def test_jk_pbc_local_fit(self):
numpy.random.seed(12)
nao = cell.nao_nr()
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
jkdf = mdf.MDF(cell)
jkdf.metric = 'S'
jkdf.auxbasis = 'weigend'
jkdf.approx_sr_level = 2
jkdf.gs = (5, ) * 3
mf = mdf_jk.density_fit(mf0, with_df=jkdf)
vj1, vk1 = mf.get_jk(cell, dm)
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 242.17560414134402, 8)
self.assertAlmostEqual(ek1, 280.27525544272237, 8)
jkdf = mdf.MDF(cell)
jkdf.metric = 'T'
jkdf.approx_sr_level = 3
jkdf.auxbasis = 'weigend'
jkdf.gs = (5, ) * 3
mf = mdf_jk.density_fit(mf0, with_df=jkdf)
vj1, vk1 = mf.get_jk(cell, dm)
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 242.1790506110278, 8)
self.assertAlmostEqual(ek1, 280.2763653230468, 8)
def test_jk_pbc_local_fit(self):
numpy.random.seed(12)
nao = cell.nao_nr()
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
jkdf = mdf.MDF(cell)
jkdf.metric = 'S'
jkdf.auxbasis = 'weigend'
jkdf.approx_sr_level = 2
jkdf.gs = (5, ) * 3
mf = mdf_jk.density_fit(mf0, with_df=jkdf)
vj1, vk1 = mf.get_jk(cell, dm)
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 242.15904061299113, 9)
self.assertAlmostEqual(ek1, 280.2553652304353, 9)
jkdf = mdf.MDF(cell)
jkdf.metric = 'T'
jkdf.approx_sr_level = 3
jkdf.auxbasis = 'weigend'
jkdf.gs = (5, ) * 3
mf = mdf_jk.density_fit(mf0, with_df=jkdf)
vj1, vk1 = mf.get_jk(cell, dm)
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 242.17554856213894, 9)
self.assertAlmostEqual(ek1, 280.27281092754305, 9)
def test_ao2mo_7d(self):
L = 3.
n = 6
cell = pgto.Cell()
cell.a = numpy.diag([L, L, L])
cell.mesh = [n, n, n]
cell.atom = '''He 2. 2.2 2.
He 1.2 1. 1.'''
cell.basis = {'He': [[0, (1.2, 1)], [1, (0.6, 1)]]}
cell.verbose = 0
cell.build(0, 0)
kpts = cell.make_kpts([1, 3, 1])
nkpts = len(kpts)
nao = cell.nao_nr()
numpy.random.seed(1)
mo = (numpy.random.random((nkpts, nao, nao)) + numpy.random.random(
(nkpts, nao, nao)) * 1j)
with_df = mdf.MDF(cell, kpts)
out = with_df.ao2mo_7d(mo, kpts)
ref = numpy.empty_like(out)
kconserv = kpts_helper.get_kconserv(cell, kpts)
for ki, kj, kk in kpts_helper.loop_kkk(nkpts):
kl = kconserv[ki, kj, kk]
tmp = with_df.ao2mo((mo[ki], mo[kj], mo[kk], mo[kl]),
kpts[[ki, kj, kk, kl]])
ref[ki, kj, kk] = tmp.reshape([nao] * 4)
self.assertAlmostEqual(abs(out - ref).max(), 0, 12)
def test_get_eri_gamma(self):
odf = mdf.MDF(cell)
odf.auxbasis = 'weigend'
odf.gs = (5, ) * 3
eri0000 = odf.get_eri()
self.assertTrue(eri0000.dtype == numpy.double)
self.assertAlmostEqual(eri0000.real.sum(), 140.52119757983661, 9)
self.assertAlmostEqual(finger(eri0000), -1.2233310290052046, 9)
eri1111 = kmdf.get_eri((kpts[0], kpts[0], kpts[0], kpts[0]))
self.assertTrue(eri1111.dtype == numpy.double)
self.assertAlmostEqual(eri1111.real.sum(), 140.52119757983661, 9)
self.assertAlmostEqual(eri1111.imag.sum(), 0, 9)
