def template_nontrivial_contraction(self, case):
refstate = cache.refstate[case]
f_oo = empty_like(refstate.fock("o1o1")).set_random()
f_vv = empty_like(refstate.fock("v1v1")).set_random()
i1 = empty_like(refstate.fock("v1v1")).set_random()
i2 = empty_like(refstate.fock("o1o1")).set_random()
oovv = empty_like(refstate.eri("o1o1v1v1")).set_random()
ovov = empty_like(refstate.eri("o1v1o1v1")).set_random()
t2 = empty_like(refstate.eri("o1o1v1v1")).set_random()
u1 = empty_like(refstate.fock("o1v1")).set_random()
nf_oo = f_oo.to_ndarray()
nf_vv = f_vv.to_ndarray()
ni1 = i1.to_ndarray()
ni2 = i2.to_ndarray()
noovv = oovv.to_ndarray()
novov = ovov.to_ndarray()
nt2 = t2.to_ndarray()
nu1 = u1.to_ndarray()
# (Slightly) modified ADC(2) singles block equation
res = (+einsum("ib,ab->ia", u1, f_vv + i1) -
einsum("ij,ja->ia", f_oo - i2, u1) -
einsum("jaib,jb->ia", ovov, u1) -
0.5 * einsum("ijab,jkbc,kc->ia", t2, oovv, u1) -
0.5 * einsum("ijab,jkbc,kc->ia", oovv, t2, u1))
ref = (+np.einsum("ib,ab->ia", nu1, nf_vv + ni1) -
np.einsum("ij,ja->ia", nf_oo - ni2, nu1) -
np.einsum("jaib,jb->ia", novov, nu1) -
0.5 * np.einsum("ijab,jkbc,kc->ia", nt2, noovv, nu1) -
0.5 * np.einsum("ijab,jkbc,kc->ia", noovv, nt2, nu1))
assert res.needs_evaluation
assert_allclose(res.to_ndarray(), ref, rtol=1e-10, atol=1e-14)
def test_nontrivial_trace(self):
import libadcc
refstate = cache.refstate["cn_sto3g"]
oovv = empty_like(refstate.eri("o1o1v1v1")).set_random()
ovov = empty_like(refstate.eri("o1v1o1v1")).set_random()
noovv = oovv.to_ndarray()
novov = ovov.to_ndarray()
res = libadcc.trace("iaai", einsum("ijab,kcja->icbk", oovv, ovov))
ref = np.einsum("ijab,ibja->", noovv, novov)
assert_allclose(res, ref, rtol=1e-10, atol=1e-14)
def test_nontrivial_diagonal(self):
refstate = cache.refstate["cn_sto3g"]
mtcs = [
nosym_like(refstate.eri("o1o1v1v1")).set_random(),
nosym_like(refstate.eri("o1v1o1v1")).set_random(),
nosym_like(refstate.eri("o1o1v1v1")).set_random()
]
mnps = [m.to_ndarray() for m in mtcs]
res = einsum("ijab,ibkc,kjad->cd", mtcs[0], mtcs[1],
mtcs[2]).diagonal()
ref = np.einsum("ijab,ibkc,kjad->cd", mnps[0], mnps[1],
mnps[2]).diagonal()
assert res.needs_evaluation
assert_allclose(res.to_ndarray(), ref, rtol=1e-10, atol=1e-14)
def test_nontrivial_direct_sum(self):
refstate = cache.refstate["cn_sto3g"]
oeo = nosym_like(refstate.orbital_energies("o1")).set_random()
oovv = empty_like(refstate.eri("o1o1v1v1")).set_random()
oev = nosym_like(refstate.orbital_energies("v1")).set_random()
interm = np.einsum("ijac,ijcb->ab", oovv.to_ndarray(),
oovv.to_ndarray())
ref = (interm[:, :, None, None] -
oeo.to_ndarray()[None, None, :, None] -
oev.to_ndarray()[None, None, None, :])
ref = ref.transpose((2, 0, 3, 1))
res = direct_sum("ab-i-c->iacb", einsum("ijac,ijcb->ab", oovv, oovv),
oeo, oev)
assert_allclose(res.to_ndarray(), ref, rtol=1e-10, atol=1e-14)
def base_test(self, contr, *arr):
arr = [a.set_random() for a in arr]
ref = np.einsum(contr, *[a.to_ndarray() for a in arr])
out = einsum(contr, *arr)
assert_allclose(out.to_ndarray(), ref, rtol=1e-10, atol=1e-14)
def test_partial_trace(self):
refstate = cache.refstate["h2o_sto3g"]
a = empty_like(refstate.ovov)
b = empty_like(refstate.fvv)
with pytest.raises(NotImplementedError, match=r"Partial traces.*"):
einsum("iaib,ba->a", a, b)