def _call_rmb_vhf1(mol, dm, key='giao'):
c1 = .5 / lib.param.LIGHT_SPEED
n2c = dm.shape[0] // 2
dmll = dm[:n2c, :n2c].copy()
dmls = dm[:n2c, n2c:].copy()
dmsl = dm[n2c:, :n2c].copy()
dmss = dm[n2c:, n2c:].copy()
vj = numpy.zeros((3, n2c * 2, n2c * 2), dtype=numpy.complex)
vk = numpy.zeros((3, n2c * 2, n2c * 2), dtype=numpy.complex)
vx = _vhf.rdirect_mapdm('int2e_' + key + '_sa10sp1spsp2_spinor', 's2kl',
('ji->s2kl', 'lk->s1ij', 'jk->s1il', 'li->s1kj'),
dmss, 3, mol._atm, mol._bas, mol._env) * c1**4
for i in range(3):
vx[0, i] = lib.hermi_triu(vx[0, i], 2)
vj[:, n2c:, n2c:] = vx[0] + vx[1]
vk[:, n2c:, n2c:] = vx[2] + vx[3]
vx = _vhf.rdirect_bindm('int2e_' + key + '_sa10sp1_spinor', 's2kl',
('lk->s1ij', 'ji->s2kl', 'jk->s1il', 'li->s1kj'),
(dmll, dmss, dmsl, dmls), 3, mol._atm, mol._bas,
mol._env) * c1**2
for i in range(3):
vx[1, i] = lib.hermi_triu(vx[1, i], 2)
vj[:, n2c:, n2c:] += vx[0]
vj[:, :n2c, :n2c] += vx[1]
vk[:, n2c:, :n2c] += vx[2]
vk[:, :n2c, n2c:] += vx[3]
for i in range(3):
vj[i] = vj[i] + vj[i].T.conj()
vk[i] = vk[i] + vk[i].T.conj()
return vj, vk
def test_unpack(self):
a = numpy.random.random((400, 400))
a = a + a * .5j
for i in range(400):
a[i, i] = a[i, i].real
b = a - a.T.conj()
b = numpy.array((b, b))
x = lib.hermi_triu(b[0].T, hermi=2, inplace=0)
self.assertAlmostEqual(abs(b[0].T - x).max(), 0, 12)
x = lib.hermi_triu(b[1], hermi=2, inplace=0)
self.assertAlmostEqual(abs(b[1] - x).max(), 0, 12)
self.assertAlmostEqual(
abs(x - lib.unpack_tril(lib.pack_tril(x), 2)).max(), 0, 12)
x = lib.hermi_triu(a, hermi=1, inplace=0)
self.assertAlmostEqual(abs(x - x.T.conj()).max(), 0, 12)
xs = numpy.asarray((x, x, x))
self.assertAlmostEqual(
abs(xs - lib.unpack_tril(lib.pack_tril(xs))).max(), 0, 12)
numpy.random.seed(1)
a = numpy.random.random((5050, 20))
self.assertAlmostEqual(lib.fp(lib.unpack_tril(a, axis=0)),
-103.03970592075423, 10)
a = numpy.zeros((5, 0))
self.assertEqual(lib.unpack_tril(a, axis=-1).shape, (5, 0, 0))
a = numpy.zeros((0, 5))
self.assertEqual(lib.unpack_tril(a, axis=0).shape, (0, 0, 5))
def make_h1_soc2e(hfcobj, dm0):
mf = hfcobj._scf
ni = mf._numint
hyb = ni.hybrid_coeff(mf.xc, spin=mol.spin)
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory * .9 - mem_now)
v1 = get_vxc_soc(ni,
mol,
mf.grids,
mf.xc,
dm0,
max_memory=max_memory,
verbose=hfcobj.verbose)
if abs(hyb) > 1e-10:
vj, vk = uhf_hfc.get_jk(mol, dm0)
v1 += vj[0] + vj[1]
v1 -= vk * hyb
else:
vj = _vhf.direct_mapdm(mol._add_suffix('int2e_p1vxp1'), 'a4ij',
'lk->s2ij', dm0, 3, mol._atm, mol._bas,
mol._env)
for i in range(3):
lib.hermi_triu(vj[0, i], hermi=2, inplace=True)
lib.hermi_triu(vj[1, i], hermi=2, inplace=True)
v1 += vj[0] + vj[1]
v1[1] *= -1
return v1
def get_j(mol, dm0):
vj = _vhf.direct_mapdm(mol._add_suffix('int2e_p1vxp1'), 'a4ij', 'lk->s2ij',
dm0, 3, mol._atm, mol._bas, mol._env)
for i in range(3):
lib.hermi_triu(vj[0, i], hermi=2, inplace=True)
lib.hermi_triu(vj[1, i], hermi=2, inplace=True)
return vj
def _call_rmb_vhf1(mol, dm, key='giao'):
c1 = .5 / lib.param.LIGHT_SPEED
n2c = dm.shape[0] // 2
dmll = dm[:n2c,:n2c].copy()
dmls = dm[:n2c,n2c:].copy()
dmsl = dm[n2c:,:n2c].copy()
dmss = dm[n2c:,n2c:].copy()
vj = numpy.zeros((3,n2c*2,n2c*2), dtype=numpy.complex)
vk = numpy.zeros((3,n2c*2,n2c*2), dtype=numpy.complex)
vx = _vhf.rdirect_mapdm('int2e_'+key+'_sa10sp1spsp2_spinor', 's2kl',
('ji->s2kl', 'lk->s1ij', 'jk->s1il', 'li->s1kj'),
dmss, 3, mol._atm, mol._bas, mol._env) * c1**4
for i in range(3):
vx[0,i] = lib.hermi_triu(vx[0,i], 2)
vj[:,n2c:,n2c:] = vx[0] + vx[1]
vk[:,n2c:,n2c:] = vx[2] + vx[3]
vx = _vhf.rdirect_bindm('int2e_'+key+'_sa10sp1_spinor', 's2kl',
('lk->s1ij', 'ji->s2kl', 'jk->s1il', 'li->s1kj'),
(dmll,dmss,dmsl,dmls), 3,
mol._atm, mol._bas, mol._env) * c1**2
for i in range(3):
vx[1,i] = lib.hermi_triu(vx[1,i], 2)
vj[:,n2c:,n2c:] += vx[0]
vj[:,:n2c,:n2c] += vx[1]
vk[:,n2c:,:n2c] += vx[2]
vk[:,:n2c,n2c:] += vx[3]
for i in range(3):
vj[i] = vj[i] + vj[i].T.conj()
vk[i] = vk[i] + vk[i].T.conj()
return vj, vk
def get_jk(mol_or_mf=None,
dm=None,
hermi=1,
with_j=True,
with_k=True,
omega=None):
'''MPI version of scf.hf.get_jk function'''
#vj = get_j(mol_or_mf, dm, hermi)
#vk = get_k(mol_or_mf, dm, hermi)
if isinstance(mol_or_mf, gto.mole.Mole):
mf = hf.SCF(mol_or_mf).view(SCF)
else:
mf = mol_or_mf
# dm may be too big for mpi4py library to serialize. Broadcast dm here.
if any(comm.allgather(dm is mpi.Message.SkippedArg)):
dm = mpi.bcast_tagged_array(dm)
mf.unpack_(comm.bcast(mf.pack()))
if mf.opt is None:
mf.opt = mf.init_direct_scf()
if omega is None:
vj, vk = _eval_jk(mf, dm, hermi, _jk_jobs_s8)
else:
with mf.mol.with_range_coulomb(omega):
vj, vk = _eval_jk(mf, dm, hermi, _jk_jobs_s8)
if rank == 0:
for i in range(vj.shape[0]):
lib.hermi_triu(vj[i], 1, inplace=True)
return vj.reshape(dm.shape), vk.reshape(dm.shape)
def _mat_hermi_(vk, hermi):
if hermi == 1:
if vk.ndim == 2:
vk = lib.hermi_triu(vk, hermi)
else:
for i in range(vk.shape[0]):
vk[i] = lib.hermi_triu(vk[i], hermi)
return vk
def get_j(mol, dm0):
vj = _vhf.direct_mapdm(mol._add_suffix('int2e_p1vxp1'),
'a4ij', 'lk->s2ij',
dm0, 3, mol._atm, mol._bas, mol._env)
for i in range(3):
lib.hermi_triu(vj[0,i], hermi=2, inplace=True)
lib.hermi_triu(vj[1,i], hermi=2, inplace=True)
return vj
def get_jk(mol, dm0):
# K_{pq} = (pi|iq) + (iq|pi)
vj, vk, vk1 = _vhf.direct_mapdm(mol._add_suffix('int2e_p1vxp1'),
'a4ij', ('lk->s2ij', 'jk->s1il', 'li->s1kj'),
dm0, 3, mol._atm, mol._bas, mol._env)
for i in range(3):
lib.hermi_triu(vj[0,i], hermi=2, inplace=True)
lib.hermi_triu(vj[1,i], hermi=2, inplace=True)
vk += vk1
return vj, vk
def get_jk(mol, dm0):
# K_{pq} = (pi|iq) + (iq|pi)
vj, vk, vk1 = _vhf.direct_mapdm(mol._add_suffix('int2e_p1vxp1'),
'a4ij', ('lk->s2ij', 'jk->s1il', 'li->s1kj'),
dm0, 3, mol._atm, mol._bas, mol._env)
for i in range(3):
lib.hermi_triu(vj[0,i], hermi=2, inplace=True)
lib.hermi_triu(vj[1,i], hermi=2, inplace=True)
vk += vk1
return vj, vk
def make_h1(mf,
mo_coeff,
mo_occ,
chkfile=None,
atmlst=None,
verbose=logger.WARN):
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mf.stdout, mf.verbose)
mol = mf.mol
if atmlst is None:
atmlst = range(mol.natm)
nao, nmo = mo_coeff.shape
mocc = mo_coeff[:, mo_occ > 0]
dm0 = numpy.dot(mocc, mocc.T) * 2
h1a = -(mol.intor('int1e_ipkin', comp=3) +
mol.intor('int1e_ipnuc', comp=3))
offsetdic = mol.offset_nr_by_atom()
h1aos = []
int2e_ip1 = mol._add_suffix('int2e_ip1')
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
mol.set_rinv_origin(mol.atom_coord(ia))
h1ao = -mol.atom_charge(ia) * mol.intor('int1e_iprinv', comp=3)
h1ao[:, p0:p1] += h1a[:, p0:p1]
h1ao = h1ao + h1ao.transpose(0, 2, 1)
shls_slice = (shl0, shl1) + (0, mol.nbas) * 3
vj1, vj2, vk1, vk2 = \
_vhf.direct_bindm(int2e_ip1, 's2kl',
('ji->s2kl', 'lk->s1ij', 'li->s1kj', 'jk->s1il'),
(-dm0[:,p0:p1], -dm0, -dm0[:,p0:p1], -dm0),
3, mol._atm, mol._bas, mol._env,
shls_slice=shls_slice)
for i in range(3):
lib.hermi_triu(vj1[i], 1)
vhf = vj1 - vk1 * .5
vhf[:, p0:p1] += vj2 - vk2 * .5
vhf = vhf + vhf.transpose(0, 2, 1)
if chkfile is None:
h1aos.append(h1ao + vhf)
else:
key = 'scf_h1ao/%d' % ia
lib.chkfile.save(chkfile, key, h1ao + vhf)
if chkfile is None:
return h1aos
else:
return chkfile
def dot_eri_dm(eri, dms, nao_v=None, eri_dot_dm=True):
assert (eri.dtype == numpy.double)
eri = numpy.asarray(eri, order='C')
dms = numpy.asarray(dms, order='C')
dms_shape = dms.shape
nao_dm = dms_shape[-1]
if nao_v is None:
nao_v = nao_dm
dms = dms.reshape(-1, nao_dm, nao_dm)
n_dm = dms.shape[0]
vj = numpy.zeros((n_dm, nao_v, nao_v))
dmsptr = []
vjkptr = []
fjkptr = []
npair_v = nao_v * (nao_v + 1) // 2
npair_dm = nao_dm * (nao_dm + 1) // 2
if eri.ndim == 2 and npair_v * npair_dm == eri.size: # 4-fold symmetry eri
if eri_dot_dm: # 'ijkl,kl->ij'
fdrv = getattr(_vhf.libcvhf, 'CVHFnrs4_incore_drv_diff_size_v_dm')
fvj = _vhf._fpointer('CVHFics4_kl_s2ij_diff_size')
else: # 'ijkl,ij->kl'
fdrv = getattr(_vhf.libcvhf, 'CVHFnrs4_incore_drv_diff_size_dm_v')
fvj = _vhf._fpointer('CVHFics4_ij_s2kl_diff_size')
for i, dm in enumerate(dms):
dmsptr.append(dm.ctypes.data_as(ctypes.c_void_p))
vjkptr.append(vj[i].ctypes.data_as(ctypes.c_void_p))
fjkptr.append(fvj)
else:
raise RuntimeError(
'Array shape not consistent: nao_v %s, DM %s, eri %s' %
(nao_v, dms_shape, eri.shape))
n_ops = len(dmsptr)
fdrv(eri.ctypes.data_as(ctypes.c_void_p),
(ctypes.c_void_p * n_ops)(*dmsptr),
(ctypes.c_void_p * n_ops)(*vjkptr), ctypes.c_int(n_ops),
ctypes.c_int(nao_v), ctypes.c_int(nao_dm),
(ctypes.c_void_p * n_ops)(*fjkptr))
for i in range(n_dm):
lib.hermi_triu(vj[i], 1, inplace=True)
if n_dm == 1:
vj = vj.reshape((nao_v, nao_v))
else:
vj = vj.reshape((n_dm, nao_v, nao_v))
return vj
def make_h1(mf, mo_coeff, mo_occ, chkfile=None, atmlst=None, verbose=logger.WARN):
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mf.stdout, mf.verbose)
mol = mf.mol
if atmlst is None:
atmlst = range(mol.natm)
nao, nmo = mo_coeff.shape
mocc = mo_coeff[:,mo_occ>0]
dm0 = numpy.dot(mocc, mocc.T) * 2
h1a =-(mol.intor('cint1e_ipkin_sph', comp=3) +
mol.intor('cint1e_ipnuc_sph', comp=3))
offsetdic = mol.offset_nr_by_atom()
h1aos = []
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
mol.set_rinv_origin(mol.atom_coord(ia))
h1ao = -mol.atom_charge(ia) * mol.intor('cint1e_iprinv_sph', comp=3)
h1ao[:,p0:p1] += h1a[:,p0:p1]
h1ao = h1ao + h1ao.transpose(0,2,1)
shls_slice = (shl0, shl1) + (0, mol.nbas)*3
vj1, vj2, vk1, vk2 = \
_vhf.direct_bindm('cint2e_ip1_sph', 's2kl',
('ji->s2kl', 'lk->s1ij', 'li->s1kj', 'jk->s1il'),
(-dm0[:,p0:p1], -dm0, -dm0[:,p0:p1], -dm0),
3, mol._atm, mol._bas, mol._env,
shls_slice=shls_slice)
for i in range(3):
lib.hermi_triu(vj1[i], 1)
vhf = vj1 - vk1*.5
vhf[:,p0:p1] += vj2 - vk2*.5
vhf = vhf + vhf.transpose(0,2,1)
if chkfile is None:
h1aos.append(h1ao+vhf)
else:
key = 'scf_h1ao/%d' % ia
lib.chkfile.save(chkfile, key, h1ao+vhf)
if chkfile is None:
return h1aos
