def get_subspace_symmetry_blocks(the_subspace,
the_blocks,
atol=params.num_zero_atol,
rtol=params.num_zero_rtol):
c2p = np.asarray(the_subspace)
new_blocks = []
remaining_space = None
for idx, c2s in enumerate(the_blocks):
s2c = c2s.conjugate().T
s2p = s2c @ c2p
svals, p2s = matrix_svd_control_options(s2p,
rspace=remaining_space,
only_nonzero_vals=True,
full_matrices=True,
sort_vecs=-1,
num_zero_atol=rtol)[1:3]
assert (
np.all(np.isclose(svals, 1, atol=atol, rtol=rtol))
), 'Subspace may not be symmetry-adapted: svals for {}th block: {}'.format(
idx, svals)
new_blocks.append(p2s[:, :len(svals)])
remaining_space = p2s[:, len(svals):]
p2s = np.concatenate(new_blocks, axis=1)
assert (is_basis_orthonormal_and_complete(p2s)
), measure_basis_nonorthonormality(p2s)
return new_blocks
def analyze_operator_blockbreaking(the_operator,
the_blocks,
block_labels=None):
if block_labels is None:
block_labels = np.arange(len(the_blocks), dtype=int)
if isinstance(the_blocks[0], np.ndarray):
c2s = np.concatenate(the_blocks, axis=1)
assert (is_basis_orthonormal_and_complete(c2s)
), "Symmetry block problem? Not a complete, orthonormal basis."
blocked_operator = represent_operator_in_basis(the_operator, c2s)
blocked_idx = np.concatenate([[
idx,
] * blk.shape[1] for idx, blk in enumerate(the_blocks)])
c2l, op_svals, c2r = analyze_operator_blockbreaking(
blocked_operator, blocked_idx, block_labels=block_labels)
c2l = [c2s @ s2l for s2l in c2l]
c2r = [c2s @ s2r for s2r in c2r]
return c2l, op_svals, c2r
elif np.asarray(the_blocks).dtype == np.asarray(block_labels).dtype:
the_indices = np.empty(len(the_blocks), dtype=int)
for idx, lbl in enumerate(block_labels):
idx_indices = (the_blocks == lbl)
the_indices[idx_indices] = idx
the_blocks = the_indices
c2l = []
c2r = []
op_svals = []
norbs = the_operator.shape[0]
my_range = [
idx for idx, bl in enumerate(block_labels) if idx in the_blocks
]
for idx1, idx2 in combinations(my_range, 2):
blk1 = block_labels[idx1]
blk2 = block_labels[idx2]
idx12 = np.ix_(the_blocks == idx1, the_blocks == idx2)
lvecs = np.eye(norbs, dtype=the_operator.dtype)[:, the_blocks == idx1]
rvecs = np.eye(norbs, dtype=the_operator.dtype)[:, the_blocks == idx2]
mat12 = the_operator[idx12]
if is_matrix_zero(mat12):
c2l.append(np.zeros((norbs, 0), dtype=the_operator.dtype))
c2r.append(np.zeros((norbs, 0), dtype=the_operator.dtype))
op_svals.append(np.zeros((0), dtype=the_operator.dtype))
continue
try:
vecs1, svals, vecs2 = matrix_svd_control_options(
mat12, sort_vecs=-1, only_nonzero_vals=False)
lvecs = lvecs @ vecs1
rvecs = rvecs @ vecs2
except ValueError as e:
if the_operator[idx12].size > 0: raise (e)
c2l.append(np.zeros((norbs, 0), dtype=the_operator.dtype))
c2r.append(np.zeros((norbs, 0), dtype=the_operator.dtype))
op_svals.append(np.zeros((0), dtype=the_operator.dtype))
continue
#print ("Coupling between {} and {}: {} svals, norm = {}".format (idx1, idx2, len (svals), linalg.norm (svals)))
c2l.append(lvecs)
c2r.append(rvecs)
op_svals.append(svals)
return c2l, op_svals, c2r
def dmet_cderi(self, loc2dmet, numAct=None):
t0 = time.clock()
w0 = time.time()
norbs_aux = self.with_df.get_naoaux()
numAct = loc2dmet.shape[1] if numAct == None else numAct
loc2imp = loc2dmet[:, :numAct]
assert (self.with_df is not None), "density fitting required"
CDERI = np.empty(
(self.with_df.get_naoaux(), numAct * (numAct + 1) // 2),
dtype=loc2dmet.dtype)
full_cderi_size = (norbs_aux * self.mol.nao_nr() *
(self.mol.nao_nr() + 1) * CDERI.itemsize // 2) / 1e6
imp_eri_size = CDERI.itemsize * (
numAct**4) / 1e6 # Since I don't use symmetry yet
imp_eri_ideal_size = CDERI.itemsize * (
numAct * (numAct + 1) // 2
)**2 / 1e6 # Eightfold symmetry is not practical because ao2mos will have to happen
imp_cderi_size = CDERI.size * CDERI.itemsize / 1e6
print(
"Size comparison: cderi is ({0},{1},{1})->{2:.0f} MB total; eri is ({1},{1},{1},{1})->{3:.0f} MB total ({4:.0f} MB ideal)"
.format(norbs_aux, numAct, imp_cderi_size, imp_eri_size,
imp_eri_ideal_size))
ao2imp = np.dot(self.ao2loc, loc2imp)
