#!/usr/bin/env python
# Copyright 2020-2021 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Authors: Qiming Sun <osirpt.sun@gmail.com>
#
'''
Range separation JK builder
Ref:
Q. Sun, arXiv:2012.07929
Q. Sun, arXiv:2302.11307
'''
import ctypes
import numpy as np
import scipy.linalg
from pyscf import gto
from pyscf import lib
from pyscf.lib import logger
from pyscf.scf import _vhf
from pyscf.pbc import gto as pbcgto
from pyscf.pbc.tools import pbc as pbctools
from pyscf.pbc.tools import k2gamma
from pyscf.pbc.scf import addons
from pyscf.pbc.df import aft, rsdf_builder, aft_jk
from pyscf.pbc.df import ft_ao
from pyscf.pbc.df.df_jk import (zdotNN, zdotCN, zdotNC, _ewald_exxdiv_for_G0,
_format_dms, _format_kpts_band, _format_jks)
from pyscf.pbc.df.incore import libpbc, _get_cache_size, LOG_ADJUST
from pyscf.pbc.lib.kpts_helper import (is_zero, kk_adapted_iter,
group_by_conj_pairs, intersection)
from pyscf import __config__
# Threshold of steep bases and local bases
RCUT_THRESHOLD = getattr(__config__, 'pbc_scf_rsjk_rcut_threshold', 1.0)
OMEGA_MIN = rsdf_builder.OMEGA_MIN
INDEX_MIN = rsdf_builder.INDEX_MIN
[docs]
class RangeSeparatedJKBuilder(lib.StreamObject):
_keys = set((
'cell', 'mesh', 'kpts', 'purify', 'omega', 'rs_cell', 'cell_d',
'bvk_kmesh', 'supmol_sr', 'supmol_ft', 'supmol_d', 'cell0_basis_mask',
'ke_cutoff', 'direct_scf_tol', 'time_reversal_symmetry',
'exclude_dd_block', 'allow_drv_nodddd', 'approx_vk_lr_missing_mo',
))
def __init__(self, cell, kpts=np.zeros((1,3))):
self.cell = cell
self.stdout = cell.stdout
self.verbose = cell.verbose
self.max_memory = cell.max_memory
self.mesh = None
self.kpts = np.reshape(kpts, (-1, 3))
self.purify = True
if cell.omega == 0:
self.omega = None
elif cell.omega < 0:
# Initialize omega to cell.omega for HF exchange of short range
# int2e in RSH functionals
self.omega = -cell.omega
else:
raise RuntimeError('RSJK does not support LR integrals')
self.rs_cell = None
self.cell_d = None
# Born-von Karman supercell
self.bvk_kmesh = None
self.supmol_sr = None
self.supmol_ft = None
self.supmol_d = None
# which shells are located in the first primitive cell
self.cell0_basis_mask = None
self.ke_cutoff = None
self.direct_scf_tol = None
# Use the k-point conjugation symmetry between k and -k
self.time_reversal_symmetry = True
self.exclude_dd_block = True
self.allow_drv_nodddd = True
self._sr_without_dddd = None
# Allow to approximate vk_lr with less mesh if mo_coeff not attached to dm.
self.approx_vk_lr_missing_mo = False
# TODO: incrementally build SR part
self._last_vs = (0, 0)
self._qindex = None
[docs]
def has_long_range(self):
'''Whether to add the long-range part computed with AFT/FFT integrals'''
return self.omega is None or abs(self.cell.omega) < self.omega
[docs]
def dump_flags(self, verbose=None):
logger.info(self, '\n')
logger.info(self, '******** %s ********', self.__class__)
logger.info(self, 'mesh = %s (%d PWs)', self.mesh, np.prod(self.mesh))
logger.info(self, 'omega = %s', self.omega)
logger.info(self, 'purify = %s', self.purify)
logger.info(self, 'bvk_kmesh = %s', self.bvk_kmesh)
logger.info(self, 'ke_cutoff = %s', self.ke_cutoff)
logger.info(self, 'time_reversal_symmetry = %s', self.time_reversal_symmetry)
logger.info(self, 'has_long_range = %s', self.has_long_range())
logger.info(self, 'exclude_dd_block = %s', self.exclude_dd_block)
logger.info(self, 'allow_drv_nodddd = %s', self.allow_drv_nodddd)
logger.debug(self, 'approx_vk_lr_missing_mo = %s', self.approx_vk_lr_missing_mo)
return self
[docs]
def reset(self, cell=None):
if cell is not None:
self.cell = cell
self.rs_cell = None
self.cell_d = None
self.supmol_sr = None
self.supmol_ft = None
self.supmol_d = None
self.exclude_dd_block = True
self.approx_vk_lr_missing_mo = False
self._last_vs = (0, 0)
self._qindex = None
return self
[docs]
def build(self, omega=None, intor='int2e'):
cpu0 = logger.process_clock(), logger.perf_counter()
log = logger.new_logger(self)
cell = self.cell
kpts = self.kpts
if omega is not None:
self.omega = omega
if self.omega is None or self.omega == 0:
# Search a proper range-separation parameter omega that can balance the
# computational cost between the real space integrals and moment space
# integrals
self.omega, self.mesh, self.ke_cutoff = _guess_omega(cell, kpts, self.mesh)
else:
self.ke_cutoff = estimate_ke_cutoff_for_omega(cell, self.omega)
self.mesh = cell.cutoff_to_mesh(self.ke_cutoff)
if cell.dimension == 2 and cell.low_dim_ft_type != 'inf_vacuum':
# To ensure trunc-coulG converged for all basis
self.mesh[2] = rsdf_builder._estimate_meshz(cell)
self.check_sanity()
log.info('omega = %.15g ke_cutoff = %s mesh = %s',
self.omega, self.ke_cutoff, self.mesh)
# AFT part exchange cost may be dominant
if cell.nao * len(kpts) > 5000:
log.debug1('Disable exclude_dd_block')
self.exclude_dd_block = False
# basis with cutoff under ~150 eV are handled by AFTDF
ke_cutoff = max(6., self.ke_cutoff)
rs_cell = ft_ao._RangeSeparatedCell.from_cell(
cell, ke_cutoff, RCUT_THRESHOLD, in_rsjk=True, verbose=log)
self.rs_cell = rs_cell
self.bvk_kmesh = kmesh = k2gamma.kpts_to_kmesh(cell, kpts)
log.debug('kmesh for bvk-cell = %s', kmesh)
exp_min = np.hstack(cell.bas_exps()).min()
lattice_sum_factor = max((2*cell.rcut)**3/cell.vol * 1/exp_min, 1)
cutoff = cell.precision / lattice_sum_factor * .1
self.direct_scf_tol = cutoff
log.debug('Set RangeSeparationJKBuilder.direct_scf_tol to %g', cutoff)
rcut_sr = estimate_rcut(rs_cell, self.omega,
exclude_dd_block=self.exclude_dd_block)
supmol_sr = ft_ao.ExtendedMole.from_cell(rs_cell, kmesh, rcut_sr.max(), log)
supmol_sr.omega = -self.omega
self.supmol_sr = supmol_sr.strip_basis(rcut_sr)
log.debug('supmol nbas = %d cGTO = %d pGTO = %d',
supmol_sr.nbas, supmol_sr.nao, supmol_sr.npgto_nr())
if self.has_long_range():
rcut = rsdf_builder.estimate_ft_rcut(
rs_cell, exclude_dd_block=self.exclude_dd_block)
supmol_ft = rsdf_builder._ExtendedMoleFT.from_cell(
rs_cell, kmesh, rcut.max(), log)
supmol_ft.exclude_dd_block = self.exclude_dd_block
self.supmol_ft = supmol_ft.strip_basis(rcut)
log.debug('sup-mol-ft nbas = %d cGTO = %d pGTO = %d',
supmol_ft.nbas, supmol_ft.nao, supmol_ft.npgto_nr())
self.cell_d = rs_cell.smooth_basis_cell()
if self.cell_d.nbas > 0:
rcut = ft_ao.estimate_rcut(self.cell_d)
supmol_d = ft_ao.ExtendedMole.from_cell(
self.cell_d, self.bvk_kmesh, rcut.max(), log)
self.supmol_d = supmol_d.strip_basis(rcut)
log.debug('supmol_d nbas = %d cGTO = %d', supmol_d.nbas, supmol_d.nao)
log.timer_debug1('initializing supmol', *cpu0)
self._cintopt = _vhf.make_cintopt(supmol_sr._atm, supmol_sr._bas,
supmol_sr._env, 'int2e')
nbas = supmol_sr.nbas
qindex = np.empty((3,nbas,nbas), dtype=np.int16)
ao_loc = supmol_sr.ao_loc
with supmol_sr.with_integral_screen(self.direct_scf_tol**2):
libpbc.PBCVHFnr_int2e_q_cond(
libpbc.int2e_sph, self._cintopt,
qindex.ctypes.data_as(ctypes.c_void_p),
ao_loc.ctypes.data_as(ctypes.c_void_p),
supmol_sr._atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(supmol_sr.natm),
supmol_sr._bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(supmol_sr.nbas),
supmol_sr._env.ctypes.data_as(ctypes.c_void_p))
libpbc.PBCVHFnr_sindex(
qindex[2:].ctypes.data_as(ctypes.c_void_p),
supmol_sr._atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(supmol_sr.natm),
supmol_sr._bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(supmol_sr.nbas),
supmol_sr._env.ctypes.data_as(ctypes.c_void_p))
if self.exclude_dd_block:
