#!/usr/bin/env python
# Copyright 2014-2020 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.
#
# Author: Timothy Berkelbach <tim.berkelbach@gmail.com>
# Qiming Sun <osirpt.sun@gmail.com>
#
import sys
import numpy
from pyscf import lib
from pyscf.dft import numint
from pyscf.dft.numint import eval_mat, _dot_ao_ao, _dot_ao_dm
from pyscf.dft.numint import _scale_ao, _contract_rho
from pyscf.dft.numint import _rks_gga_wv0, _rks_gga_wv1
from pyscf.dft.numint import _uks_gga_wv0, _uks_gga_wv1
from pyscf.dft.numint import OCCDROP
from pyscf.pbc.dft.gen_grid import make_mask, BLKSIZE
from pyscf.pbc.lib.kpts_helper import member
def eval_ao(cell, coords, kpt=numpy.zeros(3), deriv=0, relativity=0, shls_slice=None,
non0tab=None, out=None, verbose=None):
'''Collocate AO crystal orbitals (opt. gradients) on the real-space grid.
Args:
cell : instance of :class:`Cell`
coords : (nx*ny*nz, 3) ndarray
The real-space grid point coordinates.
Kwargs:
kpt : (3,) ndarray
The k-point corresponding to the crystal AO.
deriv : int
AO derivative order. It affects the shape of the return array.
If deriv=0, the returned AO values are stored in a (N,nao) array.
Otherwise the AO values are stored in an array of shape (M,N,nao).
Here N is the number of grids, nao is the number of AO functions,
M is the size associated to the derivative deriv.
Returns:
aoR : ([4,] nx*ny*nz, nao=cell.nao_nr()) ndarray
The value of the AO crystal orbitals on the real-space grid by default.
If deriv=1, also contains the value of the orbitals gradient in the
x, y, and z directions. It can be either complex or float array,
depending on the kpt argument. If kpt is not given (gamma point),
aoR is a float array.
See Also:
pyscf.dft.numint.eval_ao
'''
ao_kpts = eval_ao_kpts(cell, coords, numpy.reshape(kpt, (-1,3)), deriv,
relativity, shls_slice, non0tab, out, verbose)
return ao_kpts[0]
def eval_ao_kpts(cell, coords, kpts=None, deriv=0, relativity=0,
shls_slice=None, non0tab=None, out=None, verbose=None, **kwargs):
'''
Returns:
ao_kpts: (nkpts, [comp], ngrids, nao) ndarray
AO values at each k-point
'''
if kpts is None:
if 'kpt' in kwargs:
sys.stderr.write('WARN: KNumInt.eval_ao function finds keyword '
'argument "kpt" and converts it to "kpts"\n')
kpts = kwargs['kpt']
else:
kpts = numpy.zeros((1,3))
kpts = numpy.reshape(kpts, (-1,3))
comp = (deriv+1)*(deriv+2)*(deriv+3)//6
if cell.cart:
feval = 'GTOval_cart_deriv%d' % deriv
else:
feval = 'GTOval_sph_deriv%d' % deriv
return cell.pbc_eval_gto(feval, coords, comp, kpts,
shls_slice=shls_slice, non0tab=non0tab, out=out)
def eval_rho(cell, ao, dm, non0tab=None, xctype='LDA', hermi=0, verbose=None):
'''Collocate the *real* density (opt. gradients) on the real-space grid.
Args:
cell : instance of :class:`Mole` or :class:`Cell`
ao : ([4,] nx*ny*nz, nao=cell.nao_nr()) ndarray
The value of the AO crystal orbitals on the real-space grid by default.
If xctype='GGA', also contains the value of the gradient in the x, y,
and z directions.
Returns:
rho : ([4,] nx*ny*nz) ndarray
The value of the density on the real-space grid. If xctype='GGA',
also contains the value of the gradient in the x, y, and z
directions.
See Also:
pyscf.dft.numint.eval_rho
'''
if xctype == 'LDA' or xctype == 'HF':
ngrids, nao = ao.shape
else:
ngrids, nao = ao[0].shape
if non0tab is None:
non0tab = numpy.empty(((ngrids+BLKSIZE-1)//BLKSIZE, cell.nbas),
dtype=numpy.uint8)
non0tab[:] = 0xff
# complex orbitals or density matrix
if numpy.iscomplexobj(ao) or numpy.iscomplexobj(dm):
shls_slice = (0, cell.nbas)
ao_loc = cell.ao_loc_nr()
dm = dm.astype(numpy.complex128)
# For GGA, function eval_rho returns real(|\nabla i> D_ij <j| + |i> D_ij <\nabla j|)
# = real(|\nabla i> D_ij <j| + |i> D_ij <\nabla j|)
# = real(|\nabla i> D_ij <j| + conj(|\nabla j> conj(D_ij) < i|))
# = real(|\nabla i> D_ij <j|) + real(|\nabla j> conj(D_ij) < i|)
# = real(|\nabla i> [D_ij + (D^\dagger)_ij] <j|)
# symmetrization dm (D + D.conj().T) then /2 because the code below computes
# 2*real(|\nabla i> D_ij <j|)
if not hermi:
dm = (dm + dm.conj().T) * .5
def dot_bra(bra, aodm):
# rho = numpy.einsum('pi,pi->p', bra.conj(), aodm).real
#:rho = numpy.einsum('pi,pi->p', bra.real, aodm.real)
#:rho += numpy.einsum('pi,pi->p', bra.imag, aodm.imag)
#:return rho
return _contract_rho(bra, aodm)
if xctype == 'LDA' or xctype == 'HF':
c0 = _dot_ao_dm(cell, ao, dm, non0tab, shls_slice, ao_loc)
rho = dot_bra(ao, c0)
elif xctype == 'GGA':
rho = numpy.empty((4,ngrids))
c0 = _dot_ao_dm(cell, ao[0], dm, non0tab, shls_slice, ao_loc)
rho[0] = dot_bra(ao[0], c0)
for i in range(1, 4):
rho[i] = dot_bra(ao[i], c0) * 2
else:
# rho[4] = \nabla^2 rho, rho[5] = 1/2 |nabla f|^2
rho = numpy.empty((6,ngrids))
c0 = _dot_ao_dm(cell, ao[0], dm, non0tab, shls_slice, ao_loc)
rho[0] = dot_bra(ao[0], c0)
rho[5] = 0
for i in range(1, 4):
rho[i] = dot_bra(ao[i], c0) * 2 # *2 for +c.c.
c1 = _dot_ao_dm(cell, ao[i], dm, non0tab, shls_slice, ao_loc)
rho[5] += dot_bra(ao[i], c1)
XX, YY, ZZ = 4, 7, 9
ao2 = ao[XX] + ao[YY] + ao[ZZ]
rho[4] = dot_bra(ao2, c0)
rho[4] += rho[5]
rho[4] *= 2 # *2 for +c.c.
rho[5] *= .5
else:
# real orbitals and real DM
rho = numint.eval_rho(cell, ao, dm, non0tab, xctype, hermi, verbose)
return rho
def eval_rho2(cell, ao, mo_coeff, mo_occ, non0tab=None, xctype='LDA',
verbose=None):
'''Refer to `pyscf.dft.numint.eval_rho2` for full documentation.