ijmosym, mij_pair, moij, ijslice = ao2mo.incore._conc_mos(ao2imp,
ao2imp,
compact=True)
b0 = 0
for eri1 in self.with_df.loop():
b1 = b0 + eri1.shape[0]
eri2 = CDERI[b0:b1]
eri2 = ao2mo._ao2mo.nr_e2(eri1,
moij,
ijslice,
aosym='s2',
mosym=ijmosym,
out=eri2)
b0 = b1
t1 = time.clock()
w1 = time.time()
print(("({0}, {1}) seconds to turn {2:.0f}-MB full"
"cderi array into {3:.0f}-MP impurity cderi array").format(
t1 - t0, w1 - w0, full_cderi_size, imp_cderi_size))
sigma, vmat = matrix_svd_control_options(
CDERI,
sort_vecs=-1,
only_nonzero_vals=True,
full_matrices=False,
num_zero_atol=sqrt(LINEAR_DEP_THR))[1:]
imp_cderi_size = vmat.size * vmat.itemsize / 1e6
print(
"With SVD: {0:.0f}-MB CDERI array, compared to {1:.0f}-MB ideal eri; ({2}, {3}) seconds"
.format(imp_cderi_size, imp_eri_ideal_size,
time.clock() - t1,
time.time() - w1))
CDERI = np.ascontiguousarray((vmat * sigma).T)
return CDERI
def _svd (self, mo_lspace, mo_rspace, s=None, **kwargs):
if s is None: s = self._scf.get_ovlp ()
lsymm = getattr (mo_lspace, 'orbsym', None)
if lsymm is None:
mo_lspace = symm.symmetrize_space (self.mol, mo_lspace)
lsymm = symm.label_orb_symm(self.mol, self.mol.irrep_id,
self.mol.symm_orb, mo_lspace, s=s)
rsymm = getattr (mo_rspace, 'orbsym', None)
if rsymm is None:
mo_rspace = symm.symmetrize_space (self.mol, mo_rspace)
rsymm = symm.label_orb_symm(self.mol, self.mol.irrep_id,
self.mol.symm_orb, mo_rspace, s=s)
decomp = matrix_svd_control_options (s,
lspace=mo_lspace, rspace=mo_rspace,
lspace_symmetry=lsymm, rspace_symmetry=rsymm,
full_matrices=True, strong_symm=True)
mo_lvecs, svals, mo_rvecs, lsymm, rsymm = decomp
mo_lvecs = tag_array (mo_lvecs, orbsym=lsymm)
mo_rvecs = tag_array (mo_rvecs, orbsym=rsymm)
return mo_lvecs, svals, mo_rvecs
def get_overlapping_states (bra_basis, ket_basis, across_operator=None, inner_symmetry=None, outer_symmetry=(None, None), enforce_symmetry=False,
max_nrvecs=0, max_nlvecs=0, num_zero_atol=params.num_zero_atol, only_nonzero_vals=True, full_matrices=False):
c2p = np.asarray (bra_basis)
c2q = np.asarray (ket_basis)
cOc = 1 if across_operator is None else np.asarray (across_operator)
assert (c2p.shape[0] == c2q.shape[0]), "you need to give the two spaces in the same basis"
assert (c2p.shape[1] <= c2p.shape[0]), "you need to give the first state in a complete basis (c2p). Did you accidentally transpose it?"
assert (c2q.shape[1] <= c2q.shape[0]), "you need to give the second state in a complete basis (c2q). Did you accidentally transpose it?"
assert (max_nlvecs <= c2p.shape[1]), "you can't ask for more left states than are in your left space"
assert (max_nrvecs <= c2q.shape[1]), "you can't ask for more right states than are in your right space"
if np.any (across_operator):
assert (c2p.shape[0] == cOc.shape[0] and c2p.shape[0] == cOc.shape[1]), "when specifying an across_operator, it's dimensions need to be the same as the external basis"
get_labels = (not (inner_symmetry is None)) or (not (outer_symmetry[0] is None)) or (not (outer_symmetry[1] is None))
rets = matrix_svd_control_options (cOc, lspace=c2p, rspace=c2q, full_matrices=full_matrices,
symmetry=inner_symmetry,
lspace_symmetry=outer_symmetry[0],
rspace_symmetry=outer_symmetry[1],
strong_symm=enforce_symmetry,
sort_vecs=-1, only_nonzero_vals=only_nonzero_vals, num_zero_atol=num_zero_atol)
c2l, svals, c2r = rets[:3]
if get_labels: llab, rlab = rets[3:]
# Truncate the basis if requested
max_nlvecs = max_nlvecs or c2l.shape[1]
max_nrvecs = max_nrvecs or c2r.shape[1]
# But you can't truncate it smaller than it already is
max_nlvecs = min (max_nlvecs, c2l.shape[1])
max_nrvecs = min (max_nrvecs, c2r.shape[1])
c2l = c2l[:,:max_nlvecs]
c2r = c2r[:,:max_nrvecs]
if get_labels: return c2l, c2r, svals, llab, rlab
return c2l, c2r, svals
def _svd (self, mo_lspace, mo_rspace, s=None, **kwargs):
if s is None: s = self._scf.get_ovlp ()
return matrix_svd_control_options (s, lspace=mo_lspace, rspace=mo_rspace, full_matrices=True)[:3]
def solve (frag, guess_1RDM, chempot_imp):