else:
return chkfile
def pspace(h1e, eri, norb, nelec, hdiag=None, np=400):
'''pspace Hamiltonian to improve Davidson preconditioner. See, CPL, 169, 463
'''
if norb > 63:
raise NotImplementedError('norb > 63')
neleca, nelecb = _unpack_nelec(nelec)
h1e = numpy.ascontiguousarray(h1e)
eri = ao2mo.restore(1, eri, norb)
nb = cistring.num_strings(norb, nelecb)
if hdiag is None:
hdiag = make_hdiag(h1e, eri, norb, nelec)
if hdiag.size < np:
addr = numpy.arange(hdiag.size)
else:
try:
addr = numpy.argpartition(hdiag, np-1)[:np]
except AttributeError:
addr = numpy.argsort(hdiag)[:np]
addra, addrb = divmod(addr, nb)
stra = cistring.addrs2str(norb, neleca, addra)
strb = cistring.addrs2str(norb, nelecb, addrb)
np = len(addr)
h0 = numpy.zeros((np,np))
libfci.FCIpspace_h0tril(h0.ctypes.data_as(ctypes.c_void_p),
h1e.ctypes.data_as(ctypes.c_void_p),
eri.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(np))
for i in range(np):
h0[i,i] = hdiag[addr[i]]
h0 = lib.hermi_triu(h0)
return addr, h0
def pspace(h1e, eri, norb, nelec, hdiag, np=400):
'''pspace Hamiltonian to improve Davidson preconditioner. See, CPL, 169, 463
'''
neleca, nelecb = _unpack_nelec(nelec)
h1e = numpy.ascontiguousarray(h1e)
eri = ao2mo.restore(1, eri, norb)
nb = cistring.num_strings(norb, nelecb)
if hdiag.size < np:
addr = numpy.arange(hdiag.size)
else:
try:
addr = numpy.argpartition(hdiag, np-1)[:np]
except AttributeError:
addr = numpy.argsort(hdiag)[:np]
addra, addrb = divmod(addr, nb)
stra = numpy.array([cistring.addr2str(norb,neleca,ia) for ia in addra],
dtype=numpy.uint64)
strb = numpy.array([cistring.addr2str(norb,nelecb,ib) for ib in addrb],
dtype=numpy.uint64)
np = len(addr)
h0 = numpy.zeros((np,np))
libfci.FCIpspace_h0tril(h0.ctypes.data_as(ctypes.c_void_p),
h1e.ctypes.data_as(ctypes.c_void_p),
eri.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(np))
for i in range(np):
h0[i,i] = hdiag[addr[i]]
h0 = lib.hermi_triu(h0)
return addr, h0
def _call_giao_vhf1(mol, dm):
c1 = .5 / lib.param.LIGHT_SPEED
n2c = dm.shape[0] // 2
dmll = dm[:n2c, :n2c].copy()
dmls = dm[:n2c, n2c:].copy()
dmsl = dm[n2c:, :n2c].copy()
dmss = dm[n2c:, n2c:].copy()
vj = numpy.zeros((3, n2c * 2, n2c * 2), dtype=numpy.complex)
vk = numpy.zeros((3, n2c * 2, n2c * 2), dtype=numpy.complex)
vx = _vhf.rdirect_mapdm('int2e_g1_spinor', 'a4ij',
('lk->s2ij', 'jk->s1il'), dmll, 3, mol._atm,
mol._bas, mol._env)
vj[:, :n2c, :n2c] = vx[0]
vk[:, :n2c, :n2c] = vx[1]
vx = _vhf.rdirect_mapdm('int2e_spgsp1spsp2_spinor', 'a4ij',
('lk->s2ij', 'jk->s1il'), dmss, 3, mol._atm,
mol._bas, mol._env) * c1**4
vj[:, n2c:, n2c:] = vx[0]
vk[:, n2c:, n2c:] = vx[1]
vx = _vhf.rdirect_bindm('int2e_g1spsp2_spinor', 'a4ij',
('lk->s2ij', 'jk->s1il'), (dmss, dmls), 3,
mol._atm, mol._bas, mol._env) * c1**2
vj[:, :n2c, :n2c] += vx[0]
vk[:, :n2c, n2c:] += vx[1]
vx = _vhf.rdirect_bindm('int2e_spgsp1_spinor', 'a4ij',
('lk->s2ij', 'jk->s1il'), (dmll, dmsl), 3,
mol._atm, mol._bas, mol._env) * c1**2
vj[:, n2c:, n2c:] += vx[0]
vk[:, n2c:, :n2c] += vx[1]
for i in range(3):
vj[i] = lib.hermi_triu(vj[i], 1)
vk[i] = vk[i] + vk[i].T.conj()
return vj, vk
def _call_giao_vhf1(mol, dm):
c1 = .5 / lib.param.LIGHT_SPEED
n2c = dm.shape[0] // 2
dmll = dm[:n2c,:n2c].copy()
dmls = dm[:n2c,n2c:].copy()
dmsl = dm[n2c:,:n2c].copy()
dmss = dm[n2c:,n2c:].copy()
vj = numpy.zeros((3,n2c*2,n2c*2), dtype=numpy.complex)
vk = numpy.zeros((3,n2c*2,n2c*2), dtype=numpy.complex)
vx = _vhf.rdirect_mapdm('int2e_g1_spinor', 'a4ij',
('lk->s2ij', 'jk->s1il'), dmll, 3,
mol._atm, mol._bas, mol._env)
vj[:,:n2c,:n2c] = vx[0]
vk[:,:n2c,:n2c] = vx[1]
vx = _vhf.rdirect_mapdm('int2e_spgsp1spsp2_spinor', 'a4ij',
('lk->s2ij', 'jk->s1il'), dmss, 3,
mol._atm, mol._bas, mol._env) * c1**4
vj[:,n2c:,n2c:] = vx[0]
vk[:,n2c:,n2c:] = vx[1]
vx = _vhf.rdirect_bindm('int2e_g1spsp2_spinor', 'a4ij',
('lk->s2ij', 'jk->s1il'), (dmss,dmls), 3,
mol._atm, mol._bas, mol._env) * c1**2
vj[:,:n2c,:n2c] += vx[0]
vk[:,:n2c,n2c:] += vx[1]
vx = _vhf.rdirect_bindm('int2e_spgsp1_spinor', 'a4ij',
('lk->s2ij', 'jk->s1il'), (dmll,dmsl), 3,
mol._atm, mol._bas, mol._env) * c1**2
vj[:,n2c:,n2c:] += vx[0]
vk[:,n2c:,:n2c] += vx[1]
for i in range(3):
vj[i] = lib.hermi_triu(vj[i], 1)
vk[i] = vk[i] + vk[i].T.conj()
return vj, vk
def pspace(h1e, eri, norb, nelec, hdiag, np=400):
neleca, nelecb = direct_spin1._unpack_nelec(nelec)
h1e_a = numpy.ascontiguousarray(h1e[0])
h1e_b = numpy.ascontiguousarray(h1e[1])
g2e_aa = ao2mo.restore(1, eri[0], norb)
g2e_ab = ao2mo.restore(1, eri[1], norb)
g2e_bb = ao2mo.restore(1, eri[2], norb)
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
nb = link_indexb.shape[0]
addr = numpy.argsort(hdiag)[:np]
addra = addr // nb
addrb = addr % nb
stra = numpy.array([cistring.addr2str(norb,neleca,ia) for ia in addra],
dtype=numpy.long)
strb = numpy.array([cistring.addr2str(norb,nelecb,ib) for ib in addrb],
dtype=numpy.long)
np = len(addr)
h0 = numpy.zeros((np,np))
libfci.FCIpspace_h0tril_uhf(h0.ctypes.data_as(ctypes.c_void_p),
h1e_a.ctypes.data_as(ctypes.c_void_p),
h1e_b.ctypes.data_as(ctypes.c_void_p),
g2e_aa.ctypes.data_as(ctypes.c_void_p),
g2e_ab.ctypes.data_as(ctypes.c_void_p),
g2e_bb.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(np))
for i in range(np):
h0[i,i] = hdiag[addr[i]]
h0 = lib.hermi_triu(h0)
return addr, h0
def incore(eri, dm, hermi=0):
assert(not numpy.iscomplexobj(eri))
eri = numpy.ascontiguousarray(eri)
dm = numpy.ascontiguousarray(dm)
nao = dm.shape[0]
vj = numpy.empty((nao,nao))
vk = numpy.empty((nao,nao))
npair = nao*(nao+1)//2
if eri.ndim == 2 and npair*npair == eri.size: # 4-fold symmetry eri
fdrv = getattr(libcvhf, 'CVHFnrs4_incore_drv')
# 'ijkl,kl->ij'
fvj = _fpointer('CVHFics4_kl_s2ij')
# 'ijkl,il->jk'
fvk = _fpointer('CVHFics4_il_s1jk')
# or
## 'ijkl,ij->kl'
#fvj = _fpointer('CVHFics4_ij_s2kl')
## 'ijkl,jk->il'
#fvk = _fpointer('CVHFics4_jk_s1il')
tridm = dm
elif eri.ndim == 1 and npair*(npair+1)//2 == eri.size: # 8-fold symmetry eri
fdrv = getattr(libcvhf, 'CVHFnrs8_incore_drv')
fvj = _fpointer('CVHFics8_tridm_vj')
if hermi == 1:
fvk = _fpointer('CVHFics8_jk_s2il')
else:
fvk = _fpointer('CVHFics8_jk_s1il')
tridm = lib.pack_tril(lib.transpose_sum(dm))
i = numpy.arange(nao)
tridm[i*(i+1)//2+i] *= .5
else:
raise RuntimeError('Array shape not consistent: DM %s, eri %s'
% (dm.shape, eri.shape))
fdrv(eri.ctypes.data_as(ctypes.c_void_p),
tridm.ctypes.data_as(ctypes.c_void_p),
vj.ctypes.data_as(ctypes.c_void_p),
dm.ctypes.data_as(ctypes.c_void_p),
vk.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nao), fvj, fvk)
if hermi != 0:
vj = lib.hermi_triu(vj, hermi)
vk = lib.hermi_triu(vk, hermi)
else:
vj = lib.hermi_triu(vj, 1)
return vj, vk
def incore(eri, dm, hermi=0):
assert (not numpy.iscomplexobj(eri))
eri = numpy.ascontiguousarray(eri)
dm = numpy.ascontiguousarray(dm)
nao = dm.shape[0]
vj = numpy.empty((nao, nao))
vk = numpy.empty((nao, nao))
npair = nao * (nao + 1) // 2
if eri.ndim == 2 and npair * npair == eri.size: # 4-fold symmetry eri
fdrv = getattr(libcvhf, 'CVHFnrs4_incore_drv')
# 'ijkl,kl->ij'
fvj = _fpointer('CVHFics4_kl_s2ij')
# 'ijkl,il->jk'
fvk = _fpointer('CVHFics4_il_s1jk')
# or
## 'ijkl,ij->kl'
#fvj = _fpointer('CVHFics4_ij_s2kl')
## 'ijkl,jk->il'
#fvk = _fpointer('CVHFics4_jk_s1il')
tridm = dm
elif eri.ndim == 1 and npair * (npair +
1) // 2 == eri.size: # 8-fold symmetry eri
fdrv = getattr(libcvhf, 'CVHFnrs8_incore_drv')
fvj = _fpointer('CVHFics8_tridm_vj')
if hermi == 1:
fvk = _fpointer('CVHFics8_jk_s2il')
else:
fvk = _fpointer('CVHFics8_jk_s1il')
tridm = lib.pack_tril(lib.transpose_sum(dm))
i = numpy.arange(nao)
tridm[i * (i + 1) // 2 + i] *= .5
else:
raise RuntimeError('Array shape not consistent: DM %s, eri %s' %
(dm.shape, eri.shape))
fdrv(eri.ctypes.data_as(ctypes.c_void_p),
tridm.ctypes.data_as(ctypes.c_void_p),
vj.ctypes.data_as(ctypes.c_void_p),
dm.ctypes.data_as(ctypes.c_void_p),
vk.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(nao), fvj, fvk)
if hermi != 0:
vj = lib.hermi_triu(vj, hermi)
vk = lib.hermi_triu(vk, hermi)
else:
vj = lib.hermi_triu(vj, 1)
return vj, vk
def pspace(h1e, eri, norb, nelec, hdiag=None, np=400):
'''pspace Hamiltonian to improve Davidson preconditioner. See, CPL, 169, 463
'''
if norb > 63:
raise NotImplementedError('norb > 63')
if h1e.dtype == numpy.complex or eri.dtype == numpy.complex:
raise NotImplementedError('Complex Hamiltonian')
neleca, nelecb = _unpack_nelec(nelec)
h1e = numpy.ascontiguousarray(h1e)
eri = ao2mo.restore(1, eri, norb)
nb = cistring.num_strings(norb, nelecb)
if hdiag is None:
hdiag = make_hdiag(h1e, eri, norb, nelec)
if hdiag.size < np:
addr = numpy.arange(hdiag.size)
else:
try:
addr = numpy.argpartition(hdiag, np - 1)[:np].copy()
except AttributeError:
addr = numpy.argsort(hdiag)[:np].copy()
addra, addrb = divmod(addr, nb)
stra = cistring.addrs2str(norb, neleca, addra)
strb = cistring.addrs2str(norb, nelecb, addrb)
np = len(addr)
h0 = numpy.zeros((np, np))
libfci.FCIpspace_h0tril(h0.ctypes.data_as(ctypes.c_void_p),
h1e.ctypes.data_as(ctypes.c_void_p),
eri.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(np))
HERMITIAN_THRESHOLD = 1e-10
if (abs(h1e - h1e.T).max() < HERMITIAN_THRESHOLD and
abs(eri - eri.transpose(1, 0, 3, 2)).max() < HERMITIAN_THRESHOLD):
# symmetric Hamiltonian
h0 = lib.hermi_triu(h0)
else:
# Fill the upper triangular part
h0 = numpy.asarray(h0, order='F')
h1e = numpy.asarray(h1e.T, order='C')
eri = numpy.asarray(eri.transpose(1, 0, 3, 2), order='C')
libfci.FCIpspace_h0tril(h0.ctypes.data_as(ctypes.c_void_p),
h1e.ctypes.data_as(ctypes.c_void_p),
eri.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(np))
idx = numpy.arange(np)
h0[idx, idx] = hdiag[addr]
return addr, h0
def get_jk(mol_or_mf, dm, hermi=1):
'''MPI version of scf.hf.get_jk function'''
#vj = get_j(mol_or_mf, dm, hermi)
#vk = get_k(mol_or_mf, dm, hermi)
if isinstance(mol_or_mf, gto.mole.Mole):
mf = hf.SCF(mol_or_mf).view(SCF)
else:
mf = mol_or_mf
# dm may be too big for mpi4py library to serialize. Broadcast dm here.
if any(comm.allgather(isinstance(dm, str) and dm == 'SKIPPED_ARG')):
dm = mpi.bcast_tagged_array(dm)
mf.unpack_(comm.bcast(mf.pack()))
if mf.opt is None:
mf.opt = mf.init_direct_scf()
vj, vk = _eval_jk(mf, dm, hermi, _jk_jobs_s8)
if rank == 0:
for i in range(vj.shape[0]):
lib.hermi_triu(vj[i], 1, inplace=True)
return vj.reshape(dm.shape), vk.reshape(dm.shape)
def pspace(h1e, eri, norb, nelec, hdiag=None, np=400):
'''pspace Hamiltonian to improve Davidson preconditioner. See, CPL, 169, 463
'''
if norb > 63:
raise NotImplementedError('norb > 63')
neleca, nelecb = _unpack_nelec(nelec)
h1e = numpy.ascontiguousarray(h1e)
eri = ao2mo.restore(1, eri, norb)
nb = cistring.num_strings(norb, nelecb)
if hdiag is None:
hdiag = make_hdiag(h1e, eri, norb, nelec)
if hdiag.size < np:
addr = numpy.arange(hdiag.size)
else:
try:
addr = numpy.argpartition(hdiag, np-1)[:np]
except AttributeError:
addr = numpy.argsort(hdiag)[:np]
addra, addrb = divmod(addr, nb)
stra = cistring.addrs2str(norb, neleca, addra)
strb = cistring.addrs2str(norb, nelecb, addrb)
np = len(addr)
h0 = numpy.zeros((np,np))
libfci.FCIpspace_h0tril(h0.ctypes.data_as(ctypes.c_void_p),
h1e.ctypes.data_as(ctypes.c_void_p),
eri.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(np))
HERMITIAN_THRESHOLD = 1e-10
if (abs(h1e - h1e.T).max() < HERMITIAN_THRESHOLD and
abs(eri - eri.transpose(1,0,3,2)).max() < HERMITIAN_THRESHOLD):
# symmetric Hamiltonian
h0 = lib.hermi_triu(h0)
else:
# Fill the upper triangular part
h0 = numpy.asarray(h0, order='F')
h1e = numpy.asarray(h1e.T, order='C')
eri = numpy.asarray(eri.transpose(1,0,3,2), order='C')
libfci.FCIpspace_h0tril(h0.ctypes.data_as(ctypes.c_void_p),
h1e.ctypes.data_as(ctypes.c_void_p),
eri.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(np))
idx = numpy.arange(np)
h0[idx,idx] = hdiag[addr]
return addr, h0
def _get_jk(mol,
intor,
comp,
aosym,
script_dms,
shls_slice=None,
cintopt=None,
vhfopt=None):
intor = mol._add_suffix(intor)
scripts = script_dms[::2]
dms = script_dms[1::2]
vs = _vhf.direct_bindm(intor,
aosym,
scripts,
dms,
comp,
mol._atm,
mol._bas,
mol._env,
vhfopt=vhfopt,
cintopt=cintopt,
shls_slice=shls_slice)
for k, script in enumerate(scripts):
if 's2' in script:
hermi = 1
elif 'a2' in script:
hermi = 2
else:
continue
shape = vs[k].shape
if shape[-2] == shape[-1]:
if comp > 1:
for i in range(comp):
lib.hermi_triu(vs[k][i], hermi=hermi, inplace=True)
else:
lib.hermi_triu(vs[k], hermi=hermi, inplace=True)
return vs
def test_unpack(self):
a = numpy.random.random((400,400))
a = a+a*.5j
for i in range(400):
a[i,i] = a[i,i].real
b = a-a.T.conj()
b = numpy.array((b,b))
x = lib.hermi_triu(b[0].T, hermi=2, inplace=0)
self.assertAlmostEqual(abs(b[0].T-x).max(), 0, 12)
x = lib.hermi_triu(b[1], hermi=2, inplace=0)
self.assertAlmostEqual(abs(b[1]-x).max(), 0, 12)
self.assertAlmostEqual(abs(x - lib.unpack_tril(lib.pack_tril(x), 2)).max(), 0, 12)
x = lib.hermi_triu(a, hermi=1, inplace=0)
self.assertAlmostEqual(abs(x-x.T.conj()).max(), 0, 12)
xs = numpy.asarray((x,x,x))
self.assertAlmostEqual(abs(xs - lib.unpack_tril(lib.pack_tril(xs))).max(), 0, 12)
numpy.random.seed(1)
a = numpy.random.random((5050,20))
self.assertAlmostEqual(lib.finger(lib.unpack_tril(a, axis=0)), -103.03970592075423, 10)
def _get_jk(mol, intor, comp, aosym, script_dms,
shls_slice=None, cintopt=None):
intor = mol._add_suffix(intor)
scripts = script_dms[::2]
dms = script_dms[1::2]
vs = _vhf.direct_bindm(intor, aosym, scripts, dms, comp,
mol._atm, mol._bas, mol._env,
cintopt=cintopt, shls_slice=shls_slice)
for k, script in enumerate(scripts):
if 's2' in script:
hermi = 1
elif 'a2' in script:
hermi = 2
else:
continue
shape = vs[k].shape
if shape[-2] == shape[-1]:
if comp > 1:
for i in range(comp):
lib.hermi_triu(vs[k][i], hermi=hermi, inplace=True)
else:
lib.hermi_triu(vs[k], hermi=hermi, inplace=True)
return vs
def intor(mol):
nao = mol.nao_nr()
mat = numpy.zeros((nao,nao))
ip = 0
for ish in range(mol.nbas):
jp = 0
for jsh in range(ish+1):
buf = type1_by_shell(mol, (ish,jsh))
di, dj = buf.shape
mat[ip:ip+di,jp:jp+dj] += buf
buf = type2_by_shell(mol, (ish,jsh))
di, dj = buf.shape
mat[ip:ip+di,jp:jp+dj] += buf
jp += dj
ip += di
return lib.hermi_triu(mat)
def pspace(h1e, eri, norb, nelec, hdiag=None, np=400):
neleca, nelecb = direct_spin1._unpack_nelec(nelec)
h1e_a = numpy.ascontiguousarray(h1e[0])
h1e_b = numpy.ascontiguousarray(h1e[1])
g2e_aa = ao2mo.restore(1, eri[0], norb)
g2e_ab = ao2mo.restore(1, eri[1], norb)
g2e_bb = ao2mo.restore(1, eri[2], norb)
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
nb = link_indexb.shape[0]
if hdiag is None:
hdiag = make_hdiag(h1e, eri, norb, nelec)
if hdiag.size < np:
addr = numpy.arange(hdiag.size)
else:
try:
addr = numpy.argpartition(hdiag, np - 1)[:np]
except AttributeError:
addr = numpy.argsort(hdiag)[:np]
addra = addr // nb
addrb = addr % nb
stra = numpy.array([cistring.addr2str(norb, neleca, ia) for ia in addra],
dtype=numpy.long)
strb = numpy.array([cistring.addr2str(norb, nelecb, ib) for ib in addrb],
dtype=numpy.long)
np = len(addr)
h0 = numpy.zeros((np, np))
libfci.FCIpspace_h0tril_uhf(h0.ctypes.data_as(ctypes.c_void_p),
h1e_a.ctypes.data_as(ctypes.c_void_p),
h1e_b.ctypes.data_as(ctypes.c_void_p),
g2e_aa.ctypes.data_as(ctypes.c_void_p),
g2e_ab.ctypes.data_as(ctypes.c_void_p),
g2e_bb.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(np))
for i in range(np):
h0[i, i] = hdiag[addr[i]]
h0 = lib.hermi_triu(h0)
return addr, h0
def _jk_triu_(vj, vk, hermi):
if hermi == 0:
if vj.ndim == 2:
vj = lib.hermi_triu(vj, 1)
else:
for i in range(vj.shape[0]):
vj[i] = lib.hermi_triu(vj[i], 1)
else:
if vj.ndim == 2:
vj = lib.hermi_triu(vj, hermi)
vk = lib.hermi_triu(vk, hermi)
else:
for i in range(vj.shape[0]):
vj[i] = lib.hermi_triu(vj[i], hermi)
vk[i] = lib.hermi_triu(vk[i], hermi)
return vj, vk
def _jk_triu_(vj, vk, hermi):
if hermi == 0:
if vj.ndim == 2:
vj = lib.hermi_triu(vj, 1)
else:
for i in range(vj.shape[0]):
vj[i] = lib.hermi_triu(vj[i], 1)
else:
if vj.ndim == 2:
vj = lib.hermi_triu(vj, hermi)
vk = lib.hermi_triu(vk, hermi)
else:
for i in range(vj.shape[0]):
vj[i] = lib.hermi_triu(vj[i], hermi)
vk[i] = lib.hermi_triu(vk[i], hermi)
return vj, vk
def runjks2(dm1, ncomp, intorname, filldot, *namejk):
vjk = runjk(dm1, ncomp, intorname, filldot, *namejk)
return [lib.hermi_triu(v, 1) for v in vjk]
def test_direct_jk_s2(self):
numpy.random.seed(15)
dm1 = numpy.random.random((nao, nao))
dm1 = dm1 + dm1.T
vj0, vk0 = scf._vhf.incore(rhf._eri, dm1, 1)
vj1, vk1 = runjks2(dm1, 1, "cint2e_sph", "CVHFdot_nrs8", "CVHFnrs8_ji_s2kl", "CVHFnrs8_jk_s2il")
self.assertTrue(numpy.allclose(vj0, vj1))
self.assertTrue(numpy.allclose(vk0, vk1))
eri1 = ao2mo.restore(1, rhf._eri, nao)
vj0 = numpy.einsum("ijkl,kl->ij", eri1, dm1)
vk0 = numpy.einsum("ijkl,jk->il", eri1, dm1)
vj1, vj2 = runjks2(dm1, 1, "cint2e_sph", "CVHFdot_nrs4", "CVHFnrs4_ji_s2kl", "CVHFnrs4_jk_s2il")
self.assertTrue(numpy.allclose(vj0, vj1))
self.assertTrue(numpy.allclose(vk0, vj2))
vj1, vk1 = runjks2(dm1, 1, "cint2e_sph", "CVHFdot_nrs4", "CVHFnrs4_li_s2kj", "CVHFnrs4_jk_s2il")
self.assertTrue(numpy.allclose(vk0, vj1))
self.assertTrue(numpy.allclose(vk0, vk1))
vk0 = numpy.einsum("ijkl,jk->il", eri1, dm1)
vk1 = runjks2(
dm1,
1,
"cint2e_sph",
"CVHFdot_nrs4",
"CVHFnrs4_li_s2kj",
"CVHFnrs4_jk_s2il",
"CVHFnrs4_li_s2kj",
"CVHFnrs4_jk_s2il",
)
self.assertTrue(numpy.allclose(vk0, vk1[0]))
self.assertTrue(numpy.allclose(vk0, vk1[1]))
self.assertTrue(numpy.allclose(vk0, vk1[2]))
self.assertTrue(numpy.allclose(vk0, vk1[3]))
vj0 = numpy.einsum("ijkl,kl->ij", eri1, dm1)
vk0 = numpy.einsum("ijkl,jk->il", eri1, dm1)
vk1 = runjks2(
dm1,
1,
"cint2e_sph",
"CVHFdot_nrs2kl",
"CVHFnrs2kl_ji_s2kl",
"CVHFnrs2kl_lk_s2ij",
"CVHFnrs2kl_jk_s2il",
"CVHFnrs2kl_li_s2kj",
)
self.assertTrue(numpy.allclose(vj0, vk1[0]))
self.assertTrue(numpy.allclose(vj0, vk1[1]))
self.assertTrue(numpy.allclose(vk0, vk1[2]))
self.assertTrue(numpy.allclose(vk0, vk1[3]))
vk1 = runjks2(
dm1,
1,
"cint2e_sph",
"CVHFdot_nrs2ij",
"CVHFnrs2ij_ji_s2kl",
"CVHFnrs2ij_lk_s2ij",
"CVHFnrs2ij_jk_s2il",
"CVHFnrs2ij_li_s2kj",
)
self.assertTrue(numpy.allclose(vj0, vk1[0]))
self.assertTrue(numpy.allclose(vj0, vk1[1]))
self.assertTrue(numpy.allclose(vk0, vk1[2]))
self.assertTrue(numpy.allclose(vk0, vk1[3]))
vk1 = runjks2(
dm1,
1,
"cint2e_sph",
"CVHFdot_nrs1",
"CVHFnrs1_ji_s2kl",
"CVHFnrs1_lk_s2ij",
"CVHFnrs1_jk_s2il",
"CVHFnrs1_li_s2kj",
)
self.assertTrue(numpy.allclose(vj0, vk1[0]))
self.assertTrue(numpy.allclose(vj0, vk1[1]))
self.assertTrue(numpy.allclose(vk0, vk1[2]))
self.assertTrue(numpy.allclose(vk0, vk1[3]))
vj0, vk0 = scf._vhf.incore(rhf._eri, dm1, 1)
vj1, vk1 = runjk(dm1, 1, "cint2e_sph", "CVHFdot_nrs8", "CVHFnrs8_ji_s2kl", "CVHFnrs8_jk_s2il")
vj1 = lib.hermi_triu(vj1, 1)
vk1 = lib.hermi_triu(vk1, 1)
self.assertTrue(numpy.allclose(vj0, vj1))
self.assertTrue(numpy.allclose(vk0, vk1))
def get_jk_favorj(sgx,
dm,
hermi=1,
with_j=True,
with_k=True,
direct_scf_tol=1e-13):
t0 = time.clock(), time.time()
mol = sgx.mol
grids = sgx.grids
gthrd = sgx.grids_thrd
dms = numpy.asarray(dm)
dm_shape = dms.shape
nao = dm_shape[-1]
dms = dms.reshape(-1, nao, nao)
nset = dms.shape[0]
if sgx.debug:
batch_nuc = _gen_batch_nuc(mol)
else:
batch_jk = _gen_jk_direct(mol, 's2', with_j, with_k, direct_scf_tol)
# for basis set to shell
intor = mol._add_suffix('int3c2e')
fakemol = gto.fakemol_for_charges(grids.coords)
atm, bas, env = gto.mole.conc_env(mol._atm, mol._bas, mol._env,
fakemol._atm, fakemol._bas, fakemol._env)
ao_loc = moleintor.make_loc(bas, intor)
rao_loc = numpy.zeros((nao), dtype=int)
for i in range(mol.nbas):
for j in range(ao_loc[i], ao_loc[i + 1]):
rao_loc[j] = i
sn = numpy.zeros((nao, nao))
ngrids = grids.coords.shape[0]
