def test_sparse_operator2():
"""Test the SparseHamiltonian class"""
import pytest
import forte
import forte.utils
import psi4
from forte import det
geom = """
H
H 1 1.0
"""
scf_energy, psi4_wfn = forte.utils.psi4_scf(geom,
basis='DZ',
reference='RHF')
forte_objs = forte.utils.prepare_forte_objects(psi4_wfn, mo_spaces={})
as_ints = forte_objs['as_ints']
ham_op = forte.SparseHamiltonian(as_ints)
ref = forte.StateVector({det("20"): 1.0})
Href1 = ham_op.compute(ref, 0.0)
Href2 = ham_op.compute_on_the_fly(ref, 0.0)
assert Href1[det("20")] == pytest.approx(-1.094572, abs=1e-6)
assert Href2[det("20")] == pytest.approx(-1.094572, abs=1e-6)
psi4.core.clean()
def det(s):
return forte.det(s)
def test_sparse_operator():
import forte
import pytest
from forte import det
# test get/set
sop = forte.SparseOperator()
sop.add_term_from_str('[]')
sop.add_term_from_str('[0a+ 0b+ 0b- 0a-]')
to_str = sop.str()
assert to_str == []
to_latex = sop.latex()
assert to_latex == r'0.000000\; 0.000000\;\hat{a}_{0 \alpha}^\dagger\hat{a}_{0 \beta}^\dagger\hat{a}_{0 \beta}\hat{a}_{0 \alpha}'
sop = forte.SparseOperator(antihermitian=True)
sop.add_term_from_str('[1a+ 1b+ 0b- 0a-]', 1.0)
to_str = sop.str()
assert to_str == ['1.000000000000 * [ 1a+ 1b+ 0b- 0a- ]', '-1.000000000000 * [ 0a+ 0b+ 1b- 1a- ]']
to_latex = sop.latex()
assert to_latex == r'+\;\hat{a}_{1 \alpha}^\dagger\hat{a}_{1 \beta}^\dagger\hat{a}_{0 \beta}\hat{a}_{0 \alpha} -\;\hat{a}_{0 \alpha}^\dagger\hat{a}_{0 \beta}^\dagger\hat{a}_{1 \beta}\hat{a}_{1 \alpha}'
sop = forte.SparseOperator()
sop.add_term_from_str('[]')
sop.add_term_from_str('[0a+ 0b+ 0b- 0a-]')
coeff = sop.coefficients()
assert coeff == pytest.approx([0.0, 0.0], abs=1e-9)
sop.set_coefficient(0, 0.5)
sop.set_coefficient(1, 0.3)
coeff = sop.coefficients()
assert coeff == pytest.approx([0.5, 0.3], abs=1e-9)
# remove one term from sop
sop.pop_term()
# check the size
assert sop.size() == 1
# copy a term into a new operator
sop2 = forte.SparseOperator()
sop2.add_term(sop.term(0))
# test apply operator against safe implementation
sop = forte.SparseOperator()
sop.add_term_from_str('[2a+ 0a-]', 0.0)
sop.add_term_from_str('[1a+ 0a-]', 0.1)
sop.add_term_from_str('[1b+ 0b-]', 0.3)
sop.add_term_from_str('[1a+ 1b+ 0b- 0a-]', 0.5)
dtest = det("20")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
wfn_safe = forte.apply_operator_safe(sop, ref)
assert wfn == wfn_safe
sop = forte.SparseOperator(antihermitian=True)
sop.add_term_from_str('[2a+ 0a-]', 0.0)
sop.add_term_from_str('[1a+ 0a-]', 0.1)
sop.add_term_from_str('[1b+ 0b-]', 0.3)
sop.add_term_from_str('[1a+ 1b+ 0b- 0a-]', 0.7)
ref = forte.StateVector({det("20"): 1.0, det("02"): 0.5})
wfn = forte.apply_operator(sop, ref)
assert wfn[det("20")] == pytest.approx(-0.35, abs=1e-9)
assert wfn[det("02")] == pytest.approx(0.7, abs=1e-9)
assert wfn[det("+-")] == pytest.approx(0.25, abs=1e-9)
assert wfn[det("-+")] == pytest.approx(-0.05, abs=1e-9)
# wfn_safe = forte.apply_operator_safe(sop,ref)
# assert wfn == wfn_safe
### Operator ordering tests ###
# test repeated operator exception
sop = forte.SparseOperator()
with pytest.raises(RuntimeError):
sop.add_term_from_str('[0a+ 0a+]', 1.0)
sop = forte.SparseOperator()
with pytest.raises(RuntimeError):
sop.add_term_from_str('[1b+ 1b+]', 1.0)
sop = forte.SparseOperator()
with pytest.raises(RuntimeError):
sop.add_term_from_str('[5a- 5a-]', 1.0)
sop = forte.SparseOperator()
with pytest.raises(RuntimeError):
sop.add_term_from_str('[3b- 3b-]', 1.0)
# test ordering exception
sop = forte.SparseOperator()
