[:,:] | ||
| # B[half_size:,half_size:] = -sigma[:,:] | ||
| # #A^-1/2 | ||
| # A_neg_tmp = matrix_power(A, -0.5, 1e-14) | ||
| # M = np.dot(A_neg_tmp, B) | ||
| # M = np.dot(M,A_neg_tmp ) | ||
| # omega, Z = np.linalg.eigh(M) | ||
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| # omega = 1/omega[-k:][::-1] | ||
| # Z = Z[:, -k:][:, ::-1] | ||
| # Z = Z*(omega**0.5) | ||
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| # T = np.dot(A_neg_tmp, Z) | ||
| # x = T[:half_size,:] | ||
| # y = T[half_size:,:] | ||
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| # return omega, x, y |
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| # --- | ||
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| # auxmol = mol.copy(deep=False) | ||
| # auxmol.verbose = 0 | ||
| # auxmol_basis_keys = mol._basis.keys() | ||
| # aux_basis = get_minimal_auxbasis( | ||
| # auxmol_basis_keys, theta, fitting_basis, excludeHs=excludeHs) | ||
| # auxmol.basis = aux_basis | ||
| # auxmol._basis = auxmol.format_basis(aux_basis) | ||
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| # pre_env = np.asarray(mol._env[:gto.PTR_ENV_START], dtype=np.float64) | ||
| # auxmol._atm, auxmol._bas, auxmol._env = auxmol.make_env( | ||
| # mol._atom, auxmol._basis, pre_env, mol.nucmod, mol.nucprop) | ||
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| # auxmol._ecpbas = np.zeros((0, gto.mole.BAS_SLOTS), dtype=np.int32) | ||
| # auxmol._built = True | ||
| # return auxmol |
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now support ECP.