# Augment OEI with the chemical potential
OEI = frag.impham_OEI_C - chempot_imp
# Do I need to get the full RHF solution?
guess_orbs_av = len (frag.imp_cache) == 2 or frag.norbs_as > 0
# Get the RHF solution
mol = gto.Mole()
abs_2MS = int (round (2 * abs (frag.target_MS)))
abs_2S = int (round (2 * abs (frag.target_S)))
sign_MS = int (np.sign (frag.target_MS)) or 1
mol.spin = abs_2MS
mol.verbose = 0
if frag.mol_stdout is None:
mol.output = frag.mol_output
mol.verbose = 0 if frag.mol_output is None else lib.logger.DEBUG
mol.atom.append(('H', (0, 0, 0)))
mol.nelectron = frag.nelec_imp
if frag.enforce_symmetry:
mol.groupname = frag.symmetry
mol.symm_orb = get_subspace_symmetry_blocks (frag.loc2imp, frag.loc2symm)
mol.irrep_name = frag.ir_names
mol.irrep_id = frag.ir_ids
mol.max_memory = frag.ints.max_memory
mol.build ()
if frag.mol_stdout is None:
frag.mol_stdout = mol.stdout
else:
mol.stdout = frag.mol_stdout
mol.verbose = 0 if frag.mol_output is None else lib.logger.DEBUG
if frag.enforce_symmetry: mol.symmetry = True
#mol.incore_anyway = True
mf = scf.RHF(mol)
mf.get_hcore = lambda *args: OEI
mf.get_ovlp = lambda *args: np.eye(frag.norbs_imp)
mf.energy_nuc = lambda *args: frag.impham_CONST
if frag.impham_CDERI is not None:
mf = mf.density_fit ()
mf.with_df._cderi = frag.impham_CDERI
else:
mf._eri = ao2mo.restore(8, frag.impham_TEI, frag.norbs_imp)
mf = fix_my_RHF_for_nonsinglet_env (mf, frag.impham_OEI_S)
mf.__dict__.update (frag.mf_attr)
if guess_orbs_av: mf.max_cycle = 2
mf.scf (guess_1RDM)
if (not mf.converged) and (not guess_orbs_av):
if np.any (np.abs (frag.impham_OEI_S) > 1e-8) and mol.spin != 0:
raise NotImplementedError('Gradient and Hessian fixes for nonsinglet environment of Newton-descent ROHF algorithm')
print ("CASSCF RHF-step not converged on fixed-point iteration; initiating newton solver")
mf = mf.newton ()
mf.kernel ()
# Instability check and repeat
if not guess_orbs_av:
for i in range (frag.num_mf_stab_checks):
if np.any (np.abs (frag.impham_OEI_S) > 1e-8) and mol.spin != 0:
raise NotImplementedError('ROHF stability-check fixes for nonsinglet environment')
mf.mo_coeff = mf.stability ()[0]
guess_1RDM = mf.make_rdm1 ()
mf = scf.RHF(mol)
mf.get_hcore = lambda *args: OEI
mf.get_ovlp = lambda *args: np.eye(frag.norbs_imp)
mf._eri = ao2mo.restore(8, frag.impham_TEI, frag.norbs_imp)
mf = fix_my_RHF_for_nonsinglet_env (mf, frag.impham_OEI_S)
mf.scf (guess_1RDM)
if not mf.converged:
mf = mf.newton ()
mf.kernel ()
E_RHF = mf.e_tot
print ("CASSCF RHF-step energy: {}".format (E_RHF))
# Get the CASSCF solution
CASe = frag.active_space[0]
CASorb = frag.active_space[1]
checkCAS = (CASe <= frag.nelec_imp) and (CASorb <= frag.norbs_imp)
if (checkCAS == False):
CASe = frag.nelec_imp
CASorb = frag.norbs_imp
if (abs_2MS > abs_2S):
CASe = ((CASe + sign_MS * abs_2S) // 2, (CASe - sign_MS * abs_2S) // 2)
else:
CASe = ((CASe + sign_MS * abs_2MS) // 2, (CASe - sign_MS * abs_2MS) // 2)
if frag.impham_CDERI is not None:
mc = mcscf.DFCASSCF(mf, CASorb, CASe)
else:
mc = mcscf.CASSCF(mf, CASorb, CASe)
smult = abs_2S + 1 if frag.target_S is not None else (frag.nelec_imp % 2) + 1
mc.fcisolver = csf_solver (mf.mol, smult, symm=frag.enforce_symmetry)
if frag.enforce_symmetry: mc.fcisolver.wfnsym = frag.wfnsym
mc.max_cycle_macro = 50 if frag.imp_maxiter is None else frag.imp_maxiter
mc.conv_tol = min (1e-9, frag.conv_tol_grad**2)
mc.ah_start_tol = mc.conv_tol / 10
mc.ah_conv_tol = mc.conv_tol / 10
mc.__dict__.update (frag.corr_attr)
mc = fix_my_CASSCF_for_nonsinglet_env (mc, frag.impham_OEI_S)
norbs_amo = mc.ncas
norbs_cmo = mc.ncore
norbs_imo = frag.norbs_imp - norbs_amo
nelec_amo = sum (mc.nelecas)
norbs_occ = norbs_amo + norbs_cmo
#mc.natorb = True
# Guess orbitals
ci0 = None
dm_imp = frag.get_oneRDM_imp ()
fock_imp = mf.get_fock (dm=dm_imp)
if len (frag.imp_cache) == 2:
imp2mo, ci0 = frag.imp_cache
print ("Taking molecular orbitals and ci vector from cache")
elif frag.norbs_as > 0:
nelec_imp_guess = int (round (np.trace (frag.oneRDMas_loc)))
norbs_cmo_guess = (frag.nelec_imp - nelec_imp_guess) // 2
print ("Projecting stored amos (frag.loc2amo; spanning {} electrons) onto the impurity basis and filling the remainder with default guess".format (nelec_imp_guess))
imp2mo, my_occ = project_amo_manually (frag.loc2imp, frag.loc2amo, fock_imp, norbs_cmo_guess, dm=frag.oneRDMas_loc)
