def test_compare_returnc_interp1d_unc(interp_inputs):
# Compare the uncertainties computed from the sensitivities inside the
# interpolation range and directly.
uy_new_with_sensitivities = interp1d_unc(**interp_inputs)[2]
interp_inputs["returnC"] = False
uy_new_without_sensitivities = interp1d_unc(**interp_inputs)[2]
# Check that extrapolation results match up to machine epsilon.
assert_allclose(uy_new_with_sensitivities,
uy_new_without_sensitivities,
rtol=9e-15)
def interpolate_hyd(hyd_data, f):
# Interpolation and extrapolation of calibration data
hyd_interpolated = {"frequency": f}
N = len(f) // 2
# interpolate real part in selected frequency range
(
hyd_interpolated["frequency"],
hyd_interpolated["real"],
hyd_interpolated["varreal"],
Creal,
) = interp1d_unc(
f[:N],
hyd_data["frequency"],
hyd_data["real"],
hyd_data["varreal"],
bounds_error=False,
fill_value="extrapolate",
fill_unc="extrapolate",
returnC=True,
)
# interpolate imag part in selected frequency range
hyd_interpolated["imag"] = np.zeros((N, ))
hyd_interpolated["varimag"] = np.zeros((N, ))
(
hyd_interpolated["frequency"],
hyd_interpolated["imag"],
hyd_interpolated["varimag"],
Cimag,
) = interp1d_unc(
f[:N],
hyd_data["frequency"],
hyd_data["imag"],
hyd_data["varimag"],
bounds_error=False,
fill_value="extrapolate",
fill_unc="extrapolate",
returnC=True,
)
# adjustment of end points
hyd_interpolated["imag"][0] = 0 # Must be 0 by definition
hyd_interpolated["imag"][-1] = 0
hyd_interpolated["varimag"][0] = 0 # Must be 0 by definition
hyd_interpolated["varimag"][-1] = 0
## Use pseudo-interpolation for the covariances between real and imaginary parts
hyd_interpolated["cov"] = (Creal.dot(np.diag(hyd_data["cov"]))).dot(
Cimag.T)
return hyd_interpolated
def test_extrapolate_above_with_fill_value_interp1d_unc(interp_inputs):
# Deal with those cases where at least one of t_new is above the maximum of t and
# fill_value is a float, which means constant extrapolation with this value.
y_new = interp1d_unc(**interp_inputs)[1]
# Check that extrapolation works.
assert np.all(y_new[interp_inputs["t_new"] > np.max(interp_inputs["t"])] ==
interp_inputs["fill_value"])
def test_extrapolate_below_with_fill_uncs_interp1d_unc(interp_inputs):
# Deal with those cases where at least one of t_new is below the minimum of t and
# fill_unc is a tuple, which means constant extrapolation with its first element.
uy_new = interp1d_unc(**interp_inputs)[2]
# Check that extrapolation works.
assert np.all(uy_new[interp_inputs["t_new"] < np.min(interp_inputs["t"])]
== interp_inputs["fill_unc"][0])
def test_returnc_with_extrapolation_check_c_interp1d_unc(interp_inputs, ):
# Check if sensitivity computation parallel to linear interpolation and
# extrapolation with constant values works as expected regarding the shape and
# content of the sensitivity matrix.
C = interp1d_unc(**interp_inputs)[3]
# Check that C has the right shape.
assert C.shape == (len(interp_inputs["t_new"]), len(interp_inputs["t"]))
# Find interpolation range because we reuse it.
interp_range = (interp_inputs["t_new"] >= np.min(interp_inputs["t"])) | (
interp_inputs["t_new"] <= np.max(interp_inputs["t"]))
# Check if each row corresponding to an extrapolated value contains exactly one
# non-zero sensitivity.
assert np.all(np.count_nonzero(C[np.where(~interp_range)], 1) == 1)