# Remove the smooth-smooth basis block.
smooth_idx = supmol_sr.bas_type_to_indices(ft_ao.SMOOTH_BASIS)
qindex[0,smooth_idx[:,None], smooth_idx] = INDEX_MIN
self.qindex = qindex
log.timer('initializing qindex', *cpu0)
return self
@property
def qindex(self):
if self._qindex is None or isinstance(self._qindex, np.ndarray):
return self._qindex
return self._qindex['qindex'][:]
@qindex.setter
def qindex(self, x):
if x.size < self.max_memory*.2e6:
self._qindex = x
else:
self._qindex = lib.H5TmpFile()
self._qindex['qindex'] = x
self._qindex.flush()
def _sort_qcond_cell0(self, seg_loc, seg2sh, nbasp, qindex):
'''Sort qcond for ij-pair in cell0 so that loops in PBCVHF_direct_drv
can be "break" early
'''
qcell0_ijij = _qcond_cell0_abstract(qindex[0], seg_loc, seg2sh, nbasp)
qcell0_iijj = _qcond_cell0_abstract(qindex[1], seg_loc, seg2sh, nbasp)
idx = np.asarray(qcell0_ijij.ravel().argsort(kind='stable'), np.int32)[::-1]
jsh_idx, ish_idx = divmod(idx, nbasp)
ish_idx = np.asarray(ish_idx, dtype=np.int32, order='C')
jsh_idx = np.asarray(jsh_idx, dtype=np.int32, order='C')
return qcell0_ijij, qcell0_iijj, ish_idx, jsh_idx
def _get_jk_sr(self, dm_kpts, hermi=1, kpts=None, kpts_band=None,
with_j=True, with_k=True, omega=None, exxdiv=None):
if omega is not None: # J/K for RSH functionals
raise NotImplementedError
cpu0 = logger.process_clock(), logger.perf_counter()
log = logger.new_logger(self)
comp = 1
nkpts = kpts.shape[0]
supmol = self.supmol_sr
cell = self.cell
rs_cell = self.rs_cell
nao = cell.nao
bvk_ncells, rs_nbas, nimgs = supmol.bas_mask.shape
if dm_kpts.ndim != 4:
dm = dm_kpts.reshape(-1, nkpts, nao, nao)
else:
dm = dm_kpts
n_dm = dm.shape[0]
cutoff = int(np.log(self.direct_scf_tol) * LOG_ADJUST)
self._sr_without_dddd = (
self.allow_drv_nodddd and
not self.exclude_dd_block and
self.cell_d.nbas > 0 and
self.has_long_range() and
(cell.dimension == 3 or cell.low_dim_ft_type != 'inf_vacuum'))
if self._sr_without_dddd:
# To exclude (dd|dd) block, diffused shell needs to be independent
# segments in PBCVHF_direct_drv1. Decontract the segments in rs-shell.
# map ao indices in cell to ao indices in rs_cell
log.debug1('get_jk_sr with PBCVHF_direct_drv_nodddd')
drv = libpbc.PBCVHF_direct_drv_nodddd
ao_map = lib.locs_to_indices(cell.ao_loc, rs_cell.bas_map)
rs_nao = ao_map.size
rs_dm = np.empty((n_dm,nkpts*rs_nao,rs_nao), dtype=dm.dtype)
idx = np.arange(nkpts)[:,None] * nao + ao_map
idx = np.asarray(idx, dtype=np.int32).ravel()
for i in range(n_dm):
lib.take_2d(dm[i].reshape(nkpts*nao,nao), idx, ao_map, out=rs_dm[i])
dm = rs_dm.reshape(n_dm,nkpts,rs_nao,rs_nao)
nbasp = rs_cell.nbas
cell0_ao_loc = rs_cell.ao_loc
# uncontracted (local, diffused) basis segments in bvk-cell
seg_loc = lib.locs_to_indices(
supmol.seg_loc, np.arange(supmol.seg_loc.size-1))
seg_loc = np.append(seg_loc, supmol.seg_loc[-1]).astype(np.int32)
else:
drv = libpbc.PBCVHF_direct_drv
nbasp = cell.nbas # The number of shells in the primitive cell
cell0_ao_loc = cell.ao_loc
seg_loc = supmol.seg_loc
qindex = self.qindex
qcell0_ijij, qcell0_iijj, ish_idx, jsh_idx = \
self._sort_qcond_cell0(seg_loc, supmol.seg2sh, nbasp, qindex)
weight = 1. / nkpts
expLk = np.exp(1j*np.dot(supmol.bvkmesh_Ls, kpts.T))
# Utilized symmetry sc_dm[R,S] = sc_dm[S-R] = sc_dm[(S-R)%N]
#:phase = expLk / nkpts**.5
#:sc_dm = lib.einsum('Rk,nkuv,Sk->nRuSv', phase, sc_dm, phase.conj())
sc_dm = lib.einsum('k,Sk,nkuv->nSuv', expLk[0]*weight, expLk.conj(), dm)
dm_translation = k2gamma.double_translation_indices(self.bvk_kmesh).astype(np.int32)
dm_imag_max = abs(sc_dm.imag).max()
is_complex_dm = dm_imag_max > 1e-6
if is_complex_dm:
if dm_imag_max < 1e-2:
log.warn('DM in (BvK) cell has small imaginary part. '
'It may be a signal of symmetry broken in k-point symmetry')
sc_dm = np.vstack([sc_dm.real, sc_dm.imag])
self.purify = False
else:
sc_dm = sc_dm.real
nao1 = dm.shape[-1]
sc_dm = np.asarray(sc_dm.reshape(-1, bvk_ncells, nao1, nao1), order='C')
n_sc_dm = sc_dm.shape[0]
# * sparse_ao_loc has dimension (Nk,nbas), corresponding to the
# bvkcell with all basis
sparse_ao_loc = nao1 * np.arange(bvk_ncells)[:,None] + cell0_ao_loc[:-1]
sparse_ao_loc = np.append(sparse_ao_loc.ravel(), nao1 * bvk_ncells)
dm_cond = [lib.condense('NP_absmax', d, sparse_ao_loc, cell0_ao_loc)
for d in sc_dm.reshape(n_sc_dm, bvk_ncells*nao1, nao1)]
dm_cond = np.max(dm_cond, axis=0)
dm_cond[dm_cond < 1e-100] = 1e-100
dmindex = np.log(dm_cond)
dmindex *= LOG_ADJUST
dmindex = np.asarray(dmindex, order='C', dtype=np.int16)
dmindex = dmindex.reshape(bvk_ncells, nbasp, nbasp)
dm_cond = None
bvk_nbas = nbasp * bvk_ncells
shls_slice = (0, nbasp, 0, bvk_nbas, 0, bvk_nbas, 0, bvk_nbas)
cache_size = _get_cache_size(cell, 'int2e_sph')
cell0_dims = cell0_ao_loc[1:] - cell0_ao_loc[:-1]
cache_size += cell0_dims.max()**4 * comp * 2
if hermi:
fdot_suffix = 's2kl'
else:
fdot_suffix = 's1'
nvs = 1
if with_j and with_k:
fdot = 'PBCVHF_contract_jk_' + fdot_suffix
nvs = 2
elif with_j:
fdot = 'PBCVHF_contract_j_' + fdot_suffix
else: # with_k
fdot = 'PBCVHF_contract_k_' + fdot_suffix
vs = np.zeros((nvs, n_sc_dm, nao1, bvk_ncells, nao1))
if supmol.cart:
intor = 'PBCint2e_cart'
else:
intor = 'PBCint2e_sph'
drv(getattr(libpbc, fdot), getattr(libpbc, intor),
vs.ctypes.data_as(ctypes.c_void_p),
sc_dm.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(vs.size), ctypes.c_int(n_sc_dm),
ctypes.c_int(bvk_ncells), ctypes.c_int(nimgs), ctypes.c_int(nkpts),
ctypes.c_int(nbasp), ctypes.c_int(comp),
seg_loc.ctypes.data_as(ctypes.c_void_p),
supmol.seg2sh.ctypes.data_as(ctypes.c_void_p),
cell0_ao_loc.ctypes.data_as(ctypes.c_void_p),
rs_cell.bas_type.ctypes.data_as(ctypes.c_void_p),
(ctypes.c_int*8)(*shls_slice),
dm_translation.ctypes.data_as(ctypes.c_void_p),
qindex.ctypes.data_as(ctypes.c_void_p),
dmindex.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(cutoff),
qcell0_ijij.ctypes.data_as(ctypes.c_void_p),
qcell0_iijj.ctypes.data_as(ctypes.c_void_p),
ish_idx.ctypes.data_as(ctypes.c_void_p),
jsh_idx.ctypes.data_as(ctypes.c_void_p),
self._cintopt, ctypes.c_int(cache_size),
supmol._atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(supmol.natm),
supmol._bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(supmol.nbas),
supmol._env.ctypes.data_as(ctypes.c_void_p))
if is_complex_dm:
