def testE1(self):
bra = braE1("occ", "vir")
ket = ketE1("occ", "vir")
out = apply_wick(bra * ket)
aout = AExpression(Ex=out)
i = Idx(0, "occ")
a = Idx(0, "vir")
j = Idx(1, "occ")
b = Idx(1, "vir")
tr1 = Term(1, [],
[Tensor([a, i], ""), Tensor([j, b], "")], [],
[Delta(i, j), Delta(a, b)])
ref = Expression([tr1])
aref = AExpression(Ex=ref)
self.assertTrue(aout.pmatch(aref))
op = E1("A", ["occ"], ["vir"])
out = apply_wick(bra * op)
out.resolve()
aout = AExpression(Ex=out)
ext = Tensor([a, i], "")
ten = Tensor([a, i], "A")
at1 = ATerm(scalar=1, sums=[], tensors=[ext, ten])
self.assertTrue(len(aout.terms) == 1)
self.assertTrue(at1 == aout.terms[0])
def test_merge_external(self):
bra = braE1("occ", "vir")
ket = ketE1("occ", "vir")
out = apply_wick(bra * ket)
aout = AExpression(Ex=out)
aterm = aout.terms[0]
aterm.merge_external()
i = Idx(0, "occ")
a = Idx(0, "vir")
j = Idx(1, "occ")
b = Idx(1, "vir")
tensors = [
Tensor([a, i, j, b], ""),
tensor_from_delta(Delta(i, j)),
tensor_from_delta(Delta(a, b))
]
aref = ATerm(scalar=1, sums=[], tensors=tensors)
self.assertTrue(aterm == aref)
def test_ccsd_T1(self):
H1 = one_e("f", ["occ", "vir"], norder=True)
H2 = two_e("I", ["occ", "vir"], norder=True)
H = H1 + H2
bra = braE1("occ", "vir")
T1 = E1("t", ["occ"], ["vir"])
T2 = E2("t", ["occ"], ["vir"])
T = T1 + T2
HT = commute(H, T)
HTT = commute(HT, T)
HTTT = commute(commute(commute(H2, T1), T1), T1)
S = bra*(H + HT + Fraction('1/2')*HTT + Fraction('1/6')*HTTT)
out = apply_wick(S)
out.resolve()
final = AExpression(Ex=out)
out = str(final) + "\n"
ref = get_ref("ccsd_T1.out")
self.assertTrue(ref == out)
from wick.expression import AExpression
from wick.wick import apply_wick
from wick.convenience import one_e, two_e, braE1, ketE1, braE2, ketE2
H1 = one_e("f", ["occ", "vir"], norder=True)
H2 = two_e("I", ["occ", "vir"], norder=True)
H = H1 + H2
# first derivative wrt X*
bra = braE1("occ", "vir")
S = bra * H
out = apply_wick(S)
out.resolve()
final = AExpression(Ex=out)
final.sort_tensors()
print("dE/dX* =")
print(final)
# first derivative wrt X
ket = ketE1("occ", "vir")
S = H * ket
out = apply_wick(S)
out.resolve()
final = AExpression(Ex=out)
final.sort_tensors()
final.transpose((1, 0))
print("dE/dX =")
print(final)
print("")
# second derivative wrt X*X*
from wick.expression import AExpression
from wick.wick import apply_wick
from wick.convenience import one_e, two_e, E1, E2, braE1, commute
index_key = {
"occ": "ijklmno",
"oa": "IJKLMNO",
"va": "ABCDEFG",
"vir": "abcdefg"
}
H1 = one_e("f", ["occ", "oa", "va", "vir"], norder=True, index_key=index_key)
H2 = two_e("I", ["occ", "oa", "va", "vir"], norder=True, index_key=index_key)
H = H1 + H2
bra = braE1("occ", "vir", index_key=index_key)
T1 = E1("t", ["occ", "oa"], ["va", "vir"], index_key=index_key)
T2 = E2("t", ["occ", "oa"], ["va", "vir"], index_key=index_key)
T = T1 + T2
HT = commute(H, T)
HTT = commute(HT, T)
HTTT = commute(commute(commute(H2, T1), T1), T1)
S = bra * H
out = apply_wick(S)
out.resolve()
final = AExpression(Ex=out)
print("Constant:")
print(final)
print("")