# Check if each row corresponding to an interpolated value contains either exactly
# one or exactly two non-zero sensitivities, which are the two possible cases
# when performing Lagrangian linear interpolation.
assert np.all(
np.any(
(
np.count_nonzero(C[np.where(interp_range)], 1) == 2,
np.count_nonzero(C[np.where(interp_range)], 1) == 1,
),
0,
))
# Check if each row of sensitivities sum to one, which should hold for the
# Lagrangians and proves equality with one for extrapolation sensitivities.
assert_allclose(np.sum(C, 1), np.ones_like(interp_inputs["t_new"]))
def test_extrapolate_below_with_fill_unc_interp1d_unc(interp_inputs):
# Deal with those cases where at least one of x_new is below the minimum of x and
# fill_unc is a float, which means constant extrapolation with this value.
uy_new = interp1d_unc(**interp_inputs)[2]
# Check that extrapolation works.
assert np.all(uy_new[interp_inputs["x_new"] < np.min(interp_inputs["x"])]
== interp_inputs["fill_unc"])
def test_extrapolate_above_with_fill_uncs_interp1d_unc(interp_inputs):
# Deal with those cases where at least one of t_new is above the maximum of t and
# fill_unc is a tuple, which means constant extrapolation with its second element.
uy_new = interp1d_unc(**interp_inputs)[2]
# Check that extrapolation works.
assert np.all(uy_new[interp_inputs["t_new"] > np.max(interp_inputs["t"])]
== interp_inputs["fill_unc"][1])
def test_extrapolate_below_without_fill_value_interp1d_unc(interp_inputs):
# Deal with those cases where at least one of t_new is below the minimum of t and
# fill_value=="extrapolate", which means constant extrapolation from the boundaries.
y_new = interp1d_unc(**interp_inputs)[1]
# Check that extrapolation works, meaning in the present case, that the boundary
# value of y is taken for all t_new below the original bound.
assert np.all(y_new[interp_inputs["t_new"] < np.min(interp_inputs["t"])] ==
interp_inputs["y"][0])
def test_extrapolate_above_without_fill_unc_interp1d_unc(interp_inputs):
# Deal with those cases where at least one of t_new is above the maximum of t and
# fill_unc=="extrapolate", which means constant extrapolation from the boundaries.
uy_new = interp1d_unc(**interp_inputs)[2]
# Check that extrapolation works, meaning in the present case, that the boundary
# value of y is taken for all t_new above the original bound.
assert np.all(uy_new[interp_inputs["t_new"] > np.max(interp_inputs["t"])]
== interp_inputs["uy"][-1])
def test_returnc_with_extrapolation_check_below_bound_interp1d_unc(
interp_inputs):
# Check if extrapolation with constant values outside interpolation range and
# returning sensitivities work as expected regarding extrapolation values
# below original bound.
uy_new, C = interp1d_unc(**interp_inputs)[2:]
assert np.all(uy_new[interp_inputs["t_new"] < np.min(interp_inputs["t"])]
== interp_inputs["uy"][0])
def test_returnc_with_extrapolation_check_uy_new_above_bound_interp1d_unc(
interp_inputs, ):
# Check if extrapolation with constant values outside interpolation range and
# returning sensitivities work as expected regarding extrapolation values
# above original bound.
uy_new = interp1d_unc(**interp_inputs)[2]
assert np.all(uy_new[interp_inputs["t_new"] > np.max(interp_inputs["t"])]
== interp_inputs["uy"][-1])
def test_extrapolate_below_with_fill_values_interp1d_unc(interp_inputs):
# Deal with those cases where at least one of x_new is below the minimum of x and
# fill_value is a tuple, which means constant extrapolation with its first
# element.
y_new = interp1d_unc(**interp_inputs)[1]
# Check that extrapolation works.
assert np.all(y_new[interp_inputs["x_new"] < np.min(interp_inputs["x"])] ==
interp_inputs["fill_value"][0])
def test_linear_uy_in_interp1d_unc(n, ):