vs = vs[:,:n_dm] + vs[:,n_dm:] * 1j
if self._sr_without_dddd:
jdx = np.arange(bvk_ncells)[:,None] * nao + ao_map
jdx = np.asarray(jdx, dtype=np.int32).ravel()
rs_vs = vs.reshape(nvs*n_dm, nao1, bvk_ncells*nao1)
vs = np.zeros((nvs*n_dm, nao, bvk_ncells*nao), dtype=rs_vs.dtype)
for i in range(nvs*n_dm):
lib.takebak_2d(vs[i], rs_vs[i], ao_map, jdx, thread_safe=False)
vs = vs.reshape(nvs,n_dm,nao,bvk_ncells,nao)
if kpts_band is not None:
kpts_band = np.reshape(kpts_band, (-1, 3))
subset_only = intersection(kpts, kpts_band).size == len(kpts_band)
if not subset_only:
log.warn('Approximate J/K matrices at kpts_band '
'with the bvk-cell dervied from kpts')
expLk = np.exp(1j*np.dot(supmol.bvkmesh_Ls, kpts_band.T))
vs = lib.einsum('snpRq,Rk->snkpq', vs, expLk)
vs = np.asarray(vs, order='C')
log.timer_debug1('short range part vj and vk', *cpu0)
return vs
[docs]
def get_jk(self, dm_kpts, hermi=1, kpts=None, kpts_band=None,
with_j=True, with_k=True, omega=None, exxdiv=None):
cell = self.cell
if omega is not None: # J/K for RSH functionals
if omega > 0: # Long-range part only, call AFTDF
dfobj = aft.AFTDF(cell, self.kpts)
ke_cutoff = estimate_ke_cutoff_for_omega(cell, omega)
dfobj.mesh = cell.cutoff_to_mesh(ke_cutoff)
return dfobj.get_jk(dm_kpts, hermi, kpts, kpts_band,
with_j, with_k, omega, exxdiv)
elif omega < 0: # Short-range part only
if self.omega is not None and self.omega != omega:
raise RuntimeError(f'omega = {omega}, self.omega = {self.omega}')
raise NotImplementedError
if self.supmol_sr is None:
self.build()
# Does not support to specify arbitrary kpts
if kpts is not None and abs(kpts-self.kpts).max() > 1e-7:
raise RuntimeError('kpts error. kpts cannot be modified in RSJK')
kpts = np.asarray(self.kpts.reshape(-1, 3), order='C')
mo_coeff = getattr(dm_kpts, 'mo_coeff', None)
mo_occ = getattr(dm_kpts, 'mo_occ', None)
dm_kpts = np.asarray(dm_kpts)
dms = _format_dms(dm_kpts, kpts)
# compute delta vs if dm is obtained from SCF make_rdm1
if mo_coeff is not None:
last_dm, last_vs = self._last_vs
vs = self._get_jk_sr(dms-last_dm, hermi, kpts, kpts_band,
with_j, with_k, omega, exxdiv)
vs += last_vs
self._last_vs = (dms, vs.copy())
last_dm = last_vs = None
# dm ~= dm_factor * dm_factor.T
n_dm, nkpts, nao = dms.shape[:3]
# mo_coeff, mo_occ are not a list of aligned array if
# remove_lin_dep was applied to scf object
if dm_kpts.ndim == 4: # KUHF
nocc = max(max(np.count_nonzero(x > 0) for x in z) for z in mo_occ)
dm_factor = [[x[:,:nocc] for x in mo] for mo in mo_coeff]
occs = [[x[:nocc] for x in z] for z in mo_occ]
else: # KRHF
nocc = max(np.count_nonzero(x > 0) for x in mo_occ)
dm_factor = [[mo[:,:nocc] for mo in mo_coeff]]
occs = [[x[:nocc] for x in mo_occ]]
dm_factor = np.array(dm_factor, dtype=np.complex128, order='C')
dm_factor *= np.sqrt(np.array(occs, dtype=np.double))[:,:,None]
else:
vs = self._get_jk_sr(dms, hermi, kpts, kpts_band,
with_j, with_k, omega, exxdiv)
dm_factor = None
dms = lib.tag_array(dms, dm_factor=dm_factor)
if with_j and with_k:
vj, vk = vs
elif with_j:
vj, vk = vs[0], None
else:
vj, vk = None, vs[0]
if self.purify and kpts_band is None:
phase = np.exp(1j*np.dot(self.supmol_sr.bvkmesh_Ls, kpts.T))
phase /= np.sqrt(len(kpts))
else:
phase = None
if with_j:
if self.has_long_range():
vj += self._get_vj_lr(dms, hermi, kpts, kpts_band)
if hermi:
vj = (vj + vj.conj().transpose(0,1,3,2)) * .5
vj = _purify(vj, phase)
vj = _format_jks(vj, dm_kpts, kpts_band, kpts)
if is_zero(kpts) and dm_kpts.dtype == np.double:
vj = vj.real.copy()
if with_k:
if self.has_long_range():
approx_vk_lr = dm_factor is None and self.approx_vk_lr_missing_mo
if not approx_vk_lr:
vk += self._get_vk_lr(dms, hermi, kpts, kpts_band, exxdiv)
else:
mesh1 = np.array(self.mesh)//3*2 + 1
logger.debug(self, 'Approximate lr_k with mesh %s', mesh1)
with lib.temporary_env(self, mesh=mesh1):
vk += self._get_vk_lr(dms, hermi, kpts, kpts_band, exxdiv)
self.approx_vk_lr_missing_mo = False
if hermi:
vk = (vk + vk.conj().transpose(0,1,3,2)) * .5
vk = _purify(vk, phase)
vk = _format_jks(vk, dm_kpts, kpts_band, kpts)
if is_zero(kpts) and dm_kpts.dtype == np.double:
vk = vk.real.copy()
return vj, vk
weighted_coulG = aft.weighted_coulG
[docs]
def weighted_coulG_LR(self, kpt=np.zeros(3), exx=False, mesh=None):
# The long range part Coulomb kernel has to be computed as the
# difference between coulG(cell.omega) - coulG(self.omega). It allows this
# module to handle the SR- and regular integrals in the same framework
return (self.weighted_coulG(kpt, exx, mesh) -
self.weighted_coulG_SR(kpt, exx, mesh))
[docs]
def weighted_coulG_SR(self, kpt=np.zeros(3), exx=False, mesh=None):
return self.weighted_coulG(kpt, False, mesh, -self.omega)
def _get_vj_lr(self, dm_kpts, hermi=1, kpts=np.zeros((1,3)), kpts_band=None):
'''
Long-range part of J matrix
'''
if kpts_band is None:
return self._get_lr_j_kpts(dm_kpts, hermi, kpts)
logger.warn(self, 'Approximate kpts_band for vj with k-point projection')
vj = self._get_lr_j_kpts(dm_kpts, hermi, kpts)
pk2k = addons._k2k_projection(kpts, kpts_band, self.supmol_ft.bvkmesh_Ls)
return lib.einsum('nkpq,kh->nhpq', vj, pk2k)
def _get_lr_j_kpts(self, dm_kpts, hermi=1, kpts=np.zeros((1,3))):
'''
Long-range part of J matrix
'''
if len(kpts) == 1 and not is_zero(kpts):
raise NotImplementedError('Single k-point get-j')
cpu0 = logger.process_clock(), logger.perf_counter()
log = logger.new_logger(self)
cell = self.cell
rs_cell = self.rs_cell
if self.exclude_dd_block or self._sr_without_dddd:
cell_d = self.cell_d
naod = cell_d.nao
ngrids_d = np.prod(cell_d.mesh)
else:
cell_d = None
naod = ngrids_d = 0
kpts = np.asarray(kpts.reshape(-1, 3), order='C')
dms = dm_kpts
n_dm, nkpts, nao = dms.shape[:3]
mesh = self.mesh
ngrids = np.prod(mesh)
is_real = is_zero(kpts) and dms.dtype == np.double
if is_real:
vj_kpts = np.zeros((n_dm,nkpts,nao,nao))
else:
vj_kpts = np.zeros((n_dm,nkpts,nao,nao), dtype=np.complex128)
# TODO: aosym == 's2'
aosym = 's1'
ft_kern = self.supmol_ft.gen_ft_kernel(
aosym, return_complex=False, kpts=kpts, verbose=log)
Gv, Gvbase, kws = cell.get_Gv_weights(mesh)
gxyz = lib.cartesian_prod([np.arange(len(x)) for x in Gvbase])
kpt_allow = np.zeros(3)
coulG = self.weighted_coulG(kpt_allow, False, mesh)
if (cell.dimension == 3 or
(cell.dimension == 2 and cell.low_dim_ft_type != 'inf_vacuum')):