'''
xctype = xctype.upper()
if xctype == 'LDA' or xctype == 'HF':
ngrids, nao = ao.shape
else:
ngrids, nao = ao[0].shape
if non0tab is None:
non0tab = numpy.empty(((ngrids+BLKSIZE-1)//BLKSIZE,cell.nbas),
dtype=numpy.uint8)
non0tab[:] = 0xff
# complex orbitals or density matrix
if numpy.iscomplexobj(ao) or numpy.iscomplexobj(mo_coeff):
def dot(bra, ket):
#:rho = numpy.einsum('pi,pi->p', bra.real, ket.real)
#:rho += numpy.einsum('pi,pi->p', bra.imag, ket.imag)
#:return rho
return _contract_rho(bra, ket)
shls_slice = (0, cell.nbas)
ao_loc = cell.ao_loc_nr()
pos = mo_occ > OCCDROP
cpos = numpy.einsum('ij,j->ij', mo_coeff[:,pos], numpy.sqrt(mo_occ[pos]))
if pos.sum() > 0:
if xctype == 'LDA' or xctype == 'HF':
c0 = _dot_ao_dm(cell, ao, cpos, non0tab, shls_slice, ao_loc)
rho = dot(c0, c0)
elif xctype == 'GGA':
rho = numpy.empty((4,ngrids))
c0 = _dot_ao_dm(cell, ao[0], cpos, non0tab, shls_slice, ao_loc)
rho[0] = dot(c0, c0)
for i in range(1, 4):
c1 = _dot_ao_dm(cell, ao[i], cpos, non0tab, shls_slice, ao_loc)
rho[i] = dot(c0, c1) * 2 # *2 for +c.c.
else: # meta-GGA
# rho[4] = \nabla^2 rho, rho[5] = 1/2 |nabla f|^2
rho = numpy.empty((6,ngrids))
c0 = _dot_ao_dm(cell, ao[0], cpos, non0tab, shls_slice, ao_loc)
rho[0] = dot(c0, c0)
rho[5] = 0
for i in range(1, 4):
c1 = _dot_ao_dm(cell, ao[i], cpos, non0tab, shls_slice, ao_loc)
rho[i] = dot(c0, c1) * 2 # *2 for +c.c.
rho[5]+= dot(c1, c1)
XX, YY, ZZ = 4, 7, 9
ao2 = ao[XX] + ao[YY] + ao[ZZ]
c1 = _dot_ao_dm(cell, ao2, cpos, non0tab, shls_slice, ao_loc)
rho[4] = dot(c0, c1)
rho[4]+= rho[5]
rho[4]*= 2
rho[5]*= .5
else:
if xctype == 'LDA' or xctype == 'HF':
rho = numpy.zeros(ngrids)
elif xctype == 'GGA':
rho = numpy.zeros((4,ngrids))
else:
rho = numpy.zeros((6,ngrids))
neg = mo_occ < -OCCDROP
if neg.sum() > 0:
cneg = numpy.einsum('ij,j->ij', mo_coeff[:,neg], numpy.sqrt(-mo_occ[neg]))
if xctype == 'LDA' or xctype == 'HF':
c0 = _dot_ao_dm(cell, ao, cneg, non0tab, shls_slice, ao_loc)
rho -= dot(c0, c0)
elif xctype == 'GGA':
c0 = _dot_ao_dm(cell, ao[0], cneg, non0tab, shls_slice, ao_loc)
rho[0] -= dot(c0, c0)
for i in range(1, 4):
c1 = _dot_ao_dm(cell, ao[i], cneg, non0tab, shls_slice, ao_loc)
rho[i] -= dot(c0, c1) * 2 # *2 for +c.c.
else:
c0 = _dot_ao_dm(cell, ao[0], cneg, non0tab, shls_slice, ao_loc)
rho[0] -= dot(c0, c0)
rho5 = 0
for i in range(1, 4):
c1 = _dot_ao_dm(cell, ao[i], cneg, non0tab, shls_slice, ao_loc)
rho[i] -= dot(c0, c1) * 2 # *2 for +c.c.
rho5 -= dot(c1, c1)
XX, YY, ZZ = 4, 7, 9
ao2 = ao[XX] + ao[YY] + ao[ZZ]
c1 = _dot_ao_dm(cell, ao2, cneg, non0tab, shls_slice, ao_loc)
rho[4] -= dot(c0, c1) * 2
rho[4] -= rho5 * 2
rho[5] -= rho5 * .5
else:
rho = numint.eval_rho2(cell, ao, mo_coeff, mo_occ, non0tab, xctype, verbose)
return rho
def nr_rks(ni, cell, grids, xc_code, dms, spin=0, relativity=0, hermi=0,
kpts=None, kpts_band=None, max_memory=2000, verbose=None):
'''Calculate RKS XC functional and potential matrix for given meshgrids and density matrix
Note: This is a replica of pyscf.dft.numint.nr_rks_vxc with kpts added.
This implemented uses slow function in numint, which only calls eval_rho, eval_mat.
Faster function uses eval_rho2 which is not yet implemented.
Args:
ni : an instance of :class:`NumInt` or :class:`KNumInt`
cell : instance of :class:`Mole` or :class:`Cell`
grids : an instance of :class:`Grids`
grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
xc_code : str
XC functional description.
See :func:`parse_xc` of pyscf/dft/libxc.py for more details.
dms : 2D/3D array or a list of 2D/3D arrays
Density matrices (2D) / density matrices for k-points (3D)
Kwargs:
spin : int
spin polarized if spin = 1
relativity : int
No effects.
hermi : int
No effects
max_memory : int or float
The maximum size of cache to use (in MB).
verbose : int or object of :class:`Logger`
No effects.
kpts : (3,) ndarray or (nkpts,3) ndarray
Single or multiple k-points sampled for the DM. Default is gamma point.
kpts_band : (3,) ndarray or (*,3) ndarray
A list of arbitrary "band" k-points at which to evaluate the XC matrix.