with pytest.raises(RuntimeError):
sop.add_term_from_str('[0a+ 0b+ 0a- 0b-]', 1.0)
# test ordering exception
sop = forte.SparseOperator(antihermitian=True)
with pytest.raises(RuntimeError):
sop.add_term_from_str('[]', 1.0)
# test ordering: 0a+ 0b+ 0b- 0a- |2> = +|2>
sop = forte.SparseOperator()
sop.add_term_from_str('[0a+ 0b+ 0b- 0a-]', 1.0)
dtest = det("20")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[dtest] == pytest.approx(1.0, abs=1e-9)
# test ordering: 0a+ 0b+ 0a- 0b- |2> = -|2>
sop = forte.SparseOperator()
sop.add_term_from_str('[0a+ 0b+ 0a- 0b-]', 1.0, allow_reordering=True)
dtest = det("20")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[dtest] == pytest.approx(-1.0, abs=1e-9)
# test ordering: 0b+ 0a+ 0b- 0a- |2> = -|2>
sop = forte.SparseOperator()
sop.add_term_from_str('[0b+ 0a+ 0b- 0a-]', 1.0, allow_reordering=True)
dtest = det("20")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[dtest] == pytest.approx(-1.0, abs=1e-9)
# test ordering: 0b+ 0a+ 0a- 0b- |2> = +|2>
sop = forte.SparseOperator()
sop.add_term_from_str('[0b+ 0a+ 0a- 0b-]', 1.0, allow_reordering=True)
dtest = det("20")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[dtest] == pytest.approx(1.0, abs=1e-9)
# test ordering: 3a+ 4a+ 2b+ 1b- 0a- |22000> = + 3a+ 4a+ 2b+ 1b- |-2000>
# 3a+ 4a+ 2b+ 1b- 0a- |22000> = + 3a+ 4a+ 2b+ 1b- |-2000>
# = + 3a+ 4a+ 2b+ |-+000>
# = + 3a+ 4a+ |-+-00>
# = - 3a+ |-+-0+>
# = + 3a+ |-+-++>
sop = forte.SparseOperator()
sop.add_term_from_str('[3a+ 4a+ 2b+ 1b- 0a-]', 1.0)
ref = forte.StateVector({det("22"): 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[det("-+-++")] == pytest.approx(1.0, abs=1e-9)
sop = forte.SparseOperator()
sop.add_term_from_str('[0a+]', 1.0)
wfn = forte.apply_operator(sop, forte.StateVector({det(""): 1.0}))
assert wfn[det("+")] == pytest.approx(1.0, abs=1e-9)
sop = forte.SparseOperator()
sop.add_term_from_str('[0a+ 1a+]', 1.0)
wfn = forte.apply_operator(sop, forte.StateVector({det(""): 1.0}))
assert wfn[det("++")] == pytest.approx(1.0, abs=1e-9)
sop = forte.SparseOperator()
sop.add_term_from_str('[0a+ 1a+ 2a+]', 1.0)
wfn = forte.apply_operator(sop, forte.StateVector({det(""): 1.0}))
assert wfn[det("+++")] == pytest.approx(1.0, abs=1e-9)
sop = forte.SparseOperator()
sop.add_term_from_str('[0a+ 1a+ 2a+ 3a+]', 1.0)
wfn = forte.apply_operator(sop, forte.StateVector({det(""): 1.0}))
assert wfn[det("++++")] == pytest.approx(1.0, abs=1e-9)
sop = forte.SparseOperator()
sop.add_term_from_str('[0a+ 1a+ 2a+ 3a+ 4a+]', 1.0)
wfn = forte.apply_operator(sop, forte.StateVector({det(""): 1.0}))
assert wfn[det("+++++")] == pytest.approx(1.0, abs=1e-9)
sop = forte.SparseOperator()
sop.add_term_from_str('[2a+ 0a+ 3a+ 1a+ 4a+]', 1.0, allow_reordering=True)
wfn = forte.apply_operator(sop, forte.StateVector({det(""): 1.0}))
assert wfn[det("+++++")] == pytest.approx(-1.0, abs=1e-9)
sop = forte.SparseOperator()
sop.add_term_from_str('[0a-]', 1.0)
wfn = forte.apply_operator(sop, forte.StateVector({det("22222"): 1.0}))
assert wfn[det("-2222")] == pytest.approx(1.0, abs=1e-9)
sop = forte.SparseOperator()
sop.add_term_from_str('[1a- 0a-]', 1.0)
wfn = forte.apply_operator(sop, forte.StateVector({det("22222"): 1.0}))
assert wfn[det("--222")] == pytest.approx(1.0, abs=1e-9)
sop = forte.SparseOperator()
sop.add_term_from_str('[2a- 1a- 0a-]', 1.0)
wfn = forte.apply_operator(sop, forte.StateVector({det("22222"): 1.0}))
assert wfn[det("---22")] == pytest.approx(1.0, abs=1e-9)
sop = forte.SparseOperator()
sop.add_term_from_str('[3a- 2a- 1a- 0a-]', 1.0)
