def test_pwdf_k(self):
kpts = cell.make_kpts((2,2,2))
numpy.random.seed(1)
nao = cell.nao_nr()
dm = numpy.random.random((8,nao,nao))
mydf = pwdf.PWDF(cell)
mydf.kpts = kpts
mydf.auxbasis = 'weigend'
vk = pwdf_jk.get_k_kpts(mydf, dm, 0, mydf.kpts)
self.assertAlmostEqual(finger(vk[0]), (4.3373802352168278-0.062977052131451577j)/8, 9)
self.assertAlmostEqual(finger(vk[1]), (2.878809181709983+0.028843869853690692j) /8, 9)
self.assertAlmostEqual(finger(vk[2]), (3.7027622609953061-0.052034330663180237j)/8, 9)
self.assertAlmostEqual(finger(vk[3]), (5.0939994842559422+0.060094478876149444j)/8, 9)
self.assertAlmostEqual(finger(vk[4]), (4.2942087551592651-0.061138484763336887j)/8, 9)
self.assertAlmostEqual(finger(vk[5]), (3.9689429688683679+0.048471952758750547j)/8, 9)
self.assertAlmostEqual(finger(vk[6]), (3.6342630872923456-0.054892635365850449j)/8, 9)
self.assertAlmostEqual(finger(vk[7]), (3.3483735224533548+0.040877095049528467j)/8, 9)
numpy.random.seed(1)
dm = numpy.random.random((8,nao,nao))
dm = dm + dm.transpose(0,2,1)
vk = pwdf_jk.get_k_kpts(mydf, dm, 1, mydf.kpts)
self.assertAlmostEqual(finger(vk[0]), (8.7518173818250702-0.11793770445839372j) /8, 9)
self.assertAlmostEqual(finger(vk[1]), (5.7682393685317894+0.069482280306391239j)/8, 9)
self.assertAlmostEqual(finger(vk[2]), (7.1890462727492324-0.088727079644645671j)/8, 9)
self.assertAlmostEqual(finger(vk[3]), (10.08358152800003+0.1278144339422369j )/8, 9)
self.assertAlmostEqual(finger(vk[4]), (8.393281242945573-0.099410704957774876j) /8, 9)
self.assertAlmostEqual(finger(vk[5]), (7.9413682328898769+0.1015563120870652j) /8, 9)
self.assertAlmostEqual(finger(vk[6]), (7.3743790120272408-0.096290683129384574j)/8, 9)
self.assertAlmostEqual(finger(vk[7]), (6.8144379626901443+0.08071261392857812j) /8, 9)
def test_pwdf_k(self):
kpts = cell.make_kpts((2, 2, 2))
numpy.random.seed(1)
nao = cell.nao_nr()
dm = numpy.random.random((8, nao, nao))
mydf = pwdf.PWDF(cell)
mydf.kpts = kpts
mydf.auxbasis = 'weigend'
vk = pwdf_jk.get_k_kpts(mydf, dm, 0, mydf.kpts)
self.assertAlmostEqual(finger(
vk[0]), (4.3373802352168278 - 0.062977052131451577j) / 8, 9)
self.assertAlmostEqual(finger(vk[1]),
(2.878809181709983 + 0.028843869853690692j) / 8,
9)
self.assertAlmostEqual(finger(
vk[2]), (3.7027622609953061 - 0.052034330663180237j) / 8, 9)
self.assertAlmostEqual(finger(
vk[3]), (5.0939994842559422 + 0.060094478876149444j) / 8, 9)
self.assertAlmostEqual(finger(
vk[4]), (4.2942087551592651 - 0.061138484763336887j) / 8, 9)
self.assertAlmostEqual(finger(
vk[5]), (3.9689429688683679 + 0.048471952758750547j) / 8, 9)
self.assertAlmostEqual(finger(
vk[6]), (3.6342630872923456 - 0.054892635365850449j) / 8, 9)
self.assertAlmostEqual(finger(
vk[7]), (3.3483735224533548 + 0.040877095049528467j) / 8, 9)
numpy.random.seed(1)
dm = numpy.random.random((8, nao, nao))
