def test_ft_aoao_with_kpts(self):
numpy.random.seed(1)
kpti, kptj = numpy.random.random((2, 3))
dat = ft_ao.ft_aopair(cell, cell.Gv, kpti_kptj=(kpti, kptj))
self.assertAlmostEqual(finger(dat),
-0.80184732435570638 + 2.4078835207597176j, 9)
coords = pdft.gen_grid.gen_uniform_grids(cell)
aoi = pdft.numint.eval_ao(cell, coords, kpt=kpti)
aoj = pdft.numint.eval_ao(cell, coords, kpt=kptj)
ngs, nao = aoj.shape
q = kptj - kpti
expmikr = numpy.exp(-1j * numpy.dot(coords, q))
ref = numpy.asarray([
tools.fftk(aoi[:, i].conj() * aoj[:, j], cell.gs, expmikr)
for i in range(nao) for j in range(nao)
])
ref = ref.reshape(nao, nao, -1).transpose(2, 0, 1) * (cell.vol / ngs)
self.assertAlmostEqual(numpy.linalg.norm(ref[:, 0, 0] - dat[:, 0, 0]),
0, 5)
self.assertAlmostEqual(numpy.linalg.norm(ref[:, 1, 1] - dat[:, 1, 1]),
0.023225471785938184, 4)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 2:, 2:] - dat[:, 2:, 2:]), 0, 9)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 0, 2:] - dat[:, 0, 2:]), 0, 9)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 2:, 0] - dat[:, 2:, 0]), 0, 9)
coords = pdft.gen_grid.gen_uniform_grids(cell1)
aoi = pdft.numint.eval_ao(cell1, coords, kpt=kpti)
aoj = pdft.numint.eval_ao(cell1, coords, kpt=kptj)
ngs, nao = aoj.shape
q = kptj - kpti
dat = ft_ao.ft_aopair(cell1, cell1.Gv, kpti_kptj=(kpti, kptj), q=q)
self.assertAlmostEqual(finger(dat),
0.72664436503332241 + 3.2542145296611373j, 9)
expmikr = numpy.exp(-1j * numpy.dot(coords, q))
ref = numpy.asarray([
tools.fftk(aoi[:, i].conj() * aoj[:, j], cell1.gs, expmikr)
for i in range(nao) for j in range(nao)
])
ref = ref.reshape(nao, nao, -1).transpose(2, 0, 1) * (cell1.vol / ngs)
self.assertAlmostEqual(numpy.linalg.norm(ref[:, 0, 0] - dat[:, 0, 0]),
0, 7)
self.assertAlmostEqual(numpy.linalg.norm(ref[:, 1, 1] - dat[:, 1, 1]),
0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 2:, 2:] - dat[:, 2:, 2:]), 0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 0, 2:] - dat[:, 0, 2:]), 0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 2:, 0] - dat[:, 2:, 0]), 0, 7)
def test_ft_aoao(self):
#coords = pdft.gen_grid.gen_uniform_grids(cell)
#aoR = pdft.numint.eval_ao(cell, coords)
#ngs, nao = aoR.shape
#ref = numpy.asarray([tools.fft(aoR[:,i].conj()*aoR[:,j], cell.gs)
# for i in range(nao) for j in range(nao)])
#ref = ref.reshape(nao,nao,-1).transpose(2,0,1) * (cell.vol/ngs)
#dat = ft_ao.ft_aopair(cell, cell.Gv, aosym='s1hermi')
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,0,0]-dat[:,0,0]) , 0, 5)
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,1,1]-dat[:,1,1]) , 0.02315483195832373, 4)
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,2:,2:]-dat[:,2:,2:]), 0, 9)
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,0,2:]-dat[:,0,2:]) , 0, 9)
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,2:,0]-dat[:,2:,0]) , 0, 9)
#idx = numpy.tril_indices(nao)
#ref = dat[:,idx[0],idx[1]]
#dat = ft_ao.ft_aopair(cell, cell.Gv, aosym='s2')
#self.assertAlmostEqual(abs(dat-ref).sum(), 0, 9)
coords = pdft.gen_grid.gen_uniform_grids(cell1)
aoR = pdft.numint.eval_ao(cell1, coords)