elif frag.loc2amo_guess is not None:
print ("Projecting stored amos (frag.loc2amo_guess) onto the impurity basis (no amo dm available)")
imp2mo, my_occ = project_amo_manually (frag.loc2imp, frag.loc2amo_guess, fock_imp, norbs_cmo, dm=None)
frag.loc2amo_guess = None
else:
dm_imp = np.asarray (mf.make_rdm1 ())
while dm_imp.ndim > 2:
dm_imp = dm_imp.sum (0)
imp2mo = mf.mo_coeff
fock_imp = mf.get_fock (dm=dm_imp)
fock_mo = represent_operator_in_basis (fock_imp, imp2mo)
_, evecs = matrix_eigen_control_options (fock_mo, sort_vecs=1)
imp2mo = imp2mo @ evecs
my_occ = ((dm_imp @ imp2mo) * imp2mo).sum (0)
print ("No stored amos; using mean-field canonical MOs as initial guess")
# Guess orbital processing
if callable (frag.cas_guess_callback):
mo = reduce (np.dot, (frag.ints.ao2loc, frag.loc2imp, imp2mo))
mo = frag.cas_guess_callback (frag.ints.mol, mc, mo)
imp2mo = reduce (np.dot, (frag.imp2loc, frag.ints.ao2loc.conjugate ().T, frag.ints.ao_ovlp, mo))
frag.cas_guess_callback = None
# Guess CI vector
if len (frag.imp_cache) != 2 and frag.ci_as is not None:
loc2amo_guess = np.dot (frag.loc2imp, imp2mo[:,norbs_cmo:norbs_occ])
metric = np.arange (CASorb) + 1
gOc = np.dot (loc2amo_guess.conjugate ().T, (frag.ci_as_orb * metric[None,:]))
umat_g, svals, umat_c = matrix_svd_control_options (gOc, sort_vecs=1, only_nonzero_vals=True)
if (svals.size == norbs_amo):
print ("Loading ci guess despite shifted impurity orbitals; singular value error sum: {}".format (np.sum (svals - metric)))
imp2mo[:,norbs_cmo:norbs_occ] = np.dot (imp2mo[:,norbs_cmo:norbs_occ], umat_g)
ci0 = transform_ci_for_orbital_rotation (frag.ci_as, CASorb, CASe, umat_c)
else:
print ("Discarding stored ci guess because orbitals are too different (missing {} nonzero svals)".format (norbs_amo-svals.size))
# Symmetry align if possible
imp2unac = frag.align_imporbs_symm (np.append (imp2mo[:,:norbs_cmo], imp2mo[:,norbs_occ:], axis=1), sorting_metric=fock_imp,
sort_vecs=1, orbital_type='guess unactive', mol=mol)[0]
imp2mo[:,:norbs_cmo] = imp2unac[:,:norbs_cmo]
imp2mo[:,norbs_occ:] = imp2unac[:,norbs_cmo:]
#imp2mo[:,:norbs_cmo] = frag.align_imporbs_symm (imp2mo[:,:norbs_cmo], sorting_metric=fock_imp, sort_vecs=1, orbital_type='guess inactive', mol=mol)[0]
imp2mo[:,norbs_cmo:norbs_occ], umat = frag.align_imporbs_symm (imp2mo[:,norbs_cmo:norbs_occ], sorting_metric=fock_imp,
sort_vecs=1, orbital_type='guess active', mol=mol)
#imp2mo[:,norbs_occ:] = frag.align_imporbs_symm (imp2mo[:,norbs_occ:], sorting_metric=fock_imp, sort_vecs=1, orbital_type='guess external', mol=mol)[0]
if frag.enforce_symmetry:
imp2mo = cleanup_subspace_symmetry (imp2mo, mol.symm_orb)
err_symm = measure_subspace_blockbreaking (imp2mo, mol.symm_orb)
err_orth = measure_basis_nonorthonormality (imp2mo)
print ("Initial symmetry error after cleanup = {}".format (err_symm))
print ("Initial orthonormality error after cleanup = {}".format (err_orth))
if ci0 is not None: ci0 = transform_ci_for_orbital_rotation (ci0, CASorb, CASe, umat)
# Guess orbital printing
if frag.mfmo_printed == False and frag.ints.mol.verbose:
ao2mfmo = reduce (np.dot, [frag.ints.ao2loc, frag.loc2imp, imp2mo])
print ("Writing {} {} orbital molden".format (frag.frag_name, 'CAS guess'))
molden.from_mo (frag.ints.mol, frag.filehead + frag.frag_name + '_mfmorb.molden', ao2mfmo, occ=my_occ)
frag.mfmo_printed = True
elif len (frag.active_orb_list) > 0: # This is done AFTER everything else so that the _mfmorb.molden always has consistent ordering
print('Applying caslst: {}'.format (frag.active_orb_list))
imp2mo = mc.sort_mo(frag.active_orb_list, mo_coeff=imp2mo)
frag.active_orb_list = []
if len (frag.frozen_orb_list) > 0:
mc.frozen = copy.copy (frag.frozen_orb_list)
print ("Applying frozen-orbital list (this macroiteration only): {}".format (frag.frozen_orb_list))
frag.frozen_orb_list = []
if frag.enforce_symmetry: imp2mo = lib.tag_array (imp2mo, orbsym=label_orb_symm (mol, mol.irrep_id, mol.symm_orb, imp2mo, s=mf.get_ovlp (), check=False))
t_start = time.time()
E_CASSCF = mc.kernel(imp2mo, ci0)[0]
if (not mc.converged) and np.all (np.abs (frag.impham_OEI_S) < 1e-8):
mc = mc.newton ()
E_CASSCF = mc.kernel(mc.mo_coeff, mc.ci)[0]
if not mc.converged:
print ('Assuming ci vector is poisoned; discarding...')