Returns:
nelec, excsum, vmat.
nelec is the number of electrons generated by numerical integration.
excsum is the XC functional value. vmat is the XC potential matrix in
2D array of shape (nao,nao) where nao is the number of AO functions.
'''
if kpts is None:
kpts = numpy.zeros((1,3))
xctype = ni._xc_type(xc_code)
make_rho, nset, nao = ni._gen_rho_evaluator(cell, dms, hermi)
nelec = numpy.zeros(nset)
excsum = numpy.zeros(nset)
vmat = [0]*nset
if xctype == 'LDA':
ao_deriv = 0
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, kpts_band,
max_memory):
for i in range(nset):
rho = make_rho(i, ao_k2, mask, xctype)
exc, vxc = ni.eval_xc(xc_code, rho, spin=0,
relativity=relativity, deriv=1)[:2]
den = rho*weight
nelec[i] += den.sum()
excsum[i] += (den*exc).sum()
vmat[i] += ni.eval_mat(cell, ao_k1, weight, rho, vxc,
mask, xctype, 0, verbose)
elif xctype == 'GGA':
ao_deriv = 1
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, kpts_band,
max_memory):
for i in range(nset):
rho = make_rho(i, ao_k2, mask, xctype)
exc, vxc = ni.eval_xc(xc_code, rho, spin=0,
relativity=relativity, deriv=1)[:2]
den = rho[0]*weight
nelec[i] += den.sum()
excsum[i] += (den*exc).sum()
vmat[i] += ni.eval_mat(cell, ao_k1, weight, rho, vxc,
mask, xctype, 0, verbose)
elif xctype == 'MGGA':
if (any(x in xc_code.upper() for x in ('CC06', 'CS', 'BR89', 'MK00'))):
raise NotImplementedError('laplacian in meta-GGA method')
ao_deriv = 2
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, kpts_band,
max_memory):
for i in range(nset):
rho = make_rho(i, ao_k2, mask, xctype)
exc, vxc = ni.eval_xc(xc_code, rho, spin=0,
relativity=relativity, deriv=1)[:2]
den = rho[0]*weight
nelec[i] += den.sum()
excsum[i] += (den*exc).sum()
vmat[i] += ni.eval_mat(cell, ao_k1, weight, rho, vxc,
mask, xctype, 0, verbose)
if nset == 1:
nelec = nelec[0]
excsum = excsum[0]
vmat = vmat[0]
return nelec, excsum, numpy.asarray(vmat)
def nr_uks(ni, cell, grids, xc_code, dms, spin=1, relativity=0, hermi=0,
kpts=None, kpts_band=None, max_memory=2000, verbose=None):
'''Calculate UKS XC functional and potential matrix for given meshgrids and density matrix
Note: This is a replica of pyscf.dft.numint.nr_rks_vxc with kpts added.
This implemented uses slow function in numint, which only calls eval_rho, eval_mat.
Faster function uses eval_rho2 which is not yet implemented.
Args:
ni : an instance of :class:`NumInt` or :class:`KNumInt`
cell : instance of :class:`Mole` or :class:`Cell`
grids : an instance of :class:`Grids`
grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
xc_code : str
XC functional description.
See :func:`parse_xc` of pyscf/dft/libxc.py for more details.
dms :
Density matrices
Kwargs:
spin : int
spin polarized if spin = 1
relativity : int
No effects.
hermi : int
Input density matrices symmetric or not
max_memory : int or float
The maximum size of cache to use (in MB).
verbose : int or object of :class:`Logger`
No effects.
kpts : (3,) ndarray or (nkpts,3) ndarray
Single or multiple k-points sampled for the DM. Default is gamma point.
kpts_band : (3,) ndarray or (*,3) ndarray
A list of arbitrary "band" k-points at which to evaluate the XC matrix.
Returns:
nelec, excsum, vmat.
nelec is the number of electrons generated by numerical integration.
excsum is the XC functional value. vmat is the XC potential matrix in
2D array of shape (nao,nao) where nao is the number of AO functions.
'''
if kpts is None:
kpts = numpy.zeros((1,3))
xctype = ni._xc_type(xc_code)
dma, dmb = _format_uks_dm(dms)
nao = dma.shape[-1]
make_rhoa, nset = ni._gen_rho_evaluator(cell, dma, hermi)[:2]
make_rhob = ni._gen_rho_evaluator(cell, dmb, hermi)[0]
nelec = numpy.zeros((2,nset))
excsum = numpy.zeros(nset)
vmata = [0]*nset
vmatb = [0]*nset
if xctype == 'LDA':
ao_deriv = 0
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, kpts_band,
max_memory):
for i in range(nset):
rho_a = make_rhoa(i, ao_k2, mask, xctype)
rho_b = make_rhob(i, ao_k2, mask, xctype)
exc, vxc = ni.eval_xc(xc_code, (rho_a, rho_b), spin=1,
relativity=relativity, deriv=1,
verbose=verbose)[:2]
vrho = vxc[0]
den = rho_a * weight
nelec[0,i] += den.sum()
excsum[i] += (den*exc).sum()
den = rho_b * weight
nelec[1,i] += den.sum()
excsum[i] += (den*exc).sum()
vmata[i] += ni.eval_mat(cell, ao_k1, weight, rho_a, vrho[:,0],
mask, xctype, 1, verbose)
vmatb[i] += ni.eval_mat(cell, ao_k1, weight, rho_b, vrho[:,1],
mask, xctype, 1, verbose)
elif xctype == 'GGA':
ao_deriv = 1
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts,
kpts_band, max_memory):
for i in range(nset):
rho_a = make_rhoa(i, ao_k2, mask, xctype)
