def test_get_jk(self):
df = fft.FFTDF(cell)
dm = mf0.get_init_guess()
vj0, vk0 = get_jk(mf0, cell, dm, kpt=kpts[0])
vj1, vk1 = df.get_jk(dm, kpts=kpts[0], exxdiv=None)
self.assertTrue(vj1.dtype == numpy.complex128)
self.assertTrue(vk1.dtype == numpy.complex128)
self.assertTrue(np.allclose(vj0, vj1, atol=1e-9, rtol=1e-9))
self.assertTrue(np.allclose(vk0, vk1, atol=1e-9, rtol=1e-9))
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 2.3002596914518700, 9)
self.assertAlmostEqual(ek1, 3.3165691757797346, 9)
dm = mf0.get_init_guess()
vj0, vk0 = get_jk(mf0, cell, dm)
vj1, vk1 = df.get_jk(dm, exxdiv=None)
self.assertTrue(vj1.dtype == numpy.float64)
self.assertTrue(vk1.dtype == numpy.float64)
self.assertTrue(np.allclose(vj0, vj1, atol=1e-9, rtol=1e-9))
self.assertTrue(np.allclose(vk0, vk1, atol=1e-9, rtol=1e-9))
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 2.4673139106639925, 9)
self.assertAlmostEqual(ek1, 3.6886674521354221, 9)
def test_get_jk(self):
df = fft.FFTDF(cell)
dm = mf0.get_init_guess()
vj0, vk0 = get_jk(mf0, cell, dm, kpt=kpts[0])
vj1, vk1 = df.get_jk(dm, kpts=kpts[0], exxdiv=None)
self.assertTrue(vj1.dtype == numpy.complex128)
self.assertTrue(vk1.dtype == numpy.complex128)
self.assertTrue(np.allclose(vj0, vj1, atol=1e-9, rtol=1e-9))
self.assertTrue(np.allclose(vk0, vk1, atol=1e-9, rtol=1e-9))
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 2.3002596914518700*(6/6.82991739766009)**2, 9)
self.assertAlmostEqual(ek1, 3.3165691757797346*(6/6.82991739766009)**2, 9)
dm = mf0.get_init_guess()
vj0, vk0 = get_jk(mf0, cell, dm)
vj1, vk1 = df.get_jk(dm, exxdiv=None)
self.assertTrue(vj1.dtype == numpy.float64)
self.assertTrue(vk1.dtype == numpy.float64)
self.assertTrue(np.allclose(vj0, vj1, atol=1e-9, rtol=1e-9))
self.assertTrue(np.allclose(vk0, vk1, atol=1e-9, rtol=1e-9))
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 2.4673139106639925*(6/6.82991739766009)**2, 9)
self.assertAlmostEqual(ek1, 3.6886674521354221*(6/6.82991739766009)**2, 9)
# issue #1114
dm = numpy.eye(cell.nao, dtype=int)
vj, vk = df.get_jk(dm, exxdiv=None)
self.assertAlmostEqual(lib.fp(vj), 3.7955873127283377, 9)
self.assertAlmostEqual(lib.fp(vk), 4.290076429522121, 9)
def test_get_jk_kpts(self):
df = fft.FFTDF(cell)
dm = mf0.get_init_guess()
nkpts = len(kpts)
dms = [dm] * nkpts
vj0, vk0 = get_jk_kpts(mf0, cell, dms, kpts=kpts)
vj1, vk1 = df.get_jk(dms, kpts=kpts, exxdiv=None)
self.assertTrue(vj1.dtype == numpy.complex128)
self.assertTrue(vk1.dtype == numpy.complex128)
self.assertTrue(np.allclose(vj0, vj1, atol=1e-9, rtol=1e-9))
self.assertTrue(np.allclose(vk0, vk1, atol=1e-9, rtol=1e-9))
ej1 = numpy.einsum('xij,xji->', vj1, dms) / len(kpts)
ek1 = numpy.einsum('xij,xji->', vk1, dms) / len(kpts)