# Check for given input, if interpolated uncertainties equal 1 and
# :math:`sqrt(2) / 2`.
dt_unit = 2
dt_half = dt_unit / 2
t_new = np.arange(0, n, dt_half)
t_unit = np.arange(0, n + dt_half, dt_unit)
y = uy_unit = np.ones_like(t_unit)
uy_new = interp1d_unc(t_new, t_unit, y, uy_unit, "linear")[2]
assert np.all(uy_new[0:n:dt_unit] == 1) and np.all(
uy_new[1:n:dt_unit] == np.sqrt(2) / 2)
def test_wrong_input_lengths_call_interp1d(interp_inputs):
# Check erroneous calls with unequally long inputs.
with raises(ValueError):
interp_inputs["uy"] = np.tile(interp_inputs["uy"], 2)
interp1d_unc(**interp_inputs)
def test_value_error_for_returnc_interp1d_unc(interp_inputs):
# Check erroneous calls with returnC and wrong kind.
with raises(NotImplementedError):
interp1d_unc(**interp_inputs)
def test_usual_call_interp1d_unc(interp_inputs):
t_new, y_new, uy_new = interp1d_unc(**interp_inputs)[:]
# Check the equal dimensions of the minimum calls output.
assert len(t_new) == len(y_new) == len(uy_new)
def test_returnc_with_extrapolation_interp1d_unc(interp_inputs):
# Check if extrapolation with constant values outside interpolation range and
# returning of sensitivities is callable.
assert interp1d_unc(**interp_inputs)
def test_failing_returnc_with_extrapolation_interp1d_unc(interp_inputs):
# Since we have not implemented these cases, for now we
# check for exception being thrown.
assume(not isinstance(interp_inputs["fill_unc"], str))
with raises(NotImplementedError):
interp1d_unc(**interp_inputs)
def test_trivial_in_interp1d_unc(interp_inputs):
y_new, uy_new = interp1d_unc(**interp_inputs)[1:3]
# Check if all 'interpolated' values are present in the actual values.
assert np.all(np.isin(y_new, interp_inputs["y"]))
assert np.all(np.isin(uy_new, interp_inputs["uy"]))
def test_raise_not_implemented_yet_interp1d(interp_inputs):
# Check that not implemented versions raise exceptions.
with raises(NotImplementedError):
interp1d_unc(**interp_inputs)
def test_linear_in_interp1d_unc(interp_inputs):
y_new, uy_new = interp1d_unc(**interp_inputs)[1:3]
# Check if all interpolated values lie in the range of the original values.
assert np.all(np.min(interp_inputs["y"]) <= y_new)
assert np.all(np.max(interp_inputs["y"]) >= y_new)
def test_extrapolate_interp1d_unc(interp_inputs):
# Check that extrapolation is executable in general.
assert interp1d_unc(**interp_inputs)
def test_raise_value_error_interp1d_unc(interp_inputs):
# Check that interpolation with points outside the original domain raises
# exception if requested.
interp_inputs["bounds_error"] = True
with raises(ValueError):
interp1d_unc(**interp_inputs)
import matplotlib.pyplot as plt
import numpy as np
from PyDynamic.uncertainty.interpolate import interp1d_unc
from scipy.interpolate import interp1d
# base signal
N = 10
t = np.cumsum(0.5 * (1 + np.random.random(N)))
x = np.sin(t) # + 0.01*np.random.randn(N)
# ut = np.full_like(t, 0.05)
ux = np.full_like(x, 0.2)
# interpolate with PyDynamic
ti = np.linspace(np.min(t), np.max(t), 60)
# uti = np.full_like(ti, 0.05)
ti, xi, uxi = interp1d_unc(ti, t, x, ux, kind="cubic")
# interpolate with Monte Carlo
X_mc = []
for i in range(2000):
interp_x = interp1d(t, x + ux * np.random.randn(len(x)), kind="cubic")
xm = interp_x(ti)
X_mc.append(xm)
x_mc = np.mean(X_mc, axis=0)
ux_mc = np.std(X_mc, axis=0)
# visualize
# interpolated signal
plt.plot(ti, xi, "-or", label="interpolation PyDynamic")
plt.fill_between(ti, xi + uxi, xi - uxi, color="r", alpha=0.3)
# interpolated signal