def _test_Lambdify_Piecewise(Lambdify):
x = se.symbols('x')
p = se.Piecewise((-x, x < 0), (x * x * x, True))
f = Lambdify([x], [p])
arr = np.linspace(3, 7)
assert np.allclose(f(-arr).flat, arr, atol=1e-14, rtol=1e-15)
assert np.allclose(f(arr).flat, arr**3, atol=1e-14, rtol=1e-15)
def piecewise_matrix(*piecewise_vector):
# TODO testme
# FIXME support non 2d matrices?
dimensions = piecewise_vector[0][0].shape
for m, condition in piecewise_vector:
assert m.shape == dimensions
matrix = se.zeros(*dimensions)
for x in range(dimensions[0]):
for y in range(dimensions[1]):
piecewise_entry = []
for m, condition in piecewise_vector:
piecewise_entry.append([m[x, y], condition])
matrix[x, y] = se.Piecewise(*piecewise_entry)
return matrix
def __init__(
self,
duration: Union[int, ParameterExpression],
amp: Union[complex, ParameterExpression],
name: Optional[str] = None,
limit_amplitude: Optional[bool] = None,
):
"""Create new pulse instance.
Args:
duration: Pulse length in terms of the sampling period `dt`.
amp: The amplitude of the constant square pulse.
name: Display name for this pulse envelope.
limit_amplitude: If ``True``, then limit the amplitude of the
waveform to 1. The default is ``True`` and the amplitude is constrained to 1.
"""
parameters = {"amp": amp}
# Prepare symbolic expressions
_t, _amp, _duration = sym.symbols("t, amp, duration")
# Note this is implemented using Piecewise instead of just returning amp
# directly because otherwise the expression has no t dependence and sympy's
# lambdify will produce a function f that for an array t returns amp
# instead of amp * np.ones(t.shape). This does not work well with
# ParametricPulse.get_waveform().
#
# See: https://github.com/sympy/sympy/issues/5642
envelope_expr = _amp * sym.Piecewise((1, sym.And(_t >= 0, _t <= _duration)), (0, True))
valid_amp_conditions_expr = sym.Abs(_amp) <= 1.0
super().__init__(
pulse_type=self.__class__.__name__,
duration=duration,
parameters=parameters,
name=name,
limit_amplitude=limit_amplitude,
envelope=envelope_expr,
valid_amp_conditions=valid_amp_conditions_expr,
)
self.validate_parameters()
def test_custom_pulse(self):
"""Test defining a custom pulse which is not in the form of amp * F(t)."""
t, t1, t2, amp1, amp2 = sym.symbols("t, t1, t2, amp1, amp2")
envelope = sym.Piecewise((amp1, sym.And(t > t1, t < t2)),
(amp2, sym.true))
custom_pulse = SymbolicPulse(
pulse_type="Custom",
duration=100,
parameters={
"t1": 30,
"t2": 80,
"amp1": 0.1j,
"amp2": -0.1
},
envelope=envelope,
)
waveform = custom_pulse.get_waveform()
reference = np.concatenate(
[-0.1 * np.ones(30), 0.1j * np.ones(50), -0.1 * np.ones(20)])
np.testing.assert_array_almost_equal(waveform.samples, reference)
def fmod(a, b):
s = sign(a)
a = Abs(a)
b = Abs(b)
f1 = a - (b * floor(a / b))
return s * se.Piecewise([0, Abs(a - b) < SMALL_NUMBER], [f1, True])
def __init__(
self,
duration: Union[int, ParameterExpression],
amp: Union[complex, ParameterExpression],
sigma: Union[float, ParameterExpression],
width: Optional[Union[float, ParameterExpression]] = None,
risefall_sigma_ratio: Optional[Union[float, ParameterExpression]] = None,
name: Optional[str] = None,
limit_amplitude: Optional[bool] = None,
):
"""Create new pulse instance.
Args:
duration: Pulse length in terms of the sampling period `dt`.
amp: The amplitude of the Gaussian and of the square pulse.
sigma: A measure of how wide or narrow the Gaussian risefall is; see the class
docstring for more details.
width: The duration of the embedded square pulse.
risefall_sigma_ratio: The ratio of each risefall duration to sigma.
name: Display name for this pulse envelope.
limit_amplitude: If ``True``, then limit the amplitude of the
waveform to 1. The default is ``True`` and the amplitude is constrained to 1.
Raises:
PulseError: When width and risefall_sigma_ratio are both empty or both non-empty.
"""
# Convert risefall_sigma_ratio into width which is defined in OpenPulse spec
if width is None and risefall_sigma_ratio is None:
raise PulseError(
"Either the pulse width or the risefall_sigma_ratio parameter must be specified."
)
if width is not None and risefall_sigma_ratio is not None:
raise PulseError(
"Either the pulse width or the risefall_sigma_ratio parameter can be specified"
" but not both."
)
if width is None and risefall_sigma_ratio is not None:
width = duration - 2.0 * risefall_sigma_ratio * sigma
parameters = {"amp": amp, "sigma": sigma, "width": width}
# Prepare symbolic expressions
_t, _duration, _amp, _sigma, _width = sym.symbols("t, duration, amp, sigma, width")
_center = _duration / 2
_sq_t0 = _center - _width / 2
_sq_t1 = _center + _width / 2
_gaussian_ledge = _lifted_gaussian(_t, _sq_t0, -1, _sigma)
_gaussian_redge = _lifted_gaussian(_t, _sq_t1, _duration + 1, _sigma)
envelope_expr = _amp * sym.Piecewise(
(_gaussian_ledge, _t <= _sq_t0), (_gaussian_redge, _t >= _sq_t1), (1, True)
)
consts_expr = sym.And(_sigma > 0, _width >= 0, _duration >= _width)
valid_amp_conditions_expr = sym.Abs(_amp) <= 1.0
super().__init__(
pulse_type=self.__class__.__name__,
duration=duration,
parameters=parameters,
name=name,
limit_amplitude=limit_amplitude,
envelope=envelope_expr,
constraints=consts_expr,
valid_amp_conditions=valid_amp_conditions_expr,
)
self.validate_parameters()