dm = dm + dm.transpose(0, 2, 1)
vk = pwdf_jk.get_k_kpts(mydf, dm, 1, mydf.kpts)
self.assertAlmostEqual(finger(vk[0]),
(8.7518173818250702 - 0.11793770445839372j) / 8,
9)
self.assertAlmostEqual(finger(
vk[1]), (5.7682393685317894 + 0.069482280306391239j) / 8, 9)
self.assertAlmostEqual(finger(
vk[2]), (7.1890462727492324 - 0.088727079644645671j) / 8, 9)
self.assertAlmostEqual(finger(vk[3]),
(10.08358152800003 + 0.1278144339422369j) / 8,
9)
self.assertAlmostEqual(finger(vk[4]),
(8.393281242945573 - 0.099410704957774876j) / 8,
9)
self.assertAlmostEqual(finger(vk[5]),
(7.9413682328898769 + 0.1015563120870652j) / 8,
9)
self.assertAlmostEqual(finger(
vk[6]), (7.3743790120272408 - 0.096290683129384574j) / 8, 9)
self.assertAlmostEqual(finger(vk[7]),
(6.8144379626901443 + 0.08071261392857812j) / 8,
9)
def test_pwdf_k1(self):
kpts = cell.get_abs_kpts([[-.25,-.25,-.25],
[-.25,-.25, .25],
[-.25, .25,-.25],
[-.25, .25, .25],
[ .25,-.25,-.25],
[ .25,-.25, .25],
[ .25, .25,-.25],
[ .25, .25, .25]])
numpy.random.seed(1)
nao = cell.nao_nr()
dm = numpy.random.random((8,nao,nao))
mydf = pwdf.PWDF(cell)
mydf.kpts = kpts
mydf.auxbasis = 'weigend'
numpy.random.seed(1)
dm = numpy.random.random((8,nao,nao))
dm = dm + dm.transpose(0,2,1)
vk = pwdf_jk.get_k_kpts(mydf, dm, 1, mydf.kpts)
self.assertAlmostEqual(finger(vk[0]), (8.7518173818250702-0.11793770445839372j) /8, 9)
self.assertAlmostEqual(finger(vk[1]), (5.7682393685317894+0.069482280306391239j)/8, 9)
self.assertAlmostEqual(finger(vk[2]), (7.1890462727492324-0.088727079644645671j)/8, 9)
self.assertAlmostEqual(finger(vk[3]), (10.08358152800003+0.1278144339422369j )/8, 9)
self.assertAlmostEqual(finger(vk[4]), (8.393281242945573-0.099410704957774876j) /8, 9)
self.assertAlmostEqual(finger(vk[5]), (7.9413682328898769+0.1015563120870652j) /8, 9)
self.assertAlmostEqual(finger(vk[6]), (7.3743790120272408-0.096290683129384574j)/8, 9)
self.assertAlmostEqual(finger(vk[7]), (6.8144379626901443+0.08071261392857812j) /8, 9)
def test_pwdf_k(self):
kpts = cell.get_abs_kpts([[-.25, -.25, -.25], [-.25, -.25, .25],
[-.25, .25, -.25], [-.25, .25, .25],
[.25, -.25, -.25], [.25, -.25, .25],
[.25, .25, -.25], [.25, .25, .25]])
numpy.random.seed(1)
nao = cell.nao_nr()
dm = numpy.random.random((8, nao, nao))
mydf = pwdf.PWDF(cell)
mydf.kpts = kpts
mydf.auxbasis = 'weigend'
vk = pwdf_jk.get_k_kpts(mydf, dm, 0, mydf.kpts)
self.assertAlmostEqual(finger(
vk[0]), (4.3373802352168278 - 0.062977052131451577j) / 8, 9)
self.assertAlmostEqual(finger(vk[1]),
(2.878809181709983 + 0.028843869853690692j) / 8,
9)
self.assertAlmostEqual(finger(
vk[2]), (3.7027622609953061 - 0.052034330663180237j) / 8, 9)
self.assertAlmostEqual(finger(
vk[3]), (5.0939994842559422 + 0.060094478876149444j) / 8, 9)
self.assertAlmostEqual(finger(
vk[4]), (4.2942087551592651 - 0.061138484763336887j) / 8, 9)