G0_idx = 0 # due to np.fft.fftfreq convension
# G=0 associated to 2e integrals in real-space
coulG_SR_at_G0 = np.pi/self.omega**2
# For cell.dimension = 2, coulG is computed with truncated coulomb
# interactions. The 3d coulG_SR below is to remove the analytical
# SR from get_jk_sr (which was computed with full Coulomb) then to
# add truncated Coulomb for AFT part.
with lib.temporary_env(cell, dimension=3):
coulG_SR = self.weighted_coulG_SR(kpt_allow, False, mesh)
coulG_SR[G0_idx] += coulG_SR_at_G0 * kws
else:
coulG_SR = self.weighted_coulG_SR(kpt_allow, False, mesh)
coulG_SR_at_G0 = None
if naod > 0:
smooth_bas_mask = rs_cell.bas_type == ft_ao.SMOOTH_BASIS
smooth_bas_idx = rs_cell.bas_map[smooth_bas_mask]
ao_d_idx = rs_cell.get_ao_indices(smooth_bas_idx, cell.ao_loc)
mem_now = lib.current_memory()[0]
max_memory = self.max_memory - mem_now
log.debug1('max_memory = %d MB (%d in use)', max_memory+mem_now, mem_now)
Gblksize = max(24, int(max_memory*.8e6/16/(nao**2+naod**2)/(nkpts+1))//8*8)
Gblksize = min(Gblksize, ngrids)
log.debug1('Gblksize = %d', Gblksize)
if not self.exclude_dd_block or naod == 0:
log.debug1('get_lr_j_kpts with aft_aopair')
# Long-range part is calculated as the difference
# coulG(cell.omega) - coulG(self.omega) . It can support both regular
# integrals and LR integrals.
coulG_LR = coulG - coulG_SR
buf = np.empty(nkpts*Gblksize*nao**2*2)
for p0, p1 in lib.prange(0, ngrids, Gblksize):
Gpq = ft_kern(Gv[p0:p1], gxyz[p0:p1], Gvbase, kpt_allow, out=buf)
aft_jk._update_vj_(vj_kpts, Gpq, dms, coulG_LR[p0:p1])
Gpq = buf = None
if self._sr_without_dddd and naod > 0:
log.debug1('get_lr_j_kpts dd block with mesh %s', cell_d.mesh)
if cell.dimension < 2:
raise NotImplementedError
if cell.dimension == 2 and cell.low_dim_ft_type == 'inf_vacuum':
raise NotImplementedError
aoR_ks, aoI_ks = rsdf_builder._eval_gto(cell_d, cell_d.mesh, kpts)
# rho = einsum('nkji,kig,kjg->ng', dm, ao.conj(), ao)
rho = np.zeros((n_dm, ngrids_d))
tmpR = np.empty((naod, ngrids_d))
tmpI = np.empty((naod, ngrids_d))
dm_dd = dms[:,:,ao_d_idx[:,None],ao_d_idx]
dmR_dd = np.asarray(dm_dd.real, order='C')
dmI_dd = np.asarray(dm_dd.imag, order='C')
# vG = einsum('ij,gji->g', dm_dd[k], aoao[k]) * coulG
for i in range(n_dm):
for k in range(nkpts):
zdotNN(dmR_dd[i,k].T, dmI_dd[i,k].T,
aoR_ks[k], aoI_ks[k], 1, tmpR, tmpI)
rho[i] += np.einsum('ig,ig->g', aoR_ks[k], tmpR)
rho[i] += np.einsum('ig,ig->g', aoI_ks[k], tmpI)
if coulG_SR_at_G0 is not None:
with lib.temporary_env(cell_d, dimension=3):
coulG_SR = pbctools.get_coulG(cell_d, omega=-self.omega)
coulG_SR[G0_idx] += coulG_SR_at_G0
else:
coulG_SR = pbctools.get_coulG(cell_d, omega=-self.omega)
coulG_SR *= cell.vol / ngrids_d
vG = pbctools.fft(rho, cell_d.mesh) * coulG_SR
vR = pbctools.ifft(vG, cell_d.mesh).real
nband = nkpts
vjR_dd = np.empty((naod,naod))
vjI_dd = np.empty((naod,naod))
for i in range(n_dm):
for k in range(nband):
aowR = np.einsum('xi,x->xi', aoR_ks[k].T, vR[i])
aowI = np.einsum('xi,x->xi', aoI_ks[k].T, vR[i])
zdotCN(aoR_ks[k], aoI_ks[k], aowR, aowI, 1, vjR_dd, vjI_dd)
if is_real:
vj = vjR_dd
else:
vj = vjR_dd + vjI_dd*1j
lib.takebak_2d(vj_kpts[i,k], vj, ao_d_idx, ao_d_idx,
thread_safe=False)
elif naod > 0 and ngrids < ngrids_d:
# Prefer AFTDF for everything otherwise cell_d.mesh have to be used
# for AFTDF
log.debug1('get_lr_j_kpts dd block cached aft_aopair_dd')
ft_kern_dd = self.supmol_d.gen_ft_kernel(
aosym, return_complex=False, kpts=kpts, verbose=log)
def merge_dd(Gpq, p0, p1):
'''Merge diffused basis block into ao-pair tensor inplace'''
GpqR, GpqI = Gpq
pqG_ddR, pqG_ddI = ft_kern_dd(Gv[p0:p1], gxyz[p0:p1], Gvbase,
kpt_allow, kpts)
# Gpq should be an array of (nkpts,ni,nj,ngrids) in C order
if not GpqR[0].flags.c_contiguous:
assert GpqR[0].strides[0] == 8 # stride for grids
for k in range(nkpts):
libpbc.PBC_ft_fuse_dd_s1(
GpqR[k].ctypes.data_as(ctypes.c_void_p),
GpqI[k].ctypes.data_as(ctypes.c_void_p),
pqG_ddR[k].ctypes.data_as(ctypes.c_void_p),
pqG_ddI[k].ctypes.data_as(ctypes.c_void_p),
ao_d_idx.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nao), ctypes.c_int(naod), ctypes.c_int(p1-p0))
return (GpqR, GpqI)
buf = np.empty(nkpts*Gblksize*nao**2*2)
for p0, p1 in lib.prange(0, ngrids, Gblksize):
Gpq = ft_kern(Gv[p0:p1], gxyz[p0:p1], Gvbase, kpt_allow, out=buf)
aft_jk._update_vj_(vj_kpts, Gpq, dms, -coulG_SR[p0:p1])
Gpq = merge_dd(Gpq, p0, p1)
aft_jk._update_vj_(vj_kpts, Gpq, dms, coulG[p0:p1])
Gpq = buf = None
elif naod > 0:
log.debug1('get_lr_j_kpts dd block cached fft_aopair_dd')
aoR_ks, aoI_ks = rsdf_builder._eval_gto(cell_d, mesh, kpts)
# rho = einsum('nkji,kig,kjg->ng', dm, ao.conj(), ao)
rho = np.zeros((n_dm, ngrids))
tmpR = np.empty((naod, ngrids))
tmpI = np.empty((naod, ngrids))
dm_dd = dms[:,:,ao_d_idx[:,None],ao_d_idx]
dmR_dd = np.asarray(dm_dd.real, order='C')
dmI_dd = np.asarray(dm_dd.imag, order='C')
# vG = einsum('ij,gji->g', dm_dd[k], aoao[k]) * coulG
for i in range(n_dm):
for k in range(nkpts):
zdotNN(dmR_dd[i,k].T, dmI_dd[i,k].T, aoR_ks[k], aoI_ks[k], 1, tmpR, tmpI)
rho[i] += np.einsum('ig,ig->g', aoR_ks[k], tmpR)
rho[i] += np.einsum('ig,ig->g', aoI_ks[k], tmpI)
vG_dd = pbctools.ifft(rho, mesh) * cell.vol * coulG
tmpR = tmpI = dmR_dd = dmI_dd = None
cpu1 = log.timer_debug1('get_lr_j_kpts dd block', *cpu0)
mem_now = lib.current_memory()[0]
max_memory = self.max_memory - mem_now
log.debug1('max_memory = %d MB (%d in use)', max_memory+mem_now, mem_now)