ngs, nao = aoR.shape
ref = numpy.asarray([
tools.fft(aoR[:, i].conj() * aoR[:, j], cell1.gs)
for i in range(nao) for j in range(nao)
])
ref = ref.reshape(nao, nao, -1).transpose(2, 0, 1) * (cell1.vol / ngs)
Gv, Gvbase, kws = cell1.get_Gv_weights(cell1.gs)
b = cell1.reciprocal_vectors()
gxyz = lib.cartesian_prod([numpy.arange(len(x)) for x in Gvbase])
dat = ft_ao.ft_aopair(cell1,
cell1.Gv,
aosym='s1hermi',
b=b,
gxyz=gxyz,
Gvbase=Gvbase)
self.assertAlmostEqual(numpy.linalg.norm(ref[:, 0, 0] - dat[:, 0, 0]),
0, 7)
self.assertAlmostEqual(numpy.linalg.norm(ref[:, 1, 1] - dat[:, 1, 1]),
0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 2:, 2:] - dat[:, 2:, 2:]), 0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 0, 2:] - dat[:, 0, 2:]), 0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 2:, 0] - dat[:, 2:, 0]), 0, 7)
idx = numpy.tril_indices(nao)
ref = dat[:, idx[0], idx[1]]
dat = ft_ao.ft_aopair(cell1, cell1.Gv, aosym='s2')
self.assertAlmostEqual(abs(dat - ref).sum(), 0, 9)
def test_ft_aoao_pair_vs_fft(self):
numpy.random.seed(1)
kpti, kptj = numpy.random.random((2, 3))
coords = pdft.gen_grid.gen_uniform_grids(cell1)
aoi = pdft.numint.eval_ao(cell1, coords, kpt=kpti)
aoj = pdft.numint.eval_ao(cell1, coords, kpt=kptj)
ngrids, nao = aoj.shape
q = kptj - kpti
dat = ft_ao.ft_aopair(cell1, cell1.Gv, kpti_kptj=(kpti, kptj), q=q)
self.assertAlmostEqual(finger(dat),
0.72664436503332241 + 3.2542145296611373j, 9)
expmikr = numpy.exp(-1j * numpy.dot(coords, q))
ref = numpy.asarray([
tools.fftk(aoi[:, i].conj() * aoj[:, j], cell1.mesh, expmikr)
for i in range(nao) for j in range(nao)
])
ref = ref.reshape(nao, nao, -1).transpose(2, 0,
1) * (cell1.vol / ngrids)
self.assertAlmostEqual(numpy.linalg.norm(ref[:, 0, 0] - dat[:, 0, 0]),
0, 7)
self.assertAlmostEqual(numpy.linalg.norm(ref[:, 1, 1] - dat[:, 1, 1]),
0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 2:, 2:] - dat[:, 2:, 2:]), 0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 0, 2:] - dat[:, 0, 2:]), 0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 2:, 0] - dat[:, 2:, 0]), 0, 7)
def test_ft_aoao1(self):
cell = pgto.Cell()
cell.a = numpy.eye(3) * 5
n = 15
cell.mesh = numpy.array([n, n, n])
cell.atom = '''C 1.3 .2 .3
C .1 .1 1.1
'''
cell.basis = {'C': [[1, (0.6, 1)]]}
cell.unit = 'B'
cell.build(0, 0)
ao2 = ft_ao.ft_aopair(cell, cell.Gv)
nao = cell.nao_nr()
coords = cell.get_uniform_grids()
aoR = cell.pbc_eval_gto('GTOval', coords)
aoR2 = numpy.einsum('ki,kj->kij', aoR.conj(), aoR)
ngrids = aoR.shape[0]
ao2ref = [
tools.fft(aoR2[:, i, j], cell.mesh) * cell.vol / ngrids
for i in range(nao) for j in range(nao)
]
ao2ref = numpy.array(ao2ref).reshape(6, 6, -1).transpose(2, 0, 1)
self.assertAlmostEqual(abs(ao2ref - ao2).max(), 0, 6)
aoG = ft_ao.ft_ao(cell, cell.Gv)
aoref = [
tools.fft(aoR[:, i], cell.mesh) * cell.vol / ngrids
for i in range(nao)
]
self.assertAlmostEqual(abs(numpy.array(aoref).T - aoG).max(), 0, 6)
def test_ft_aoao(self):
coords = pdft.gen_grid.gen_uniform_grids(cell)
aoR = pdft.numint.eval_ao(cell, coords)
ngs, nao = aoR.shape
