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Fix second order integral regression #117

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Merged
thangleiter merged 2 commits into from
Mar 1, 2026
Merged

Fix second order integral regression #117

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594371c
Add failing test for limiting case
thangleiter Feb 28, 2026
f24933c
Fix second order integral limiting cases
thangleiter Feb 28, 2026
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56 changes: 20 additions & 36 deletions filter_functions/numeric.py
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Original file line number Diff line number Diff line change
Expand Up @@ -170,7 +170,7 @@ def _first_order_integral(E: ndarray, eigvals: ndarray, dt: float,
def _second_order_integral(E: ndarray, eigvals: ndarray, dt: float,
int_buf: ndarray, frc_bufs: Tuple[ndarray, ndarray],
dE_bufs: Tuple[ndarray, ndarray, ndarray],
msk_bufs: Tuple[ndarray, ndarray, ndarray, ndarray]) -> ndarray:
msk_bufs: Tuple[ndarray, ndarray]) -> ndarray:
r"""Calculate the nested integral of second order Magnus expansion.

The integral is evaluated as
Expand Down Expand Up @@ -200,32 +200,21 @@ def _second_order_integral(E: ndarray, eigvals: ndarray, dt: float,
# frc_buf1 has shape (len(E), *dE.shape), frc_buf2 has shape dE.shape*2
frc_buf1, frc_buf2 = frc_bufs
dEdE, EdE, dEE = dE_bufs
mask_nE_dE_dE, mask_nE_ndE_dE, mask_nE_dE_ndE, mask_nEdE_ndEE = msk_bufs
mask_nEdE_dEE, mask_nEdE_ndEE = msk_bufs

dE = np.subtract.outer(eigvals, eigvals)
dEdE = np.add.outer(dE, dE, out=dEdE)
EdE = np.add.outer(E, dE, out=EdE)
dEE = np.add.outer(-E, dE, out=dEE)

mask_E = E != 0
mask_dE = dE != 0
mask_dEE = dEE != 0
mask_EdE = EdE != 0
mask_dEdE = dEdE != 0
mask_dE_dE = mask_dE[..., None, None] & mask_dE
mask_ndE_dE = ~mask_dE[..., None, None] & mask_dE
mask_dE_ndE = mask_dE[..., None, None] & ~mask_dE
mask_ndE_ndE = ~mask_dE[..., None, None] & ~mask_dE
mask_nE_dE_dE = np.logical_and(~mask_E[:, None, None, None, None], mask_dE_dE,
out=mask_nE_dE_dE)
mask_nE_ndE_dE = np.logical_and(~mask_E[:, None, None, None, None], mask_ndE_dE,
out=mask_nE_ndE_dE)
mask_nE_dE_ndE = np.logical_and(~mask_E[:, None, None, None, None], mask_dE_ndE,
out=mask_nE_dE_ndE)
mask_nEdE_ndEE = np.logical_and(~mask_E[:, None, None, None, None], mask_ndE_ndE,
out=mask_nEdE_ndEE)
mask_EdE_dEE = np.broadcast_to(mask_EdE[:, None, None], int_buf.shape)
mask_EdE = np.broadcast_to((EdE != 0)[:, None, None], int_buf.shape)
mask_nEdE_dEE = np.logical_and(~mask_EdE, mask_dEE[..., None, None], out=mask_nEdE_dEE)
mask_nEdE_ndEE = np.logical_and(~mask_EdE, ~mask_dEE[..., None, None], out=mask_nEdE_ndEE)

# ω + Ω_mn != 0
# This buffer holds the term (exp(Ω_ij - ω) - 1)/(Ω_ij - ω), which we reuse later.
frc_buf1 = util.cexpm1(dEE*dt, where=mask_dEE, out=frc_buf1)
frc_buf1 = np.divide(frc_buf1, dEE, where=mask_dEE, out=frc_buf1)
frc_buf1[~mask_dEE] = 1j*dt
Expand All @@ -235,23 +224,18 @@ def _second_order_integral(E: ndarray, eigvals: ndarray, dt: float,
frc_buf2[~mask_dEdE] = 1j*dt

int_buf = np.subtract(frc_buf1[..., None, None], frc_buf2[None, ...],
out=int_buf, where=mask_EdE_dEE)
int_buf = np.divide(int_buf, EdE[:, None, None], out=int_buf, where=mask_EdE_dEE)