wfn = forte.apply_operator(sop, forte.StateVector({det("22222"): 1.0}))
assert wfn[det("----2")] == pytest.approx(1.0, abs=1e-9)
sop = forte.SparseOperator()
sop.add_term_from_str('[4a- 3a- 2a- 1a- 0a-]', 1.0)
wfn = forte.apply_operator(sop, forte.StateVector({det("22222"): 1.0}))
assert wfn[det("-----")] == pytest.approx(1.0, abs=1e-9)
sop = forte.SparseOperator()
sop.add_term_from_str('[1a- 3a- 2a- 4a- 0a-]', 1.0, allow_reordering=True)
wfn = forte.apply_operator(sop, forte.StateVector({det("22222"): 1.0}))
assert wfn[det("-----")] == pytest.approx(-1.0, abs=1e-9)
### Test for cases that are supposed to return zero ###
# test destroying empty orbitals: (0a+ 0b+ 0b- 0a-) |0> = 0
sop = forte.SparseOperator()
sop.add_term_from_str('[0a+ 0b+ 0b- 0a-]', 1.0)
dtest = det("00")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert dtest not in wfn
# test destroying empty orbitals: (0a+ 0b+ 0b- 0a-) |0> = 0
sop = forte.SparseOperator()
sop.add_term_from_str('[0a+ 0b+ 0b-]', 1.0)
dtest = det("00")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert dtest not in wfn
# test creating in filled orbitals: (0a+ 1a+ 0a-) |22> = 0
sop = forte.SparseOperator()
sop.add_term_from_str('[1a+ 0a+ 0a-]', 1.0, allow_reordering=True)
dtest = det("+")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert dtest not in wfn
# test creating in filled orbitals: (0a+ 1a+ 0a-) |22> = 0
sop = forte.SparseOperator()
sop.add_term_from_str('[1b+ 0a+ 0a-]', 1.0, allow_reordering=True)
dtest = det("+")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert dtest not in wfn
### Number operator tests ###
# test number operator: (0a+ 0a-) |0> = 0
sop = forte.SparseOperator()
sop.add_term_from_str('[0a+ 0a-]', 1.0)
dtest = det("0")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert dtest not in wfn
# test number operator: (0a+ 0a-) |+> = |+>
sop = forte.SparseOperator()
sop.add_term_from_str('[0a+ 0a-]', 1.0)
dtest = det("+")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[dtest] == pytest.approx(1.0, abs=1e-9)
# test number operator: (0a+ 0a-) |-> = 0
sop = forte.SparseOperator()
sop.add_term_from_str('[0a+ 0a-]', 1.0)
dtest = det("-")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert dtest not in wfn
# test number operator: (0a+ 0a-) |2> = |2>
sop = forte.SparseOperator()
sop.add_term_from_str('[0a+ 0a-]', 1.0)
dtest = det("2")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[dtest] == pytest.approx(1.0, abs=1e-9)
# test number operator: (0b+ 0b-) |0> = 0
sop = forte.SparseOperator()
sop.add_term_from_str('[0b+ 0b-]', 1.0)
dtest = det("0")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert dtest not in wfn
# test number operator: (0b+ 0b-) |+> = 0
sop = forte.SparseOperator()
sop.add_term_from_str('[0b+ 0b-]', 1.0)
dtest = det("+")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert dtest not in wfn
# test number operator: (0b+ 0b-) |-> = |->
sop = forte.SparseOperator()
sop.add_term_from_str('[0b+ 0b-]', 1.0)
dtest = det("-")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[dtest] == pytest.approx(1.0, abs=1e-9)
# test number operator: (0b+ 0b-) |2> = |2>
sop = forte.SparseOperator()
sop.add_term_from_str('[0b+ 0b-]', 1.0)
ref = forte.StateVector({det("2"): 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[det("2")] == pytest.approx(1.0, abs=1e-9)
# test number operator: (2a+ 2a- + 2b+ 2b-) |222> = |222>
sop = forte.SparseOperator()
sop.add_term_from_str('[2a+ 2a-]', 1.0)
sop.add_term_from_str('[2b+ 2b-]', 1.0)
ref = forte.StateVector({det("222"): 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[det("222")] == pytest.approx(2.0, abs=1e-9)