ref = numpy.asarray([tools.fft(aoR[:,i].conj()*aoR[:,j], cell.gs)
for i in range(nao) for j in range(nao)])
ref = ref.reshape(nao,nao,-1).transpose(2,0,1) * (cell.vol/ngs)
dat = ft_ao.ft_aopair(cell, cell.Gv, aosym='s1hermi')
self.assertAlmostEqual(numpy.linalg.norm(ref[:,0,0]-dat[:,0,0]) , 1.869103994619606e-06 , 7)
self.assertAlmostEqual(numpy.linalg.norm(ref[:,1,1]-dat[:,1,1]) , 0.02315483195832373 , 4)
self.assertAlmostEqual(numpy.linalg.norm(ref[:,2:,2:]-dat[:,2:,2:]), 5.4648896424693173e-14, 9)
self.assertAlmostEqual(numpy.linalg.norm(ref[:,0,2:]-dat[:,0,2:]) , 4.0352047774658308e-11, 9)
self.assertAlmostEqual(numpy.linalg.norm(ref[:,2:,0]-dat[:,2:,0]) , 4.0352047774658308e-11, 9)
idx = numpy.tril_indices(nao)
ref = dat[:,idx[0],idx[1]]
dat = ft_ao.ft_aopair(cell, cell.Gv, aosym='s2')
self.assertAlmostEqual(abs(dat-ref).sum(), 0, 9)
def test_ft_aoao_with_kpts(self):
numpy.random.seed(1)
kpti, kptj = kpts = numpy.random.random((2,3))
Gv = cell.get_Gv([5]*3)
kpt = numpy.random.random(3)
dat = ft_ao._ft_aopair_kpts(cell, Gv, kpt=kpt, kptjs=kpts)
self.assertAlmostEqual(finger(dat[0]), (2.3753953914129382-2.5365192689115088j), 9)
self.assertAlmostEqual(finger(dat[1]), (2.4951510097641840-3.1990956672116355j), 9)
dat = ft_ao.ft_aopair(cell, Gv)
self.assertAlmostEqual(finger(dat), (1.2534723618134684+1.830086071817564j), 9)
def test_ft_aoao_pdotp(self):
coords = pdft.gen_grid.gen_uniform_grids(cell1)
Gv, Gvbase, kws = cell1.get_Gv_weights(cell1.mesh)
dat = ft_ao.ft_aopair(cell1,
cell1.Gv,
aosym='s1',
intor='GTO_ft_pdotp_sph')
self.assertAlmostEqual(finger(dat),
5.7858606710458078 - 8.654809509773056j, 9)
aoR = pdft.numint.eval_ao(cell1, coords, deriv=1)
ngrids, nao = aoR.shape[1:]
aoaoR = numpy.einsum('xpi,xpj->ijp', aoR[1:4], aoR[1:4])
ref = tools.fft(aoaoR.reshape(nao * nao, -1), cell1.mesh)
ref = ref.reshape(nao, nao, -1).transpose(2, 0,
1) * (cell1.vol / ngrids)
self.assertAlmostEqual(abs(ref - dat).max(), 0, 7)
def test_ft_aoao_with_kpts(self):
numpy.random.seed(1)
kpti, kptj = numpy.random.random((2,3))
coords = pdft.gen_grid.gen_uniform_grids(cell)
aoi = pdft.numint.eval_ao(cell, coords, kpt=kpti)
aoj = pdft.numint.eval_ao(cell, coords, kpt=kptj)
ngs, nao = aoj.shape
q = kptj - kpti
ref = numpy.asarray([tools.fftk(aoi[:,i].conj()*aoj[:,j], cell.gs, coords, q)
for i in range(nao) for j in range(nao)])
ref = ref.reshape(nao,nao,-1).transpose(2,0,1) * (cell.vol/ngs)
dat = ft_ao.ft_aopair(cell, cell.Gv, kpti_kptj=(kpti,kptj))
self.assertAlmostEqual(numpy.linalg.norm(ref[:,0,0]-dat[:,0,0]) , 1.8912693795904546e-06, 7)
self.assertAlmostEqual(numpy.linalg.norm(ref[:,1,1]-dat[:,1,1]) , 0.023225471785938184 , 4)
self.assertAlmostEqual(numpy.linalg.norm(ref[:,2:,2:]-dat[:,2:,2:]), 3.9231124086361633e-14, 9)
self.assertAlmostEqual(numpy.linalg.norm(ref[:,0,2:]-dat[:,0,2:]) , 3.6949758392853562e-11, 9)
self.assertAlmostEqual(numpy.linalg.norm(ref[:,2:,0]-dat[:,2:,0]) , 4.1245047267152665e-11, 9)
def test_ft_aoao_pxp(self):
coords = pdft.gen_grid.gen_uniform_grids(cell1)
Gv, Gvbase, kws = cell1.get_Gv_weights(cell1.mesh)
dat = ft_ao.ft_aopair(cell1,
cell1.Gv,
aosym='s1',