self.assertAlmostEqual(finger(eri1111), -1.2233310290052046, 9)
self.assertTrue(numpy.allclose(eri1111, eri0000))
eri4444 = kmdf.get_eri((kpts[4], kpts[4], kpts[4], kpts[4]))
self.assertTrue(eri4444.dtype == numpy.complex128)
self.assertAlmostEqual(eri4444.real.sum(), 259.45414408787667, 9)
self.assertAlmostEqual(
abs(eri4444.imag).sum(), 0.00044186526697869387, 9)
self.assertAlmostEqual(finger(eri4444),
1.968178030116118 - 3.6128363791369754e-07j, 8)
eri0000 = ao2mo.restore(1, eri0000,
cell.nao_nr()).reshape(eri4444.shape)
self.assertTrue(numpy.allclose(eri0000, eri4444, atol=1e-7))
def test_jk(self):
mf = mdf_jk.density_fit(mf0, auxbasis='weigend', gs=(5, ) * 3)
dm = mf.get_init_guess()
vj, vk = mf.get_jk(cell, dm)
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1, 46.698952864038205, 8)
self.assertAlmostEqual(ek1, 31.724297969654103, 8)
numpy.random.seed(12)
nao = cell.nao_nr()
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
vj1, vk1 = mf.get_jk(cell, dm, hermi=0)
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 242.19367653513686, 8)
self.assertAlmostEqual(ek1, 280.28452000317549, 8)
numpy.random.seed(1)
kpt = numpy.random.random(3)
mydf = mdf.MDF(cell, [kpt])
vj, vk = mydf.get_jk(dm, 1, kpt)
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1, 241.29943526257196 + 0j, 8)
self.assertAlmostEqual(ek1, 691.7685639227974 + 0j, 8)
def test_k_kpts_1(self):
cell = pgto.Cell()
cell.atom = 'He 1. .5 .5; He .1 1.3 2.1'
cell.basis = {'He': [(0, (2.5, 1)), (0, (1., 1))]}
cell.a = numpy.eye(3) * 2.5
cell.mesh = [11] * 3
cell.build()
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 = mdf.MDF(cell).set(auxbasis='weigend')
mydf.linear_dep_threshold = 1e-7
mydf.kpts = kpts
mydf.auxbasis = 'weigend'
mydf.exxdiv = None
mydf.mesh = numpy.asarray((11,)*3)
mydf.eta = 0.3
vk = mdf_jk.get_k_kpts(mydf, dm, 0, mydf.kpts)
self.assertAlmostEqual(finger(vk[0]), (0.54208542933016668-0.007872205456027636j ), 9)
self.assertAlmostEqual(finger(vk[1]), (0.35976730327192219+0.0036055469686362227j), 9)
self.assertAlmostEqual(finger(vk[2]), (0.46276307618592272-0.006504349523994527j ), 9)
self.assertAlmostEqual(finger(vk[3]), (0.63667731843923825+0.0075118647005158034j), 9)
self.assertAlmostEqual(finger(vk[4]), (0.53670632359622572-0.00764236264065816j ), 9)
self.assertAlmostEqual(finger(vk[5]), (0.4960454361832054 +0.0060590376596187257j), 9)
self.assertAlmostEqual(finger(vk[6]), (0.45421052168235576-0.006861624162215218j ), 9)
self.assertAlmostEqual(finger(vk[7]), (0.41848054629487041+0.0051096775483082746j), 9)
def setUpModule():
global cell, cell1, kdf0, kpts, kpt0
cell = pgto.Cell()
cell.atom = 'He 1. .5 .5; C .1 1.3 2.1'
cell.basis = {
'He': [(0, (2.5, 1)), (0, (1., 1))],
'C': 'gth-szv',
}
cell.pseudo = {'C': 'gth-pade'}
cell.a = np.eye(3) * 2.5
cell.mesh = [21] * 3