# test number operator: (2a+ 2a- + 2b+ 2b-) |22+> = |22+>
sop = forte.SparseOperator()
sop.add_term_from_str('[2a+ 2a-]', 1.0)
sop.add_term_from_str('[2b+ 2b-]', 1.0)
ref = forte.StateVector({det("22+"): 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[det("22+")] == pytest.approx(1.0, abs=1e-9)
# test number operator: (2a+ 2a- + 2b+ 2b-) |22-> = |22->
sop = forte.SparseOperator()
sop.add_term_from_str('[2a+ 2a-]', 1.0)
sop.add_term_from_str('[2b+ 2b-]', 1.0)
ref = forte.StateVector({det("22-"): 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[det("22-")] == pytest.approx(1.0, abs=1e-9)
# test number operator: (2a+ 2a- + 2b+ 2b-) |220> = |220>
sop = forte.SparseOperator()
sop.add_term_from_str('[2a+ 2a-]', 1.0)
sop.add_term_from_str('[2b+ 2b-]', 1.0)
ref = forte.StateVector({det("220"): 1.0})
wfn = forte.apply_operator(sop, ref)
assert dtest not in wfn
### Excitation operator tests ###
# test excitation operator: (3a+ 0a-) |2200> = 3a+ |-200> = -|-20+>
sop = forte.SparseOperator()
sop.add_term_from_str('[3a+ 0a-]', 1.0)
dtest = det("22")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[det("-20+")] == pytest.approx(-1.0, abs=1e-9)
# test excitation operator: (0a- 3a+) |22> = 0a- |220+> = |-20+>
sop = forte.SparseOperator()
sop.add_term_from_str('[0a- 3a+]', 1.0, allow_reordering=True)
dtest = det("22")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[det("-20+")] == pytest.approx(1.0, abs=1e-9)
# test number operator: (3b+ 0b-) |2200> = 3b+ |+200> = |+20->
sop = forte.SparseOperator()
sop.add_term_from_str('[3b+ 0b-]', 1.0)
dtest = det("22")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(sop, ref)
assert wfn[det("+20-")] == pytest.approx(-1.0, abs=1e-9)
def test_sparse_vector():
import pytest
import forte
from forte import det
### Overlap tests ###
ref = forte.StateVector({
det(""): 1.0,
det("+"): 1.0,
det("-"): 1.0,
det("2"): 1.0,
det("02"): 1.0
})
ref2 = forte.StateVector({det("02"): 0.3})
ref3 = forte.StateVector({det("002"): 0.5})
assert forte.overlap(ref, ref) == pytest.approx(5.0, abs=1e-9)
assert forte.overlap(ref, ref2) == pytest.approx(0.3, abs=1e-9)
assert forte.overlap(ref2, ref) == pytest.approx(0.3, abs=1e-9)
assert forte.overlap(ref, ref3) == pytest.approx(0.0, abs=1e-9)
ref_str = ref.str(2)
### Number projection tests ###
proj1 = forte.StateVector({det("2"): 1.0, det("02"): 1.0})
test_proj1 = forte.apply_number_projector(1, 1, ref)
assert proj1 == test_proj1
proj2 = forte.StateVector({det(""): 1.0})
test_proj2 = forte.apply_number_projector(0, 0, ref)
assert proj2 == test_proj2
proj3 = forte.StateVector({det("+"): 1.0})
test_proj3 = forte.apply_number_projector(1, 0, ref)
assert proj3 == test_proj3
proj4 = forte.StateVector({det("-"): 1.0})
test_proj4 = forte.apply_number_projector(0, 1, ref)
assert proj4 == test_proj4
def test_sparse_ci4():
import pytest
from forte import det
### Test the linear operator ###
op = forte.SparseOperator()
ref = forte.StateVector({det("22"): 1.0})
op.add_term_from_str('[2a+ 0a-]', 0.1)
op.add_term_from_str('[2b+ 0b-]', 0.2)
op.add_term_from_str('[2a+ 0a-]', 0.2)
op.add_term_from_str('[2b+ 0b-]', 0.1)
op.add_term_from_str('[2a+ 2b+ 0b- 0a-]', 0.15)
op.add_term_from_str('[3a+ 3b+ 1b- 1a-]', -0.21)
op.add_term_from_str('[1a+ 1b+ 3b- 3a-]', 0.13 * 0.17)
wfn = forte.apply_operator(op, ref)
assert det("2200") not in wfn
assert wfn[det("+2-0")] == pytest.approx(-0.3, abs=1e-9)
assert wfn[det("-2+0")] == pytest.approx(-0.3, abs=1e-9)
assert wfn[det("0220")] == pytest.approx(0.15, abs=1e-9)