max_memory = sgx.max_memory - lib.current_memory()[0]
sblk = sgx.blockdim
blksize = min(ngrids, max(4, int(min(sblk,
max_memory * 1e6 / 8 / nao**2))))
for i0, i1 in lib.prange(0, ngrids, blksize):
coords = grids.coords[i0:i1]
ao = mol.eval_gto('GTOval', coords)
wao = ao * grids.weights[i0:i1, None]
sn += lib.dot(ao.T, wao)
ovlp = mol.intor_symmetric('int1e_ovlp')
proj = scipy.linalg.solve(sn, ovlp)
proj_dm = lib.einsum('ki,xij->xkj', proj, dms)
t1 = logger.timer_debug1(mol, "sgX initialziation", *t0)
vj = numpy.zeros_like(dms)
vk = numpy.zeros_like(dms)
tnuc = 0, 0
for i0, i1 in lib.prange(0, ngrids, blksize):
coords = grids.coords[i0:i1]
ao = mol.eval_gto('GTOval', coords)
wao = ao * grids.weights[i0:i1, None]
fg = lib.einsum('gi,xij->xgj', wao, proj_dm)
mask = numpy.zeros(i1 - i0, dtype=bool)
for i in range(nset):
gmaxfg = numpy.amax(numpy.absolute(fg[i]), axis=1)
gmaxwao_v = numpy.amax(numpy.absolute(ao), axis=1)
gmaxtt = gmaxfg * gmaxwao_v
mask |= numpy.any(gmaxtt > 1e-7)
mask |= numpy.any(gmaxtt < -1e-7)
if not numpy.all(mask):
ao = ao[mask]
wao = wao[mask]
fg = fg[:, mask]
coords = coords[mask]
# screening u by value of grids
umaxg = numpy.amax(numpy.absolute(wao), axis=0)
usi = numpy.argwhere(umaxg > 1e-7).reshape(-1)
if len(usi) != 0:
# screening v by ovlp
uovl = ovlp[usi, :]
vmaxu = numpy.amax(numpy.absolute(uovl), axis=0)
osi = numpy.argwhere(vmaxu > 1e-4).reshape(-1)
udms = proj_dm[0][usi, :]
# screening v by dm and ovlp then triangle matrix bn
dmaxg = numpy.amax(numpy.absolute(udms), axis=0)
dsi = numpy.argwhere(dmaxg > 1e-4).reshape(-1)
vsi = numpy.intersect1d(dsi, osi)
if len(vsi) != 0:
vsh = numpy.unique(rao_loc[vsi])
mol._bvv = vsh
# screening u by value of grids
umaxg = numpy.amax(numpy.absolute(wao), axis=0)
usi = numpy.argwhere(umaxg > 1e-7).reshape(-1)
if len(usi) != 0:
# screening v by ovlp
uovl = ovlp[usi, :]
vmaxu = numpy.amax(numpy.absolute(uovl), axis=0)
osi = numpy.argwhere(vmaxu > 1e-4).reshape(-1)
if len(osi) != 0:
vsh = numpy.unique(rao_loc[osi])
#print(vsh.shape,'eew',vsh)
mol._bvv = vsh
fg = lib.einsum('gi,xij->xgj', wao, proj_dm)
mask = numpy.zeros(i1 - i0, dtype=bool)
for i in range(nset):
mask |= numpy.any(fg[i] > gthrd, axis=1)
mask |= numpy.any(fg[i] < -gthrd, axis=1)
if not numpy.all(mask):
ao = ao[mask]
fg = fg[:, mask]
coords = coords[mask]
if with_j:
rhog = numpy.einsum('xgu,gu->xg', fg, ao)
else:
rhog = None
if sgx.debug:
tnuc = tnuc[0] - time.clock(), tnuc[1] - time.time()
gbn = batch_nuc(mol, coords)
tnuc = tnuc[0] + time.clock(), tnuc[1] + time.time()
if with_j:
jpart = numpy.einsum('guv,xg->xuv', gbn, rhog)
if with_k:
gv = lib.einsum('gtv,xgt->xgv', gbn, fg)
gbn = None
else:
tnuc = tnuc[0] - time.clock(), tnuc[1] - time.time()
jpart, gv = batch_jk(mol, coords, rhog, fg)
tnuc = tnuc[0] + time.clock(), tnuc[1] + time.time()
if with_j:
vj += jpart
if with_k:
for i in range(nset):
vk[i] += lib.einsum('gu,gv->uv', ao, gv[i])
jpart = gv = None
t2 = logger.timer_debug1(mol, "sgX J/K builder", *t1)
tdot = t2[0] - t1[0] - tnuc[0], t2[1] - t1[1] - tnuc[1]
logger.debug1(
sgx, '(CPU, wall) time for integrals (%.2f, %.2f); '
'for tensor contraction (%.2f, %.2f)', tnuc[0], tnuc[1], tdot[0],
tdot[1])
for i in range(nset):
lib.hermi_triu(vj[i], inplace=True)
if with_k and hermi == 1:
vk = (vk + vk.transpose(0, 2, 1)) * .5
logger.timer(mol, "vj and vk", *t0)
return vj.reshape(dm_shape), vk.reshape(dm_shape)
def intor_cross(intor, cell1, cell2, comp=1, hermi=0, kpts=None, kpt=None):
r'''1-electron integrals from two cells like
.. math::
\langle \mu | intor | \nu \rangle, \mu \in cell1, \nu \in cell2
'''
intor = moleintor.ascint3(intor)
if kpts is None:
if kpt is not None:
kpts_lst = np.reshape(kpt, (1, 3))
else:
kpts_lst = np.zeros((1, 3))
else:
kpts_lst = np.reshape(kpts, (-1, 3))
nkpts = len(kpts_lst)
atm, bas, env = conc_env(cell1._atm, cell1._bas, cell1._env, cell2._atm,
cell2._bas, cell2._env)
atm = np.asarray(atm, dtype=np.int32)
bas = np.asarray(bas, dtype=np.int32)
env = np.asarray(env, dtype=np.double)
natm = len(atm)
nbas = len(bas)
shls_slice = (0, cell1.nbas, cell1.nbas, nbas)
ao_loc = moleintor.make_loc(bas, intor)
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
nj = ao_loc[shls_slice[3]] - ao_loc[shls_slice[2]]
out = np.empty((nkpts, comp, ni, nj), dtype=np.complex128)
if hermi == 0:
aosym = 's1'
else:
aosym = 's2'
fill = getattr(libpbc, 'PBCnr2c_fill_k' + aosym)
fintor = getattr(moleintor.libcgto, intor)
intopt = lib.c_null_ptr()
Ls = cell1.get_lattice_Ls(rcut=max(cell1.rcut, cell2.rcut))
expkL = np.asarray(np.exp(1j * np.dot(kpts_lst, Ls.T)), order='C')
drv = libpbc.PBCnr2c_drv
drv(fintor, fill, out.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(nkpts),
ctypes.c_int(comp), ctypes.c_int(len(Ls)),
Ls.ctypes.data_as(ctypes.c_void_p),
expkL.ctypes.data_as(ctypes.c_void_p),
(ctypes.c_int * 4)(*(shls_slice[:4])),
ao_loc.ctypes.data_as(ctypes.c_void_p), intopt,
atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(natm),
bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(nbas),
env.ctypes.data_as(ctypes.c_void_p))
mat = []
for k, kpt in enumerate(kpts_lst):
v = out[k]
if hermi != 0:
for ic in range(comp):
lib.hermi_triu(v[ic], hermi=hermi, inplace=True)
if comp == 1:
v = v[0]
if abs(kpt).sum() < 1e-9: # gamma_point
v = v.real
mat.append(v)
if kpts is None or np.shape(kpts) == (3, ): # A single k-point
mat = mat[0]
return mat
def runjks2(dm1, ncomp, intorname, filldot, *namejk):
vjk = runjk(dm1, ncomp, intorname, filldot, *namejk)
return [lib.hermi_triu(v, 1) for v in vjk]
def make_hdiag_csf_slower (h1e, eri, norb, nelec, transformer, hdiag_det=None):
''' This is tricky because I need the diagonal blocks for each configuration in order to get
the correct csf hdiag values, not just the diagonal elements for each determinant. '''
smult = transformer.smult
t0, w0 = time.process_time (), time.time ()
tstr = tlib = tloop = wstr = wlib = wloop = 0
if hdiag_det is None:
hdiag_det = make_hdiag_det (None, h1e, eri, norb, nelec)
eri = ao2mo.restore(1, eri, norb)
neleca, nelecb = _unpack_nelec (nelec)
min_npair, npair_csd_offset, npair_dconf_size, npair_sconf_size, npair_sdet_size = get_csdaddrs_shape (norb, neleca, nelecb)
_, npair_csf_offset, _, _, npair_csf_size = get_csfvec_shape (norb, neleca, nelecb, smult)
npair_econf_size = npair_dconf_size * npair_sconf_size
max_npair = min (neleca, nelecb)
ncsf_all = count_all_csfs (norb, neleca, nelecb, smult)
ndeta_all = cistring.num_strings(norb, neleca)
ndetb_all = cistring.num_strings(norb, nelecb)
ndet_all = ndeta_all * ndetb_all
hdiag_csf = np.ascontiguousarray (np.zeros (ncsf_all, dtype=np.float64))
hdiag_csf_check = np.ones (ncsf_all, dtype=np.bool)
for npair in range (min_npair, max_npair+1):
ipair = npair - min_npair
nconf = npair_econf_size[ipair]
ndet = npair_sdet_size[ipair]
ncsf = npair_csf_size[ipair]
if ncsf == 0:
continue
nspin = neleca + nelecb - 2*npair
csd_offset = npair_csd_offset[ipair]
csf_offset = npair_csf_offset[ipair]
hdiag_conf = np.ascontiguousarray (np.zeros ((nconf, ndet, ndet), dtype=np.float64))
det_addr = transformer.csd_mask[csd_offset:][:nconf*ndet]
if ndet == 1:
# Closed-shell singlets
assert (ncsf == 1)
hdiag_csf[csf_offset:][:nconf] = hdiag_det[det_addr.flat]
hdiag_csf_check[csf_offset:][:nconf] = False
continue
umat = get_spin_evecs (nspin, neleca, nelecb, smult)
det_addra, det_addrb = divmod (det_addr, ndetb_all)
t1, w1 = time.process_time (), time.time ()
det_stra = cistring.addrs2str (norb, neleca, det_addra).reshape (nconf, ndet, order='C')
det_strb = cistring.addrs2str (norb, nelecb, det_addrb).reshape (nconf, ndet, order='C')
tstr += time.process_time () - t1
wstr += time.time () - w1
det_addr = det_addr.reshape (nconf, ndet, order='C')
diag_idx = np.diag_indices (ndet)
triu_idx = np.triu_indices (ndet)
ipair_check = 0
# It looks like the library call below is, itself, usually responsible for about 50% of the
# clock and wall time that this function consumes.
t1, w1 = time.process_time (), time.time ()
for iconf in range (nconf):
addr = det_addr[iconf]
assert (len (addr) == ndet)
stra = det_stra[iconf]
strb = det_strb[iconf]
t2, w2 = time.process_time (), time.time ()
libfci.FCIpspace_h0tril(hdiag_conf[iconf].ctypes.data_as(ctypes.c_void_p),
h1e.ctypes.data_as(ctypes.c_void_p),
eri.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(ndet))
tlib += time.process_time () - t2
wlib += time.time () - w2
#hdiag_conf[iconf][diag_idx] = hdiag_det[addr]
#hdiag_conf[iconf] = lib.hermi_triu(hdiag_conf[iconf])
for iconf in range (nconf): hdiag_conf[iconf] = lib.hermi_triu (hdiag_conf[iconf])
for iconf in range (nconf): hdiag_conf[iconf][diag_idx] = hdiag_det[det_addr[iconf]]
tloop += time.process_time () - t1
wloop += time.time () - w1
hdiag_conf = np.tensordot (hdiag_conf, umat, axes=1)
hdiag_conf = (hdiag_conf * umat[np.newaxis,:,:]).sum (1)
hdiag_csf[csf_offset:][:nconf*ncsf] = hdiag_conf.ravel (order='C')
hdiag_csf_check[csf_offset:][:nconf*ncsf] = False
assert (np.count_nonzero (hdiag_csf_check) == 0), np.count_nonzero (hdiag_csf_check)
#print ("Total time in hdiag_csf: {}, {}".format (time.process_time () - t0, time.time () - w0))
#print (" Loop: {}, {}".format (tloop, wloop))
#print (" Library: {}, {}".format (tlib, wlib))
#print (" Cistring: {}, {}".format (tstr, wstr))
return hdiag_csf
def _eval_jk(mf, dm, hermi, gen_jobs):
cpu0 = (logger.process_clock(), logger.perf_counter())
mol = mf.mol
ao_loc = mol.ao_loc_nr()
nao = ao_loc[-1]
bas_groups = _partition_bas(mol)
jobs = gen_jobs(len(bas_groups), hermi)
njobs = len(jobs)
logger.debug1(mf, 'njobs %d', njobs)
# Each job has multiple recipes.
n_recipes = len(jobs[0][1:])
dm = numpy.asarray(dm).reshape(-1, nao, nao)
n_dm = dm.shape[0]
vk = numpy.zeros((n_recipes, n_dm, nao, nao))
if mf.opt is None:
vhfopt = mf.init_direct_scf(mol)
else:
vhfopt = mf.opt
# Assign the entire dm_cond to vhfopt.
# The prescreen function CVHFnrs8_prescreen will index q_cond and dm_cond
# over the entire basis. "set_dm" in function jk.get_jk/direct_bindm only
# creates a subblock of dm_cond which is not compatible with
# CVHFnrs8_prescreen.
vhfopt.set_dm(dm, mol._atm, mol._bas, mol._env)
# Then skip the "set_dm" initialization in function jk.get_jk/direct_bindm.
vhfopt._dmcondname = None
logger.timer_debug1(mf, 'get_jk initialization', *cpu0)
for job_id in mpi.work_stealing_partition(range(njobs)):
group_ids = jobs[job_id][0]
recipes = jobs[job_id][1:]
shls_slice = lib.flatten([bas_groups[i] for i in group_ids])
loc = ao_loc[shls_slice].reshape(4, 2)
dm_blks = []
for i_dm in range(n_dm):
for ir, recipe in enumerate(recipes):
for i, rec in enumerate(recipe):
p0, p1 = loc[rec[0]]
q0, q1 = loc[rec[1]]
dm_blks.append(dm[i_dm, p0:p1, q0:q1])
scripts = [
'ijkl,%s%s->%s%s' % tuple(['ijkl'[x] for x in rec])
for recipe in recipes for rec in recipe
] * n_dm
kparts = jk.get_jk(mol,
dm_blks,
scripts,
shls_slice=shls_slice,
vhfopt=vhfopt)
for i_dm in range(n_dm):
for ir, recipe in enumerate(recipes):
for i, rec in enumerate(recipe):
p0, p1 = loc[rec[2]]
q0, q1 = loc[rec[3]]
vk[ir, i_dm, p0:p1, q0:q1] += kparts[i]
# Pop the results of one recipe
kparts = kparts[i + 1:]
vk = mpi.reduce(vk)
if rank == 0:
if hermi:
for i in range(n_recipes):
for j in range(n_dm):
lib.hermi_triu(vk[i, j], hermi, inplace=True)
else:
# Zero out vk on workers. If reduce(get_jk()) is called twice,
# non-zero vk on workers can cause error.
vk[:] = 0
logger.timer(mf, 'get_jk', *cpu0)
return vk
def direct(dms, atm, bas, env, vhfopt=None, hermi=0, cart=False):
c_atm = numpy.asarray(atm, dtype=numpy.int32, order='C')
c_bas = numpy.asarray(bas, dtype=numpy.int32, order='C')
c_env = numpy.asarray(env, dtype=numpy.double, order='C')
natm = ctypes.c_int(c_atm.shape[0])
nbas = ctypes.c_int(c_bas.shape[0])
if isinstance(dms, numpy.ndarray) and dms.ndim == 2:
dms = dms[numpy.newaxis, :, :]
n_dm = len(dms)
nao = dms[0].shape[0]
dms = numpy.asarray(dms, order='C')
if vhfopt is None:
if cart:
intor = 'int2e_cart'
else:
intor = 'int2e_sph'
cintopt = make_cintopt(c_atm, c_bas, c_env, intor)
cvhfopt = lib.c_null_ptr()
else:
vhfopt.set_dm(dms, atm, bas, env)
cvhfopt = vhfopt._this
cintopt = vhfopt._cintopt
intor = vhfopt._intor
cintor = _fpointer(intor)
fdrv = getattr(libcvhf, 'CVHFnr_direct_drv')
fdot = _fpointer('CVHFdot_nrs8')
fvj = _fpointer('CVHFnrs8_ji_s2kl')
if hermi == 1:
fvk = _fpointer('CVHFnrs8_li_s2kj')
else:
fvk = _fpointer('CVHFnrs8_li_s1kj')
vjk = numpy.empty((2, n_dm, nao, nao))
fjk = (ctypes.c_void_p * (2 * n_dm))()
dmsptr = (ctypes.c_void_p * (2 * n_dm))()
vjkptr = (ctypes.c_void_p * (2 * n_dm))()
for i in range(n_dm):
dmsptr[i] = dms[i].ctypes.data_as(ctypes.c_void_p)
vjkptr[i] = vjk[0, i].ctypes.data_as(ctypes.c_void_p)
fjk[i] = fvj
for i in range(n_dm):
dmsptr[n_dm + i] = dms[i].ctypes.data_as(ctypes.c_void_p)
vjkptr[n_dm + i] = vjk[1, i].ctypes.data_as(ctypes.c_void_p)
fjk[n_dm + i] = fvk
shls_slice = (ctypes.c_int * 8)(*([0, c_bas.shape[0]] * 4))
ao_loc = make_loc(bas, intor)
fdrv(cintor, fdot, fjk, dmsptr, vjkptr, ctypes.c_int(n_dm * 2),
ctypes.c_int(1), shls_slice, ao_loc.ctypes.data_as(ctypes.c_void_p),
cintopt, cvhfopt, c_atm.ctypes.data_as(ctypes.c_void_p), natm,
c_bas.ctypes.data_as(ctypes.c_void_p), nbas,
c_env.ctypes.data_as(ctypes.c_void_p))
# vj must be symmetric
for idm in range(n_dm):
vjk[0, idm] = lib.hermi_triu(vjk[0, idm], 1)
if hermi != 0: # vk depends
for idm in range(n_dm):
vjk[1, idm] = lib.hermi_triu(vjk[1, idm], hermi)
if n_dm == 1:
vjk = vjk.reshape(2, nao, nao)
return vjk
def direct(dms,
atm,
bas,
env,
vhfopt=None,
hermi=0,
cart=False,
with_j=True,
with_k=True):
c_atm = numpy.asarray(atm, dtype=numpy.int32, order='C')
c_bas = numpy.asarray(bas, dtype=numpy.int32, order='C')
c_env = numpy.asarray(env, dtype=numpy.double, order='C')
natm = ctypes.c_int(c_atm.shape[0])
nbas = ctypes.c_int(c_bas.shape[0])
dms = numpy.asarray(dms, order='C')
dms_shape = dms.shape
nao = dms_shape[-1]
dms = dms.reshape(-1, nao, nao)
n_dm = dms.shape[0]
if vhfopt is None:
if cart:
intor = 'int2e_cart'
else:
intor = 'int2e_sph'
cintopt = make_cintopt(c_atm, c_bas, c_env, intor)
cvhfopt = lib.c_null_ptr()
else:
vhfopt.set_dm(dms, atm, bas, env)
cvhfopt = vhfopt._this
cintopt = vhfopt._cintopt
intor = vhfopt._intor
cintor = _fpointer(intor)
fdrv = getattr(libcvhf, 'CVHFnr_direct_drv')
fdot = _fpointer('CVHFdot_nrs8')
vj = vk = None
dmsptr = []
vjkptr = []
fjk = []
if with_j:
fvj = _fpointer('CVHFnrs8_ji_s2kl')
vj = numpy.empty((n_dm, nao, nao))
for i, dm in enumerate(dms):
dmsptr.append(dm.ctypes.data_as(ctypes.c_void_p))
vjkptr.append(vj[i].ctypes.data_as(ctypes.c_void_p))
fjk.append(fvj)
if with_k:
if hermi == 1:
fvk = _fpointer('CVHFnrs8_li_s2kj')
else:
fvk = _fpointer('CVHFnrs8_li_s1kj')
vk = numpy.empty((n_dm, nao, nao))
for i, dm in enumerate(dms):
dmsptr.append(dm.ctypes.data_as(ctypes.c_void_p))
vjkptr.append(vk[i].ctypes.data_as(ctypes.c_void_p))
fjk.append(fvk)
shls_slice = (ctypes.c_int * 8)(*([0, c_bas.shape[0]] * 4))
ao_loc = make_loc(bas, intor)
n_ops = len(dmsptr)
comp = 1
fdrv(cintor, fdot, (ctypes.c_void_p * n_ops)(*fjk),
(ctypes.c_void_p * n_ops)(*dmsptr),
(ctypes.c_void_p * n_ops)(*vjkptr), ctypes.c_int(n_ops),
ctypes.c_int(comp), shls_slice,
ao_loc.ctypes.data_as(ctypes.c_void_p), cintopt, cvhfopt,
c_atm.ctypes.data_as(ctypes.c_void_p), natm,
c_bas.ctypes.data_as(ctypes.c_void_p), nbas,
c_env.ctypes.data_as(ctypes.c_void_p))
if with_j:
# vj must be symmetric
for i in range(n_dm):
lib.hermi_triu(vj[i], 1, inplace=True)
vj = vj.reshape(dms_shape)
if with_k:
if hermi != 0:
for i in range(n_dm):
lib.hermi_triu(vk[i], hermi, inplace=True)
vk = vk.reshape(dms_shape)
return vj, vk
def get_jk(mols, dms, scripts=['ijkl,ji->kl'], intor='int2e_sph',
aosym='s1', comp=None, hermi=0, shls_slice=None,
verbose=logger.WARN, vhfopt=None):
'''Compute J/K matrices for the given density matrix
Args:
mols : an instance of :class:`Mole` or a list of `Mole` objects
dms : ndarray or list of ndarrays
A density matrix or a list of density matrices
Kwargs:
hermi : int
Whether the returned J (K) matrix is hermitian
| 0 : no hermitian or symmetric
| 1 : hermitian
| 2 : anti-hermitian
intor : str
2-electron integral name. See :func:`getints` for the complete
list of available 2-electron integral names
aosym : int or str
Permutation symmetry for the AO integrals
| 4 or '4' or 's4': 4-fold symmetry (default)
| '2ij' or 's2ij' : symmetry between i, j in (ij|kl)
| '2kl' or 's2kl' : symmetry between k, l in (ij|kl)
| 1 or '1' or 's1': no symmetry
| 'a4ij' : 4-fold symmetry with anti-symmetry between i, j in (ij|kl)
| 'a4kl' : 4-fold symmetry with anti-symmetry between k, l in (ij|kl)
| 'a2ij' : anti-symmetry between i, j in (ij|kl)
| 'a2kl' : anti-symmetry between k, l in (ij|kl)
comp : int
Components of the integrals, e.g. cint2e_ip_sph has 3 components.
scripts : string or a list of strings
Contraction description (following numpy.einsum convention) based on
letters [ijkl]. Each script will be one-to-one applied to each
entry of dms. So it must have the same number of elements as the
dms, len(scripts) == len(dms).
shls_slice : 8-element list
(ish_start, ish_end, jsh_start, jsh_end, ksh_start, ksh_end, lsh_start, lsh_end)
Returns:
Depending on the number of density matrices, the function returns one
J/K matrix or a list of J/K matrices (the same number of entries as the
input dms).
Each JK matrices may be a 2D array or 3D array if the AO integral
has multiple components.