# Limiting cases for ω -> 0
dEt = dE*dt
# Ω_ij == 0, Ω_mn != 0
int_buf = np.divide(1j*dt - np.divide(util.cexpm1(dEt), dE, where=mask_dE), dE,
where=mask_nE_ndE_dE, out=int_buf)
# Ω_ij != 0, Ω_mn == 0
int_buf = np.divide((np.divide(util.cexpm1(dEt), dE, where=mask_dE)
- 1j*dt*util.cexp(dEt))[..., None, None],
dE[..., None, None], where=mask_nE_dE_ndE, out=int_buf)
# Ω_ij != 0, Ω_mn != 0
int_buf = np.subtract(np.divide(util.cexpm1(dEt), dE, where=mask_dE)[..., None, None],
frc_buf2, where=mask_nE_dE_dE, out=int_buf)
int_buf = np.divide(int_buf, dE, where=mask_nE_dE_dE, out=int_buf)
# Ω_ij == 0, Ω_mn == 0
out=int_buf, where=mask_EdE)
int_buf = np.divide(int_buf, EdE[:, None, None], out=int_buf, where=mask_EdE)

# Limiting cases
# ω + Ω_mn = 0, Ω_ij - ω != 0
frc_buf1 = np.subtract(frc_buf1, 1j*dt*util.cexp(dEE*dt, where=mask_dEE),
where=mask_dEE, out=frc_buf1)
frc_buf1 = np.divide(frc_buf1, dEE, where=mask_dEE, out=frc_buf1)
int_buf[mask_nEdE_dEE] = np.broadcast_to(frc_buf1[..., None, None], int_buf.shape)[
mask_nEdE_dEE
]
# ω + Ω_mn = 0, Ω_ij - ω = 0
int_buf[mask_nEdE_ndEE] = dt**2 / 2
return int_buf

Expand Down Expand Up @@ -1586,7 +1570,7 @@ def calculate_second_order_filter_function_from_scratch(
np.empty((n_omega, d, d), dtype=float),
np.empty((n_omega, d, d), dtype=float))
frc_bufs = (np.empty((n_omega, d, d), dtype=complex), np.empty((d, d, d, d), dtype=complex))
msk_bufs = np.empty((4, n_omega, d, d, d, d), dtype=bool)
msk_bufs = np.empty((2, n_omega, d, d, d, d), dtype=bool)
n_opers_basis_buf = np.empty((n_nops, n_basis, d, d), dtype=complex)
complete_steps = np.zeros((n_nops, n_nops, n_basis, n_basis, n_omega), dtype=complex)
incomplete_steps = np.zeros_like(complete_steps)
Expand Down
18 changes: 17 additions & 1 deletion tests/test_precision.py
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Original file line number Diff line number Diff line change
Expand Up @@ -54,7 +54,7 @@ def _get_integrals_second_order(d, E, eigval, dt, t0):
frc_bufs = (np.empty((len(E), d, d), dtype=complex),
np.empty((d, d, d, d), dtype=complex))
int_buf = np.empty((len(E), d, d, d, d), dtype=complex)
msk_bufs = np.empty((4, len(E), d, d, d, d), dtype=bool)
msk_bufs = np.empty((2, len(E), d, d, d, d), dtype=bool)
tspace = np.linspace(0, dt, 1001) + t0
dE = np.subtract.outer(eigval, eigval)

Expand Down Expand Up @@ -492,6 +492,22 @@ def test_integration(self):
integral, integral_numeric = _get_integrals_second_order(d, E, eigval, dt, t)
self.assertArrayAlmostEqual(integral, integral_numeric, atol=1e-4)

def test_integration_edge_cases(self):
pulse = testutil.rand_pulse_sequence(testutil.rng.integers(2, 10),
testutil.rng.integers(1, 5))
for i, (eigval, dt, t) in enumerate(zip(pulse.eigvals, pulse.dt, pulse.t)):
# \Omega_ij = \omega or \Omega_mn = -\omega
omega = np.repeat(testutil.rng.choice([-1, 1])
* np.diff(testutil.rng.choice(eigval, 2, replace=False)),
3)
omega[0] -= 1e-10
omega[2] += 1e-10
integral, integral_numeric = _get_integrals_first_order(pulse.d, omega, eigval, dt, t)
self.assertArrayAlmostEqual(integral, integral_numeric, atol=1e-4)

integral, integral_numeric = _get_integrals_second_order(pulse.d, omega, eigval, dt, t)
self.assertArrayAlmostEqual(integral, integral_numeric, atol=1e-4)

def test_infidelity(self):
"""Benchmark infidelity results against previous version's results"""
rng = np.random.default_rng(seed=123456789)
Expand Down
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