assert wfn[det("2002")] == pytest.approx(-0.21, abs=1e-9)
### Test the exponential operator with excitation operator ###
op = forte.SparseOperator()
ref = forte.StateVector({det("22"): 1.0})
op.add_term_from_str('[2a+ 0a-]', 0.1)
op.add_term_from_str('[2b+ 0b-]', 0.1)
op.add_term_from_str('[2a+ 2b+ 0b- 0a-]', 0.15)
op.add_term_from_str('[3a+ 3b+ 1b- 1a-]', -0.077)
exp = forte.SparseExp()
wfn = exp.compute(op, ref)
assert wfn[det("2200")] == pytest.approx(1.0, abs=1e-9)
assert wfn[det("0220")] == pytest.approx(0.16, abs=1e-9)
assert wfn[det("+2-0")] == pytest.approx(-0.1, abs=1e-9)
assert wfn[det("-2+0")] == pytest.approx(-0.1, abs=1e-9)
assert wfn[det("2002")] == pytest.approx(-0.077, abs=1e-9)
assert wfn[det("+0-2")] == pytest.approx(-0.0077, abs=1e-9)
assert wfn[det("-0+2")] == pytest.approx(-0.0077, abs=1e-9)
wfn = exp.compute(op, ref, algorithm='onthefly')
assert wfn[det("2200")] == pytest.approx(1.0, abs=1e-9)
assert wfn[det("0220")] == pytest.approx(0.16, abs=1e-9)
assert wfn[det("+2-0")] == pytest.approx(-0.1, abs=1e-9)
assert wfn[det("-2+0")] == pytest.approx(-0.1, abs=1e-9)
assert wfn[det("2002")] == pytest.approx(-0.077, abs=1e-9)
assert wfn[det("+0-2")] == pytest.approx(-0.0077, abs=1e-9)
assert wfn[det("-0+2")] == pytest.approx(-0.0077, abs=1e-9)
wfn = exp.compute(op, ref, algorithm='ontheflystd')
assert wfn[det("2200")] == pytest.approx(1.0, abs=1e-9)
assert wfn[det("0220")] == pytest.approx(0.16, abs=1e-9)
assert wfn[det("+2-0")] == pytest.approx(-0.1, abs=1e-9)
assert wfn[det("-2+0")] == pytest.approx(-0.1, abs=1e-9)
assert wfn[det("2002")] == pytest.approx(-0.077, abs=1e-9)
assert wfn[det("+0-2")] == pytest.approx(-0.0077, abs=1e-9)
assert wfn[det("-0+2")] == pytest.approx(-0.0077, abs=1e-9)
### Test the exponential operator with antihermitian operator ###
op = forte.SparseOperator(antihermitian=True)
ref = forte.StateVector({det("22"): 1.0})
op.add_term_from_str('[2a+ 0a-]', 0.1)
op.add_term_from_str('[2b+ 0b-]', 0.1)
op.add_term_from_str('[2a+ 2b+ 0b- 0a-]', 0.15)
exp = forte.SparseExp()
wfn = exp.compute(op, ref)
assert wfn[det("-2+0")] == pytest.approx(-0.091500564912, abs=1e-9)
assert wfn[det("+2-0")] == pytest.approx(-0.091500564912, abs=1e-9)
assert wfn[det("0220")] == pytest.approx(+0.158390400605, abs=1e-9)
assert wfn[det("2200")] == pytest.approx(+0.978860446763, abs=1e-9)
exp = forte.SparseExp()
wfn = exp.compute(op, ref, algorithm='onthefly')
assert wfn[det("-2+0")] == pytest.approx(-0.091500564912, abs=1e-9)
assert wfn[det("+2-0")] == pytest.approx(-0.091500564912, abs=1e-9)
assert wfn[det("0220")] == pytest.approx(+0.158390400605, abs=1e-9)
assert wfn[det("2200")] == pytest.approx(+0.978860446763, abs=1e-9)
exp = forte.SparseExp()
wfn = exp.compute(op, ref, algorithm='ontheflystd')
assert wfn[det("-2+0")] == pytest.approx(-0.091500564912, abs=1e-9)
assert wfn[det("+2-0")] == pytest.approx(-0.091500564912, abs=1e-9)
assert wfn[det("0220")] == pytest.approx(+0.158390400605, abs=1e-9)
assert wfn[det("2200")] == pytest.approx(+0.978860446763, abs=1e-9)
exp = forte.SparseExp()
wfn = exp.compute(op, ref)
wfn2 = exp.compute(op, wfn, scaling_factor=-1.0)
assert wfn2[det("2200")] == pytest.approx(1.0, abs=1e-9)
assert wfn2[det("0220")] == pytest.approx(0.0, abs=1e-9)
assert wfn2[det("+2-0")] == pytest.approx(0.0, abs=1e-9)
assert wfn2[det("-2+0")] == pytest.approx(0.0, abs=1e-9)
exp = forte.SparseExp()
wfn = exp.compute(op, ref, algorithm='onthefly')
wfn2 = exp.compute(op, wfn, scaling_factor=-1.0, algorithm='onthefly')