self.assertAlmostEqual(ej1, 2.3163352969873445, 9)
self.assertAlmostEqual(ek1, 7.7311228144548600, 9)
numpy.random.seed(1)
kpts_band = numpy.random.random((2, 3))
vj1, vk1 = df.get_jk(dms, kpts=kpts, kpts_band=kpts_band, exxdiv=None)
self.assertAlmostEqual(lib.finger(vj1),
3.437188138446714 + 0.1360466492092307j, 9)
self.assertAlmostEqual(lib.finger(vk1),
7.479986541097368 + 1.1980593415201204j, 9)
nao = dm.shape[0]
mo_coeff = numpy.random.random((nkpts, nao, nao))
mo_occ = numpy.array(numpy.random.random((nkpts, nao)) > .6,
dtype=numpy.double)
dms = numpy.einsum('kpi,ki,kqi->kpq', mo_coeff, mo_occ, mo_coeff)
dms = lib.tag_array(lib.asarray(dms), mo_coeff=mo_coeff, mo_occ=mo_occ)
vk1 = df.get_jk(dms, kpts=kpts, kpts_band=kpts_band, exxdiv=None)[1]
self.assertAlmostEqual(lib.finger(vk1),
10.239828255099447 + 2.1190549216896182j, 9)
def test_get_jk(self):
df = fft.FFTDF(cell)
dm = mf0.get_init_guess()
vj0, vk0 = get_jk(mf0, cell, dm, kpt=kpts[0])
vj1, vk1 = df.get_jk(dm, kpts=kpts[0], exxdiv=None)
self.assertTrue(vj1.dtype == numpy.complex128)
self.assertTrue(vk1.dtype == numpy.complex128)
self.assertTrue(np.allclose(vj0, vj1, atol=1e-9, rtol=1e-9))
self.assertTrue(np.allclose(vk0, vk1, atol=1e-9, rtol=1e-9))
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 2.2642719646779832, 9)
self.assertAlmostEqual(ek1, 3.2581479552187513, 9)
dm = mf0.get_init_guess()
vj0, vk0 = get_jk(mf0, cell, dm)
vj1, vk1 = df.get_jk(dm, exxdiv=None)
self.assertTrue(vj1.dtype == numpy.float64)
self.assertTrue(vk1.dtype == numpy.float64)
self.assertTrue(np.allclose(vj0, vj1, atol=1e-9, rtol=1e-9))
self.assertTrue(np.allclose(vk0, vk1, atol=1e-9, rtol=1e-9))
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 2.4216815457582102, 9)
self.assertAlmostEqual(ek1, 3.6061858403253977, 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 = fft.FFTDF(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_0123(self):
odf = aft.AFTDF(cell1)
ref = kdf0.get_eri(kpts)
eri1111 = odf.get_eri(kpts)
self.assertTrue(np.allclose(eri1111, ref, atol=1e-8, rtol=1e-8))
self.assertAlmostEqual(finger(eri1111), (1.2917759427391706-0.013340252488069412j), 9)
ref = fft.FFTDF(cell1).get_mo_eri([numpy.eye(cell1.nao_nr())]*4, kpts)
self.assertTrue(np.allclose(eri1111, ref, atol=1e-8, rtol=1e-8))
def test_get_mo_eri1(self):
df = fft.FFTDF(cell2)
nao = cell2.nao_nr()
numpy.random.seed(5)
mos = (numpy.random.random((4, nao, nao)) + numpy.random.random(
(4, nao, nao)) * 1j)
eri_mo0 = get_mo_eri(cell2, mos, kpts1)
eri_mo1 = df.get_mo_eri(mos, kpts1)
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-9, rtol=1e-9))
def test_get_eri_0123(self):
odf = aft.AFTDF(cell1)
ref = kdf0.get_eri(kpts)
eri1111 = odf.get_eri(kpts)