cell.build()
np.random.seed(1)
kpts = np.random.random((4, 3))
kpts[3] = kpts[0] - kpts[1] + kpts[2]
kpt0 = np.zeros(3)
cell1 = pgto.Cell()
cell1.atom = 'He 1. .5 .5; He .1 1.3 2.1'
cell1.basis = {'He': [(0, (2.5, 1)), (0, (1., 1))]}
cell1.a = np.eye(3) * 2.5
cell1.mesh = [21] * 3
cell1.build()
kdf0 = mdf.MDF(cell1)
kdf0.auxbasis = 'weigend'
kdf0.mesh = [21] * 3
kdf0.kpts = kpts
def test_jk_single_kpt(self):
mf = mdf_jk.density_fit(mf0, auxbasis='weigend', gs=(5, ) * 3)
mf.with_df.gs = [5] * 3
mf.with_df.eta = 0.3
dm = mf.get_init_guess()
vj, vk = mf.get_jk(cell, dm)
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1, 46.698952864035398, 8)
self.assertAlmostEqual(ek1, 31.724297969652138, 8)
numpy.random.seed(12)
nao = cell.nao_nr()
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
vj1, vk1 = mf.get_jk(cell, dm, hermi=0)
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 242.19367653513683, 8)
self.assertAlmostEqual(ek1, 280.28452000317401, 8)
numpy.random.seed(1)
kpt = numpy.random.random(3)
mydf = mdf.MDF(cell, [kpt]).set(auxbasis='weigend')
mydf.gs = [5] * 3
mydf.eta = 0.3
vj, vk = mydf.get_jk(dm, 1, kpt)
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1, 241.29943526257165 + 0j, 8)
self.assertAlmostEqual(ek1, 691.76856392279456 + 0j, 8)
def density_fit(mf, auxbasis=None, gs=None, with_df=None):
'''Generte density-fitting SCF object
Args:
auxbasis : str or basis dict
Same format to the input attribute mol.basis.
The default basis 'weigend+etb' means weigend-coulomb-fit basis
for light elements and even-tempered basis for heavy elements.
gs : tuple
number of grids in each (+)direction
with_df : MDF object
'''
from pyscf.pbc.df import mdf
if with_df is None:
if hasattr(mf, 'kpts'):
kpts = mf.kpts
else:
kpts = numpy.reshape(mf.kpt, (1,3))
with_df = mdf.MDF(mf.cell, kpts)
with_df.max_memory = mf.max_memory
with_df.stdout = mf.stdout
with_df.verbose = mf.verbose
with_df.auxbasis = auxbasis
if gs is not None:
with_df.gs = gs
mf = copy.copy(mf)
mf.with_df = with_df
return mf
def test_k_kpts_1(self):
cell = pgto.Cell()
cell.atom = 'He 1. .5 .5; He .1 1.3 2.1'
cell.basis = {'He': [(0, (2.5, 1)), (0, (1., 1))]}
cell.a = numpy.eye(3) * 2.5
cell.gs = [5] * 3
cell.build()
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 = mdf.MDF(cell)
mydf.kpts = kpts
mydf.auxbasis = 'weigend'
mydf.exxdiv = None
vk = mdf_jk.get_k_kpts(mydf, dm, 0, mydf.kpts)
self.assertAlmostEqual(finger(vk[0]), (0.54208523897216732-0.0078722056426767627j), 9)
self.assertAlmostEqual(finger(vk[1]), (0.35976712320322424+0.0036055471233112256j), 9)
self.assertAlmostEqual(finger(vk[2]), (0.46276289905549617-0.0065043496646110801j), 9)
self.assertAlmostEqual(finger(vk[3]), (0.63667714700745526+0.0075118648848031978j), 9)
self.assertAlmostEqual(finger(vk[4]), (0.53670615076993111-0.0076423628684680065j), 9)