assert wfn2[det("2200")] == pytest.approx(1.0, abs=1e-9)
assert wfn2[det("0220")] == pytest.approx(0.0, abs=1e-9)
assert wfn2[det("+2-0")] == pytest.approx(0.0, abs=1e-9)
assert wfn2[det("-2+0")] == pytest.approx(0.0, abs=1e-9)
exp = forte.SparseExp()
wfn = exp.compute(op, ref, algorithm='ontheflystd')
wfn2 = exp.compute(op, wfn, scaling_factor=-1.0, algorithm='ontheflystd')
assert wfn2[det("2200")] == pytest.approx(1.0, abs=1e-9)
assert wfn2[det("0220")] == pytest.approx(0.0, abs=1e-9)
assert wfn2[det("+2-0")] == pytest.approx(0.0, abs=1e-9)
assert wfn2[det("-2+0")] == pytest.approx(0.0, abs=1e-9)
### Test the factorized exponential operator ###
op = forte.SparseOperator(antihermitian=True)
op.add_term_from_str('[2a+ 0a-]', 0.1)
op.add_term_from_str('[2b+ 0b-]', 0.2)
op.add_term_from_str('[2a+ 2b+ 0b- 0a-]', 0.15)
ref = forte.StateVector({det("22"): 1.0})
factexp = forte.SparseFactExp()
wfn = factexp.compute(op, ref)
assert wfn[det("+2-0")] == pytest.approx(-0.197676811654, abs=1e-9)
assert wfn[det("-2+0")] == pytest.approx(-0.097843395007, abs=1e-9)
assert wfn[det("0220")] == pytest.approx(+0.165338757995, abs=1e-9)
assert wfn[det("2200")] == pytest.approx(+0.961256283877, abs=1e-9)
wfn2 = factexp.compute(op, wfn, inverse=True)
assert wfn2[det("2200")] == pytest.approx(1.0, abs=1e-9)
factexp = forte.SparseFactExp()
wfn = factexp.compute(op, ref, algorithm='onthefly')
assert wfn[det("+2-0")] == pytest.approx(-0.197676811654, abs=1e-9)
assert wfn[det("-2+0")] == pytest.approx(-0.097843395007, abs=1e-9)
assert wfn[det("0220")] == pytest.approx(+0.165338757995, abs=1e-9)
assert wfn[det("2200")] == pytest.approx(+0.961256283877, abs=1e-9)
wfn2 = factexp.compute(op, wfn, inverse=True, algorithm='onthefly')
assert wfn2[det("2200")] == pytest.approx(1.0, abs=1e-9)
op = forte.SparseOperator(antihermitian=True)
op.add_term_from_str('[1a+ 0a-]', 0.1)
op.add_term_from_str('[1a+ 1b+ 0b- 0a-]', -0.3)
op.add_term_from_str('[1b+ 0b-]', 0.05)
op.add_term_from_str('[2a+ 2b+ 1b- 1a-]', -0.07)
dtest = det("20")
ref = forte.StateVector({det("20"): 0.5, det("02"): 0.8660254038})
factexp = forte.SparseFactExp()
wfn = factexp.compute(op, ref)
assert wfn[det("200")] == pytest.approx(0.733340213919, abs=1e-9)
assert wfn[det("+-0")] == pytest.approx(-0.049868863373, abs=1e-9)
assert wfn[det("002")] == pytest.approx(-0.047410073759, abs=1e-9)
assert wfn[det("020")] == pytest.approx(0.676180171388, abs=1e-9)
assert wfn[det("-+0")] == pytest.approx(0.016058887563, abs=1e-9)
wfn = factexp.compute(op, ref, algorithm='onthefly')
assert wfn[det("200")] == pytest.approx(0.733340213919, abs=1e-9)
assert wfn[det("+-0")] == pytest.approx(-0.049868863373, abs=1e-9)
assert wfn[det("002")] == pytest.approx(-0.047410073759, abs=1e-9)
assert wfn[det("020")] == pytest.approx(0.676180171388, abs=1e-9)
assert wfn[det("-+0")] == pytest.approx(0.016058887563, abs=1e-9)
def test_sparse_ci3():
import forte
import pytest
from forte import det
### Operator ordering tests ###
# test ordering: 0a+ 0b+ 0b- 0a- |2> = +|2>
op = forte.SparseOperator()
op.add_term_from_str('[0a+ 0b+ 0b- 0a-]', 1.0)
dtest = det("20")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert wfn[dtest] == pytest.approx(1.0, abs=1e-9)
# test ordering: 0a+ 0b+ 0a- 0b- |2> = -|2>
op = forte.SparseOperator()
op.add_term_from_str('[0a+ 0b+ 0a- 0b-]', 1.0, allow_reordering=True)
dtest = det("20")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert wfn[dtest] == pytest.approx(-1.0, abs=1e-9)
# test ordering: 0b+ 0a+ 0b- 0a- |2> = -|2>
op = forte.SparseOperator()