Examples:
>>> from pyscf import gto
>>> mol = gto.M(atom='H 0 -.5 0; H 0 .5 0', basis='cc-pvdz')
>>> nao = mol.nao_nr()
>>> dm = numpy.random.random((nao,nao))
>>> # Default, Coulomb matrix
>>> vj = get_jk(mol, dm)
>>> # Coulomb matrix with 8-fold permutation symmetry for AO integrals
>>> vj = get_jk(mol, dm, 'ijkl,ji->kl', aosym='s8')
>>> # Exchange matrix with 8-fold permutation symmetry for AO integrals
>>> vk = get_jk(mol, dm, 'ijkl,jk->il', aosym='s8')
>>> # Compute coulomb and exchange matrices together
>>> vj, vk = get_jk(mol, (dm,dm), ('ijkl,ji->kl','ijkl,li->kj'), aosym='s8')
>>> # Analytical gradients for coulomb matrix
>>> j1 = get_jk(mol, dm, 'ijkl,lk->ij', intor='int2e_ip1_sph', aosym='s2kl', comp=3)
>>> # contraction across two molecules
>>> mol1 = gto.M(atom='He 2 0 0', basis='6-31g')
>>> nao1 = mol1.nao_nr()
>>> dm1 = numpy.random.random((nao1,nao1))
>>> # Coulomb interaction between two molecules, note 4-fold symmetry can be applied
>>> jcross = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', aosym='s4')
>>> ecoul = numpy.einsum('ij,ij', jcross, dm1)
>>> # Exchange interaction between two molecules, no symmetry can be used
>>> kcross = get_jk((mol1,mol,mol,mol1), dm, scripts='ijkl,jk->il')
>>> ex = numpy.einsum('ij,ji', kcross, dm1)
>>> # Analytical gradients for coulomb matrix between two molecules
>>> jcros1 = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='int2e_ip1_sph', comp=3)
>>> # Analytical gradients for coulomb interaction between 1s density and the other molecule
>>> jpart1 = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='int2e_ip1_sph', comp=3,
... shls_slice=(0,1,0,1,0,mol.nbas,0,mol.nbas))
'''
if isinstance(mols, (tuple, list)):
intor, comp = gto.moleintor._get_intor_and_comp(mols[0]._add_suffix(intor), comp)
assert(len(mols) == 4)
assert(mols[0].cart == mols[1].cart == mols[2].cart == mols[3].cart)
if shls_slice is None:
shls_slice = numpy.array([(0, mol.nbas) for mol in mols])
else:
shls_slice = numpy.asarray(shls_slice).reshape(4,2)
# concatenate unique mols and build corresponding shls_slice
mol_ids = [id(mol) for mol in mols]
atm, bas, env = mols[0]._atm, mols[0]._bas, mols[0]._env
bas_start = numpy.zeros(4, dtype=int)
for m in range(1,4):
first = mol_ids.index(mol_ids[m])
if first == m: # the unique mol, not repeated in mols
bas_start[m] = bas.shape[0]
atm, bas, env = gto.conc_env(atm, bas, env, mols[m]._atm,
mols[m]._bas, mols[m]._env)
else:
bas_start[m] = bas_start[first]
shls_slice[m] += bas_start[m]
shls_slice = shls_slice.flatten()
else:
intor, comp = gto.moleintor._get_intor_and_comp(mols._add_suffix(intor), comp)
atm, bas, env = mols._atm, mols._bas, mols._env
if shls_slice is None:
shls_slice = (0, mols.nbas) * 4
single_script = isinstance(scripts, str)
if single_script:
scripts = [scripts]
if isinstance(dms, numpy.ndarray) and dms.ndim == 2:
dms = [dms]
assert(len(scripts) == len(dms))
#format scripts
descript = []
for script in scripts:
dmsym, vsym = script.lower().split(',')[1].split('->')
if vsym[:2] in ('a2', 's2', 's1'):
descript.append(dmsym + '->' + vsym)
elif hermi == 0:
descript.append(dmsym + '->s1' + vsym)
else:
descript.append(dmsym + '->s2' + vsym)
vs = _vhf.direct_bindm(intor, aosym, descript, dms, comp, atm, bas, env,
vhfopt=vhfopt, shls_slice=shls_slice)
if hermi != 0:
for v in vs:
if v.ndim == 3:
for vi in v:
lib.hermi_triu(vi, hermi, inplace=True)
else:
lib.hermi_triu(v, hermi, inplace=True)
if single_script:
vs = vs[0]
return vs
def get_jk_favorj(sgx, dm, hermi=1, with_j=True, with_k=True,
direct_scf_tol=1e-13):
t0 = time.clock(), time.time()
mol = sgx.mol
grids = sgx.grids
gthrd = sgx.grids_thrd
dms = numpy.asarray(dm)
dm_shape = dms.shape
nao = dm_shape[-1]
dms = dms.reshape(-1,nao,nao)
nset = dms.shape[0]
if sgx.debug:
batch_nuc = _gen_batch_nuc(mol)
else:
batch_jk = _gen_jk_direct(mol, 's2', with_j, with_k, direct_scf_tol,
sgx._opt)
sn = numpy.zeros((nao,nao))
ngrids = grids.coords.shape[0]
max_memory = sgx.max_memory - lib.current_memory()[0]
sblk = sgx.blockdim
blksize = min(ngrids, max(4, int(min(sblk, max_memory*1e6/8/nao**2))))
for i0, i1 in lib.prange(0, ngrids, blksize):
coords = grids.coords[i0:i1]
ao = mol.eval_gto('GTOval', coords)
wao = ao * grids.weights[i0:i1,None]
sn += lib.dot(ao.T, wao)
ovlp = mol.intor_symmetric('int1e_ovlp')
proj = scipy.linalg.solve(sn, ovlp)
proj_dm = lib.einsum('ki,xij->xkj', proj, dms)
t1 = logger.timer_debug1(mol, "sgX initialziation", *t0)
vj = numpy.zeros_like(dms)
vk = numpy.zeros_like(dms)
tnuc = 0, 0
for i0, i1 in lib.prange(0, ngrids, blksize):
coords = grids.coords[i0:i1]
ao = mol.eval_gto('GTOval', coords)
wao = ao * grids.weights[i0:i1,None]
fg = lib.einsum('gi,xij->xgj', wao, proj_dm)
mask = numpy.zeros(i1-i0, dtype=bool)
for i in range(nset):
mask |= numpy.any(fg[i]>gthrd, axis=1)
mask |= numpy.any(fg[i]<-gthrd, axis=1)
if not numpy.all(mask):
ao = ao[mask]
fg = fg[:,mask]
coords = coords[mask]
if with_j:
rhog = numpy.einsum('xgu,gu->xg', fg, ao)
else:
rhog = None
if sgx.debug:
tnuc = tnuc[0] - time.clock(), tnuc[1] - time.time()
gbn = batch_nuc(mol, coords)
tnuc = tnuc[0] + time.clock(), tnuc[1] + time.time()
if with_j:
jpart = numpy.einsum('guv,xg->xuv', gbn, rhog)
if with_k:
gv = lib.einsum('gtv,xgt->xgv', gbn, fg)
gbn = None
else:
tnuc = tnuc[0] - time.clock(), tnuc[1] - time.time()
if with_j: rhog = rhog.copy()
jpart, gv = batch_jk(mol, coords, rhog, fg.copy())
tnuc = tnuc[0] + time.clock(), tnuc[1] + time.time()
if with_j:
vj += jpart
if with_k:
for i in range(nset):
vk[i] += lib.einsum('gu,gv->uv', ao, gv[i])
jpart = gv = None
t2 = logger.timer_debug1(mol, "sgX J/K builder", *t1)
tdot = t2[0] - t1[0] - tnuc[0] , t2[1] - t1[1] - tnuc[1]
logger.debug1(sgx, '(CPU, wall) time for integrals (%.2f, %.2f); '
'for tensor contraction (%.2f, %.2f)',
tnuc[0], tnuc[1], tdot[0], tdot[1])
for i in range(nset):
lib.hermi_triu(vj[i], inplace=True)
if with_k and hermi == 1:
vk = (vk + vk.transpose(0,2,1))*.5
logger.timer(mol, "vj and vk", *t0)
return vj.reshape(dm_shape), vk.reshape(dm_shape)
def make_h1(mf,
mo_coeff,
mo_occ,
chkfile=None,
atmlst=None,
verbose=logger.WARN):
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mf.stdout, mf.verbose)
mol = mf.mol
if atmlst is None:
atmlst = range(mol.natm)
nao, nmo = mo_coeff.shape
mocc = mo_coeff[:, mo_occ > 0]
dm0 = numpy.dot(mocc, mocc.T) * 2
ni = copy.copy(mf._numint)
if USE_XCFUN:
try:
ni.libxc = dft.xcfun
xctype = ni._xc_type(mf.xc)
except (ImportError, KeyError, NotImplementedError):
ni.libxc = dft.libxc
xctype = ni._xc_type(mf.xc)
else:
xctype = ni._xc_type(mf.xc)
grids = mf.grids
hyb = ni.libxc.hybrid_coeff(mf.xc)
max_memory = 4000
h1a = -(mol.intor('int1e_ipkin', comp=3) +
mol.intor('int1e_ipnuc', comp=3))
offsetdic = mol.offset_nr_by_atom()
h1aos = []
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
mol.set_rinv_origin(mol.atom_coord(ia))
h1ao = -mol.atom_charge(ia) * mol.intor('int1e_iprinv', comp=3)
h1ao[:, p0:p1] += h1a[:, p0:p1]
h1ao = h1ao + h1ao.transpose(0, 2, 1)
shls_slice = (shl0, shl1) + (0, mol.nbas) * 3
int2e_ip1 = mol._add_suffix('int2e_ip1')
if abs(hyb) > 1e-10:
vj1, vj2, vk1, vk2 = \
_vhf.direct_bindm(int2e_ip1, 's2kl',
('ji->s2kl', 'lk->s1ij', 'li->s1kj', 'jk->s1il'),
(-dm0[:,p0:p1], -dm0, -dm0[:,p0:p1], -dm0),
3, mol._atm, mol._bas, mol._env,
shls_slice=shls_slice)
for i in range(3):
lib.hermi_triu(vj1[i], 1)
veff = vj1 - hyb * .5 * vk1
veff[:, p0:p1] += vj2 - hyb * .5 * vk2
else:
vj1, vj2 = \
_vhf.direct_bindm(int2e_ip1, 's2kl',
('ji->s2kl', 'lk->s1ij'),
(-dm0[:,p0:p1], -dm0),
3, mol._atm, mol._bas, mol._env,
shls_slice=shls_slice)
for i in range(3):
lib.hermi_triu(vj1[i], 1)
veff = vj1
veff[:, p0:p1] += vj2
if xctype == 'LDA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, 'LDA')
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
vrho = vxc[0]
frr = fxc[0]
half = lib.dot(ao[0], dm0[:, p0:p1].copy())
rho1 = numpy.einsum('xpi,pi->xp', ao[1:, :, p0:p1], half)
aow = numpy.einsum('pi,xp->xpi', ao[0], weight * frr * rho1)
aow1 = numpy.einsum('xpi,p->xpi', ao[1:, :, p0:p1],
weight * vrho)
aow[:, :, p0:p1] += aow1
veff[0] += lib.dot(-aow[0].T, ao[0])
veff[1] += lib.dot(-aow[1].T, ao[0])
veff[2] += lib.dot(-aow[2].T, ao[0])
half = aow = aow1 = None
elif xctype == 'GGA':
def get_wv(rho, rho1, weight, vxc, fxc):
vgamma = vxc[1]
frr, frg, fgg = fxc[:3]
ngrid = weight.size
sigma1 = numpy.einsum('xi,xi->i', rho[1:], rho1[1:])
wv = numpy.empty((4, ngrid))
wv[0] = frr * rho1[0]
wv[0] += frg * sigma1 * 2
wv[1:] = (fgg * sigma1 * 4 + frg * rho1[0] * 2) * rho[1:]
wv[1:] += vgamma * rho1[1:] * 2
wv *= weight
return wv
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao[:4], mo_coeff, mo_occ, mask, 'GGA')
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
vrho, vgamma = vxc[:2]
# (d_X \nabla_x mu) nu DM_{mu,nu}
half = lib.dot(ao[0], dm0[:, p0:p1].copy())
rho1X = numpy.einsum('xpi,pi->xp', ao[[1, XX, XY, XZ], :,
p0:p1], half)
rho1Y = numpy.einsum('xpi,pi->xp', ao[[2, YX, YY, YZ], :,
p0:p1], half)
rho1Z = numpy.einsum('xpi,pi->xp', ao[[3, ZX, ZY, ZZ], :,
p0:p1], half)
# (d_X mu) (\nabla_x nu) DM_{mu,nu}
half = lib.dot(ao[1], dm0[:, p0:p1].copy())
rho1X[1] += numpy.einsum('pi,pi->p', ao[1, :, p0:p1], half)
rho1Y[1] += numpy.einsum('pi,pi->p', ao[2, :, p0:p1], half)
rho1Z[1] += numpy.einsum('pi,pi->p', ao[3, :, p0:p1], half)
half = lib.dot(ao[2], dm0[:, p0:p1].copy())
rho1X[2] += numpy.einsum('pi,pi->p', ao[1, :, p0:p1], half)
rho1Y[2] += numpy.einsum('pi,pi->p', ao[2, :, p0:p1], half)
rho1Z[2] += numpy.einsum('pi,pi->p', ao[3, :, p0:p1], half)
half = lib.dot(ao[3], dm0[:, p0:p1].copy())
rho1X[3] += numpy.einsum('pi,pi->p', ao[1, :, p0:p1], half)
rho1Y[3] += numpy.einsum('pi,pi->p', ao[2, :, p0:p1], half)
rho1Z[3] += numpy.einsum('pi,pi->p', ao[3, :, p0:p1], half)
wv = get_wv(rho, rho1X, weight, vxc, fxc)
wv[0] *= .5
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
veff[0] -= lib.transpose_sum(lib.dot(aow.T, ao[0]))
wv = get_wv(rho, rho1Y, weight, vxc, fxc)
wv[0] *= .5
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
veff[1] -= lib.transpose_sum(lib.dot(aow.T, ao[0]))
wv = get_wv(rho, rho1Z, weight, vxc, fxc)
wv[0] *= .5
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
veff[2] -= lib.transpose_sum(lib.dot(aow.T, ao[0]))
wv = numpy.empty_like(rho)
wv[0] = weight * vrho
wv[1:] = rho[1:] * (weight * vgamma * 2)
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
veff[0, p0:p1] -= lib.dot(ao[1, :, p0:p1].T.copy(), aow)
veff[1, p0:p1] -= lib.dot(ao[2, :, p0:p1].T.copy(), aow)
veff[2, p0:p1] -= lib.dot(ao[3, :, p0:p1].T.copy(), aow)
aow = numpy.einsum('npi,np->pi', ao[[XX, XY, XZ], :, p0:p1],
wv[1:4])
veff[0, p0:p1] -= lib.dot(aow.T, ao[0])
aow = numpy.einsum('npi,np->pi', ao[[YX, YY, YZ], :, p0:p1],
wv[1:4])
veff[1, p0:p1] -= lib.dot(aow.T, ao[0])
aow = numpy.einsum('npi,np->pi', ao[[ZX, ZY, ZZ], :, p0:p1],
wv[1:4])
veff[2, p0:p1] -= lib.dot(aow.T, ao[0])
else:
raise NotImplementedError('meta-GGA')
veff = veff + veff.transpose(0, 2, 1)
if chkfile is None:
h1aos.append(h1ao + veff)
else:
key = 'scf_h1ao/%d' % ia
lib.chkfile.save(chkfile, key, h1ao + veff)
if chkfile is None:
return h1aos
else:
return chkfile
def get_jk(mols,
dms,
scripts=['ijkl,ji->kl'],
intor='int2e_sph',
aosym='s1',
comp=None,
hermi=0,
shls_slice=None,
verbose=logger.WARN,
vhfopt=None):
'''Compute J/K matrices for the given density matrix
Args:
mols : an instance of :class:`Mole` or a list of `Mole` objects
dms : ndarray or list of ndarrays
A density matrix or a list of density matrices
Kwargs:
hermi : int
Whether the returned J (K) matrix is hermitian
| 0 : no hermitian or symmetric
| 1 : hermitian
| 2 : anti-hermitian
intor : str
2-electron integral name. See :func:`getints` for the complete
list of available 2-electron integral names
aosym : int or str
Permutation symmetry for the AO integrals
| 4 or '4' or 's4': 4-fold symmetry (default)
| '2ij' or 's2ij' : symmetry between i, j in (ij|kl)
| '2kl' or 's2kl' : symmetry between k, l in (ij|kl)
| 1 or '1' or 's1': no symmetry
| 'a4ij' : 4-fold symmetry with anti-symmetry between i, j in (ij|kl)
| 'a4kl' : 4-fold symmetry with anti-symmetry between k, l in (ij|kl)
| 'a2ij' : anti-symmetry between i, j in (ij|kl)
| 'a2kl' : anti-symmetry between k, l in (ij|kl)
comp : int
Components of the integrals, e.g. cint2e_ip_sph has 3 components.
scripts : string or a list of strings
Contraction description (following numpy.einsum convention) based on
letters [ijkl]. Each script will be one-to-one applied to each
entry of dms. So it must have the same number of elements as the
dms, len(scripts) == len(dms).
shls_slice : 8-element list
(ish_start, ish_end, jsh_start, jsh_end, ksh_start, ksh_end, lsh_start, lsh_end)
Returns:
Depending on the number of density matrices, the function returns one
J/K matrix or a list of J/K matrices (the same number of entries as the
input dms).
Each JK matrices may be a 2D array or 3D array if the AO integral
has multiple components.