self.assertAlmostEqual(finger(
vk[5]), (3.9689429688683679 + 0.048471952758750547j) / 8, 9)
self.assertAlmostEqual(finger(
vk[6]), (3.6342630872923456 - 0.054892635365850449j) / 8, 9)
self.assertAlmostEqual(finger(
vk[7]), (3.3483735224533548 + 0.040877095049528467j) / 8, 9)
def get_jk(self,
dm,
hermi=1,
kpts=None,
kpt_band=None,
with_j=True,
with_k=True,
exxdiv='ewald'):
if kpts is None:
if numpy.all(self.kpts == 0):
# Gamma-point calculation by default
kpts = numpy.zeros(3)
else:
kpts = self.kpts
if kpts.shape == (3, ):
return pwdf_jk.get_jk(self, dm, hermi, kpts, kpt_band, with_j,
with_k, exxdiv)
vj = vk = None
if with_k:
vk = pwdf_jk.get_k_kpts(self, dm, hermi, kpts, kpt_band, exxdiv)
if with_j:
vj = pwdf_jk.get_j_kpts(self, dm, hermi, kpts, kpt_band)
return vj, vk
def get_jk(self, dm, hermi=1, kpts=None, kpt_band=None,
with_j=True, with_k=True, exxdiv='ewald'):
if kpts is None:
if numpy.all(self.kpts == 0):
# Gamma-point calculation by default
kpts = numpy.zeros(3)
else:
kpts = self.kpts
if kpts.shape == (3,):
return pwdf_jk.get_jk(self, dm, hermi, kpts, kpt_band, with_j,
with_k, exxdiv)
vj = vk = None
if with_k:
vk = pwdf_jk.get_k_kpts(self, dm, hermi, kpts, kpt_band, exxdiv)
if with_j:
vj = pwdf_jk.get_j_kpts(self, dm, hermi, kpts, kpt_band)
return vj, vk
def test_pwdf_k(self):
kpts = cell.get_abs_kpts([[-.25,-.25,-.25],
[-.25,-.25, .25],
[-.25, .25,-.25],
[-.25, .25, .25],
[ .25,-.25,-.25],
[ .25,-.25, .25],
[ .25, .25,-.25],
[ .25, .25, .25]])
numpy.random.seed(1)
nao = cell.nao_nr()
dm = numpy.random.random((8,nao,nao))
mydf = pwdf.PWDF(cell)
mydf.kpts = kpts
mydf.auxbasis = 'weigend'
vk = pwdf_jk.get_k_kpts(mydf, dm, 0, mydf.kpts)
self.assertAlmostEqual(finger(vk[0]), (4.3373802352168278-0.062977052131451577j)/8, 9)
self.assertAlmostEqual(finger(vk[1]), (2.878809181709983+0.028843869853690692j) /8, 9)
self.assertAlmostEqual(finger(vk[2]), (3.7027622609953061-0.052034330663180237j)/8, 9)
self.assertAlmostEqual(finger(vk[3]), (5.0939994842559422+0.060094478876149444j)/8, 9)
self.assertAlmostEqual(finger(vk[4]), (4.2942087551592651-0.061138484763336887j)/8, 9)
self.assertAlmostEqual(finger(vk[5]), (3.9689429688683679+0.048471952758750547j)/8, 9)
self.assertAlmostEqual(finger(vk[6]), (3.6342630872923456-0.054892635365850449j)/8, 9)
self.assertAlmostEqual(finger(vk[7]), (3.3483735224533548+0.040877095049528467j)/8, 9)
def test_pwdf_k1(self):
kpts = cell.get_abs_kpts([[-.25, -.25, -.25], [-.25, -.25, .25],
[-.25, .25, -.25], [-.25, .25, .25],
[.25, -.25, -.25], [.25, -.25, .25],
[.25, .25, -.25], [.25, .25, .25]])
numpy.random.seed(1)
nao = cell.nao_nr()
dm = numpy.random.random((8, nao, nao))
mydf = pwdf.PWDF(cell)
mydf.kpts = kpts
mydf.auxbasis = 'weigend'
numpy.random.seed(1)
dm = numpy.random.random((8, nao, nao))
dm = dm + dm.transpose(0, 2, 1)
vk = pwdf_jk.get_k_kpts(mydf, dm, 1, mydf.kpts)