Gblksize = min(Gblksize, int(max_memory*.8e6/16/(nao**2+naod**2)/(nkpts+1))//8*8)
log.debug1('Gblksize = %d', Gblksize)
buf = np.empty(nkpts*Gblksize*nao**2*2)
for p0, p1 in lib.prange(0, ngrids, Gblksize):
Gpq = ft_kern(Gv[p0:p1], gxyz[p0:p1], Gvbase, kpt_allow, out=buf)
#: aft_jk._update_vj_(vj_kpts, aoaoks, dms, coulG[p0:p1], 1)
#: aft_jk._update_vj_(vj_kpts, aoaoks, dms, coulG_SR[p0:p1], -1)
GpqR, GpqI = Gpq
for i in range(n_dm):
rhoR = np.einsum('kij,kgij->g', dms[i].real, GpqR)
rhoI = -np.einsum('kij,kgij->g', dms[i].real, GpqI)
if not is_real:
rhoR += np.einsum('kij,kgij->g', dms[i].imag, GpqI)
rhoI += np.einsum('kij,kgij->g', dms[i].imag, GpqR)
rho = rhoR + rhoI * 1j
vG = vG_dd[i,p0:p1]
# Update vG_dd inplace to include rho contributions
vG += coulG[p0:p1] * rho
vG_SR = coulG_SR[p0:p1] * rho
# vG_LR contains full vG of dd-block and vG_LR of rest blocks
vG_LR = vG - vG_SR
vj_kpts[i].real += np.einsum('g,kgij->kij', vG_LR.real, GpqR)
vj_kpts[i].real -= np.einsum('g,kgij->kij', vG_LR.imag, GpqI)
if not is_real:
vj_kpts[i].imag += np.einsum('g,kgij->kij', vG_LR.real, GpqI)
vj_kpts[i].imag += np.einsum('g,kgij->kij', vG_LR.imag, GpqR)
Gpq = None
log.timer_debug1('get_lr_j_kpts ft_aopair', *cpu1)
vR = pbctools.fft(vG_dd, mesh).real * (cell.vol/ngrids)
vjR_dd = np.empty((naod, naod))
vjI_dd = np.empty((naod, naod))
for i in range(n_dm):
for k in range(nkpts):
tmpR = aoR_ks[k] * vR[i]
tmpI = aoI_ks[k] * vR[i]
zdotCN(aoR_ks[k], aoI_ks[k], tmpR.T, tmpI.T, 1, vjR_dd, vjI_dd)
if is_real:
vj_dd = vjR_dd
else:
vj_dd = vjR_dd + vjI_dd * 1j
lib.takebak_2d(vj_kpts[i,k], vj_dd, ao_d_idx, ao_d_idx,
thread_safe=False)
else:
raise RuntimeError(f'exclude_dd_block={self.exclude_dd_block} '
f'sr_without_dddd={self._sr_without_dddd} naod={naod}')
if nkpts > 1:
vj_kpts *= 1./nkpts
log.timer_debug1('get_lr_j_kpts', *cpu0)
return vj_kpts
def _get_vk_lr(self, dm_kpts, hermi=1, kpts=np.zeros((1,3)), kpts_band=None,
exxdiv=None):
'''
Long-range part of K matrix
'''
if kpts_band is None:
return self._get_lr_k_kpts(dm_kpts, hermi, kpts, exxdiv)
# Note: Errors in k2k-projection for vj is relatively small.
# k2k-projection for vk has significant finite-size errors.
logger.warn(self, 'Approximate kpts_band for vk with k-point projection')
vk = self._get_lr_k_kpts(dm_kpts, hermi, kpts, exxdiv=None)
pk2k = addons._k2k_projection(kpts, kpts_band, self.supmol_ft.bvkmesh_Ls)
vk = lib.einsum('nkpq,kh->nhpq', vk, pk2k)
if exxdiv == 'ewald':
_ewald_exxdiv_for_G0(self.cell, kpts, dm_kpts, vk, kpts_band)
return vk
def _get_lr_k_kpts(self, dm_kpts, hermi=1, kpts=np.zeros((1,3)), exxdiv=None):
'''
Long-range part of K matrix
'''
cpu0 = cpu1 = logger.process_clock(), logger.perf_counter()
log = logger.new_logger(self)
cell = self.cell
rs_cell = self.rs_cell
if self.exclude_dd_block or self._sr_without_dddd:
cell_d = self.cell_d
naod = cell_d.nao
ngrids_d = np.prod(cell_d.mesh)
else:
cell_d = None
naod = ngrids_d = 0
mesh = self.mesh
ngrids = np.prod(mesh)
dms = dm_kpts
n_dm, nkpts, nao = dms.shape[:3]
vkR = np.zeros((n_dm,nkpts,nao,nao))
vkI = np.zeros((n_dm,nkpts,nao,nao))
vk = [vkR, vkI]
weight = 1. / nkpts
# Test if vk[k] == vk[k_conj].conj()
t_rev_pairs = group_by_conj_pairs(cell, kpts, return_kpts_pairs=False)
try:
t_rev_pairs = np.asarray(t_rev_pairs, dtype=np.int32, order='F')
except TypeError:
t_rev_pairs = [[k, k] if k_conj is None else [k, k_conj]
for k, k_conj in t_rev_pairs]
t_rev_pairs = np.asarray(t_rev_pairs, dtype=np.int32, order='F')
log.debug1('Num kpts conj_pairs %d', len(t_rev_pairs))
time_reversal_symmetry = self.time_reversal_symmetry
if time_reversal_symmetry:
for k, k_conj in t_rev_pairs:
if k != k_conj and abs(dms[:,k_conj] - dms[:,k].conj()).max() > 1e-6:
time_reversal_symmetry = False
log.debug2('Disable time_reversal_symmetry')
break
# TODO: aosym == 's2'
aosym = 's1'
if time_reversal_symmetry:
k_to_compute = np.zeros(nkpts, dtype=np.int8)
k_to_compute[t_rev_pairs[:,0]] = 1
else:
k_to_compute = np.ones(nkpts, dtype=np.int8)
t_rev_pairs = None
dm_factor = getattr(dm_kpts, 'dm_factor', None)
contract_mo_early = False
if dm_factor is None:
dmsR = np.asarray(dms.real, order='C')
dmsI = np.asarray(dms.imag, order='C')
dm = [dmsR, dmsI]
dm_factor = None
if np.count_nonzero(k_to_compute) >= 2 * lib.num_threads():
update_vk = aft_jk._update_vk1_
else:
update_vk = aft_jk._update_vk_
else:
# dm ~= dm_factor * dm_factor.T
nocc = dm_factor.shape[-1]
if nocc == 0:
return vkR
bvk_ncells, rs_nbas, nimgs = self.supmol_ft.bas_mask.shape
s_nao = self.supmol_ft.nao
contract_mo_early = (time_reversal_symmetry and naod == 0 and
bvk_ncells*nao*6 > s_nao*nocc*n_dm)
log.debug2('time_reversal_symmetry = %s bvk_ncells = %d '
's_nao = %d nocc = %d n_dm = %d',
time_reversal_symmetry, bvk_ncells, s_nao, nocc, n_dm)
log.debug2('Use algorithm contract_mo_early = %s', contract_mo_early)
if contract_mo_early:
bvk_kmesh = self.bvk_kmesh
rcut = ft_ao.estimate_rcut(cell)
supmol = ft_ao.ExtendedMole.from_cell(cell, bvk_kmesh, rcut.max())
supmol = supmol.strip_basis(rcut)
s_nao = supmol.nao
moR, moI = aft_jk._mo_k2gamma(supmol, dm_factor, kpts, t_rev_pairs)
if abs(moI).max() < 1e-5:
dm = [moR, None]
ft_kern = aft_jk._gen_ft_kernel_fake_gamma(cell, supmol, aosym)
update_vk = aft_jk._update_vk_fake_gamma
else:
contract_mo_early = False
moR = moI = None
if not contract_mo_early:
dm = [np.asarray(dm_factor.real, order='C'),
np.asarray(dm_factor.imag, order='C')]
if np.count_nonzero(k_to_compute) >= 2 * lib.num_threads():
update_vk = aft_jk._update_vk1_dmf
else:
update_vk = aft_jk._update_vk_dmf
log.debug2('set update_vk to %s', update_vk)
if not contract_mo_early:
ft_kern = self.supmol_ft.gen_ft_kernel(
aosym, return_complex=False, kpts=kpts, verbose=log)
Gv, Gvbase, kws = cell.get_Gv_weights(mesh)
Gv = np.asarray(Gv, order='F')
gxyz = lib.cartesian_prod([np.arange(len(x)) for x in Gvbase])
G0_idx = 0
if (cell.dimension == 3 or
(cell.dimension == 2 and cell.low_dim_ft_type != 'inf_vacuum')):
coulG_SR_at_G0 = np.pi/self.omega**2 * kws
else:
coulG_SR_at_G0 = None
if naod > 0:
smooth_bas_mask = rs_cell.bas_type == ft_ao.SMOOTH_BASIS
smooth_bas_idx = rs_cell.bas_map[smooth_bas_mask]
ao_d_idx = rs_cell.get_ao_indices(smooth_bas_idx, cell.ao_loc)
mem_now = lib.current_memory()[0]
max_memory = max(2000, (self.max_memory - mem_now))
log.debug1('max_memory = %d MB (%d in use)', max_memory+mem_now, mem_now)
if self.exclude_dd_block and not self._sr_without_dddd and naod > 0:
cache_size = (naod*(naod+1)*ngrids*(nkpts+1))*16e-6
log.debug1('naod = %d cache_size = %d', naod, cache_size)
# fft_aopair_dd seems less efficient than aft_aopair_dd
if 0 and max_memory * .5 > cache_size and cell.dimension >= 2:
from pyscf.pbc.dft.multigrid import _take_5d
mesh_d = cell_d.mesh
log.debug1('merge_dd with cached fft_aopair_dd')
aoR_ks, aoI_ks = rsdf_builder._eval_gto(cell_d, mesh_d, kpts)
coords = cell_d.get_uniform_grids(mesh_d)
max_memory -= cache_size
gx = np.fft.fftfreq(mesh[0], 1./mesh[0]).astype(np.int32)
gy = np.fft.fftfreq(mesh[1], 1./mesh[1]).astype(np.int32)
gz = np.fft.fftfreq(mesh[2], 1./mesh[2]).astype(np.int32)
def fft_aopair_dd(ki, kj, expmikr):
# einsum('g,ig,jg->ijg', expmikr, ao_ki.conj(), ao_kj)
pqG_ddR = np.empty((naod**2, ngrids_d))
pqG_ddI = np.empty((naod**2, ngrids_d))
expmikrR, expmikrI = expmikr
libpbc.PBC_zjoin_fCN_s1(
pqG_ddR.ctypes.data_as(ctypes.c_void_p),
pqG_ddI.ctypes.data_as(ctypes.c_void_p),
expmikrR.ctypes.data_as(ctypes.c_void_p),
expmikrI.ctypes.data_as(ctypes.c_void_p),
aoR_ks[ki].ctypes.data_as(ctypes.c_void_p),
aoI_ks[ki].ctypes.data_as(ctypes.c_void_p),
aoR_ks[kj].ctypes.data_as(ctypes.c_void_p),
aoI_ks[kj].ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(naod), ctypes.c_int(naod), ctypes.c_int(ngrids_d))
pqG_dd = np.empty((naod**2, ngrids_d), dtype=np.complex128)
pqG_dd.real = pqG_ddR
pqG_dd.imag = pqG_ddI
pqG_ddR = pqG_ddI = None
pqG_dd *= cell.vol / ngrids_d
pqG_dd = pbctools.fft(pqG_dd, mesh_d).reshape(naod, naod, *mesh_d)
pqG_dd = _take_5d(pqG_dd, (None, None, gx, gy, gz))
return np.asarray(pqG_dd.reshape(naod, naod, ngrids), order='C')
cache = {}
def merge_dd(Gpq, p0, p1, ki_lst, kj_lst):
'''Merge diffused basis block into ao-pair tensor inplace'''
expmikr = np.exp(-1j * np.dot(coords, kpts[kj_lst[0]]-kpts[ki_lst[0]]))
expmikrR = np.asarray(expmikr.real, order='C')
expmikrI = np.asarray(expmikr.imag, order='C')
GpqR, GpqI = Gpq
# Gpq should be an array of (nkpts,ni,nj,ngrids) in C order
if not GpqR[0].flags.c_contiguous:
assert GpqR[0].strides[0] == 8 # stride for grids
cpu0 = logger.process_clock(), logger.perf_counter()
for k, (ki, kj) in enumerate(zip(ki_lst, kj_lst)):
if (ki, kj) not in cache:
log.debug3('cache dd block (%d, %d)', ki, kj)
cache[ki, kj] = fft_aopair_dd(ki, kj, (expmikrR, expmikrI))
pqG_dd = cache[ki, kj]
libpbc.PBC_ft_zfuse_dd_s1(
GpqR[kj].ctypes.data_as(ctypes.c_void_p),
GpqI[kj].ctypes.data_as(ctypes.c_void_p),
pqG_dd.ctypes.data_as(ctypes.c_void_p),
ao_d_idx.ctypes.data_as(ctypes.c_void_p),
(ctypes.c_int*2)(p0, p1), ctypes.c_int(nao),
ctypes.c_int(naod), ctypes.c_int(ngrids))
log.timer_debug1('merge_dd', *cpu0)
return (GpqR, GpqI)
cpu1 = log.timer_debug1('get_lr_k_kpts initializing dd block', *cpu1)
else:
log.debug1('merge_dd with aft_aopair_dd')
ft_kern_dd = self.supmol_d.gen_ft_kernel(
aosym, return_complex=False, kpts=kpts, verbose=log)
buf1 = None
def merge_dd(Gpq, p0, p1, ki_lst, kj_lst):
'''Merge diffused basis block into ao-pair tensor inplace'''
kpt = kpts[kj_lst[0]] - kpts[ki_lst[0]]
GpqR, GpqI = Gpq
pqG_ddR, pqG_ddI = ft_kern_dd(Gv[p0:p1], gxyz[p0:p1], Gvbase,
kpt, out=buf1)
# Gpq should be an array of (nkpts,ni,nj,ngrids) in C order
if not GpqR[0].flags.c_contiguous:
assert GpqR[0].strides[0] == 8 # stride for grids
for k in range(nkpts):
libpbc.PBC_ft_fuse_dd_s1(
GpqR[k].ctypes.data_as(ctypes.c_void_p),
GpqI[k].ctypes.data_as(ctypes.c_void_p),
pqG_ddR[k].ctypes.data_as(ctypes.c_void_p),
pqG_ddI[k].ctypes.data_as(ctypes.c_void_p),
ao_d_idx.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nao), ctypes.c_int(naod), ctypes.c_int(p1-p0))
return (GpqR, GpqI)
if contract_mo_early:
Gblksize = max(24, int((max_memory*1e6/16-nkpts*nao**2*3)/
(nao*s_nao+nao*nkpts*nocc))//8*8)
Gblksize = min(Gblksize, ngrids, 200000)
log.debug1('Gblksize = %d', Gblksize)
buf = np.empty(Gblksize*s_nao*nao*2)
else:
Gblksize = max(24, int(max_memory*.8e6/16/(nao**2+naod**2)/(nkpts+3))//8*8)
Gblksize = min(Gblksize, ngrids, 200000)
log.debug1('Gblksize = %d', Gblksize)
buf = np.empty(nkpts*Gblksize*nao**2*2)
if naod > 0:
buf1 = np.empty(nkpts*Gblksize*naod**2*2)
for group_id, (kpt, ki_idx, kj_idx, self_conj) \
in enumerate(kk_adapted_iter(cell, kpts)):
coulG = self.weighted_coulG(kpt, exxdiv, mesh)
if coulG_SR_at_G0 is not None:
# For cell.dimension = 2, coulG is computed with truncated coulomb
# interactions. The 3d coulG_SR below is to remove the analytical
# SR from get_jk_sr (which was computed with full Coulomb) then
# add the truncated Coulomb for AFT part.
with lib.temporary_env(cell, dimension=3):
coulG_SR = self.weighted_coulG_SR(kpt, False, mesh)
if is_zero(kpt):
coulG_SR[G0_idx] += coulG_SR_at_G0
else:
coulG_SR = self.weighted_coulG_SR(kpt, False, mesh)
if self.exclude_dd_block and not self._sr_without_dddd and naod > 0:
for p0, p1 in lib.prange(0, ngrids, Gblksize):
# C ~ compact basis, D ~ diffused basis
# K matrix with coulG_LR:
# (CC|CC) (CC|CD) (CC|DC) (CD|CC) (CD|CD) (CD|DC) (DC|CC) (DC|CD) (DC|DC)
# K matrix with full coulG:
# (CC|DD) (CD|DD) (DC|DD) (DD|CC) (DD|CD) (DD|DC) (DD|DD)
log.debug3('update_vk [%s:%s]', p0, p1)
Gpq = ft_kern(Gv[p0:p1], gxyz[p0:p1], Gvbase, kpt, out=buf)
update_vk(vk, Gpq, dm, coulG_SR[p0:p1] * -weight, ki_idx,
kj_idx, not self_conj, k_to_compute, t_rev_pairs)
Gpq = merge_dd(Gpq, p0, p1, ki_idx, kj_idx)
update_vk(vk, Gpq, dm, coulG[p0:p1] * weight, ki_idx,
kj_idx, not self_conj, k_to_compute, t_rev_pairs)
Gpq = None
# clear cache to release memory for merge_dd function
cache = {}
else:
coulG_LR = coulG - coulG_SR
for p0, p1 in lib.prange(0, ngrids, Gblksize):
log.debug3('update_vk [%s:%s]', p0, p1)
Gpq = ft_kern(Gv[p0:p1], gxyz[p0:p1], Gvbase, kpt, out=buf)
update_vk(vk, Gpq, dm, coulG_LR[p0:p1] * weight, ki_idx,
kj_idx, not self_conj, k_to_compute, t_rev_pairs)
Gpq = None
cpu1 = log.timer_debug1(f'ft_aopair group {group_id}', *cpu1)
if self._sr_without_dddd and naod > 0:
# (DD|DD) with full coulG, rest terms with coulG_LR
log.debug1('ft_aopair dd-blcok for dddd-block ERI')
if cell.dimension < 2:
raise NotImplementedError
if cell.dimension == 2 and cell.low_dim_ft_type == 'inf_vacuum':
raise NotImplementedError
vkR_dd = np.zeros((n_dm,nkpts,naod,naod))
vkI_dd = np.zeros((n_dm,nkpts,naod,naod))
vk_dd = [vkR_dd, vkI_dd]
if dm_factor is None:
dmsR, dmsI = dm
dmR_dd = np.asarray(dmsR[:,:,ao_d_idx[:,None],ao_d_idx], order='C')
dmI_dd = np.asarray(dmsI[:,:,ao_d_idx[:,None],ao_d_idx], order='C')
dm_dd = [dmR_dd, dmI_dd]
else:
assert update_vk is not aft_jk._update_vk_fake_gamma
dmfR, dmfI = dm
dmfR_dd = np.asarray(dmfR[:,:,ao_d_idx], order='C')
dmfI_dd = np.asarray(dmfI[:,:,ao_d_idx], order='C')
dm_dd = [dmfR_dd, dmfI_dd]
# AFT mesh for ERI is usually smaller than cell_d.mesh
ke_cutoff = aft.estimate_ke_cutoff(cell_d)
mesh_d = cell_d.cutoff_to_mesh(ke_cutoff)
log.debug1('lr_k dd-block ke_cutoff = %s mesh = %s', ke_cutoff, mesh_d)
ft_kern_dd = self.supmol_d.gen_ft_kernel(
aosym, return_complex=False, kpts=kpts, verbose=log)
Gv, Gvbase, kws = cell_d.get_Gv_weights(mesh_d)
gxyz = lib.cartesian_prod([np.arange(len(x)) for x in Gvbase])
ngrids_d = len(Gv)
Gblksize = max(24, int(max_memory*.8e6/16/naod**2/(nkpts+max(nkpts,3)))//8*8)
Gblksize = min(Gblksize, ngrids_d)
log.debug1('Gblksize = %d', Gblksize)
buf = np.empty(nkpts*Gblksize*naod**2*2)
for group_id, (kpt, ki_idx, kj_idx, self_conj) \
in enumerate(kk_adapted_iter(cell, kpts)):
with lib.temporary_env(cell, dimension=3):
coulG_SR = self.weighted_coulG_SR(kpt, False, mesh_d)
if is_zero(kpt) and coulG_SR_at_G0 is not None:
coulG_SR[G0_idx] += coulG_SR_at_G0
for p0, p1 in lib.prange(0, ngrids_d, Gblksize):
Gpq = ft_kern_dd(Gv[p0:p1], gxyz[p0:p1], Gvbase, kpt, out=buf)
update_vk(vk_dd, Gpq, dm_dd, coulG_SR[p0:p1] * weight,
ki_idx, kj_idx, not self_conj, k_to_compute, t_rev_pairs)
Gpq = None
cpu1 = log.timer_debug1(f'ft_aopair dd-block group {group_id}', *cpu1)
for i in range(n_dm):
for k in range(nkpts):
lib.takebak_2d(vkR[i,k], vkR_dd[i,k], ao_d_idx, ao_d_idx,
thread_safe=False)
lib.takebak_2d(vkI[i,k], vkI_dd[i,k], ao_d_idx, ao_d_idx,
thread_safe=False)
buf = buf1 = None
if is_zero(kpts) and not np.iscomplexobj(dm_kpts):
vk_kpts = vkR
else:
vk_kpts = vkR + vkI * 1j
# Add ewald_exxdiv contribution because G=0 was not included in the
# non-uniform grids
if (exxdiv == 'ewald' and
(cell.dimension < 2 or # 0D and 1D are computed with inf_vacuum
(cell.dimension == 2 and cell.low_dim_ft_type == 'inf_vacuum'))):
_ewald_exxdiv_for_G0(cell, kpts, dms, vk_kpts, kpts)
if time_reversal_symmetry:
for k, k_conj in t_rev_pairs:
if k != k_conj:
vk_kpts[:,k_conj] = vk_kpts[:,k].conj()
log.timer_debug1('get_lr_k_kpts', *cpu0)
return vk_kpts
RangeSeparationJKBuilder = RangeSeparatedJKBuilder
def _purify(mat_kpts, phase):
if phase is None:
return mat_kpts
#:mat_bvk = np.einsum('Rk,nkij,Sk->nRSij', phase, mat_kpts, phase.conj())
#:return np.einsum('Rk,nRSij,Sk->nkij', phase.conj(), mat_bvk.real, phase)
nkpts = phase.shape[1]
mat_bvk = lib.einsum('k,Sk,nkuv->nSuv', phase[0], phase.conj(), mat_kpts)
return lib.einsum('S,Sk,nSuv->nkuv', nkpts*phase[:,0].conj(), phase, mat_bvk.real)
[docs]
def estimate_rcut(rs_cell, omega, precision=None,
exclude_dd_block=True):
'''Estimate rcut for 2e SR-integrals'''
if precision is None:
precision = rs_cell.precision
rs_cell = rs_cell
exps, cs = pbcgto.cell._extract_pgto_params(rs_cell, 'min')
ls = rs_cell._bas[:,gto.ANG_OF]
exp_min_idx = exps.argmin()