op.add_term_from_str('[0b+ 0a+ 0b- 0a-]', 1.0, allow_reordering=True)
dtest = det("20")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert wfn[dtest] == pytest.approx(-1.0, abs=1e-9)
# test ordering: 0b+ 0a+ 0a- 0b- |2> = +|2>
op = forte.SparseOperator()
op.add_term_from_str('[0b+ 0a+ 0a- 0b-]', 1.0, allow_reordering=True)
dtest = det("20")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert wfn[dtest] == pytest.approx(1.0, abs=1e-9)
# test ordering: 3a+ 4a+ 2b+ 1b- 0a- |22000> = + 3a+ 4a+ 2b+ 1b- |-2000>
# 3a+ 4a+ 2b+ 1b- 0a- |22000> = + 3a+ 4a+ 2b+ 1b- |-2000>
# = + 3a+ 4a+ 2b+ |-+000>
# = + 3a+ 4a+ |-+-00>
# = - 3a+ |-+-0+>
# = + 3a+ |-+-++>
op = forte.SparseOperator()
op.add_term_from_str('[3a+ 4a+ 2b+ 1b- 0a-]', 1.0)
ref = forte.StateVector({det("22"): 1.0})
wfn = forte.apply_operator(op, ref)
assert wfn[det("-+-++")] == pytest.approx(1.0, abs=1e-9)
op = forte.SparseOperator()
op.add_term_from_str('[0a+]', 1.0)
wfn = forte.apply_operator(op, forte.StateVector({det(""): 1.0}))
assert wfn[det("+")] == pytest.approx(1.0, abs=1e-9)
op = forte.SparseOperator()
op.add_term_from_str('[0a+ 1a+]', 1.0)
wfn = forte.apply_operator(op, forte.StateVector({det(""): 1.0}))
assert wfn[det("++")] == pytest.approx(1.0, abs=1e-9)
op = forte.SparseOperator()
op.add_term_from_str('[0a+ 1a+ 2a+]', 1.0)
wfn = forte.apply_operator(op, forte.StateVector({det(""): 1.0}))
assert wfn[det("+++")] == pytest.approx(1.0, abs=1e-9)
op = forte.SparseOperator()
op.add_term_from_str('[0a+ 1a+ 2a+ 3a+]', 1.0)
wfn = forte.apply_operator(op, forte.StateVector({det(""): 1.0}))
assert wfn[det("++++")] == pytest.approx(1.0, abs=1e-9)
op = forte.SparseOperator()
op.add_term_from_str('[0a+ 1a+ 2a+ 3a+ 4a+]', 1.0)
wfn = forte.apply_operator(op, forte.StateVector({det(""): 1.0}))
assert wfn[det("+++++")] == pytest.approx(1.0, abs=1e-9)
op = forte.SparseOperator()
op.add_term_from_str('[2a+ 0a+ 3a+ 1a+ 4a+]', 1.0, allow_reordering=True)
wfn = forte.apply_operator(op, forte.StateVector({det(""): 1.0}))
assert wfn[det("+++++")] == pytest.approx(-1.0, abs=1e-9)
op = forte.SparseOperator()
op.add_term_from_str('[0a-]', 1.0)
wfn = forte.apply_operator(op, forte.StateVector({det("22222"): 1.0}))
assert wfn[det("-2222")] == pytest.approx(1.0, abs=1e-9)
op = forte.SparseOperator()
op.add_term_from_str('[1a- 0a-]', 1.0)
wfn = forte.apply_operator(op, forte.StateVector({det("22222"): 1.0}))
assert wfn[det("--222")] == pytest.approx(1.0, abs=1e-9)
op = forte.SparseOperator()
op.add_term_from_str('[2a- 1a- 0a-]', 1.0)
wfn = forte.apply_operator(op, forte.StateVector({det("22222"): 1.0}))
assert wfn[det("---22")] == pytest.approx(1.0, abs=1e-9)
op = forte.SparseOperator()
op.add_term_from_str('[3a- 2a- 1a- 0a-]', 1.0)
wfn = forte.apply_operator(op, forte.StateVector({det("22222"): 1.0}))
assert wfn[det("----2")] == pytest.approx(1.0, abs=1e-9)
op = forte.SparseOperator()
op.add_term_from_str('[4a- 3a- 2a- 1a- 0a-]', 1.0)
wfn = forte.apply_operator(op, forte.StateVector({det("22222"): 1.0}))
assert wfn[det("-----")] == pytest.approx(1.0, abs=1e-9)
op = forte.SparseOperator()
op.add_term_from_str('[1a- 3a- 2a- 4a- 0a-]', 1.0, allow_reordering=True)
wfn = forte.apply_operator(op, forte.StateVector({det("22222"): 1.0}))
assert wfn[det("-----")] == pytest.approx(-1.0, abs=1e-9)
### Test for cases that are supposed to return zero ###
# test destroying empty orbitals: (0a+ 0b+ 0b- 0a-) |0> = 0
op = forte.SparseOperator()
op.add_term_from_str('[0a+ 0b+ 0b- 0a-]', 1.0)
dtest = det("00")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert dtest not in wfn