rho_b = make_rhob(i, ao_k2, mask, xctype)
exc, vxc = ni.eval_xc(xc_code, (rho_a, rho_b), spin=1,
relativity=relativity, deriv=1,
verbose=verbose)[:2]
vrho, vsigma = vxc[:2]
den = rho_a[0]*weight
nelec[0,i] += den.sum()
excsum[i] += (den*exc).sum()
den = rho_b[0]*weight
nelec[1,i] += den.sum()
excsum[i] += (den*exc).sum()
vmata[i] += ni.eval_mat(cell, ao_k1, weight, (rho_a,rho_b),
(vrho[:,0], (vsigma[:,0],vsigma[:,1])),
mask, xctype, 1, verbose)
vmatb[i] += ni.eval_mat(cell, ao_k1, weight, (rho_b,rho_a),
(vrho[:,1], (vsigma[:,2],vsigma[:,1])),
mask, xctype, 1, verbose)
elif xctype == 'MGGA':
assert(all(x not in xc_code.upper() for x in ('CC06', 'CS', 'BR89', 'MK00')))
ao_deriv = 2
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, kpts_band,
max_memory):
for i in range(nset):
rho_a = make_rhoa(i, ao_k2, mask, xctype)
rho_b = make_rhob(i, ao_k2, mask, xctype)
exc, vxc = ni.eval_xc(xc_code, (rho_a, rho_b), spin=1,
relativity=relativity, deriv=1,
verbose=verbose)[:2]
vrho, vsigma, vlapl, vtau = vxc
den = rho_a[0]*weight
nelec[0,i] += den.sum()
excsum[i] += (den*exc).sum()
den = rho_b[0]*weight
nelec[1,i] += den.sum()
excsum[i] += (den*exc).sum()
v = (vrho[:,0], (vsigma[:,0],vsigma[:,1]), None, vtau[:,0])
vmata[i] += ni.eval_mat(cell, ao_k1, weight, (rho_a,rho_b), v,
mask, xctype, 1, verbose)
v = (vrho[:,1], (vsigma[:,2],vsigma[:,1]), None, vtau[:,1])
vmatb[i] += ni.eval_mat(cell, ao_k1, weight, (rho_b,rho_a), v,
mask, xctype, 1, verbose)
v = None
if dma.ndim == vmata[0].ndim: # One set of DMs in the input
nelec = nelec[:,0]
excsum = excsum[0]
vmata = vmata[0]
vmatb = vmatb[0]
return nelec, excsum, numpy.asarray((vmata,vmatb))
def _format_uks_dm(dms):
dma, dmb = dms
if getattr(dms, 'mo_coeff', None) is not None:
#TODO: test whether dm.mo_coeff matching dm
mo_coeff = dms.mo_coeff
mo_occ = dms.mo_occ
if (isinstance(mo_coeff[0], numpy.ndarray) and
mo_coeff[0].ndim < dma.ndim): # handle ROKS
mo_occa = [numpy.array(occ> 0, dtype=numpy.double) for occ in mo_occ]
mo_occb = [numpy.array(occ==2, dtype=numpy.double) for occ in mo_occ]
dma = lib.tag_array(dma, mo_coeff=mo_coeff, mo_occ=mo_occa)
dmb = lib.tag_array(dmb, mo_coeff=mo_coeff, mo_occ=mo_occb)
else:
dma = lib.tag_array(dma, mo_coeff=mo_coeff[0], mo_occ=mo_occ[0])
dmb = lib.tag_array(dmb, mo_coeff=mo_coeff[1], mo_occ=mo_occ[1])
return dma, dmb
nr_rks_vxc = nr_rks
nr_uks_vxc = nr_uks
def nr_rks_fxc(ni, cell, grids, xc_code, dm0, dms, relativity=0, hermi=0,
rho0=None, vxc=None, fxc=None, kpts=None, max_memory=2000,
verbose=None):
'''Contract RKS XC kernel matrix with given density matrices
Args:
ni : an instance of :class:`NumInt` or :class:`KNumInt`
cell : instance of :class:`Mole` or :class:`Cell`
grids : an instance of :class:`Grids`
grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
xc_code : str
XC functional description.
See :func:`parse_xc` of pyscf/dft/libxc.py for more details.
dms : 2D/3D array or a list of 2D/3D arrays
Density matrices (2D) / density matrices for k-points (3D)
Kwargs:
hermi : int
Input density matrices symmetric or not
max_memory : int or float
The maximum size of cache to use (in MB).
rho0 : float array
Zero-order density (and density derivative for GGA). Giving kwargs rho0,
vxc and fxc to improve better performance.
vxc : float array
First order XC derivatives
fxc : float array
Second order XC derivatives
Examples:
'''
if kpts is None:
kpts = numpy.zeros((1,3))
xctype = ni._xc_type(xc_code)
make_rho, nset, nao = ni._gen_rho_evaluator(cell, dms, hermi)
if ((xctype == 'LDA' and fxc is None) or
(xctype == 'GGA' and rho0 is None)):
make_rho0 = ni._gen_rho_evaluator(cell, dm0, 1)[0]
ao_loc = cell.ao_loc_nr()
vmat = [0] * nset
if xctype == 'LDA':
ao_deriv = 0
ip = 0
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, None, max_memory):
ngrid = weight.size
if fxc is None:
rho = make_rho0(0, ao_k1, mask, xctype)
fxc0 = ni.eval_xc(xc_code, rho, spin=0,
relativity=relativity, deriv=2,
verbose=verbose)[2]
frr = fxc0[0]
else:
frr = fxc[0][ip:ip+ngrid]
ip += ngrid
for i in range(nset):
rho1 = make_rho(i, ao_k1, mask, xctype)
wv = weight * frr * rho1
vmat[i] += ni._fxc_mat(cell, ao_k1, wv, mask, xctype, ao_loc)
elif xctype == 'GGA':
ao_deriv = 1
ip = 0
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, None, max_memory):
ngrid = weight.size
if rho0 is None:
rho = make_rho0(0, ao_k1, mask, xctype)
else:
rho = numpy.asarray(rho0[:,ip:ip+ngrid], order='C')
if vxc is None or fxc is None:
vxc0, fxc0 = ni.eval_xc(xc_code, rho, spin=0,
relativity=relativity, deriv=2,
verbose=verbose)[1:3]
else:
vxc0 = (None, vxc[1][ip:ip+ngrid])