self.assertAlmostEqual(abs(eri1111-ref).max(), 0, 9)
self.assertAlmostEqual(finger(eri1111), (1.2917759427391706-0.013340252488069412j), 9)
ref = fft.FFTDF(cell1).get_mo_eri([numpy.eye(cell1.nao_nr())]*4, kpts)
self.assertAlmostEqual(abs(eri1111-ref).max(), 0, 9)
def test_get_eri_0011(self):
odf = aft.AFTDF(cell1)
ref = kdf0.get_eri((kpts[0],kpts[0],kpts[1],kpts[1]))
eri0011 = odf.get_eri((kpts[0],kpts[0],kpts[1],kpts[1]))
self.assertTrue(np.allclose(eri0011, ref, atol=1e-3, rtol=1e-3))
self.assertAlmostEqual(finger(eri0011), (1.2410162858084512+0.00074485383749912936j), 9)
ref = fft.FFTDF(cell1).get_mo_eri([numpy.eye(cell1.nao_nr())]*4, (kpts[0],kpts[0],kpts[1],kpts[1]))
eri0011 = odf.get_eri((kpts[0],kpts[0],kpts[1],kpts[1]))
self.assertTrue(np.allclose(eri0011, ref, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri0011), (1.2410162860852818+0.00074485383748954838j), 9)
def test_get_j_non_hermitian(self):
kpt = kpts[0]
numpy.random.seed(2)
nao = cell2.nao
dm = numpy.random.random((nao,nao))
mydf = fft.FFTDF(cell2)
v1 = mydf.get_jk(dm, hermi=0, kpts=kpts[1], with_k=False)[0]
eri = mydf.get_eri([kpts[1]]*4).reshape(nao,nao,nao,nao)
ref = numpy.einsum('ijkl,ji->kl', eri, dm)
self.assertAlmostEqual(abs(ref - v1).max(), 0, 12)
self.assertTrue(abs(ref-ref.T.conj()).max() > 1e-5)
def test_get_pp(self):
v0 = pgto.pseudo.get_pp(cell, kpts[0])
v1 = fft.FFTDF(cell).get_pp(kpts)
self.assertTrue(np.allclose(v0, v1[0], atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(v1[0]), (-5.6240249083785869+0.22094834302524968j), 8)
v0 = pgto.pseudo.get_pp(cell, kpts[1])
self.assertTrue(np.allclose(v0, v1[1], atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(v1[1]), (-5.5387702576467603+1.0439333717227581j) , 8)
self.assertAlmostEqual(finger(v1[2]), (-6.0530899866313366+0.2817289667029651j), 8)
self.assertAlmostEqual(finger(v1[3]), (-5.6011543542444446+0.27597306418805201j), 8)
def test_get_nuc(self):
v0 = get_nuc(cell, kpts[0])
v1 = fft.FFTDF(cell).get_nuc(kpts)
self.assertTrue(np.allclose(v0, v1[0], atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(v1[0]), (-5.7646608099493841+0.19126294430138713j), 8)
v0 = get_nuc(cell, kpts[1])
self.assertTrue(np.allclose(v0, v1[1], atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(v1[1]), (-5.6567258309199193+0.86813371243952175j), 8)
self.assertAlmostEqual(finger(v1[2]), (-6.1528952645454895+0.09517054428060109j), 8)
self.assertAlmostEqual(finger(v1[3]), (-5.7445962879770942+0.24611951427601772j), 8)
def test_aft_get_ao_eri(self):
df0 = fft.FFTDF(cell1)
df = aft.AFTDF(cell1)
eri0 = df0.get_ao_eri(compact=True)
eri1 = df.get_ao_eri(compact=True)
self.assertAlmostEqual(abs(eri0 - eri1).max(), 0, 9)
eri0 = df0.get_ao_eri(kpts[0])