self.assertAlmostEqual(finger(vk[5]), (0.49604529705337863+0.0060590377882828398j), 9)
self.assertAlmostEqual(finger(vk[6]), (0.45421039104866701-0.0068616242937238692j), 9)
self.assertAlmostEqual(finger(vk[7]), (0.41848041777106704+0.0051096776806240215j), 9)
def test_jk_single_kpt(self):
mf = mdf_jk.density_fit(mf0, auxbasis='weigend', mesh=(11,)*3)
mf.with_df.mesh = [11]*3
mf.with_df.eta = 0.3
mf.with_df.linear_dep_threshold = 1e-7
dm = mf.get_init_guess()
vj, vk = mf.get_jk(cell, dm)
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1, 46.698950904264514, 8)
self.assertAlmostEqual(ek1, 31.724297945923094, 8)
numpy.random.seed(12)
nao = cell.nao_nr()
dm = numpy.random.random((nao,nao))
dm = dm + dm.T
vj1, vk1 = mf.get_jk(cell, dm, hermi=0)
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 242.19379703364774, 8)
self.assertAlmostEqual(ek1, 280.28450527230103, 8)
numpy.random.seed(1)
kpt = numpy.random.random(3)
mydf = mdf.MDF(cell, [kpt]).set(auxbasis='weigend')
mydf.linear_dep_threshold = 1e-7
mydf.mesh = [11]*3
mydf.eta = 0.3
vj, vk = mydf.get_jk(dm, 1, kpt, exxdiv='ewald')
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1, 241.29955504573206+0j, 8)
self.assertAlmostEqual(ek1, 691.76854602384913+0j, 8)
def test_k_kpts_2(self):
cell = pgto.Cell()
cell.atom = 'He 1. .5 .5; He .1 1.3 2.1'
cell.basis = {'He': [(0, (2.5, 1)), (0, (1., 1))]}
cell.a = numpy.eye(3) * 2.5
cell.mesh = [11] * 3
cell.build()
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]])
mydf = mdf.MDF(cell).set(auxbasis='weigend')
mydf.linear_dep_threshold = 1e-7
mydf.kpts = kpts
mydf.auxbasis = 'weigend'
mydf.exxdiv = None
mydf.mesh = numpy.asarray((11,)*3)
mydf.eta = 0.3
nao = cell.nao_nr()
numpy.random.seed(1)
dm = numpy.random.random((8,nao,nao))
dm = dm + dm.transpose(0,2,1)
vk = mdf_jk.get_k_kpts(mydf, dm, 1, mydf.kpts)
self.assertAlmostEqual(finger(vk[0]), (1.0938028454012594 -0.014742352047969521j), 9)
self.assertAlmostEqual(finger(vk[1]), (0.72086205228975953+0.008685417852198867j), 9)
self.assertAlmostEqual(finger(vk[2]), (0.89846608130483796-0.011091006902191843j), 9)
self.assertAlmostEqual(finger(vk[3]), (1.260302267937254 +0.015976908047169756j), 9)
self.assertAlmostEqual(finger(vk[4]), (1.0490207113210688 -0.012426436820904021j), 9)
self.assertAlmostEqual(finger(vk[5]), (0.99252601243537697+0.012694645170334074j), 9)
self.assertAlmostEqual(finger(vk[6]), (0.92165252496655681-0.012036431811316108j), 9)
self.assertAlmostEqual(finger(vk[7]), (0.85167195537981 +0.010089165459944484j), 9)
def density_fit(mf, auxbasis=None, mesh=None, with_df=None):
'''Generte density-fitting SCF object
Args:
auxbasis : str or basis dict
Same format to the input attribute mol.basis. If auxbasis is
None, auxiliary basis based on AO basis (if possible) or
even-tempered Gaussian basis will be used.