# test destroying empty orbitals: (0a+ 0b+ 0b- 0a-) |0> = 0
op = forte.SparseOperator()
op.add_term_from_str('[0a+ 0b+ 0b-]', 1.0)
dtest = det("00")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert dtest not in wfn
# test creating in filled orbitals: (0a+ 1a+ 0a-) |22> = 0
op = forte.SparseOperator()
op.add_term_from_str('[1a+ 0a+ 0a-]', 1.0, allow_reordering=True)
dtest = det("+")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert dtest not in wfn
# test creating in filled orbitals: (0a+ 1a+ 0a-) |22> = 0
op = forte.SparseOperator()
op.add_term_from_str('[1b+ 0a+ 0a-]', 1.0, allow_reordering=True)
dtest = det("+")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert dtest not in wfn
### Number operator tests ###
# test number operator: (0a+ 0a-) |0> = 0
op = forte.SparseOperator()
op.add_term_from_str('[0a+ 0a-]', 1.0)
dtest = det("0")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert dtest not in wfn
# test number operator: (0a+ 0a-) |+> = |+>
op = forte.SparseOperator()
op.add_term_from_str('[0a+ 0a-]', 1.0)
dtest = det("+")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert wfn[dtest] == pytest.approx(1.0, abs=1e-9)
# test number operator: (0a+ 0a-) |-> = 0
op = forte.SparseOperator()
op.add_term_from_str('[0a+ 0a-]', 1.0)
dtest = det("-")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert dtest not in wfn
# test number operator: (0a+ 0a-) |2> = |2>
op = forte.SparseOperator()
op.add_term_from_str('[0a+ 0a-]', 1.0)
dtest = det("2")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert wfn[dtest] == pytest.approx(1.0, abs=1e-9)
# test number operator: (0b+ 0b-) |0> = 0
op = forte.SparseOperator()
op.add_term_from_str('[0b+ 0b-]', 1.0)
dtest = det("0")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert dtest not in wfn
# test number operator: (0b+ 0b-) |+> = 0
op = forte.SparseOperator()
op.add_term_from_str('[0b+ 0b-]', 1.0)
dtest = det("+")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert dtest not in wfn
# test number operator: (0b+ 0b-) |-> = |->
op = forte.SparseOperator()
op.add_term_from_str('[0b+ 0b-]', 1.0)
dtest = det("-")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert wfn[dtest] == pytest.approx(1.0, abs=1e-9)
# test number operator: (0b+ 0b-) |2> = |2>
op = forte.SparseOperator()
op.add_term_from_str('[0b+ 0b-]', 1.0)
ref = forte.StateVector({det("2"): 1.0})
wfn = forte.apply_operator(op, ref)
assert wfn[det("2")] == pytest.approx(1.0, abs=1e-9)
# make sure that the number operator throws an exception: (2a+ 2a- + 2b+ 2b-) |222> = |222>
op = forte.SparseOperator()
with pytest.raises(RuntimeError):
op.add_term_from_str('[2a+ 2a-] + [2b+ 2b-]', 1.0)
### Excitation operator tests ###
# test excitation operator: (3a+ 0a-) |2200> = 3a+ |-200> = -|-20+>
op = forte.SparseOperator()
op.add_term_from_str('[3a+ 0a-]', 1.0)
dtest = det("22")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert wfn[det("-20+")] == pytest.approx(-1.0, abs=1e-9)
# test excitation operator: (0a- 3a+) |22> = 0a- |220+> = |-20+>
op = forte.SparseOperator()
op.add_term_from_str('[0a- 3a+]', 1.0, allow_reordering=True)
dtest = det("22")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert wfn[det("-20+")] == pytest.approx(1.0, abs=1e-9)
# test number operator: (3b+ 0b-) |2200> = 3b+ |+200> = |+20->
op = forte.SparseOperator()
op.add_term_from_str('[3b+ 0b-]', 1.0)
dtest = det("22")
ref = forte.StateVector({dtest: 1.0})
wfn = forte.apply_operator(op, ref)
assert wfn[det("+20-")] == pytest.approx(-1.0, abs=1e-9)