imp2mo = mc.mo_coeff.copy ()
mc = mcscf.CASSCF(mf, CASorb, CASe)
smult = abs_2S + 1 if frag.target_S is not None else (frag.nelec_imp % 2) + 1
mc.fcisolver = csf_solver (mf.mol, smult)
E_CASSCF = mc.kernel(imp2mo)[0]
if not mc.converged:
if np.any (np.abs (frag.impham_OEI_S) > 1e-8):
raise NotImplementedError('Gradient and Hessian fixes for nonsinglet environment of Newton-descent CASSCF algorithm')
mc = mc.newton ()
E_CASSCF = mc.kernel(mc.mo_coeff, mc.ci)[0]
assert (mc.converged)
'''
mc.conv_tol = 1e-12
mc.ah_start_tol = 1e-10
mc.ah_conv_tol = 1e-12
E_CASSCF = mc.kernel(mc.mo_coeff, mc.ci)[0]
if not mc.converged:
mc = mc.newton ()
E_CASSCF = mc.kernel(mc.mo_coeff, mc.ci)[0]
#assert (mc.converged)
'''
# Get twoRDM + oneRDM. cs: MC-SCF core, as: MC-SCF active space
# I'm going to need to keep some representation of the active-space orbitals
# Symmetry align if possible
oneRDM_amo, twoRDM_amo = mc.fcisolver.make_rdm12 (mc.ci, mc.ncas, mc.nelecas)
fock_imp = mc.get_fock ()
mc.mo_coeff[:,:norbs_cmo] = frag.align_imporbs_symm (mc.mo_coeff[:,:norbs_cmo], sorting_metric=fock_imp, sort_vecs=1, orbital_type='optimized inactive', mol=mol)[0]
mc.mo_coeff[:,norbs_cmo:norbs_occ], umat = frag.align_imporbs_symm (mc.mo_coeff[:,norbs_cmo:norbs_occ],
sorting_metric=oneRDM_amo, sort_vecs=-1, orbital_type='optimized active', mol=mol)
mc.mo_coeff[:,norbs_occ:] = frag.align_imporbs_symm (mc.mo_coeff[:,norbs_occ:], sorting_metric=fock_imp, sort_vecs=1, orbital_type='optimized external', mol=mol)[0]
if frag.enforce_symmetry:
amo2imp = mc.mo_coeff[:,norbs_cmo:norbs_occ].conjugate ().T
mc.mo_coeff = cleanup_subspace_symmetry (mc.mo_coeff, mol.symm_orb)
umat = umat @ (amo2imp @ mc.mo_coeff[:,norbs_cmo:norbs_occ])
err_symm = measure_subspace_blockbreaking (mc.mo_coeff, mol.symm_orb)
err_orth = measure_basis_nonorthonormality (mc.mo_coeff)
print ("Final symmetry error after cleanup = {}".format (err_symm))
print ("Final orthonormality error after cleanup = {}".format (err_orth))
mc.ci = transform_ci_for_orbital_rotation (mc.ci, CASorb, CASe, umat)
# Cache stuff
imp2mo = mc.mo_coeff #mc.cas_natorb()[0]
loc2mo = np.dot (frag.loc2imp, imp2mo)
imp2amo = imp2mo[:,norbs_cmo:norbs_occ]
loc2amo = loc2mo[:,norbs_cmo:norbs_occ]
frag.imp_cache = [mc.mo_coeff, mc.ci]
frag.ci_as = mc.ci
frag.ci_as_orb = loc2amo.copy ()
t_end = time.time()
# oneRDM
oneRDM_imp = mc.make_rdm1 ()
# twoCDM
oneRDM_amo, twoRDM_amo = mc.fcisolver.make_rdm12 (mc.ci, mc.ncas, mc.nelecas)
oneRDMs_amo = np.stack (mc.fcisolver.make_rdm1s (mc.ci, mc.ncas, mc.nelecas), axis=0)
oneSDM_amo = oneRDMs_amo[0] - oneRDMs_amo[1] if frag.target_MS >= 0 else oneRDMs_amo[1] - oneRDMs_amo[0]
oneSDM_imp = represent_operator_in_basis (oneSDM_amo, imp2amo.conjugate ().T)
print ("Norm of spin density: {}".format (linalg.norm (oneSDM_amo)))
# Note that I do _not_ do the *real* cumulant decomposition; I do one assuming oneSDM_amo = 0.
# This is fine as long as I keep it consistent, since it is only in the orbital gradients for this impurity that
# the spin density matters. But it has to stay consistent!
twoCDM_amo = get_2CDM_from_2RDM (twoRDM_amo, oneRDM_amo)
twoCDM_imp = represent_operator_in_basis (twoCDM_amo, imp2amo.conjugate ().T)
print('Impurity CASSCF energy (incl chempot): {}; spin multiplicity: {}; time to solve: {}'.format (E_CASSCF, spin_square (mc)[1], t_end - t_start))
# Active-space RDM data
frag.oneRDMas_loc = symmetrize_tensor (represent_operator_in_basis (oneRDM_amo, loc2amo.conjugate ().T))
frag.oneSDMas_loc = symmetrize_tensor (represent_operator_in_basis (oneSDM_amo, loc2amo.conjugate ().T))
frag.twoCDMimp_amo = twoCDM_amo
frag.loc2mo = loc2mo
frag.loc2amo = loc2amo
frag.E2_cum = np.tensordot (ao2mo.restore (1, mc.get_h2eff (), mc.ncas), twoCDM_amo, axes=4) / 2
frag.E2_cum += (mf.get_k (dm=oneSDM_imp) * oneSDM_imp).sum () / 4
# The second line compensates for my incorrect cumulant decomposition. Anything to avoid changing the checkpoint files...
# General impurity data
frag.oneRDM_loc = frag.oneRDMfroz_loc + symmetrize_tensor (represent_operator_in_basis (oneRDM_imp, frag.imp2loc))
frag.oneSDM_loc = frag.oneSDMfroz_loc + frag.oneSDMas_loc
frag.twoCDM_imp = None # Experiment: this tensor is huge. Do I actually need to keep it? In principle, of course not.
frag.E_imp = E_CASSCF + np.einsum ('ab,ab->', chempot_imp, oneRDM_imp)
return None
def solve(frag, guess_1RDM, chempot_imp):