Examples:
>>> from pyscf import gto
>>> mol = gto.M(atom='H 0 -.5 0; H 0 .5 0', basis='cc-pvdz')
>>> nao = mol.nao_nr()
>>> dm = numpy.random.random((nao,nao))
>>> # Default, Coulomb matrix
>>> vj = get_jk(mol, dm)
>>> # Coulomb matrix with 8-fold permutation symmetry for AO integrals
>>> vj = get_jk(mol, dm, 'ijkl,ji->kl', aosym='s8')
>>> # Exchange matrix with 8-fold permutation symmetry for AO integrals
>>> vk = get_jk(mol, dm, 'ijkl,jk->il', aosym='s8')
>>> # Compute coulomb and exchange matrices together
>>> vj, vk = get_jk(mol, (dm,dm), ('ijkl,ji->kl','ijkl,li->kj'), aosym='s8')
>>> # Analytical gradients for coulomb matrix
>>> j1 = get_jk(mol, dm, 'ijkl,lk->ij', intor='int2e_ip1_sph', aosym='s2kl', comp=3)
>>> # contraction across two molecules
>>> mol1 = gto.M(atom='He 2 0 0', basis='6-31g')
>>> nao1 = mol1.nao_nr()
>>> dm1 = numpy.random.random((nao1,nao1))
>>> # Coulomb interaction between two molecules, note 4-fold symmetry can be applied
>>> jcross = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', aosym='s4')
>>> ecoul = numpy.einsum('ij,ij', jcross, dm1)
>>> # Exchange interaction between two molecules, no symmetry can be used
>>> kcross = get_jk((mol1,mol,mol,mol1), dm, scripts='ijkl,jk->il')
>>> ex = numpy.einsum('ij,ji', kcross, dm1)
>>> # Analytical gradients for coulomb matrix between two molecules
>>> jcros1 = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='int2e_ip1_sph', comp=3)
>>> # Analytical gradients for coulomb interaction between 1s density and the other molecule
>>> jpart1 = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='int2e_ip1_sph', comp=3,
... shls_slice=(0,1,0,1,0,mol.nbas,0,mol.nbas))
'''
if isinstance(mols, (tuple, list)):
intor, comp = gto.moleintor._get_intor_and_comp(
mols[0]._add_suffix(intor), comp)
assert (len(mols) == 4)
assert (mols[0].cart == mols[1].cart == mols[2].cart == mols[3].cart)
if shls_slice is None:
shls_slice = numpy.array([(0, mol.nbas) for mol in mols])
else:
shls_slice = numpy.asarray(shls_slice).reshape(4, 2)
# concatenate unique mols and build corresponding shls_slice
mol_ids = [id(mol) for mol in mols]
atm, bas, env = mols[0]._atm, mols[0]._bas, mols[0]._env
bas_start = numpy.zeros(4, dtype=int)
for m in range(1, 4):
first = mol_ids.index(mol_ids[m])
if first == m: # the unique mol, not repeated in mols
bas_start[m] = bas.shape[0]
atm, bas, env = gto.conc_env(atm, bas, env, mols[m]._atm,
mols[m]._bas, mols[m]._env)
else:
bas_start[m] = bas_start[first]
shls_slice[m] += bas_start[m]
shls_slice = shls_slice.flatten()
else:
intor, comp = gto.moleintor._get_intor_and_comp(
mols._add_suffix(intor), comp)
atm, bas, env = mols._atm, mols._bas, mols._env
if shls_slice is None:
shls_slice = (0, mols.nbas) * 4
single_script = isinstance(scripts, str)
if single_script:
scripts = [scripts]
# Check if letters other than ijkl were provided.
if set(''.join(scripts[:4])).difference('ijkl,->as12'):
# Translate these letters to ijkl if possible
scripts = [
script.translate({
ord(script[0]): 'i',
ord(script[1]): 'j',
ord(script[2]): 'k',
ord(script[3]): 'l'
}) for script in scripts
]
if set(''.join(scripts[:4])).difference('ijkl,->as12'):
raise RuntimeError('Scripts unsupported %s' % scripts)
if isinstance(dms, numpy.ndarray) and dms.ndim == 2:
dms = [dms]
assert (len(scripts) == len(dms))
#format scripts
descript = []
for script in scripts:
dmsym, vsym = script.lower().split(',')[1].split('->')
if vsym[:2] in ('a2', 's2', 's1'):
descript.append(dmsym + '->' + vsym)
elif hermi == 0:
descript.append(dmsym + '->s1' + vsym)
else:
descript.append(dmsym + '->s2' + vsym)
vs = _vhf.direct_bindm(intor,
aosym,
descript,
dms,
comp,
atm,
bas,
env,
vhfopt=vhfopt,
shls_slice=shls_slice)
if hermi != 0:
for v in vs:
if v.ndim == 3:
for vi in v:
lib.hermi_triu(vi, hermi, inplace=True)
else:
lib.hermi_triu(v, hermi, inplace=True)
if single_script:
vs = vs[0]
return vs
def pspace (fci, h1e, eri, norb, nelec, transformer, hdiag_det=None, hdiag_csf=None, npsp=200):
''' Note that getting pspace for npsp CSFs is substantially more costly than getting it for npsp determinants,
until I write code than can evaluate Hamiltonian matrix elements of CSFs directly. On the other hand
a pspace of determinants contains many redundant degrees of freedom for the same reason. Therefore I have
reduced the default pspace size by a factor of 2.'''
if norb > 63:
raise NotImplementedError('norb > 63')
t0 = (time.process_time (), time.time ())
neleca, nelecb = _unpack_nelec(nelec)
h1e = np.ascontiguousarray(h1e)
eri = ao2mo.restore(1, eri, norb)
nb = cistring.num_strings(norb, nelecb)
if hdiag_det is None:
hdiag_det = fci.make_hdiag(h1e, eri, norb, nelec)
if hdiag_csf is None:
hdiag_csf = fci.make_hdiag_csf(h1e, eri, norb, nelec, hdiag_det=hdiag_det)
csf_addr = np.arange (hdiag_csf.size, dtype=np.int)
if transformer.wfnsym is None:
ncsf_sym = hdiag_csf.size
else:
idx_sym = transformer.confsym[transformer.econf_csf_mask] == transformer.wfnsym
ncsf_sym = np.count_nonzero (idx_sym)
csf_addr = csf_addr[idx_sym]
if ncsf_sym > npsp:
try:
csf_addr = csf_addr[np.argpartition(hdiag_csf[csf_addr], npsp-1)[:npsp]]
except AttributeError:
csf_addr = csf_addr[np.argsort(hdiag_csf[csf_addr])[:npsp]]
# To build
econf_addr = np.unique (transformer.econf_csf_mask[csf_addr])
det_addr = np.concatenate ([np.nonzero (transformer.econf_det_mask == conf)[0]
for conf in econf_addr])
lib.logger.debug (fci, ("csf.pspace: Lowest-energy %s CSFs correspond to %s configurations"
" which are spanned by %s determinants"), npsp, econf_addr.size, det_addr.size)
addra, addrb = divmod(det_addr, nb)
stra = cistring.addrs2str(norb, neleca, addra)
strb = cistring.addrs2str(norb, nelecb, addrb)
npsp_det = len(det_addr)
h0 = np.zeros((npsp_det,npsp_det))
h1e_ab = unpack_h1e_ab (h1e)
h1e_a = np.ascontiguousarray(h1e_ab[0])
h1e_b = np.ascontiguousarray(h1e_ab[1])
g2e = ao2mo.restore(1, eri, norb)
g2e_ab = g2e_bb = g2e_aa = g2e
_debug_g2e (fci, g2e, eri, norb) # Exploring g2e nan bug; remove later?
t0 = lib.logger.timer (fci, "csf.pspace: index manipulation", *t0)
libfci.FCIpspace_h0tril_uhf(h0.ctypes.data_as(ctypes.c_void_p),
h1e_a.ctypes.data_as(ctypes.c_void_p),
h1e_b.ctypes.data_as(ctypes.c_void_p),
g2e_aa.ctypes.data_as(ctypes.c_void_p),
g2e_ab.ctypes.data_as(ctypes.c_void_p),
g2e_bb.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(npsp_det))
t0 = lib.logger.timer (fci, "csf.pspace: pspace Hamiltonian in determinant basis", *t0)
for i in range(npsp_det):
h0[i,i] = hdiag_det[det_addr[i]]
h0 = lib.hermi_triu(h0)
try:
if fci.verbose >= lib.logger.DEBUG: evals_before = scipy.linalg.eigh (h0)[0]
except ValueError as e:
lib.logger.debug (fci, ("ERROR: h0 has {} infs, {} nans; h1e_a has {} infs, {} nans; "
"h1e_b has {} infs, {} nans; g2e has {} infs, {} nans, norb = {}, npsp_det = {}").format (
np.count_nonzero (np.isinf (h0)), np.count_nonzero (np.isnan (h0)),
np.count_nonzero (np.isinf (h1e_a)), np.count_nonzero (np.isnan (h1e_a)),
np.count_nonzero (np.isinf (h1e_b)), np.count_nonzero (np.isnan (h1e_b)),
np.count_nonzero (np.isinf (g2e)), np.count_nonzero (np.isnan (g2e)),
norb, npsp_det))
evals_before = np.zeros (npsp_det)
h0, csf_addr = transformer.mat_det2csf_confspace (h0, econf_addr)
t0 = lib.logger.timer (fci, "csf.pspace: transform pspace Hamiltonian into CSF basis", *t0)
if fci.verbose >= lib.logger.DEBUG:
lib.logger.debug2 (fci, "csf.pspace: eigenvalues of h0 before transformation %s", evals_before)
evals_after = scipy.linalg.eigh (h0)[0]
lib.logger.debug2 (fci, "csf.pspace: eigenvalues of h0 after transformation %s", evals_after)
idx = [np.argmin (np.abs (evals_before - ev)) for ev in evals_after]
resid = evals_after - evals_before[idx]
lib.logger.debug2 (fci, "csf.pspace: best h0 eigenvalue matching differences after transformation: %s", resid)
lib.logger.debug (fci, "csf.pspace: if the transformation of h0 worked the following number will be zero: %s", np.max (np.abs(resid)))
# We got extra CSFs from building the configurations most of the time.
if csf_addr.size > npsp:
try:
csf_addr_2 = np.argpartition(np.diag (h0), npsp-1)[:npsp]
except AttributeError:
csf_addr_2 = np.argsort(np.diag (h0))[:npsp]
csf_addr = csf_addr[csf_addr_2]
h0 = h0[np.ix_(csf_addr_2,csf_addr_2)]
npsp_csf = csf_addr.size
lib.logger.debug (fci, "csf_solver.pspace: asked for %s-CSF pspace; found %s CSFs", npsp, npsp_csf)
t0 = lib.logger.timer (fci, "csf.pspace wrapup", *t0)
return csf_addr, h0
def test_direct_jk_s2(self):
numpy.random.seed(15)
dm1 = numpy.random.random((nao,nao))
dm1 = dm1 + dm1.T
vj0, vk0 = scf._vhf.incore(rhf._eri, dm1, 1)
vj1, vk1 = runjks2(dm1, 1, 'cint2e_sph', 'CVHFdot_nrs8',
'CVHFnrs8_ji_s2kl', 'CVHFnrs8_jk_s2il')
self.assertTrue(numpy.allclose(vj0,vj1))
self.assertTrue(numpy.allclose(vk0,vk1))
eri1 = ao2mo.restore(1, rhf._eri, nao)
vj0 = numpy.einsum('ijkl,kl->ij', eri1, dm1)
vk0 = numpy.einsum('ijkl,jk->il', eri1, dm1)
vj1, vj2 = runjks2(dm1, 1, 'cint2e_sph', 'CVHFdot_nrs4',
'CVHFnrs4_ji_s2kl', 'CVHFnrs4_jk_s2il')
self.assertTrue(numpy.allclose(vj0,vj1))
self.assertTrue(numpy.allclose(vk0,vj2))
vj1, vk1 = runjks2(dm1, 1, 'cint2e_sph', 'CVHFdot_nrs4',
'CVHFnrs4_li_s2kj', 'CVHFnrs4_jk_s2il')
self.assertTrue(numpy.allclose(vk0,vj1))
self.assertTrue(numpy.allclose(vk0,vk1))
vk0 = numpy.einsum('ijkl,jk->il', eri1, dm1)
vk1 = runjks2(dm1, 1, 'cint2e_sph', 'CVHFdot_nrs4',
'CVHFnrs4_li_s2kj', 'CVHFnrs4_jk_s2il',
'CVHFnrs4_li_s2kj', 'CVHFnrs4_jk_s2il')
self.assertTrue(numpy.allclose(vk0,vk1[0]))
self.assertTrue(numpy.allclose(vk0,vk1[1]))
self.assertTrue(numpy.allclose(vk0,vk1[2]))
self.assertTrue(numpy.allclose(vk0,vk1[3]))
vj0 = numpy.einsum('ijkl,kl->ij', eri1, dm1)
vk0 = numpy.einsum('ijkl,jk->il', eri1, dm1)
vk1 = runjks2(dm1, 1, 'cint2e_sph', 'CVHFdot_nrs2kl',
'CVHFnrs2kl_ji_s2kl', 'CVHFnrs2kl_lk_s2ij',
'CVHFnrs2kl_jk_s2il', 'CVHFnrs2kl_li_s2kj')
self.assertTrue(numpy.allclose(vj0,vk1[0]))
self.assertTrue(numpy.allclose(vj0,vk1[1]))
self.assertTrue(numpy.allclose(vk0,vk1[2]))
self.assertTrue(numpy.allclose(vk0,vk1[3]))
vk1 = runjks2(dm1, 1, 'cint2e_sph', 'CVHFdot_nrs2ij',
'CVHFnrs2ij_ji_s2kl', 'CVHFnrs2ij_lk_s2ij',
'CVHFnrs2ij_jk_s2il', 'CVHFnrs2ij_li_s2kj')
self.assertTrue(numpy.allclose(vj0,vk1[0]))