intor='GTO_ft_pxp_sph',
comp=3)
self.assertAlmostEqual(finger(dat),
(6.4124798727215779 - 10.673712733378771j), 9)
aoR = pdft.numint.eval_ao(cell1, coords, deriv=1)
ngrids, nao = aoR.shape[1:]
aox, aoy, aoz = aoR[1:]
aoaoR = (numpy.einsum('pi,pj->ijp', aoy, aoz) -
numpy.einsum('pi,pj->ijp', aoz, aoy),
numpy.einsum('pi,pj->ijp', aoz, aox) -
numpy.einsum('pi,pj->ijp', aox, aoz),
numpy.einsum('pi,pj->ijp', aox, aoy) -
numpy.einsum('pi,pj->ijp', aoy, aox))
ref = tools.fft(
numpy.array(aoaoR).reshape(3 * nao * nao, -1), cell1.mesh)
ref = ref.reshape(3, nao, nao, -1).transpose(0, 3, 1,
2) * (cell1.vol / ngrids)
self.assertAlmostEqual(abs(ref - dat).max(), 0, 7)
def test_ft_aoao(self):
#coords = pdft.gen_grid.gen_uniform_grids(cell)
#aoR = pdft.numint.eval_ao(cell, coords)
#ngrids, nao = aoR.shape
#ref = numpy.asarray([tools.fft(aoR[:,i].conj()*aoR[:,j], cell.mesh)
# for i in range(nao) for j in range(nao)])
#ref = ref.reshape(nao,nao,-1).transpose(2,0,1) * (cell.vol/ngrids)
#dat = ft_ao.ft_aopair(cell, cell.Gv, aosym='s1hermi')
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,0,0]-dat[:,0,0]) , 0, 5)
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,1,1]-dat[:,1,1]) , 0.02315483195832373, 4)
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,2:,2:]-dat[:,2:,2:]), 0, 9)
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,0,2:]-dat[:,0,2:]) , 0, 9)
#self.assertAlmostEqual(numpy.linalg.norm(ref[:,2:,0]-dat[:,2:,0]) , 0, 9)
#idx = numpy.tril_indices(nao)
#ref = dat[:,idx[0],idx[1]]
#dat = ft_ao.ft_aopair(cell, cell.Gv, aosym='s2')
#self.assertAlmostEqual(abs(dat-ref).sum(), 0, 9)
coords = pdft.gen_grid.gen_uniform_grids(cell1)
Gv, Gvbase, kws = cell1.get_Gv_weights(cell1.mesh)
b = cell1.reciprocal_vectors()
gxyz = lib.cartesian_prod([numpy.arange(len(x)) for x in Gvbase])
dat = ft_ao.ft_aopair(cell1,
cell1.Gv,
aosym='s1',
b=b,
gxyz=gxyz,
Gvbase=Gvbase)
self.assertAlmostEqual(finger(dat),
1.5666516306798806 + 1.953555017583245j, 9)
dat = ft_ao.ft_aopair(cell1,
cell1.Gv,
aosym='s2',
b=b,
gxyz=gxyz,
Gvbase=Gvbase)
self.assertAlmostEqual(finger(dat),
-0.85276967757297917 + 1.0378751267506394j, 9)
dat = ft_ao.ft_aopair(cell1,
cell1.Gv,
aosym='s1hermi',
b=b,
gxyz=gxyz,
Gvbase=Gvbase)
self.assertAlmostEqual(finger(dat),
1.5666516306798806 + 1.953555017583245j, 9)
aoR = pdft.numint.eval_ao(cell1, coords)
ngrids, nao = aoR.shape
aoaoR = numpy.einsum('pi,pj->ijp', aoR, aoR)
ref = tools.fft(aoaoR.reshape(nao * nao, -1), cell1.mesh)
ref = ref.reshape(nao, nao, -1).transpose(2, 0,
1) * (cell1.vol / ngrids)
self.assertAlmostEqual(numpy.linalg.norm(ref[:, 0, 0] - dat[:, 0, 0]),
0, 7)
self.assertAlmostEqual(numpy.linalg.norm(ref[:, 1, 1] - dat[:, 1, 1]),
0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 2:, 2:] - dat[:, 2:, 2:]), 0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 0, 2:] - dat[:, 0, 2:]), 0, 7)
self.assertAlmostEqual(
numpy.linalg.norm(ref[:, 2:, 0] - dat[:, 2:, 0]), 0, 7)
idx = numpy.tril_indices(nao)
ref = dat[:, idx[0], idx[1]]
dat = ft_ao.ft_aopair(cell1, cell1.Gv, aosym='s2')
self.assertAlmostEqual(abs(dat - ref).sum(), 0, 9)