# Augment OEI with the chemical potential
OEI = frag.impham_OEI - chempot_imp
# Do I need to get the full RHF solution?
guess_orbs_av = len(frag.imp_cache) == 2 or frag.norbs_as > 0
# Get the RHF solution
mol = gto.Mole()
mol.spin = int(round(2 * frag.target_MS))
mol.verbose = 0 if frag.mol_output is None else lib.logger.DEBUG
mol.output = frag.mol_output
mol.atom.append(('H', (0, 0, 0)))
mol.nelectron = frag.nelec_imp
mol.build()
#mol.incore_anyway = True
mf = scf.RHF(mol)
mf.get_hcore = lambda *args: OEI
mf.get_ovlp = lambda *args: np.eye(frag.norbs_imp)
mf.energy_nuc = lambda *args: frag.impham_CONST
if frag.impham_CDERI is not None:
mf = mf.density_fit()
mf.with_df._cderi = frag.impham_CDERI
else:
mf._eri = ao2mo.restore(8, frag.impham_TEI, frag.norbs_imp)
mf.__dict__.update(frag.mf_attr)
if guess_orbs_av: mf.max_cycle = 2
mf.scf(guess_1RDM)
if (not mf.converged) and (not guess_orbs_av):
print(
"CASSCF RHF-step not converged on fixed-point iteration; initiating newton solver"
)
mf = mf.newton()
mf.kernel()
# Instability check and repeat
if not guess_orbs_av:
for i in range(frag.num_mf_stab_checks):
mf.mo_coeff = mf.stability()[0]
guess_1RDM = mf.make_rdm1()
mf = scf.RHF(mol)
mf.get_hcore = lambda *args: OEI
mf.get_ovlp = lambda *args: np.eye(frag.norbs_imp)
mf._eri = ao2mo.restore(8, frag.impham_TEI, frag.norbs_imp)
mf.scf(guess_1RDM)
if not mf.converged:
mf = mf.newton()
mf.kernel()
print("CASSCF RHF-step energy: {}".format(mf.e_tot))
#print(mf.mo_occ)
'''
idx = mf.mo_energy.argsort()
mf.mo_energy = mf.mo_energy[idx]
mf.mo_coeff = mf.mo_coeff[:,idx]'''
# Get the CASSCF solution
CASe = frag.active_space[0]
CASorb = frag.active_space[1]
checkCAS = (CASe <= frag.nelec_imp) and (CASorb <= frag.norbs_imp)
if (checkCAS == False):
CASe = frag.nelec_imp
CASorb = frag.norbs_imp
if (frag.target_MS > frag.target_S):
CASe = ((CASe // 2) + frag.target_S, (CASe // 2) - frag.target_S)
else:
CASe = ((CASe // 2) + frag.target_MS, (CASe // 2) - frag.target_MS)
if frag.impham_CDERI is not None:
mc = mcscf.DFCASSCF(mf, CASorb, CASe)
else:
mc = mcscf.CASSCF(mf, CASorb, CASe)
norbs_amo = mc.ncas
norbs_cmo = mc.ncore
norbs_imo = frag.norbs_imp - norbs_amo
nelec_amo = sum(mc.nelecas)
norbs_occ = norbs_amo + norbs_cmo
#mc.natorb = True
# Guess orbitals
ci0 = None
if len(frag.imp_cache) == 2:
imp2mo, ci0 = frag.imp_cache
print("Taking molecular orbitals and ci vector from cache")
elif frag.norbs_as > 0:
nelec_imp_guess = int(round(np.trace(frag.oneRDMas_loc)))
norbs_cmo_guess = (frag.nelec_imp - nelec_imp_guess) // 2
print(
"Projecting stored amos (frag.loc2amo; spanning {} electrons) onto the impurity basis and filling the remainder with default guess"
.format(nelec_imp_guess))
imp2mo, my_occ = project_amo_manually(
frag.loc2imp,
frag.loc2amo,
mf.get_fock(dm=frag.get_oneRDM_imp()),
norbs_cmo_guess,
dm=frag.oneRDMas_loc)
elif frag.loc2amo_guess is not None:
print(
"Projecting stored amos (frag.loc2amo_guess) onto the impurity basis (no dm available)"
)
imp2mo, my_occ = project_amo_manually(
frag.loc2imp,
frag.loc2amo_guess,
mf.get_fock(dm=frag.get_oneRDM_imp()),
norbs_cmo,
dm=None)
frag.loc2amo_guess = None
else:
imp2mo = mc.mo_coeff
my_occ = mf.mo_occ
print(
"No stored amos; using mean-field canonical MOs as initial guess")
# Guess orbital processing
if callable(frag.cas_guess_callback):
mo = reduce(np.dot, (frag.ints.ao2loc, frag.loc2imp, imp2mo))
mo = frag.cas_guess_callback(frag.ints.mol, mc, mo)
imp2mo = reduce(np.dot, (frag.imp2loc, frag.ints.ao2loc.conjugate().T,
frag.ints.ao_ovlp, mo))
frag.cas_guess_callback = None
elif len(frag.active_orb_list) > 0:
print('Applying caslst: {}'.format(frag.active_orb_list))
imp2mo = mc.sort_mo(frag.active_orb_list, mo_coeff=imp2mo)
frag.active_orb_list = []
if len(frag.frozen_orb_list) > 0:
mc.frozen = copy.copy(frag.frozen_orb_list)
print("Applying frozen-orbital list (this macroiteration only): {}".
format(frag.frozen_orb_list))
frag.frozen_orb_list = []
# Guess orbital printing
if frag.mfmo_printed == False:
ao2mfmo = reduce(np.dot, [frag.ints.ao2loc, frag.loc2imp, imp2mo])
molden.from_mo(frag.ints.mol,
frag.filehead + frag.frag_name + '_mfmorb.molden',
ao2mfmo,
occ=my_occ)
frag.mfmo_printed = True
# Guess CI vector
if len(frag.imp_cache) != 2 and frag.ci_as is not None:
loc2amo_guess = np.dot(frag.loc2imp, imp2mo[:, norbs_cmo:norbs_occ])
gOc = np.dot(loc2amo_guess.conjugate().T, frag.ci_as_orb)
umat_g, svals, umat_c = matrix_svd_control_options(
gOc, sort_vecs=-1, only_nonzero_vals=True)
if (svals.size == norbs_amo):
print(
"Loading ci guess despite shifted impurity orbitals; singular value sum: {}"
.format(np.sum(svals)))
imp2mo[:, norbs_cmo:norbs_occ] = np.dot(
imp2mo[:, norbs_cmo:norbs_occ], umat_g)
ci0 = transform_ci_for_orbital_rotation(frag.ci_as, CASorb, CASe,
umat_c)
else:
print(
"Discarding stored ci guess because orbitals are too different (missing {} nonzero svals)"
.format(norbs_amo - svals.size))
t_start = time.time()
smult = 2 * frag.target_S + 1 if frag.target_S is not None else (
frag.nelec_imp % 2) + 1
mc.fcisolver = csf_solver(mf.mol, smult)
mc.max_cycle_macro = 50 if frag.imp_maxiter is None else frag.imp_maxiter
mc.ah_start_tol = 1e-10
mc.ah_conv_tol = 1e-10
mc.conv_tol = 1e-9
mc.__dict__.update(frag.corr_attr)
E_CASSCF = mc.kernel(imp2mo, ci0)[0]
if not mc.converged:
mc = mc.newton()
E_CASSCF = mc.kernel(mc.mo_coeff, mc.ci)[0]
if not mc.converged:
print('Assuming ci vector is poisoned; discarding...')
