def test_2d_uu(self):
m = np.random.random((2, 5, 5))
c1 = np.random.random((2, 5, 10))
c2 = np.random.random((2, 5, 10))
t1 = util.ao2mo(m, c1, c2)
t2 = util.einsum('spq,spi,sqj->sij', m, c1, c2)
self.assertAlmostEqual(np.max(np.absolute(t1 - t2)), 0, 8)
def test_2d_rr(self):
m = np.random.random((5, 5))
c1 = np.random.random((5, 10))
c2 = np.random.random((5, 10))
t1 = util.ao2mo(m, c1, c2)
t2 = util.einsum('pq,pi,qj->ij', m, c1, c2)
self.assertAlmostEqual(np.max(np.absolute(t1 - t2)), 0, 8)
def test_4d_uu(self):
m = np.random.random((2, 2, 5, 5, 5, 5))
c1 = np.random.random((2, 5, 10))
c2 = np.random.random((2, 5, 10))
c3 = np.random.random((2, 5, 10))
c4 = np.random.random((2, 5, 10))
t1 = util.ao2mo(m, c1, c2, c3, c4)
t2 = util.einsum('abpqrs,api,aqj,brk,bsl->abijkl', m, c1, c2, c3, c4)
self.assertAlmostEqual(np.max(np.absolute(t1 - t2)), 0, 8)
def test_4d_rr(self):
m = np.random.random((5, 5, 5, 5))
c1 = np.random.random((5, 10))
c2 = np.random.random((5, 10))
c3 = np.random.random((5, 10))
c4 = np.random.random((5, 10))
t1 = util.ao2mo(m, c1, c2, c3, c4)
t2 = util.einsum('pqrs,pi,qj,rk,sl->ijkl', m, c1, c2, c3, c4)
self.assertAlmostEqual(np.max(np.absolute(t1 - t2)), 0, 8)
def setup(self):
self.eri_ao = util.spin_block(self.hf.eri_ao, self.hf.eri_ao)
self.h1e_ao = util.spin_block(self.hf.h1e_ao, self.hf.h1e_ao)
if isinstance(self.hf, hf.RHF):
self.e = util.spin_block(self.hf.e, self.hf.e)
self.c = util.spin_block(self.hf.c, self.hf.c)
elif isinstance(self.hf, hf.UHF):
self.e = util.spin_block(*list(self.hf.e))
self.c = util.spin_block(*list(self.hf.c))
mask = np.argsort(self.e)
self.e = self.e[mask]
self.c = self.c[:,mask]
self.eri_ao = self.eri_ao.transpose(0,2,1,3) - \
self.eri_ao.transpose(0,2,3,1)
self.h1e_mo = util.ao2mo(self.h1e_ao, self.c, self.c)
self.eri_mo = util.ao2mo(self.eri_ao, self.c, self.c, self.c, self.c)
def solve_casida(self):
#TODO: this step is n^6 and inefficient in memory, rethink
e_ia = util.outer_sum([-self.gf.e_occ, self.gf.e_vir])
co = self.gf.v[:self.nphys, self.gf.e < self.chempot]
cv = self.gf.v[:self.nphys, self.gf.e >= self.chempot]
iajb = util.ao2mo(self.eri, co, cv, co, cv).reshape((e_ia.size, ) * 2)
apb = np.diag(e_ia.flatten()) + 4.0 * iajb
amb = np.diag(np.sqrt(e_ia.flatten()))
h_rpa = util.dots((amb, apb, amb))
e_rpa, v_rpa = util.eigh(h_rpa)
e_rpa = np.sqrt(e_rpa)
xpy = util.einsum('ij,jk,k->ik', amb, v_rpa, 1.0 / np.sqrt(e_rpa))
xpy *= np.sqrt(2.0)
self.rpa = (e_rpa, v_rpa, xpy)
return self.rpa
def run(self):
t_amp = np.zeros((self.nvir, self.nvir, self.nocc, self.nocc), dtype=types.float64)