fxc0 = (fxc[0][ip:ip+ngrid], fxc[1][ip:ip+ngrid], fxc[2][ip:ip+ngrid])
ip += ngrid
for i in range(nset):
rho1 = make_rho(i, ao_k1, mask, xctype)
wv = _rks_gga_wv1(rho, rho1, vxc0, fxc0, weight)
vmat[i] += ni._fxc_mat(cell, ao_k1, wv, mask, xctype, ao_loc)
# call swapaxes method to swap last two indices because vmat may be a 3D
# array (nset,nao,nao) in single k-point mode or a 4D array
# (nset,nkpts,nao,nao) in k-points mode
for i in range(nset): # for (\nabla\mu) \nu + \mu (\nabla\nu)
vmat[i] = vmat[i] + vmat[i].swapaxes(-2,-1).conj()
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
if isinstance(dms, numpy.ndarray) and dms.ndim == vmat[0].ndim:
# One set of DMs in the input
vmat = vmat[0]
return numpy.asarray(vmat)
def nr_rks_fxc_st(ni, cell, grids, xc_code, dm0, dms_alpha, relativity=0, singlet=True,
rho0=None, vxc=None, fxc=None, kpts=None, max_memory=2000,
verbose=None):
'''Associated to singlet or triplet Hessian
Note the difference to nr_rks_fxc, dms_alpha is the response density
matrices of alpha spin, alpha+/-beta DM is applied due to singlet/triplet
coupling
Ref. CPL, 256, 454
'''
if kpts is None:
kpts = numpy.zeros((1,3))
xctype = ni._xc_type(xc_code)
make_rho, nset, nao = ni._gen_rho_evaluator(cell, dms_alpha)
if ((xctype == 'LDA' and fxc is None) or
(xctype == 'GGA' and rho0 is None)):
make_rho0 = ni._gen_rho_evaluator(cell, dm0, 1)[0]
ao_loc = cell.ao_loc_nr()
vmat = [0] * nset
if xctype == 'LDA':
ao_deriv = 0
ip = 0
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, None, max_memory):
ngrid = weight.size
if fxc is None:
rho = make_rho0(0, ao_k1, mask, xctype)
rho *= .5 # alpha density
fxc0 = ni.eval_xc(xc_code, (rho,rho), spin=1, deriv=2)[2]
u_u, u_d, d_d = fxc0[0].T
else:
u_u, u_d, d_d = fxc[0][ip:ip+ngrid].T
ip += ngrid
if singlet:
frho = u_u + u_d
else:
frho = u_u - u_d
for i in range(nset):
rho1 = make_rho(i, ao_k1, mask, xctype)
wv = weight * frho * rho1
vmat[i] += ni._fxc_mat(cell, ao_k1, wv, mask, xctype, ao_loc)
elif xctype == 'GGA':
ao_deriv = 1
ip = 0
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, None, max_memory):
ngrid = weight.size
if vxc is None or fxc is None:
rho = make_rho0(0, ao_k1, mask, xctype)
rho *= .5 # alpha density
vxc0, fxc0 = ni.eval_xc(xc_code, (rho,rho), spin=1, deriv=2)[1:3]
vsigma = vxc0[1].T
u_u, u_d, d_d = fxc0[0].T # v2rho2
u_uu, u_ud, u_dd, d_uu, d_ud, d_dd = fxc0[1].T # v2rhosigma
uu_uu, uu_ud, uu_dd, ud_ud, ud_dd, dd_dd = fxc0[2].T # v2sigma2
else:
rho = rho0[0][:,ip:ip+ngrid]
vsigma = vxc[1][ip:ip+ngrid].T
u_u, u_d, d_d = fxc[0][ip:ip+ngrid].T # v2rho2
u_uu, u_ud, u_dd, d_uu, d_ud, d_dd = fxc[1][ip:ip+ngrid].T # v2rhosigma
uu_uu, uu_ud, uu_dd, ud_ud, ud_dd, dd_dd = fxc[2][ip:ip+ngrid].T # v2sigma2
if singlet:
fgamma = vsigma[0] + vsigma[1] * .5
frho = u_u + u_d
fgg = uu_uu + .5*ud_ud + 2*uu_ud + uu_dd
frhogamma = u_uu + u_dd + u_ud
else:
fgamma = vsigma[0] - vsigma[1] * .5
frho = u_u - u_d
fgg = uu_uu - uu_dd
frhogamma = u_uu - u_dd
for i in range(nset):
# rho1[0 ] = |b><j| z_{bj}
# rho1[1:] = \nabla(|b><j|) z_{bj}
rho1 = make_rho(i, ao_k1, mask, xctype)
wv = _rks_gga_wv1(rho, rho1, (None,fgamma),
(frho,frhogamma,fgg), weight)
vmat[i] += ni._fxc_mat(cell, ao_k1, wv, mask, xctype, ao_loc)
for i in range(nset): # for (\nabla\mu) \nu + \mu (\nabla\nu)
vmat[i] = vmat[i] + vmat[i].swapaxes(-2,-1).conj()
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
if isinstance(dms_alpha, numpy.ndarray) and dms_alpha.ndim == vmat[0].ndim:
vmat = vmat[0]
return numpy.asarray(vmat)
def nr_uks_fxc(ni, cell, grids, xc_code, dm0, dms, relativity=0, hermi=0,
rho0=None, vxc=None, fxc=None, kpts=None, max_memory=2000,
verbose=None):
'''Contract UKS XC kernel matrix with given density matrices
Args:
ni : an instance of :class:`NumInt` or :class:`KNumInt`
cell : instance of :class:`Mole` or :class:`Cell`
grids : an instance of :class:`Grids`
grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
xc_code : str
XC functional description.
See :func:`parse_xc` of pyscf/dft/libxc.py for more details.
dms : 2D array a list of 2D arrays
Density matrix or multiple density matrices
Kwargs:
hermi : int
Input density matrices symmetric or not
max_memory : int or float
The maximum size of cache to use (in MB).
rho0 : float array
Zero-order density (and density derivative for GGA). Giving kwargs rho0,
vxc and fxc to improve better performance.
vxc : float array
First order XC derivatives
fxc : float array
Second order XC derivatives
Returns:
nelec, excsum, vmat.
nelec is the number of electrons generated by numerical integration.