mesh : tuple
number of grids in each direction
with_df : MDF object
'''
from pyscf.pbc.df import mdf
if with_df is None:
if getattr(mf, 'kpts', None) is not None:
kpts = mf.kpts
else:
kpts = numpy.reshape(mf.kpt, (1, 3))
with_df = mdf.MDF(mf.cell, kpts)
with_df.max_memory = mf.max_memory
with_df.stdout = mf.stdout
with_df.verbose = mf.verbose
with_df.auxbasis = auxbasis
if mesh is not None:
with_df.mesh = mesh
mf = copy.copy(mf)
mf.with_df = with_df
mf._eri = None
return mf
def test_jk(self):
mf = mdf_jk.density_fit(mf0, auxbasis='weigend', gs=(5, ) * 3)
dm = mf.get_init_guess()
vj, vk = mf.get_jk(cell, dm)
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1, 46.698944426560104, 8)
self.assertAlmostEqual(ek1, 31.723136985575099, 8)
numpy.random.seed(12)
nao = cell.nao_nr()
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
vj1, vk1 = mf.get_jk(cell, dm, hermi=0)
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 242.18066893105836, 8)
self.assertAlmostEqual(ek1, 280.27749933492305, 8)
numpy.random.seed(1)
kpt = numpy.random.random(3)
mydf = mdf.MDF(cell, [kpt])
vj, vk = mydf.get_jk(dm, 1, kpt)
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1, 240.96370951556852, 8)
self.assertAlmostEqual(ek1, 691.41117108086291, 8)
def test_get_eri_gamma_high_cost(self):
odf = mdf.MDF(cell)
odf.linear_dep_threshold = 1e-7
odf.auxbasis = 'weigend'
odf.mesh = (11, ) * 3
odf.eta = 0.154728892598
eri0000 = odf.get_eri()
self.assertTrue(eri0000.dtype == numpy.double)
self.assertAlmostEqual(eri0000.real.sum(), 140.52553833398147, 6)
self.assertAlmostEqual(finger(eri0000), -1.2234059928846319, 6)
eri1111 = kmdf.get_eri((kpts[0], kpts[0], kpts[0], kpts[0]))
self.assertTrue(eri1111.dtype == numpy.double)
self.assertAlmostEqual(eri1111.real.sum(), 140.52553833398153, 6)
self.assertAlmostEqual(eri1111.imag.sum(), 0, 7)
self.assertAlmostEqual(finger(eri1111), -1.2234059928846333, 6)
self.assertTrue(numpy.allclose(eri1111, eri0000))
eri4444 = kmdf.get_eri((kpts[4], kpts[4], kpts[4], kpts[4]))
self.assertTrue(eri4444.dtype == numpy.complex128)
self.assertAlmostEqual(eri4444.real.sum(), 259.46539833377523, 6)
self.assertAlmostEqual(
abs(eri4444.imag).sum(), 0.00044187056294873458, 9)
self.assertAlmostEqual(finger(eri4444),
1.9705270829923354 - 3.6097479693720031e-07j, 6)
eri0000 = ao2mo.restore(1, eri0000,
cell.nao_nr()).reshape(eri4444.shape)
self.assertTrue(numpy.allclose(eri0000, eri4444, atol=1e-7))
def test_jk(self):
mf = mdf_jk.density_fit(mf0, auxbasis='weigend', gs=(5,)*3)
dm = mf.get_init_guess()
vj, vk = mf.get_jk(cell, dm)
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1, 46.698951249368726, 8)
self.assertAlmostEqual(ek1, 31.724431026527277, 8)
numpy.random.seed(12)
nao = cell.nao_nr()
dm = numpy.random.random((nao,nao))
dm = dm + dm.T
vj1, vk1 = mf.get_jk(cell, dm, hermi=0)
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 242.19444220341163, 8)
self.assertAlmostEqual(ek1, 280.28473250798748, 8)
numpy.random.seed(1)
kpt = numpy.random.random(3)
mydf = mdf.MDF(cell, [kpt])
vj, vk = mydf.get_jk(dm, 1, kpt)
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1, 241.30019902835264+0j, 8)
self.assertAlmostEqual(ek1, 691.76877471308376+0j, 8)
def test_k_kpts_2(self):