self.assertAlmostEqual(finger(vk[0]),
(8.7518173818250702 - 0.11793770445839372j) / 8,
9)
self.assertAlmostEqual(finger(
vk[1]), (5.7682393685317894 + 0.069482280306391239j) / 8, 9)
self.assertAlmostEqual(finger(
vk[2]), (7.1890462727492324 - 0.088727079644645671j) / 8, 9)
self.assertAlmostEqual(finger(vk[3]),
(10.08358152800003 + 0.1278144339422369j) / 8,
9)
self.assertAlmostEqual(finger(vk[4]),
(8.393281242945573 - 0.099410704957774876j) / 8,
9)
self.assertAlmostEqual(finger(vk[5]),
(7.9413682328898769 + 0.1015563120870652j) / 8,
9)
self.assertAlmostEqual(finger(
vk[6]), (7.3743790120272408 - 0.096290683129384574j) / 8, 9)
self.assertAlmostEqual(finger(vk[7]),
(6.8144379626901443 + 0.08071261392857812j) / 8,
9)
def get_k_kpts(mydf, dm_kpts, hermi=1, kpts=numpy.zeros((1,3)), kpt_band=None,
exxdiv=None):
cell = mydf.cell
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = (time.clock(), time.time())
if mydf._cderi is None:
mydf.build()
t1 = log.timer_debug1('Init get_k_kpts', *t1)
dm_kpts = lib.asarray(dm_kpts, order='C')
dms = _format_dms(dm_kpts, kpts)
nset, nkpts, nao = dms.shape[:3]
naux = mydf.auxcell.nao_nr()
nao_pair = nao * (nao+1) // 2
if kpt_band is None:
kpts_band = kpts
swap_2e = True
else:
kpts_band = numpy.reshape(kpt_band, (-1,3))
nband = len(kpts_band)
kk_table = kpts_band.reshape(-1,1,3) - kpts.reshape(1,-1,3)
kk_todo = numpy.ones(kk_table.shape[:2], dtype=bool)
vkR = numpy.zeros((nset,nband,nao,nao))
vkI = numpy.zeros((nset,nband,nao,nao))
dmsR = numpy.asarray(dms.real, order='C')
dmsI = numpy.asarray(dms.imag, order='C')
mem_now = lib.current_memory()[0]
max_memory = max(2000, (mydf.max_memory - mem_now)) * .8
log.debug1('max_memory = %d MB (%d in use)', max_memory, mem_now)
# K_pq = ( p{k1} i{k2} | i{k2} q{k1} )
def make_kpt(kpt): # kpt = kptj - kpti
# search for all possible ki and kj that has ki-kj+kpt=0
kk_match = numpy.einsum('ijx->ij', abs(kk_table + kpt)) < 1e-9
kpti_idx, kptj_idx = numpy.where(kk_todo & kk_match)
nkptj = len(kptj_idx)
kk_todo[kpti_idx,kptj_idx] = False
if swap_2e and not is_zero(kpt):
kk_todo[kptj_idx,kpti_idx] = False
# Note: kj-ki for electorn 1 and ki-kj for electron 2
# j2c ~ ({kj-ki}|{ks-kr}) ~ ({kj-ki}|-{kj-ki}) ~ ({kj-ki}|{ki-kj})
# j3c ~ (Q|kj,ki) = j3c{ji} = (Q|ki,kj)* = conj(transpose(j3c{ij}, (0,2,1)))
bufR = numpy.empty((mydf.blockdim*nao**2))
bufI = numpy.empty((mydf.blockdim*nao**2))
for ki,kj in zip(kpti_idx,kptj_idx):
kpti = kpts_band[ki]
kptj = kpts[kj]
kptij = numpy.asarray((kpti,kptj))
for LpqR, LpqI, j3cR, j3cI in mydf.sr_loop(kptij, max_memory, False):
nrow = LpqR.shape[0]
pLqR = numpy.ndarray((nao,nrow,nao), buffer=bufR)
pLqI = numpy.ndarray((nao,nrow,nao), buffer=bufI)
pjqR = numpy.ndarray((nao,nrow,nao), buffer=LpqR)
pjqI = numpy.ndarray((nao,nrow,nao), buffer=LpqI)
tmpR = numpy.ndarray((nao,nrow*nao), buffer=j3cR)