excsum is the XC functional value. vmat is the XC potential matrix in
2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
'''
if kpts is None:
kpts = numpy.zeros((1,3))
xctype = ni._xc_type(xc_code)
dma, dmb = _format_uks_dm(dms)
nao = dma.shape[-1]
make_rhoa, nset = ni._gen_rho_evaluator(cell, dma, hermi)[:2]
make_rhob = ni._gen_rho_evaluator(cell, dmb, hermi)[0]
if ((xctype == 'LDA' and fxc is None) or
(xctype == 'GGA' and rho0 is None)):
dm0a, dm0b = _format_uks_dm(dm0)
make_rho0a = ni._gen_rho_evaluator(cell, dm0a, 1)[0]
make_rho0b = ni._gen_rho_evaluator(cell, dm0b, 1)[0]
ao_loc = cell.ao_loc_nr()
vmata = [0] * nset
vmatb = [0] * nset
if xctype == 'LDA':
ao_deriv = 0
ip = 0
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, None, max_memory):
ngrid = weight.size
if fxc is None:
rho0a = make_rho0a(0, ao_k1, mask, xctype)
rho0b = make_rho0b(0, ao_k1, mask, xctype)
fxc0 = ni.eval_xc(xc_code, (rho0a,rho0b), spin=1,
relativity=relativity, deriv=2,
verbose=verbose)[2]
u_u, u_d, d_d = fxc0[0].T
else:
u_u, u_d, d_d = fxc[0][ip:ip+ngrid].T
ip += ngrid
for i in range(nset):
rho1a = make_rhoa(i, ao_k1, mask, xctype)
rho1b = make_rhob(i, ao_k1, mask, xctype)
wv = u_u * rho1a + u_d * rho1b
wv *= weight
vmata[i] += ni._fxc_mat(cell, ao_k1, wv, mask, xctype, ao_loc)
wv = u_d * rho1a + d_d * rho1b
wv *= weight
vmatb[i] += ni._fxc_mat(cell, ao_k1, wv, mask, xctype, ao_loc)
elif xctype == 'GGA':
ao_deriv = 1
ip = 0
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, None, max_memory):
ngrid = weight.size
if rho0 is None:
rho0a = make_rho0a(0, ao_k1, mask, xctype)
rho0b = make_rho0b(0, ao_k1, mask, xctype)
else:
rho0a = rho0[0][:,ip:ip+ngrid]
rho0b = rho0[1][:,ip:ip+ngrid]
if vxc is None or fxc is None:
vxc0, fxc0 = ni.eval_xc(xc_code, (rho0a,rho0b), spin=1,
relativity=relativity, deriv=2,
verbose=verbose)[1:3]
else:
vxc0 = (None, vxc[1][ip:ip+ngrid])
fxc0 = (fxc[0][ip:ip+ngrid], fxc[1][ip:ip+ngrid], fxc[2][ip:ip+ngrid])
ip += ngrid
for i in range(nset):
rho1a = make_rhoa(i, ao_k1, mask, xctype)
rho1b = make_rhob(i, ao_k1, mask, xctype)
wva, wvb = _uks_gga_wv1((rho0a,rho0b), (rho1a,rho1b),
vxc0, fxc0, weight)
vmata[i] += ni._fxc_mat(cell, ao_k1, wva, mask, xctype, ao_loc)
vmatb[i] += ni._fxc_mat(cell, ao_k1, wvb, mask, xctype, ao_loc)
for i in range(nset): # for (\nabla\mu) \nu + \mu (\nabla\nu)
vmata[i] = vmata[i] + vmata[i].swapaxes(-1,-2).conj()
vmatb[i] = vmatb[i] + vmatb[i].swapaxes(-1,-2).conj()
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
if dma.ndim == vmata[0].ndim: # One set of DMs in the input
vmata = vmata[0]
vmatb = vmatb[0]
return numpy.asarray((vmata,vmatb))
def _fxc_mat(cell, ao, wv, non0tab, xctype, ao_loc):
shls_slice = (0, cell.nbas)
if xctype == 'LDA' or xctype == 'HF':
#:aow = numpy.einsum('pi,p->pi', ao, wv)
aow = _scale_ao(ao, wv)
mat = _dot_ao_ao(cell, ao, aow, non0tab, shls_slice, ao_loc)
else:
#:aow = numpy.einsum('npi,np->pi', ao, wv)
aow = _scale_ao(ao, wv)
mat = _dot_ao_ao(cell, ao[0], aow, non0tab, shls_slice, ao_loc)
return mat
def cache_xc_kernel(ni, cell, grids, xc_code, mo_coeff, mo_occ, spin=0,
kpts=None, max_memory=2000):
'''Compute the 0th order density, Vxc and fxc. They can be used in TDDFT,
DFT hessian module etc.
'''
if kpts is None:
kpts = numpy.zeros((1,3))
xctype = ni._xc_type(xc_code)
ao_deriv = 0
if xctype == 'GGA':
ao_deriv = 1
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
nao = cell.nao_nr()
if spin == 0:
rho = []
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, None, max_memory):
rho.append(ni.eval_rho2(cell, ao_k1, mo_coeff, mo_occ, mask, xctype))
rho = numpy.hstack(rho)
else:
rhoa = []
rhob = []
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, None, max_memory):
rhoa.append(ni.eval_rho2(cell, ao_k1, mo_coeff[0], mo_occ[0], mask, xctype))
rhob.append(ni.eval_rho2(cell, ao_k1, mo_coeff[1], mo_occ[1], mask, xctype))
rho = (numpy.hstack(rhoa), numpy.hstack(rhob))
vxc, fxc = ni.eval_xc(xc_code, rho, spin=spin, relativity=0, deriv=2,
verbose=0)[1:3]
return rho, vxc, fxc
def get_rho(ni, cell, dm, grids, kpts=numpy.zeros((1,3)), max_memory=2000):
'''Density in real space
'''
make_rho, nset, nao = ni._gen_rho_evaluator(cell, dm)
assert(nset == 1)
rho = numpy.empty(grids.weights.size)
p1 = 0
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, 0, kpts, None, max_memory):
p0, p1 = p1, p1 + weight.size
rho[p0:p1] = make_rho(0, ao_k1, mask, 'LDA')
return rho
class NumInt(numint.NumInt):
'''Generalization of pyscf's NumInt class for a single k-point shift and
periodic images.
'''
def eval_ao(self, cell, coords, kpt=numpy.zeros(3), deriv=0, relativity=0,
shls_slice=None, non0tab=None, out=None, verbose=None):
return eval_ao(cell, coords, kpt, deriv, relativity, shls_slice,
non0tab, out, verbose)
@lib.with_doc(make_mask.__doc__)
def make_mask(self, cell, coords, relativity=0, shls_slice=None,
verbose=None):
return make_mask(cell, coords, relativity, shls_slice, verbose)
@lib.with_doc(eval_rho.__doc__)
def eval_rho(self, cell, ao, dm, non0tab=None, xctype='LDA', hermi=0, verbose=None):
return eval_rho(cell, ao, dm, non0tab, xctype, hermi, verbose)
def eval_rho2(self, cell, ao, mo_coeff, mo_occ, non0tab=None, xctype='LDA',
verbose=None):
return eval_rho2(cell, ao, mo_coeff, mo_occ, non0tab, xctype, verbose)
def nr_vxc(self, cell, grids, xc_code, dms, spin=0, relativity=0, hermi=0,
kpt=None, kpts_band=None, max_memory=2000, verbose=None):
'''Evaluate RKS/UKS XC functional and potential matrix.
See :func:`nr_rks` and :func:`nr_uks` for more details.