o = slice(None, self.nocc)
v = slice(self.nocc, None)
opdm_corr = np.zeros((self.nso,)*2, dtype=types.float64)
opdm_ref = opdm_corr.copy()
opdm_ref[o,o] = np.eye(self.nocc)
tpdm_corr = np.zeros((self.nso,)*4, dtype=types.float64)
x = opdm_corr.copy()
eija = util.outer_sum([-self.e[v], -self.e[v], self.e[o], self.e[o]])
eija = 1.0 / eija
if self.diis:
diis = util.DIIS(self.diis_space)
for niter in range(1, self.maxiter+1):
f = self.h1e_mo + util.einsum('piqi->pq', self.eri_mo[:,o,:,o])
fp = f.copy()
np.fill_diagonal(fp, 0.0)
e = f.diagonal()
t1 = self.eri_mo[v,v,o,o]
t2 = util.einsum('ac,cbij->abij', fp[v,v], t_amp)
t3 = util.einsum('ki,abkj->abij', fp[o,o], t_amp)
t_amp = t1.copy()
t_amp += t2 - t2.transpose(1,0,2,3)
t_amp -= t3 - t3.transpose(0,1,3,2)
t_amp *= eija
if niter > 1:
if self.diis:
t_amp = diis.update(t_amp)
if self.damping > 0.0:
damping = self.damping
t_amp = (1.0 - damping) * t_amp + damping * self._t_prev
if self.damping > 0.0:
self._t_prev = t_amp.copy()
opdm_corr[v,v] = util.einsum('ijac,bcij->ba', t_amp.T, t_amp) * 0.5
opdm_corr[o,o] = util.einsum('jkab,abik->ji', t_amp.T, t_amp) * -0.5
opdm = opdm_corr + opdm_ref
tpdm_corr[v,v,o,o] = t_amp
tpdm_corr[o,o,v,v] = t_amp.T
tpdm2 = util.einsum('rp,sq->rspq', opdm_corr, opdm_ref)
tpdm3 = util.einsum('rp,sq->rspq', opdm_ref, opdm_ref)
tpdm = tpdm_corr.copy()
tpdm += tpdm2 - tpdm2.transpose(1,0,2,3)
tpdm -= tpdm2.transpose(0,1,3,2) - tpdm2.transpose(1,0,3,2)
tpdm += tpdm3 - tpdm3.transpose(1,0,2,3)
fnr = util.einsum('pr,rq->pq', self.h1e_mo, opdm)
fnr += util.einsum('prst,stqr->pq', self.eri_mo, tpdm) * 0.5
x[v,o] = ((fnr - fnr.T)[v,o]) / util.outer_sum([-self.e[v], self.e[o]])
u = expm(x - x.T)
c = np.dot(self.c, u)
self.c = c
self.h1e_mo = util.ao2mo(self.h1e_ao, c, c)
self.eri_mo = util.ao2mo(self.eri_ao, c, c, c, c)
e_prev = self.e_tot
self.e_1body = util.einsum('pq,qp->', self.h1e_mo, opdm)
self.e_1body += self.hf.e_nuc
self.e_2body = 0.25 * util.einsum('pqrs,rspq->', self.eri_mo, tpdm)
if abs(self.e_tot - e_prev) < self.etol:
break
return self
def get_eri(self, coeffs):
return util.ao2mo(self.eri_ao, *coeffs)
def eri_mo(self):
if not self.with_df:
return util.ao2mo(self.eri_ao, self.c, self.c, self.c, self.c)
else:
return util.ao2mo(self.eri_ao, self.c, self.c)
def rdm1_mo(self):
sds = util.ao2mo(self.rdm1_ao, self.ovlp_ao, self.ovlp_ao)
return util.ao2mo(sds, self.c, self.c)
def fock_mo(self):
return util.ao2mo(self.fock_ao, self.c, self.c)
def h1e_mo(self):
return util.ao2mo(self.h1e_ao, self.c, self.c)