eri1 = df.get_ao_eri(kpts[0])
self.assertAlmostEqual(abs(eri0 - eri1).max(), 0, 9)
eri0 = df0.get_ao_eri(kpts)
eri1 = df.get_ao_eri(kpts)
self.assertAlmostEqual(abs(eri0 - eri1).max(), 0, 9)
def test_get_ao_eri(self):
df = fft.FFTDF(cell)
eri0 = get_ao_eri(cell)
eri1 = df.get_ao_eri(compact=True)
self.assertTrue(np.allclose(eri0, eri1, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri1), 0.80425358275734926, 8)
eri0 = get_ao_eri(cell, kpts[0])
eri1 = df.get_ao_eri(kpts[0])
self.assertTrue(np.allclose(eri0, eri1, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri1), (2.9346374584901898-0.20479054936744959j), 8)
eri4 = df.get_ao_eri(kpts)
self.assertAlmostEqual(finger(eri4), (0.33709288394542991-0.94185725001175313j), 8)
def test_get_jk_kpts(self):
df = fft.FFTDF(cell)
dm = mf0.get_init_guess()
dms = [dm] * len(kpts)
vj0, vk0 = get_jk_kpts(mf0, cell, dms, kpts=kpts)
vj1, vk1 = df.get_jk(dms, kpts=kpts, exxdiv=None)
self.assertTrue(vj1.dtype == numpy.complex128)
self.assertTrue(vk1.dtype == numpy.complex128)
self.assertTrue(np.allclose(vj0, vj1, atol=1e-9, rtol=1e-9))
self.assertTrue(np.allclose(vk0, vk1, atol=1e-9, rtol=1e-9))
ej1 = numpy.einsum('xij,xji->', vj1, dms) / len(kpts)
ek1 = numpy.einsum('xij,xji->', vk1, dms) / len(kpts)
self.assertAlmostEqual(ej1, 2.2785994326264971, 9)
self.assertAlmostEqual(ek1, 7.5122832961825941, 9)
def test_get_eri_0110(self):
odf = aft.AFTDF(cell1)
ref = kdf0.get_eri((kpts[0],kpts[1],kpts[1],kpts[0]))
eri0110 = odf.get_eri((kpts[0],kpts[1],kpts[1],kpts[0]))
self.assertTrue(np.allclose(eri0110, ref, atol=1e-6, rtol=1e-6))
eri0110 = odf.get_eri((kpts[0]+1e-8,kpts[1]+1e-8,kpts[1],kpts[0]))
self.assertTrue(np.allclose(eri0110, ref, atol=1e-6, rtol=1e-6))
self.assertAlmostEqual(finger(eri0110), (1.2928399254827956-0.011820590601969154j), 9)
ref = fft.FFTDF(cell1).get_mo_eri([numpy.eye(cell1.nao_nr())]*4, (kpts[0],kpts[1],kpts[1],kpts[0]))
eri0110 = odf.get_eri((kpts[0],kpts[1],kpts[1],kpts[0]))
self.assertTrue(np.allclose(eri0110, ref, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri0110), (1.2928399254827956-0.011820590601969154j), 9)
eri0110 = odf.get_eri((kpts[0]+1e-8,kpts[1]+1e-8,kpts[1],kpts[0]))
self.assertTrue(np.allclose(eri0110, ref, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri0110), (1.2928399254827956-0.011820590601969154j), 9)
def test_get_eri_gamma(self):
odf = aft.AFTDF(cell1)
ref = odf.get_eri(compact=True)
df = fft.FFTDF(cell1)
eri0000 = df.get_eri(compact=True)
self.assertTrue(eri0000.dtype == numpy.double)
self.assertTrue(np.allclose(eri0000, ref, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri0000), 0.23714016293926865, 9)
ref = odf.get_eri((kpts[0],kpts[0],kpts[0],kpts[0]))
eri1111 = df.get_eri((kpts[0],kpts[0],kpts[0],kpts[0]))