self.assertTrue(numpy.allclose(vj0,vk1[1]))
self.assertTrue(numpy.allclose(vk0,vk1[2]))
self.assertTrue(numpy.allclose(vk0,vk1[3]))
vk1 = runjks2(dm1, 1, 'cint2e_sph', 'CVHFdot_nrs1',
'CVHFnrs1_ji_s2kl', 'CVHFnrs1_lk_s2ij',
'CVHFnrs1_jk_s2il', 'CVHFnrs1_li_s2kj')
self.assertTrue(numpy.allclose(vj0,vk1[0]))
self.assertTrue(numpy.allclose(vj0,vk1[1]))
self.assertTrue(numpy.allclose(vk0,vk1[2]))
self.assertTrue(numpy.allclose(vk0,vk1[3]))
vj0, vk0 = scf._vhf.incore(rhf._eri, dm1, 1)
vj1, vk1 = runjk(dm1, 1, 'cint2e_sph', 'CVHFdot_nrs8',
'CVHFnrs8_ji_s2kl', 'CVHFnrs8_jk_s2il')
vj1 = lib.hermi_triu(vj1, 1)
vk1 = lib.hermi_triu(vk1, 1)
self.assertTrue(numpy.allclose(vj0,vj1))
self.assertTrue(numpy.allclose(vk0,vk1))
def incore(eri, dms, hermi=0, with_j=True, with_k=True):
assert (eri.dtype == numpy.double)
eri = numpy.asarray(eri, order='C')
dms = numpy.asarray(dms, order='C')
dms_shape = dms.shape
nao = dms_shape[-1]
dms = dms.reshape(-1, nao, nao)
n_dm = dms.shape[0]
vj = vk = None
if with_j:
vj = numpy.zeros((n_dm, nao, nao))
if with_k:
vk = numpy.zeros((n_dm, nao, nao))
dmsptr = []
vjkptr = []
fjkptr = []
npair = nao * (nao + 1) // 2
if eri.ndim == 2 and npair * npair == eri.size: # 4-fold symmetry eri
fdrv = getattr(libcvhf, 'CVHFnrs4_incore_drv')
if with_j:
# 'ijkl,kl->ij'
fvj = _fpointer('CVHFics4_kl_s2ij')
# or
## 'ijkl,ij->kl'
#fvj = _fpointer('CVHFics4_ij_s2kl')
for i, dm in enumerate(dms):
dmsptr.append(dm.ctypes.data_as(ctypes.c_void_p))
vjkptr.append(vj[i].ctypes.data_as(ctypes.c_void_p))
fjkptr.append(fvj)
if with_k:
# 'ijkl,il->jk'
fvk = _fpointer('CVHFics4_il_s1jk')
# or
## 'ijkl,jk->il'
#fvk = _fpointer('CVHFics4_jk_s1il')
for i, dm in enumerate(dms):
dmsptr.append(dm.ctypes.data_as(ctypes.c_void_p))
vjkptr.append(vk[i].ctypes.data_as(ctypes.c_void_p))
fjkptr.append(fvk)
elif eri.ndim == 1 and npair * (npair +
1) // 2 == eri.size: # 8-fold symmetry eri
fdrv = getattr(libcvhf, 'CVHFnrs8_incore_drv')
if with_j:
fvj = _fpointer('CVHFics8_tridm_vj')
tridms = lib.pack_tril(lib.hermi_sum(dms, axes=(0, 2, 1)))
idx = numpy.arange(nao)
tridms[:, idx * (idx + 1) // 2 + idx] *= .5
for i, tridm in enumerate(tridms):
dmsptr.append(tridm.ctypes.data_as(ctypes.c_void_p))
vjkptr.append(vj[i].ctypes.data_as(ctypes.c_void_p))
fjkptr.append(fvj)
if with_k:
if hermi == 1:
fvk = _fpointer('CVHFics8_jk_s2il')
else:
fvk = _fpointer('CVHFics8_jk_s1il')
for i, dm in enumerate(dms):
dmsptr.append(dm.ctypes.data_as(ctypes.c_void_p))
vjkptr.append(vk[i].ctypes.data_as(ctypes.c_void_p))
fjkptr.append(fvk)
else:
raise RuntimeError('Array shape not consistent: DM %s, eri %s' %
(dms_shape, eri.shape))
n_ops = len(dmsptr)
fdrv(eri.ctypes.data_as(ctypes.c_void_p),
(ctypes.c_void_p * n_ops)(*dmsptr),
(ctypes.c_void_p * n_ops)(*vjkptr), ctypes.c_int(n_ops),
ctypes.c_int(nao), (ctypes.c_void_p * n_ops)(*fjkptr))
if with_j:
for i in range(n_dm):
lib.hermi_triu(vj[i], 1, inplace=True)
vj = vj.reshape(dms_shape)
if with_k:
if hermi != 0:
for i in range(n_dm):
lib.hermi_triu(vk[i], hermi, inplace=True)
vk = vk.reshape(dms_shape)
return vj, vk
def direct(dms, atm, bas, env, vhfopt=None, hermi=0, cart=False):
c_atm = numpy.asarray(atm, dtype=numpy.int32, order='C')
c_bas = numpy.asarray(bas, dtype=numpy.int32, order='C')
c_env = numpy.asarray(env, dtype=numpy.double, order='C')
natm = ctypes.c_int(c_atm.shape[0])
nbas = ctypes.c_int(c_bas.shape[0])
if isinstance(dms, numpy.ndarray) and dms.ndim == 2:
dms = dms[numpy.newaxis,:,:]
n_dm = len(dms)
nao = dms[0].shape[0]
dms = numpy.asarray(dms, order='C')
if vhfopt is None:
if cart:
intor = 'int2e_cart'
else:
intor = 'int2e_sph'
cintopt = make_cintopt(c_atm, c_bas, c_env, intor)
cvhfopt = lib.c_null_ptr()
else:
vhfopt.set_dm(dms, atm, bas, env)
cvhfopt = vhfopt._this
cintopt = vhfopt._cintopt
intor = vhfopt._intor
cintor = _fpointer(intor)
fdrv = getattr(libcvhf, 'CVHFnr_direct_drv')
fdot = _fpointer('CVHFdot_nrs8')
fvj = _fpointer('CVHFnrs8_ji_s2kl')
if hermi == 1:
fvk = _fpointer('CVHFnrs8_li_s2kj')
else:
fvk = _fpointer('CVHFnrs8_li_s1kj')
vjk = numpy.empty((2,n_dm,nao,nao))
fjk = (ctypes.c_void_p*(2*n_dm))()
dmsptr = (ctypes.c_void_p*(2*n_dm))()
vjkptr = (ctypes.c_void_p*(2*n_dm))()
for i in range(n_dm):
dmsptr[i] = dms[i].ctypes.data_as(ctypes.c_void_p)
vjkptr[i] = vjk[0,i].ctypes.data_as(ctypes.c_void_p)
fjk[i] = fvj
for i in range(n_dm):
dmsptr[n_dm+i] = dms[i].ctypes.data_as(ctypes.c_void_p)
vjkptr[n_dm+i] = vjk[1,i].ctypes.data_as(ctypes.c_void_p)
fjk[n_dm+i] = fvk
shls_slice = (ctypes.c_int*8)(*([0, c_bas.shape[0]]*4))
ao_loc = make_loc(bas, intor)
fdrv(cintor, fdot, fjk, dmsptr, vjkptr,
ctypes.c_int(n_dm*2), ctypes.c_int(1),
shls_slice, ao_loc.ctypes.data_as(ctypes.c_void_p), cintopt, cvhfopt,
c_atm.ctypes.data_as(ctypes.c_void_p), natm,
c_bas.ctypes.data_as(ctypes.c_void_p), nbas,
c_env.ctypes.data_as(ctypes.c_void_p))
# vj must be symmetric
for idm in range(n_dm):
vjk[0,idm] = lib.hermi_triu(vjk[0,idm], 1)
if hermi != 0: # vk depends
for idm in range(n_dm):
vjk[1,idm] = lib.hermi_triu(vjk[1,idm], hermi)
if n_dm == 1:
vjk = vjk.reshape(2,nao,nao)
return vjk
def make_h1(mf, mo_coeff, mo_occ, chkfile=None, atmlst=None, verbose=logger.WARN):
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mf.stdout, mf.verbose)
mol = mf.mol
if atmlst is None:
atmlst = range(mol.natm)
nao, nmo = mo_coeff.shape
mocc = mo_coeff[:,mo_occ>0]
dm0 = numpy.dot(mocc, mocc.T) * 2
ni = copy.copy(mf._numint)
if USE_XCFUN:
try:
ni.libxc = dft.xcfun
xctype = ni._xc_type(mf.xc)
except (ImportError, KeyError, NotImplementedError):
ni.libxc = dft.libxc
xctype = ni._xc_type(mf.xc)
else:
xctype = ni._xc_type(mf.xc)
grids = mf.grids
hyb = ni.libxc.hybrid_coeff(mf.xc)
max_memory = 4000
h1a =-(mol.intor('cint1e_ipkin_sph', comp=3) +
mol.intor('cint1e_ipnuc_sph', comp=3))
offsetdic = mol.offset_nr_by_atom()
h1aos = []
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
mol.set_rinv_origin(mol.atom_coord(ia))
h1ao = -mol.atom_charge(ia) * mol.intor('cint1e_iprinv_sph', comp=3)
h1ao[:,p0:p1] += h1a[:,p0:p1]
h1ao = h1ao + h1ao.transpose(0,2,1)
shls_slice = (shl0, shl1) + (0, mol.nbas)*3
if abs(hyb) > 1e-10:
vj1, vj2, vk1, vk2 = \
_vhf.direct_bindm('cint2e_ip1_sph', 's2kl',
('ji->s2kl', 'lk->s1ij', 'li->s1kj', 'jk->s1il'),
(-dm0[:,p0:p1], -dm0, -dm0[:,p0:p1], -dm0),
3, mol._atm, mol._bas, mol._env,
shls_slice=shls_slice)
for i in range(3):
lib.hermi_triu(vj1[i], 1)
veff = vj1 - hyb*.5*vk1
veff[:,p0:p1] += vj2 - hyb*.5*vk2
else:
vj1, vj2 = \
_vhf.direct_bindm('cint2e_ip1_sph', 's2kl',
('ji->s2kl', 'lk->s1ij'),
(-dm0[:,p0:p1], -dm0),
3, mol._atm, mol._bas, mol._env,
shls_slice=shls_slice)
for i in range(3):
lib.hermi_triu(vj1[i], 1)
veff = vj1
veff[:,p0:p1] += vj2
if xctype == 'LDA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory, ni.non0tab):
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, 'LDA')
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
vrho = vxc[0]
frr = fxc[0]
half = lib.dot(ao[0], dm0[:,p0:p1].copy())
rho1 = numpy.einsum('xpi,pi->xp', ao[1:,:,p0:p1], half)
aow = numpy.einsum('pi,xp->xpi', ao[0], weight*frr*rho1)
aow1 = numpy.einsum('xpi,p->xpi', ao[1:,:,p0:p1], weight*vrho)
aow[:,:,p0:p1] += aow1
veff[0] += lib.dot(-aow[0].T, ao[0])
veff[1] += lib.dot(-aow[1].T, ao[0])
veff[2] += lib.dot(-aow[2].T, ao[0])
half = aow = aow1 = None
elif xctype == 'GGA':
def get_wv(rho, rho1, weight, vxc, fxc):
vgamma = vxc[1]
frr, frg, fgg = fxc[:3]
ngrid = weight.size
sigma1 = numpy.einsum('xi,xi->i', rho[1:], rho1[1:])
wv = numpy.empty((4,ngrid))
wv[0] = frr * rho1[0]
wv[0] += frg * sigma1 * 2
wv[1:] = (fgg * sigma1 * 4 + frg * rho1[0] * 2) * rho[1:]
wv[1:] += vgamma * rho1[1:] * 2
wv *= weight
return wv
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory, ni.non0tab):
rho = ni.eval_rho2(mol, ao[:4], mo_coeff, mo_occ, mask, 'GGA')
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
vrho, vgamma = vxc[:2]
# (d_X \nabla_x mu) nu DM_{mu,nu}
half = lib.dot(ao[0], dm0[:,p0:p1].copy())
rho1X = numpy.einsum('xpi,pi->xp', ao[[1,XX,XY,XZ],:,p0:p1], half)
rho1Y = numpy.einsum('xpi,pi->xp', ao[[2,YX,YY,YZ],:,p0:p1], half)
rho1Z = numpy.einsum('xpi,pi->xp', ao[[3,ZX,ZY,ZZ],:,p0:p1], half)
# (d_X mu) (\nabla_x nu) DM_{mu,nu}
half = lib.dot(ao[1], dm0[:,p0:p1].copy())
rho1X[1] += numpy.einsum('pi,pi->p', ao[1,:,p0:p1], half)
rho1Y[1] += numpy.einsum('pi,pi->p', ao[2,:,p0:p1], half)
rho1Z[1] += numpy.einsum('pi,pi->p', ao[3,:,p0:p1], half)
half = lib.dot(ao[2], dm0[:,p0:p1].copy())
rho1X[2] += numpy.einsum('pi,pi->p', ao[1,:,p0:p1], half)
rho1Y[2] += numpy.einsum('pi,pi->p', ao[2,:,p0:p1], half)
rho1Z[2] += numpy.einsum('pi,pi->p', ao[3,:,p0:p1], half)
half = lib.dot(ao[3], dm0[:,p0:p1].copy())
rho1X[3] += numpy.einsum('pi,pi->p', ao[1,:,p0:p1], half)
rho1Y[3] += numpy.einsum('pi,pi->p', ao[2,:,p0:p1], half)
rho1Z[3] += numpy.einsum('pi,pi->p', ao[3,:,p0:p1], half)
wv = get_wv(rho, rho1X, weight, vxc, fxc)
wv[0] *= .5
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
veff[0] -= lib.transpose_sum(lib.dot(aow.T, ao[0]))
wv = get_wv(rho, rho1Y, weight, vxc, fxc)
wv[0] *= .5
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
veff[1] -= lib.transpose_sum(lib.dot(aow.T, ao[0]))
wv = get_wv(rho, rho1Z, weight, vxc, fxc)
wv[0] *= .5
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
veff[2] -= lib.transpose_sum(lib.dot(aow.T, ao[0]))
wv = numpy.empty_like(rho)
wv[0] = weight * vrho
wv[1:] = rho[1:] * (weight * vgamma * 2)
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
veff[0,p0:p1] -= lib.dot(ao[1,:,p0:p1].T.copy(), aow)
veff[1,p0:p1] -= lib.dot(ao[2,:,p0:p1].T.copy(), aow)
veff[2,p0:p1] -= lib.dot(ao[3,:,p0:p1].T.copy(), aow)
aow = numpy.einsum('npi,np->pi', ao[[XX,XY,XZ],:,p0:p1], wv[1:4])
veff[0,p0:p1] -= lib.dot(aow.T, ao[0])
aow = numpy.einsum('npi,np->pi', ao[[YX,YY,YZ],:,p0:p1], wv[1:4])
veff[1,p0:p1] -= lib.dot(aow.T, ao[0])
aow = numpy.einsum('npi,np->pi', ao[[ZX,ZY,ZZ],:,p0:p1], wv[1:4])
veff[2,p0:p1] -= lib.dot(aow.T, ao[0])
else:
raise NotImplementedError('meta-GGA')
veff = veff + veff.transpose(0,2,1)
if chkfile is None:
h1aos.append(h1ao+veff)
else:
key = 'scf_h1ao/%d' % ia
lib.chkfile.save(chkfile, key, h1ao+veff)
if chkfile is None:
return h1aos
else:
return chkfile