cost = cs * (.5*abs(omega)*rs_cell.rcut)**ls / (2*exps)**(ls/2+.75)
ai_idx = ak_idx = cost.argmax()
compact_mask = rs_cell.bas_type != ft_ao.SMOOTH_BASIS
compact_idx = np.where(compact_mask)[0]
if exclude_dd_block and compact_idx.size > 0:
ak_idx = compact_idx[cost[compact_idx].argmax()]
logger.debug2(rs_cell, 'ai_idx=%d ak_idx=%d', ai_idx, ak_idx)
# Case 1: l in cell0, product kl ~ dc, product ij ~ dd and dc
# This includes interactions (dc|dd)
ak = exps[ak_idx]
lk = rs_cell._bas[ak_idx,gto.ANG_OF]
ck = cs[ak_idx]
aj = exps
lj = ls
cj = cs
ai = exps[ai_idx]
li = rs_cell._bas[ai_idx,gto.ANG_OF]
ci = cs[ai_idx]
al = exps[exp_min_idx]
ll = rs_cell._bas[exp_min_idx,gto.ANG_OF]
cl = cs[exp_min_idx]
aij = ai + aj
akl = ak + al
lij = li + lj
lkl = lk + ll
l4 = lij + lkl
norm_ang = ((2*li+1)*(2*lj+1)*(2*lk+1)*(2*ll+1)/(4*np.pi)**4)**.5
c1 = ci * cj * ck * cl * norm_ang
theta = omega**2*aij*akl/(aij*akl + (aij+akl)*omega**2)
sfac = omega**2*aj*al/(aj*al + (aj+al)*omega**2) / theta
fl = 2
fac = 2**(li+lk)*np.pi**2.5*c1 * theta**(l4-.5)
fac *= 2*np.pi/rs_cell.vol/theta
fac /= aij**(li+1.5) * akl**(lk+1.5) * aj**lj * al**ll
fac *= fl / precision
r0 = rs_cell.rcut
r0 = (np.log(fac * r0 * (sfac*r0)**(l4-1) + 1.) / (sfac*theta))**.5
r0 = (np.log(fac * r0 * (sfac*r0)**(l4-1) + 1.) / (sfac*theta))**.5
rcut = r0
if exclude_dd_block and 0 < compact_idx.size < rs_cell.nbas:
# Case 2: l in cell0, product kl ~ dc, product ij ~ cd
# so as to exclude interaction (dc|dd)
smooth_mask = ~compact_mask
ai, li, ci = ak, lk, ck
aj = exps[smooth_mask]
lj = ls[smooth_mask]
cj = cs[smooth_mask]
aij = ai + aj
lij = li + lj
l4 = lij + lkl
norm_ang = ((2*li+1)*(2*lj+1)*(2*lk+1)*(2*ll+1)/(4*np.pi)**4)**.5
c1 = ci * cj * ck * cl * norm_ang
theta = omega**2*aij*akl/(aij*akl + (aij+akl)*omega**2)
sfac = omega**2*aj*al/(aj*al + (aj+al)*omega**2) / theta
fl = 2
fac = 2**(li+lk)*np.pi**2.5*c1 * theta**(l4-.5)
fac *= 2*np.pi/rs_cell.vol/theta
fac /= aij**(li+1.5) * akl**(lk+1.5) * aj**lj * al**ll
fac *= fl / precision
r0 = rcut[smooth_mask]
r0 = (np.log(fac * r0 * (sfac*r0)**(l4-1) + 1.) / (sfac*theta))**.5
r0 = (np.log(fac * r0 * (sfac*r0)**(l4-1) + 1.) / (sfac*theta))**.5
rcut[smooth_mask] = r0
return rcut
def _guess_omega(cell, kpts, mesh=None):
a = cell.lattice_vectors()
if cell.dimension == 0:
if mesh is None:
mesh = cell.mesh
ke_cutoff = pbctools.mesh_to_cutoff(a, mesh).min()
return 0, mesh, ke_cutoff
precision = cell.precision
nkpts = len(kpts)
if mesh is None:
omega_min = OMEGA_MIN
ke_min = estimate_ke_cutoff_for_omega(cell, omega_min)
nk = nkpts**(1./3)
ke_cutoff = 50 / (.7+.25*nk+.05*nk**3)
ke_cutoff = max(ke_cutoff, ke_min)
mesh = cell.cutoff_to_mesh(ke_cutoff)
else:
mesh = np.asarray(mesh)
ke_cutoff = min(pbctools.mesh_to_cutoff(a, mesh)[:cell.dimension])
omega = estimate_omega_for_ke_cutoff(cell, ke_cutoff, precision)
return omega, mesh, ke_cutoff
[docs]
def estimate_ke_cutoff_for_omega(cell, omega, precision=None):
'''Energy cutoff for FFTDF to converge attenuated Coulomb in moment space
'''
if precision is None:
precision = cell.precision
ai = np.hstack(cell.bas_exps()).max()
theta = 1./(1./ai + omega**-2)
fac = 32*np.pi**2 * theta / precision
Ecut = 20.
Ecut = np.log(fac / (2*Ecut) + 1.) * 2*theta
Ecut = np.log(fac / (2*Ecut) + 1.) * 2*theta
return Ecut
[docs]
def estimate_omega_for_ke_cutoff(cell, ke_cutoff, precision=None):
'''The minimal omega in attenuated Coulombl given energy cutoff
'''
if precision is None:
precision = cell.precision
# # esitimation based on \int dk 4pi/k^2 exp(-k^2/4omega) sometimes is not
# # enough to converge the 2-electron integrals. A penalty term here is to
# # reduce the error in integrals
# precision *= 1e-2
# kmax = (ke_cutoff*2)**.5
# log_rest = np.log(precision / (16*np.pi**2 * kmax**lmax))
# omega = (-.5 * ke_cutoff / log_rest)**.5
# return omega
ai = np.hstack(cell.bas_exps()).max()
aij = ai * 2
fac = 32*np.pi**2 / precision
omega = .3
theta = 1./(1./ai + omega**-2)
omega2 = 1./(np.log(fac * theta/ (2*ke_cutoff) + 1.)*2/ke_cutoff - 1./aij)
if omega2 > 0:
theta = 1./(1./ai + 1./omega2)
omega2 = 1./(np.log(fac * theta/ (2*ke_cutoff) + 1.)*2/ke_cutoff - 1./aij)
omega = max(omega2, 0)**.5
if omega < OMEGA_MIN:
logger.warn(cell, 'omega=%g smaller than the required minimal value %g. '
'Set omega to %g', omega2, OMEGA_MIN, OMEGA_MIN)
omega = OMEGA_MIN
return omega
def _qcond_cell0_abstract(qcond, seg_loc, seg2sh, nbasp):
'''Find the max qcond for ij pair'''
# The first shell in each seg_loc[i]:seg_loc[i+1] is inside cell0
cell0_prim_idx = seg2sh[np.arange(seg_loc[nbasp])]
qcond_sub = qcond[:,cell0_prim_idx]
sh_loc = seg2sh[seg_loc]
nbas_bvk = sh_loc.size - 1
qtmp = np.empty((nbas_bvk, cell0_prim_idx.size), dtype=qcond.dtype)
for i, (i0, i1) in enumerate(zip(sh_loc[:-1], sh_loc[1:])):
if i0 != i1:
qtmp[i] = qcond_sub[i0:i1].max(axis=0)
else:
qtmp[i] = INDEX_MIN
qcond_cell0 = np.empty((nbas_bvk, nbasp), dtype=qcond.dtype)
for j, (j0, j1) in enumerate(zip(seg_loc[:nbasp], seg_loc[1:nbasp+1])):
if j0 != j1:
qcond_cell0[:,j] = qtmp[:,j0:j1].max(axis=1)
else:
qcond_cell0[:,j] = INDEX_MIN
return qcond_cell0