imp2mo = mc.mo_coeff.copy()
mc = mcscf.CASSCF(mf, CASorb, CASe)
smult = 2 * frag.target_S + 1 if frag.target_S is not None else (
frag.nelec_imp % 2) + 1
mc.fcisolver = csf_solver(mf.mol, smult)
E_CASSCF = mc.kernel(imp2mo)[0]
if not mc.converged:
mc = mc.newton()
E_CASSCF = mc.kernel(mc.mo_coeff, mc.ci)[0]
assert (mc.converged)
'''
mc.conv_tol = 1e-12
mc.ah_start_tol = 1e-10
mc.ah_conv_tol = 1e-12
E_CASSCF = mc.kernel(mc.mo_coeff, mc.ci)[0]
if not mc.converged:
mc = mc.newton ()
E_CASSCF = mc.kernel(mc.mo_coeff, mc.ci)[0]
#assert (mc.converged)
'''
# Get twoRDM + oneRDM. cs: MC-SCF core, as: MC-SCF active space
# I'm going to need to keep some representation of the active-space orbitals
imp2mo = mc.mo_coeff #mc.cas_natorb()[0]
loc2mo = np.dot(frag.loc2imp, imp2mo)
imp2amo = imp2mo[:, norbs_cmo:norbs_occ]
loc2amo = loc2mo[:, norbs_cmo:norbs_occ]
frag.imp_cache = [mc.mo_coeff, mc.ci]
frag.ci_as = mc.ci
frag.ci_as_orb = loc2amo.copy()
t_end = time.time()
print(
'Impurity CASSCF energy (incl chempot): {}; spin multiplicity: {}; time to solve: {}'
.format(E_CASSCF,
spin_square(mc)[1], t_end - t_start))
# oneRDM
oneRDM_imp = mc.make_rdm1()
# twoCDM
oneRDM_amo, twoRDM_amo = mc.fcisolver.make_rdm12(mc.ci, mc.ncas,
mc.nelecas)
# Note that I do _not_ do the *real* cumulant decomposition; I do one assuming oneRDMs_amo_alpha = oneRDMs_amo_beta
# This is fine as long as I keep it consistent, since it is only in the orbital gradients for this impurity that
# the spin density matters. But it has to stay consistent!
twoCDM_amo = get_2CDM_from_2RDM(twoRDM_amo, oneRDM_amo)
twoCDM_imp = represent_operator_in_basis(twoCDM_amo, imp2amo.conjugate().T)
# General impurity data
frag.oneRDM_loc = symmetrize_tensor(
frag.oneRDMfroz_loc +
represent_operator_in_basis(oneRDM_imp, frag.imp2loc))
frag.twoCDM_imp = None # Experiment: this tensor is huge. Do I actually need to keep it? In principle, of course not.
frag.E_imp = E_CASSCF + np.einsum('ab,ab->', chempot_imp, oneRDM_imp)
# Active-space RDM data
frag.oneRDMas_loc = symmetrize_tensor(
represent_operator_in_basis(oneRDM_amo,
loc2amo.conjugate().T))
frag.twoCDMimp_amo = twoCDM_amo
frag.loc2mo = loc2mo
frag.loc2amo = loc2amo
frag.E2_cum = 0.5 * np.tensordot(
ao2mo.restore(1, mc.get_h2eff(), mc.ncas), twoCDM_amo, axes=4)
return None
def get_overlapping_states (bra_basis, ket_basis, across_operator=None, inner_symmetry=None, outer_symmetry=(None, None), enforce_symmetry=False,
max_nrvecs=0, max_nlvecs=0, num_zero_atol=params.num_zero_atol, only_nonzero_vals=True, full_matrices=False):
c2p = np.asarray (bra_basis)
c2q = np.asarray (ket_basis)
cOc = 1 if across_operator is None else np.asarray (across_operator)
assert (c2p.shape[0] == c2q.shape[0]), "you need to give the two spaces in the same basis"
assert (c2p.shape[1] <= c2p.shape[0]), "you need to give the first state in a complete basis (c2p). Did you accidentally transpose it?"
assert (c2q.shape[1] <= c2q.shape[0]), "you need to give the second state in a complete basis (c2q). Did you accidentally transpose it?"
assert (max_nlvecs <= c2p.shape[1]), "you can't ask for more left states than are in your left space"
assert (max_nrvecs <= c2q.shape[1]), "you can't ask for more right states than are in your right space"
if np.any (across_operator):
assert (c2p.shape[0] == cOc.shape[0] and c2p.shape[0] == cOc.shape[1]), "when specifying an across_operator, it's dimensions need to be the same as the external basis"
get_labels = (not (inner_symmetry is None)) or (not (outer_symmetry[0] is None)) or (not (outer_symmetry[1] is None))
try:
rets = matrix_svd_control_options (cOc, lspace=c2p, rspace=c2q, full_matrices=full_matrices,
symmetry=inner_symmetry,
lspace_symmetry=outer_symmetry[0],
rspace_symmetry=outer_symmetry[1],
strong_symm=enforce_symmetry,
sort_vecs=-1, only_nonzero_vals=only_nonzero_vals, num_zero_atol=num_zero_atol)
c2l, svals, c2r = rets[:3]
if get_labels: llab, rlab = rets[3:]
except linalg.LinAlgError as e:
print ("LinAlgError in SVD! Analyzing...")