self.assertTrue(np.allclose(eri1111, ref, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri1111), (1.2410388899583582-5.2370501878355006e-06j), 9)
eri1111 = df.get_eri((kpts[0]+1e-8,kpts[0]+1e-8,kpts[0],kpts[0]))
self.assertTrue(np.allclose(eri1111, ref, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri1111), (1.2410388899583582-5.2370501878355006e-06j), 9)
def test_aft_get_ao_eri(self):
df0 = fft.FFTDF(cell)
df = aft.AFTDF(cell)
eri0 = df0.get_ao_eri(compact=True)
eri1 = df.get_ao_eri(compact=True)
self.assertTrue(np.allclose(eri0, eri1, atol=1e-5, rtol=1e-5))
self.assertAlmostEqual(finger(eri1), 0.80425361966560172, 8)
eri0 = df0.get_ao_eri(kpts[0])
eri1 = df.get_ao_eri(kpts[0])
self.assertTrue(np.allclose(eri0, eri1, atol=1e-5, rtol=1e-5))
self.assertAlmostEqual(finger(eri1), (2.9346374476387949-0.20479054936779137j), 8)
eri0 = df0.get_ao_eri(kpts)
eri1 = df.get_ao_eri(kpts)
self.assertTrue(np.allclose(eri0, eri1, atol=1e-5, rtol=1e-5))
self.assertAlmostEqual(finger(eri1), (0.33709287302019619-0.94185725020966538j), 8)
def test_get_mo_eri(self):
df0 = fft.FFTDF(cell)
odf = aft.AFTDF(cell)
nao = cell.nao_nr()
numpy.random.seed(5)
mo =(numpy.random.random((nao,nao)) +
numpy.random.random((nao,nao))*1j)
eri_mo0 = df0.get_mo_eri((mo,)*4, kpts)
eri_mo1 = odf.get_mo_eri((mo,)*4, kpts)
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
kpts_t = (kpts[2],kpts[3],kpts[0],kpts[1])
eri_mo2 = df0.get_mo_eri((mo,)*4, kpts_t)
eri_mo2 = eri_mo2.reshape((nao,)*4).transpose(2,3,0,1).reshape(nao**2,-1)
self.assertTrue(np.allclose(eri_mo2, eri_mo0, atol=1e-7, rtol=1e-7))
eri_mo0 = df0.get_mo_eri((mo,)*4, (kpts[0],)*4)
eri_mo1 = odf.get_mo_eri((mo,)*4, (kpts[0],)*4)
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
eri_mo0 = df0.get_mo_eri((mo,)*4, (kpts[0],kpts[1],kpts[1],kpts[0],))
eri_mo1 = odf.get_mo_eri((mo,)*4, (kpts[0],kpts[1],kpts[1],kpts[0],))
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
eri_mo0 = df0.get_mo_eri((mo,)*4, (kpt0,kpt0,kpts[0],kpts[0],))
eri_mo1 = odf.get_mo_eri((mo,)*4, (kpt0,kpt0,kpts[0],kpts[0],))
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
eri_mo0 = df0.get_mo_eri((mo,)*4, (kpts[0],kpts[0],kpt0,kpt0,))
eri_mo1 = odf.get_mo_eri((mo,)*4, (kpts[0],kpts[0],kpt0,kpt0,))
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
mo1 = mo[:,:nao//2+1]
eri_mo0 = df0.get_mo_eri((mo1,mo,mo,mo1), (kpts[0],)*4)
eri_mo1 = odf.get_mo_eri((mo1,mo,mo,mo1), (kpts[0],)*4)
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
eri_mo0 = df0.get_mo_eri((mo1,mo,mo1,mo), (kpts[0],kpts[1],kpts[1],kpts[0],))
eri_mo1 = odf.get_mo_eri((mo1,mo,mo1,mo), (kpts[0],kpts[1],kpts[1],kpts[0],))
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