cell = pgto.Cell()
cell.atom = 'He 1. .5 .5; He .1 1.3 2.1'
cell.basis = {'He': [(0, (2.5, 1)), (0, (1., 1))]}
cell.a = numpy.eye(3) * 2.5
cell.gs = [5] * 3
cell.build()
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]])
mydf = mdf.MDF(cell)
mydf.kpts = kpts
mydf.auxbasis = 'weigend'
mydf.exxdiv = None
nao = cell.nao_nr()
numpy.random.seed(1)
dm = numpy.random.random((8,nao,nao))
dm = dm + dm.transpose(0,2,1)
vk = mdf_jk.get_k_kpts(mydf, dm, 1, mydf.kpts)
self.assertAlmostEqual(finger(vk[0]), (1.093802464678856 -0.014742352431919676j), 9)
self.assertAlmostEqual(finger(vk[1]), (0.72086169197091587+0.008685418217133528j), 9)
self.assertAlmostEqual(finger(vk[2]), (0.89846572708244654-0.011091007223188223j), 9)
self.assertAlmostEqual(finger(vk[3]), (1.2603019232380572 +0.015976908426091924j), 9)
self.assertAlmostEqual(finger(vk[4]), (1.0490203655653567 -0.012426437226316521j), 9)
self.assertAlmostEqual(finger(vk[5]), (0.99252573352507678+0.012694645461974137j), 9)
self.assertAlmostEqual(finger(vk[6]), (0.92165226277159285-0.012036432073368958j), 9)
self.assertAlmostEqual(finger(vk[7]), (0.85167169839559342+0.010089165714668009j), 9)
def test_get_eri_gamma(self):
odf = mdf.MDF(cell)
odf.auxbasis = 'weigend'
odf.gs = (5, ) * 3
eri0000 = odf.get_eri()
self.assertTrue(eri0000.dtype == numpy.double)
self.assertAlmostEqual(eri0000.real.sum(), 140.52297323243539, 9)
self.assertAlmostEqual(finger(eri0000), -1.2233877452643904, 9)
eri1111 = kmdf.get_eri((kpts[0], kpts[0], kpts[0], kpts[0]))
self.assertTrue(eri1111.dtype == numpy.double)
self.assertAlmostEqual(eri1111.real.sum(), 140.52297323243539, 9)
self.assertAlmostEqual(eri1111.imag.sum(), 0, 9)
self.assertAlmostEqual(finger(eri1111), -1.2233877452643904, 9)
self.assertTrue(numpy.allclose(eri1111, eri0000))
eri4444 = kmdf.get_eri((kpts[4], kpts[4], kpts[4], kpts[4]))
self.assertTrue(eri4444.dtype == numpy.complex128)
self.assertAlmostEqual(eri4444.real.sum(), 259.45730831500038, 9)
self.assertAlmostEqual(
abs(eri4444.imag).sum(), 0.00044186906554179585, 9)
self.assertAlmostEqual(finger(eri4444),
1.9676993803147795 - 3.6138386194340396e-07j, 8)
eri0000 = ao2mo.restore(1, eri0000,
cell.nao_nr()).reshape(eri4444.shape)
self.assertTrue(numpy.allclose(eri0000, eri4444, atol=1e-7))
def test_jk(self):
mf = mdf_jk.density_fit(mf0, auxbasis='weigend', gs=(5, ) * 3)
dm = mf.get_init_guess()
vj, vk = mf.get_jk(cell, dm)
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1, 46.698923699173982, 9)
self.assertAlmostEqual(ek1, 31.722934801807845, 9)
numpy.random.seed(12)
nao = cell.nao_nr()
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
vj1, vk1 = mf.get_jk(cell, dm, hermi=0)
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 242.17738846073865, 9)
self.assertAlmostEqual(ek1, 280.27434674577881, 9)
numpy.random.seed(1)
kpt = numpy.random.random(3)
mydf = mdf.MDF(cell, [kpt])
vj, vk = mydf.get_jk(dm, 0, kpt)
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1, 240.96357256500787, 9)
self.assertAlmostEqual(ek1, 691.41111361623132, 9)
def setUpModule():
global cell, cell1, mf0, kmdf, kmdf1, kpts
L = 5.
n = 11
cell = pgto.Cell()
cell.a = numpy.diag([L,L,L])
cell.mesh = numpy.array([n,n,n])
cell.atom = '''C 3. 2. 3.