if isinstance (cOc, np.ndarray):
print ("Shape of across_operator: {}".format (cOc.shape))
print ("Any NANs in across_operator? {}".format (np.count_nonzero (np.isnan (cOc))))
print ("Any INFs in across_operator? {}".format (np.count_nonzero (np.isinf (cOc))))
print ("min/max across_operator: {}/{}".format (np.amin (cOc), np.amax (cOc)))
print ("Shape of bra_basis: {}".format (c2p.shape))
print ("Any NANs in bra_basis? {}".format (np.count_nonzero (np.isnan (c2p))))
print ("Any INFs in bra_basis? {}".format (np.count_nonzero (np.isinf (c2p))))
print ("min/max bra_basis: {}/{}".format (np.amin (c2p), np.amax (c2p)))
print ("Shape of ket_basis: {}".format (c2p.shape))
print ("Any NANs in ket_basis? {}".format (np.count_nonzero (np.isnan (c2p))))
print ("Any INFs in ket_basis? {}".format (np.count_nonzero (np.isinf (c2p))))
print ("min/max ket_basis: {}/{}".format (np.amin (c2p), np.amax (c2p)))
proj_l = c2p @ c2p.conjugate ().T
if isinstance (cOc, np.ndarray):
proj_l = cOc @ proj_l @ cOc
r_symmetry = inner_symmetry if outer_symmetry[1] is None else outer_symmetry[1]
rets = matrix_eigen_control_options (proj_l, subspace=c2q, symmetry=r_symmetry, strong_symm=enforce_symmetry, sort_vecs=-1,
only_nonzero_vals=False, num_zero_atol=num_zero_atol)
evals_r, c2r = rets[:2]
if get_labels: rlab = rets[2]
proj_r = c2q @ c2q.conjugate ().T
if isinstance (cOc, np.ndarray):
proj_r = cOc @ proj_r @ cOc
l_symmetry = inner_symmetry if outer_symmetry[0] is None else outer_symmetry[0]
rets = matrix_eigen_control_options (proj_r, subspace=c2p, symmetry=l_symmetry, strong_symm=enforce_symmetry, sort_vecs=-1,
only_nonzero_vals=False, num_zero_atol=num_zero_atol)
evals_l, c2l = rets[:2]
if get_labels: llab = rets[2]
print ("These pairs of eigenvalues should be equal and all positive:")
for el, er in zip (evals_l, evals_r):
print (el, er)
mlen = min (len (evals_l), len (evals_r))
if len (evals_l) > mlen: print ("More left-hand eigenvalues: {}".format (evals_l[mlen:]))
if len (evals_r) > mlen: print ("More left-hand eigenvalues: {}".format (evals_r[mlen:]))
raise (e)
# Truncate the basis if requested
max_nlvecs = max_nlvecs or c2l.shape[1]
max_nrvecs = max_nrvecs or c2r.shape[1]
# But you can't truncate it smaller than it already is
max_nlvecs = min (max_nlvecs, c2l.shape[1])
max_nrvecs = min (max_nrvecs, c2r.shape[1])
c2l = c2l[:,:max_nlvecs]
c2r = c2r[:,:max_nrvecs]
if get_labels: return c2l, c2r, svals, llab, rlab
return c2l, c2r, svals
def dmet_cderi(self, loc2dmet, numAct=None):
t0 = time.clock()
w0 = time.time()
norbs_aux = self.with_df.get_naoaux()
numAct = loc2dmet.shape[1] if numAct == None else numAct
loc2imp = loc2dmet[:, :numAct]
assert (self.with_df is not None), "density fitting required"
npair = numAct * (numAct + 1) // 2
CDERI = np.empty((self.with_df.get_naoaux(), npair),
dtype=loc2dmet.dtype)
full_cderi_size = (norbs_aux * self.mol.nao_nr() *
(self.mol.nao_nr() + 1) * CDERI.itemsize // 2) / 1e6
imp_eri_size = (CDERI.itemsize * npair * (npair + 1) // 2) / 1e6
imp_cderi_size = CDERI.size * CDERI.itemsize / 1e6
print(
"Size comparison: cderi is ({0},{1},{1})->{2:.0f} MB compacted; eri is ({1},{1},{1},{1})->{3:.0f} MB compacted"
.format(norbs_aux, numAct, imp_cderi_size, imp_eri_size))
ao2imp = np.dot(self.ao2loc, loc2imp)
ijmosym, mij_pair, moij, ijslice = ao2mo.incore._conc_mos(ao2imp,
ao2imp,
compact=True)
b0 = 0
for eri1 in self.with_df.loop():
b1 = b0 + eri1.shape[0]
eri2 = CDERI[b0:b1]
eri2 = ao2mo._ao2mo.nr_e2(eri1,
moij,
ijslice,
aosym='s2',
mosym=ijmosym,
out=eri2)
b0 = b1
t1 = time.clock()
w1 = time.time()
print(("({0}, {1}) seconds to turn {2:.0f}-MB full"
"cderi array into {3:.0f}-MP impurity cderi array").format(
t1 - t0, w1 - w0, full_cderi_size, imp_cderi_size))
# Compression step 1: remove zero rows
idx_nonzero = np.amax(np.abs(CDERI), axis=1) > sqrt(LINEAR_DEP_THR)
print(
"From {} auxiliary functions, {} have nonzero rows of the 3-center integral"
.format(norbs_aux, np.count_nonzero(idx_nonzero)))
CDERI = CDERI[idx_nonzero]
# Compression step 2: svd
sigma, vmat = matrix_svd_control_options(
CDERI,
sort_vecs=-1,
only_nonzero_vals=True,
full_matrices=False,
num_zero_atol=sqrt(LINEAR_DEP_THR))[1:]
imp_cderi_size = vmat.size * vmat.itemsize / 1e6
print(
"From {} nonzero aux-function rows, {} nonzero singular values found"
.format(np.count_nonzero(idx_nonzero), len(sigma)))
print(
"With SVD: {0:.0f}-MB CDERI array, compared to {1:.0f}-MB eri; ({2}, {3}) seconds"
.format(imp_cderi_size, imp_eri_size,
time.clock() - t1,
time.time() - w1))
CDERI = np.ascontiguousarray((vmat * sigma).T)
return CDERI