'''
if spin == 0:
return self.nr_rks(cell, grids, xc_code, dms, hermi,
kpt, kpts_band, max_memory, verbose)
else:
return self.nr_uks(cell, grids, xc_code, dms, hermi,
kpt, kpts_band, max_memory, verbose)
@lib.with_doc(nr_rks.__doc__)
def nr_rks(self, cell, grids, xc_code, dms, hermi=0,
kpt=numpy.zeros(3), kpts_band=None, max_memory=2000, verbose=None):
if kpts_band is not None:
# To compute Vxc on kpts_band, convert the NumInt object to KNumInt object.
ni = KNumInt()
ni.__dict__.update(self.__dict__)
nao = dms.shape[-1]
return ni.nr_rks(cell, grids, xc_code, dms.reshape(-1,1,nao,nao),
hermi, kpt.reshape(1,3), kpts_band, max_memory,
verbose)
return nr_rks(self, cell, grids, xc_code, dms,
0, 0, hermi, kpt, kpts_band, max_memory, verbose)
@lib.with_doc(nr_uks.__doc__)
def nr_uks(self, cell, grids, xc_code, dms, hermi=0,
kpt=numpy.zeros(3), kpts_band=None, max_memory=2000, verbose=None):
if kpts_band is not None:
# To compute Vxc on kpts_band, convert the NumInt object to KNumInt object.
ni = KNumInt()
ni.__dict__.update(self.__dict__)
nao = dms[0].shape[-1]
return ni.nr_uks(cell, grids, xc_code, dms.reshape(-1,1,nao,nao),
hermi, kpt.reshape(1,3), kpts_band, max_memory,
verbose)
return nr_uks(self, cell, grids, xc_code, dms,
1, 0, hermi, kpt, kpts_band, max_memory, verbose)
def eval_mat(self, cell, ao, weight, rho, vxc,
non0tab=None, xctype='LDA', spin=0, verbose=None):
# Guess whether ao is evaluated for kpts_band. When xctype is LDA, ao on grids
# should be a 2D array. For other xc functional, ao should be a 3D array.
if ao.ndim == 2 or (xctype != 'LDA' and ao.ndim == 3):
mat = eval_mat(cell, ao, weight, rho, vxc, non0tab, xctype, spin, verbose)
else:
nkpts = len(ao)
nao = ao[0].shape[-1]
mat = numpy.empty((nkpts,nao,nao), dtype=numpy.complex128)
for k in range(nkpts):
mat[k] = eval_mat(cell, ao[k], weight, rho, vxc,
non0tab, xctype, spin, verbose)
return mat
def _fxc_mat(self, cell, ao, wv, non0tab, xctype, ao_loc):
return _fxc_mat(cell, ao, wv, non0tab, xctype, ao_loc)
def block_loop(self, cell, grids, nao=None, deriv=0, kpt=numpy.zeros(3),
kpts_band=None, max_memory=2000, non0tab=None, blksize=None):
'''Define this macro to loop over grids by blocks.
'''
# For UniformGrids, grids.coords does not indicate whehter grids are initialized
if grids.non0tab is None:
grids.build(with_non0tab=True)
if nao is None:
nao = cell.nao
grids_coords = grids.coords
grids_weights = grids.weights
ngrids = grids_coords.shape[0]
comp = (deriv+1)*(deriv+2)*(deriv+3)//6
# NOTE to index grids.non0tab, the blksize needs to be the integer multiplier of BLKSIZE
if blksize is None:
blksize = int(max_memory*1e6/(comp*2*nao*16*BLKSIZE))*BLKSIZE
blksize = max(BLKSIZE, min(blksize, ngrids, BLKSIZE*1200))
if non0tab is None:
non0tab = grids.non0tab
if non0tab is None:
non0tab = numpy.empty(((ngrids+BLKSIZE-1)//BLKSIZE,cell.nbas),
dtype=numpy.uint8)
non0tab[:] = 0xff
kpt = numpy.reshape(kpt, 3)
if kpts_band is None:
kpt1 = kpt2 = kpt
else:
kpt1 = kpts_band
kpt2 = kpt
for ip0 in range(0, ngrids, blksize):
ip1 = min(ngrids, ip0+blksize)
coords = grids_coords[ip0:ip1]
weight = grids_weights[ip0:ip1]
non0 = non0tab[ip0//BLKSIZE:]
ao_k2 = self.eval_ao(cell, coords, kpt2, deriv=deriv, non0tab=non0)
if abs(kpt1-kpt2).sum() < 1e-9:
ao_k1 = ao_k2
else:
ao_k1 = self.eval_ao(cell, coords, kpt1, deriv=deriv)
yield ao_k1, ao_k2, non0, weight, coords
ao_k1 = ao_k2 = None
def _gen_rho_evaluator(self, cell, dms, hermi=0):
return numint.NumInt._gen_rho_evaluator(self, cell, dms, hermi)
nr_rks_fxc = nr_rks_fxc
nr_uks_fxc = nr_uks_fxc
cache_xc_kernel = cache_xc_kernel
get_rho = get_rho
_NumInt = NumInt
class KNumInt(numint.NumInt):
'''Generalization of pyscf's NumInt class for k-point sampling and
periodic images.
'''
def __init__(self, kpts=numpy.zeros((1,3))):
numint.NumInt.__init__(self)
self.kpts = numpy.reshape(kpts, (-1,3))
def eval_ao(self, cell, coords, kpts=numpy.zeros((1,3)), deriv=0, relativity=0,
shls_slice=None, non0tab=None, out=None, verbose=None, **kwargs):
return eval_ao_kpts(cell, coords, kpts, deriv,
relativity, shls_slice, non0tab, out, verbose)
@lib.with_doc(make_mask.__doc__)
def make_mask(self, cell, coords, relativity=0, shls_slice=None,
verbose=None):
return make_mask(cell, coords, relativity, shls_slice, verbose)
def eval_rho(self, cell, ao_kpts, dm_kpts, non0tab=None, xctype='LDA',
hermi=0, verbose=None):
'''Collocate the *real* density (opt. gradients) on the real-space grid.
Args:
cell : Mole or Cell object
ao_kpts : (nkpts, ngrids, nao) ndarray
AO values at each k-point
dm_kpts: (nkpts, nao, nao) ndarray
Density matrix at each k-point
Returns:
rhoR : (ngrids,) ndarray
'''
nkpts = len(ao_kpts)
rhoR = 0
for k in range(nkpts):
rhoR += eval_rho(cell, ao_kpts[k], dm_kpts[k], non0tab, xctype,
hermi, verbose)
rhoR *= 1./nkpts
return rhoR
def eval_rho2(self, cell, ao_kpts, mo_coeff_kpts, mo_occ_kpts,
non0tab=None, xctype='LDA', verbose=None):
nkpts = len(ao_kpts)
rhoR = 0
for k in range(nkpts):
rhoR += eval_rho2(cell, ao_kpts[k], mo_coeff_kpts[k],
mo_occ_kpts[k], non0tab, xctype, verbose)
rhoR *= 1./nkpts
return rhoR
def nr_vxc(self, cell, grids, xc_code, dms, spin=0, relativity=0, hermi=0,
kpts=None, kpts_band=None, max_memory=2000, verbose=None):
'''Evaluate RKS/UKS XC functional and potential matrix.