C 1. 1. 1.'''
cell.basis = 'ccpvdz'
cell.verbose = 0
cell.rcut = 17
cell.build(0,0)
mf0 = pscf.RHF(cell)
mf0.exxdiv = 'vcut_sph'
numpy.random.seed(1)
kpts = numpy.random.random((5,3))
kpts[0] = 0
kpts[3] = kpts[0]-kpts[1]+kpts[2]
kpts[4] *= 1e-5
kmdf = mdf.MDF(cell)
kmdf.linear_dep_threshold = 1e-7
kmdf.auxbasis = 'weigend'
kmdf.kpts = kpts
kmdf.mesh = (11,)*3
kmdf.eta = 0.154728892598
cell1 = pgto.Cell()
cell1.a = numpy.eye(3) * 3.
cell1.mesh = [10]*3
cell1.atom = '''C 3. 2. 3.
C 1. 1. 1.'''
cell1.basis = [[0, (3.5, 1)], [0, (1.0, 1)], [1, (0.6, 1)]]
cell1.rcut = 9.5
cell1.build(0,0)
kmdf1 = mdf.MDF(cell1)
kmdf1.linear_dep_threshold = 1e-7
kmdf1.auxbasis = df.aug_etb(cell1, 1.8)
kmdf1.kpts = kpts
kmdf1.mesh = [6]*3
kmdf1.eta = 0.1
def test_get_eri_gamma(self):
odf0 = mdf.MDF(cell1)
odf = aft.AFTDF(cell1)
ref = odf0.get_eri()
eri0000 = odf.get_eri(compact=True)
self.assertTrue(eri0000.dtype == numpy.double)
self.assertTrue(np.allclose(eri0000, ref, atol=1e-6, rtol=1e-6))
self.assertAlmostEqual(finger(eri0000), 0.23714016293926865, 9)
def test_hcore(self):
mf = pscf.RHF(cell)
odf = mdf.MDF(cell)
odf.auxbasis = 'weigend'
odf.gs = (10, ) * 3
dm = mf.get_init_guess()
self.assertAlmostEqual(numpy.einsum('ij,ji->', odf.get_nuc(), dm),
-150.61096872500249, 9)
def test_eri1111(self):
kpts = numpy.random.random((4,3)) * .25
kpts[3] = -numpy.einsum('ij->j', kpts[:3])
with_df = mdf.MDF(cell)
with_df.kpts = kpts
mo =(numpy.random.random((nao,nao)) +
numpy.random.random((nao,nao))*1j)
eri = with_df.get_eri(kpts).reshape((nao,)*4)
eri0 = numpy.einsum('pjkl,pi->ijkl', eri , mo.conj())
eri0 = numpy.einsum('ipkl,pj->ijkl', eri0, mo )
eri0 = numpy.einsum('ijpl,pk->ijkl', eri0, mo.conj())
eri0 = numpy.einsum('ijkp,pl->ijkl', eri0, mo )
eri1 = with_df.ao2mo(mo, kpts)
self.assertAlmostEqual(abs(eri1.reshape(eri0.shape)-eri0).sum(), 0, 9)
def test_j_kpts(self):
numpy.random.seed(1)
nao = cell.nao_nr()
dm = numpy.random.random((4,nao,nao))
dm = dm + dm.transpose(0,2,1)
mydf = mdf.MDF(cell)
mydf.kpts = numpy.random.random((4,3))
mydf.gs = numpy.asarray((5,)*3)
mydf.auxbasis = 'weigend'
vj = mdf_jk.get_j_kpts(mydf, dm, 1, mydf.kpts)
self.assertAlmostEqual(finger(vj[0]), (0.48227656190426815-0.11872564582011846j ), 9)
self.assertAlmostEqual(finger(vj[1]), (0.54073739901923457-0.046133364517070521j), 9)
self.assertAlmostEqual(finger(vj[2]), (0.52806808175231224-0.083705005021225326j), 9)
self.assertAlmostEqual(finger(vj[3]), (0.54351987747190522+0.008843499422802630j), 9)
def test_jk_hermi0(self):
numpy.random.seed(12)
nao = cell.nao_nr()
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
dm[:2, -3:] *= .5
jkdf = mdf.MDF(cell).set(auxbasis='weigend')
jkdf.gs = (5, ) * 3
jkdf.eta = 0.3
vj0, vk0 = jkdf.get_jk(dm, hermi=0, exxdiv=None)