tmpI = numpy.ndarray((nao,nrow*nao), buffer=j3cI)
pLqR[:] = LpqR.reshape(-1,nao,nao).transpose(1,0,2)
pLqI[:] = LpqI.reshape(-1,nao,nao).transpose(1,0,2)
pjqR[:] = j3cR.reshape(-1,nao,nao).transpose(1,0,2)
pjqI[:] = j3cI.reshape(-1,nao,nao).transpose(1,0,2)
#:Lpq = LpqR + LpqI*1j
#:j3c = j3cR + j3cI*1j
#:for i in range(nset):
#: dm = dms[i,ki]
#: tmp = numpy.dot(dm, j3c.reshape(nao,-1))
#: vk1 = numpy.dot(Lpq.reshape(-1,nao).conj().T, tmp.reshape(-1,nao))
#: tmp = numpy.dot(dm, Lpq.reshape(nao,-1))
#: vk1+= numpy.dot(j3c.reshape(-1,nao).conj().T, tmp.reshape(-1,nao))
#: vkR[i,kj] += vk1.real
#: vkI[i,kj] += vk1.imag
#:if swap_2e and not is_zero(kpt):
#: # K ~ 'Lij,Llk*,jk->il' + 'Llk*,Lij,jk->il'
#: for i in range(nset):
#: dm = dms[i,kj]
#: tmp = numpy.dot(j3c.reshape(-1,nao), dm)
#: vk1 = numpy.dot(tmp.reshape(nao,-1), Lpq.reshape(nao,-1).conj().T)
#: tmp = numpy.dot(Lpq.reshape(-1,nao), dm)
#: vk1+= numpy.dot(tmp.reshape(nao,-1), j3c.reshape(nao,-1).conj().T)
#: vkR[i,ki] += vk1.real
#: vkI[i,ki] += vk1.imag
# K ~ 'iLj,lLk*,li->kj' + 'lLk*,iLj,li->kj'
for i in range(nset):
tmpR, tmpI = zdotNN(dmsR[i,ki], dmsI[i,ki], pjqR.reshape(nao,-1),
pjqI.reshape(nao,-1), 1, tmpR, tmpI)
vk1R, vk1I = zdotCN(pLqR.reshape(-1,nao).T, pLqI.reshape(-1,nao).T,
tmpR.reshape(-1,nao), tmpI.reshape(-1,nao))
vkR[i,kj] += vk1R
vkI[i,kj] += vk1I
if hermi:
vkR[i,kj] += vk1R.T
vkI[i,kj] -= vk1I.T
else:
tmpR, tmpI = zdotNN(dmsR[i,ki], dmsI[i,ki], pLqR.reshape(nao,-1),
pLqI.reshape(nao,-1), 1, tmpR, tmpI)
zdotCN(pjqR.reshape(-1,nao).T, pjqI.reshape(-1,nao).T,
tmpR.reshape(-1,nao), tmpI.reshape(-1,nao),
1, vkR[i,kj], vkI[i,kj], 1)
if swap_2e and not is_zero(kpt):
tmpR = tmpR.reshape(nao*nrow,nao)
tmpI = tmpI.reshape(nao*nrow,nao)
# K ~ 'iLj,lLk*,jk->il' + 'lLk*,iLj,jk->il'
for i in range(nset):
tmpR, tmpI = zdotNN(pjqR.reshape(-1,nao), pjqI.reshape(-1,nao),
dmsR[i,kj], dmsI[i,kj], 1, tmpR, tmpI)
vk1R, vk1I = zdotNC(tmpR.reshape(nao,-1), tmpI.reshape(nao,-1),
pLqR.reshape(nao,-1).T, pLqI.reshape(nao,-1).T)
vkR[i,ki] += vk1R
vkI[i,ki] += vk1I
if hermi:
vkR[i,ki] += vk1R.T
vkI[i,ki] -= vk1I.T
else:
tmpR, tmpI = zdotNN(pLqR.reshape(-1,nao), pLqI.reshape(-1,nao),
dmsR[i,kj], dmsI[i,kj], 1, tmpR, tmpI)
zdotNC(tmpR.reshape(nao,-1), tmpI.reshape(nao,-1),
pjqR.reshape(nao,-1).T, pjqI.reshape(nao,-1).T,
1, vkR[i,ki], vkI[i,ki], 1)
LpqR = LpqI = j3cR = j3cI = tmpR = tmpI = None
return None
for ki, kpti in enumerate(kpts_band):
for kj, kptj in enumerate(kpts):
if kk_todo[ki,kj]:
make_kpt(kptj-kpti)
vkR *= 1./nkpts
vkI *= 1./nkpts
vk_kpts = pwdf_jk.get_k_kpts(mydf, dm_kpts, hermi, kpts, kpt_band, exxdiv)
if (gamma_point(kpts) and gamma_point(kpts_band) and
not numpy.iscomplexobj(dm_kpts)):
vk_kpts += vkR.reshape(vk_kpts.shape)
else:
vk_kpts += (vkR+vkI*1j).reshape(vk_kpts.shape)
return vk_kpts