See :func:`nr_rks` and :func:`nr_uks` for more details.
'''
if spin == 0:
return self.nr_rks(cell, grids, xc_code, dms, hermi,
kpts, kpts_band, max_memory, verbose)
else:
return self.nr_uks(cell, grids, xc_code, dms, hermi,
kpts, kpts_band, max_memory, verbose)
@lib.with_doc(nr_rks.__doc__)
def nr_rks(self, cell, grids, xc_code, dms, hermi=0, kpts=None, kpts_band=None,
max_memory=2000, verbose=None, **kwargs):
if kpts is None:
if 'kpt' in kwargs:
sys.stderr.write('WARN: KNumInt.nr_rks function finds keyword '
'argument "kpt" and converts it to "kpts"\n')
kpts = kwargs['kpt']
else:
kpts = self.kpts
kpts = kpts.reshape(-1,3)
return nr_rks(self, cell, grids, xc_code, dms, 0, 0,
hermi, kpts, kpts_band, max_memory, verbose)
@lib.with_doc(nr_uks.__doc__)
def nr_uks(self, cell, grids, xc_code, dms, hermi=0, kpts=None, kpts_band=None,
max_memory=2000, verbose=None, **kwargs):
if kpts is None:
if 'kpt' in kwargs:
sys.stderr.write('WARN: KNumInt.nr_uks function finds keyword '
'argument "kpt" and converts it to "kpts"\n')
kpts = kwargs['kpt']
else:
kpts = self.kpts
kpts = kpts.reshape(-1,3)
return nr_uks(self, cell, grids, xc_code, dms, 1, 0,
hermi, kpts, kpts_band, max_memory, verbose)
def eval_mat(self, cell, ao_kpts, weight, rho, vxc,
non0tab=None, xctype='LDA', spin=0, verbose=None):
nkpts = len(ao_kpts)
nao = ao_kpts[0].shape[-1]
dtype = numpy.result_type(*ao_kpts)
mat = numpy.empty((nkpts,nao,nao), dtype=dtype)
for k in range(nkpts):
mat[k] = eval_mat(cell, ao_kpts[k], weight, rho, vxc,
non0tab, xctype, spin, verbose)
return mat
def _fxc_mat(self, cell, ao_kpts, wv, non0tab, xctype, ao_loc):
nkpts = len(ao_kpts)
nao = ao_kpts[0].shape[-1]
dtype = numpy.result_type(*ao_kpts)
mat = numpy.empty((nkpts,nao,nao), dtype=dtype)
for k in range(nkpts):
mat[k] = _fxc_mat(cell, ao_kpts[k], wv, non0tab, xctype, ao_loc)
return mat
def block_loop(self, cell, grids, nao=None, deriv=0, kpts=numpy.zeros((1,3)),
kpts_band=None, max_memory=2000, non0tab=None, blksize=None):
'''Define this macro to loop over grids by blocks.
'''
if grids.coords is None:
grids.build(with_non0tab=True)
if nao is None:
nao = cell.nao
grids_coords = grids.coords
grids_weights = grids.weights
ngrids = grids_coords.shape[0]
nkpts = len(kpts)
comp = (deriv+1)*(deriv+2)*(deriv+3)//6
# NOTE to index grids.non0tab, the blksize needs to be the integer multiplier of BLKSIZE
if blksize is None:
blksize = int(max_memory*1e6/(comp*2*nkpts*nao*16*BLKSIZE))*BLKSIZE
blksize = max(BLKSIZE, min(blksize, ngrids, BLKSIZE*1200))
if non0tab is None:
non0tab = grids.non0tab
if non0tab is None:
non0tab = numpy.empty(((ngrids+BLKSIZE-1)//BLKSIZE,cell.nbas),
dtype=numpy.uint8)
non0tab[:] = 0xff
if kpts_band is not None:
kpts_band = numpy.reshape(kpts_band, (-1,3))
where = [member(k, kpts) for k in kpts_band]
where = [k_id[0] if len(k_id)>0 else None for k_id in where]
for ip0 in range(0, ngrids, blksize):
ip1 = min(ngrids, ip0+blksize)
coords = grids_coords[ip0:ip1]
weight = grids_weights[ip0:ip1]
non0 = non0tab[ip0//BLKSIZE:]
ao_k1 = ao_k2 = self.eval_ao(cell, coords, kpts, deriv=deriv, non0tab=non0)
if kpts_band is not None:
ao_k1 = self.eval_ao(cell, coords, kpts_band, deriv=deriv, non0tab=non0)
yield ao_k1, ao_k2, non0, weight, coords
ao_k1 = ao_k2 = None
def _gen_rho_evaluator(self, cell, dms, hermi=0):
if getattr(dms, 'mo_coeff', None) is not None:
mo_coeff = dms.mo_coeff
mo_occ = dms.mo_occ
if isinstance(dms[0], numpy.ndarray) and dms[0].ndim == 2:
mo_coeff = [mo_coeff]
mo_occ = [mo_occ]
nao = cell.nao_nr()
ndms = len(mo_occ)
def make_rho(idm, ao, non0tab, xctype):
return self.eval_rho2(cell, ao, mo_coeff[idm], mo_occ[idm],
non0tab, xctype)
else:
if isinstance(dms[0], numpy.ndarray) and dms[0].ndim == 2:
dms = [numpy.stack(dms)]
#if not hermi:
# Density (or response of density) is always real for DFT.
# Symmetrizing DM for gamma point should not change the value of
# density. However, when k-point is considered, unless dm and
# dm.conj().transpose produce the same real part of density, the
# symmetrization code below may be incorrect (proof is needed).
# # dm.shape = (nkpts, nao, nao)
# dms = [(dm+dm.conj().transpose(0,2,1))*.5 for dm in dms]
nao = dms[0].shape[-1]
ndms = len(dms)
def make_rho(idm, ao_kpts, non0tab, xctype):
return self.eval_rho(cell, ao_kpts, dms[idm], non0tab, xctype,
hermi=hermi)
return make_rho, ndms, nao
nr_rks_fxc = nr_rks_fxc
nr_uks_fxc = nr_uks_fxc
cache_xc_kernel = cache_xc_kernel
get_rho = get_rho
_KNumInt = KNumInt