ej0 = numpy.einsum('ij,ji->', vj0, dm)
ek0 = numpy.einsum('ij,ji->', vk0, dm)
self.assertAlmostEqual(ej0, 242.18855706416096, 8)
self.assertAlmostEqual(ek0, 280.70982164657647, 8)
def test_jk_hermi0(self):
numpy.random.seed(12)
nao = cell.nao_nr()
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
dm[:2, -3:] *= .5
jkdf = mdf.MDF(cell)
jkdf.auxbasis = 'weigend'
jkdf.gs = (5, ) * 3
vj0, vk0 = jkdf.get_jk(dm, hermi=0, exxdiv=None)
ej0 = numpy.einsum('ij,ji->', vj0, dm)
ek0 = numpy.einsum('ij,ji->', vk0, dm)
self.assertAlmostEqual(ej0, 242.18843656969429, 8)
self.assertAlmostEqual(ek0, 280.70983914362279, 8)
def test_jk_hermi0(self):
numpy.random.seed(12)
nao = cell.nao_nr()
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
dm[:2, -3:] *= .5
jkdf = mdf.MDF(cell)
jkdf.auxbasis = 'weigend'
jkdf.gs = (5, ) * 3
vj0, vk0 = jkdf.get_jk(dm, hermi=0, exxdiv=None)
ej0 = numpy.einsum('ij,ji->', vj0, dm)
ek0 = numpy.einsum('ij,ji->', vk0, dm)
self.assertAlmostEqual(ej0, 242.17214791834408, 9)
self.assertAlmostEqual(ek0, 280.69967132048043, 9)
def test_eri0110(self):
kpts = numpy.random.random((4,3)) * .25
kpts[3] = kpts[0]
kpts[2] = kpts[1]
with_df = mdf.MDF(cell).set(auxbasis='weigend')
with_df.kpts = kpts
mo =(numpy.random.random((nao,nao)) +
numpy.random.random((nao,nao))*1j)
eri = with_df.get_eri(kpts).reshape((nao,)*4)
eri0 = numpy.einsum('pjkl,pi->ijkl', eri , mo.conj())
eri0 = numpy.einsum('ipkl,pj->ijkl', eri0, mo )
eri0 = numpy.einsum('ijpl,pk->ijkl', eri0, mo.conj())
eri0 = numpy.einsum('ijkp,pl->ijkl', eri0, mo )
eri1 = with_df.ao2mo(mo, kpts)
self.assertAlmostEqual(abs(eri1.reshape(eri0.shape)-eri0).sum(), 0, 8)
def test_jk_metric(self):
numpy.random.seed(12)
nao = cell.nao_nr()
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
jkdf = mdf.MDF(cell)
jkdf.metric = 'S'
jkdf.auxbasis = 'weigend'
jkdf.gs = (5, ) * 3
vj1, vk1 = jkdf.get_jk(dm, exxdiv=None)
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 242.1754481772021, 8)
self.assertAlmostEqual(ek1, 280.2751263818186, 8)
jkdf = mdf.MDF(cell)
jkdf.metric = 'T'
jkdf.auxbasis = 'weigend'
jkdf.gs = (5, ) * 3
vj1, vk1 = jkdf.get_jk(dm, exxdiv=None)
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 242.18066893105842, 8)
self.assertAlmostEqual(ek1, 280.27749933492305, 8)
def test_jk_hermi0(self):
numpy.random.seed(12)
nao = cell0.nao_nr()
dm = numpy.random.random((nao,nao))
dm = dm + dm.T
dm[:2,-3:] *= .5
jkdf = mdf.MDF(cell0).set(auxbasis='weigend')
jkdf.linear_dep_threshold = 1e-7
jkdf.mesh = (11,)*3
jkdf.eta = 0.3
vj0, vk0 = jkdf.get_jk(dm, hermi=0, exxdiv=None)
ej0 = numpy.einsum('ij,ji->', vj0, dm)
ek0 = numpy.einsum('ij,ji->', vk0, dm)
self.assertAlmostEqual(ej0, 25.77582611607388 , 8)
self.assertAlmostEqual(ek0, 30.814555613338555, 8)