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C_fb = 0
R_hv = calibration.R_hv[df.hv_resistor.values]
C_hv = calibration.C_hv[df.hv_resistor.values]
# Solve feedback transfer function for the actuation voltage, _(i.e.,
# `V1`)_, based on the high-voltage measurements.
# Note that the transfer function definition depends on the hardware
# version.
V_actuation = compute_from_transfer_function(calibration.hw_version
.major, 'V1', V2=df.V_hv,
R1=Z, R2=R_hv, C2=C_hv,
f=df.frequency)
# Solve feedback transfer function for the expected impedance feedback
# voltage, _(i.e., `V2`)_, based on the actuation voltage, the proposed
# values for `R2` and `C2`, and the reported `C1` value from the
# feedback measurements.
# Note that the transfer function definition depends on the hardware
# version.
# __NB__ If we do not specify a value for `R1`, a symbolic value of
# infinity is used. However, in this case, we have `R1` in both the
# numerator and denominator. The result is a value of zero returned
# regardless of the values of the other arguments. We avoid this issue
# by specifying a *very large* value for `R1`.
# TODO Update comment if this works...
V_impedance = compute_from_transfer_function(calibration.hw_version
.major, 'V2',
V1=V_actuation,
C1=df.test_capacitor,
R2=R_fb, C2=C_fb,
f=df.frequency)
return df.V_fb - V_impedance
# Perform a nonlinear least-squares fit of the data.
def fit_model(p0, df, calibration):
p1, cov_x, infodict, mesg, ier = scipy.optimize.leastsq(
error, p0, args=(df, calibration), full_output=True)
p1 = np.abs(p1)
E = error(p1, df, calibration)
return p1, E, cov_x
CI = []
feedback_records = []
# Fit feedback parameters for each feedback resistor.
for i in range(len(calibration.R_fb)):
# Only include data points for the given feedback resistor (and where
# `hv_resistor` is a valid index).
df_i = df.loc[(df.fb_resistor == i)].dropna()
if df_i.shape[0] < 2:
CI.append([0, 0])
continue
# Fit the data assuming no parasitic capacitance (model 1).
p0_1 = [R_fb[i]]
p1_1, E_1, cov_x_1 = fit_model(p0_1, df_i, calibration)
df_1 = (len(E_1) - len(p0_1))
chi2_1 = np.sum(E_1 ** 2)
chi2r_1 = chi2_1 / (df_1 - 1)
# fit the data including parasitic capacitance (model 2)
p0_2 = [R_fb[i], C_fb[i]]
p1_2, E_2, cov_x_2 = fit_model(p0_2, df_i, calibration)
df_2 = (len(E_2) - len(p0_2))
chi2_2 = np.sum(E_2 ** 2)
chi2r_2 = chi2_2 / (df_2 - 1)
# do an F-test to compare the models
F = (chi2_1 - chi2_2) / chi2r_2
p_value = scipy.stats.f.cdf(F, 1, df_2-1)
# if the p_value is > 0.95, we assume that the capacitive term is
# necessary
if p_value > .95 and cov_x_2 is not None:
model = 'w/Parasitic C'
chi2r = chi2r_2
R_fb_i = p1_2[0]
C_fb_i = p1_2[1]
CI.append((100 * np.sqrt(chi2r_2 * np.diag(cov_x_2)) / p1_2))
else: # otherwise, set the capacitance to zero
model = 'w/o Parasitic C'
chi2r = chi2r_2
R_fb_i = p1_1[0]
C_fb_i = 0
if cov_x_1 is None:
cov_x_1 = [0]
CI.append((100 * np.sqrt(chi2r_1 * np.diag(cov_x_1)) /
p1_1).tolist() + [0])
feedback_records.append([int(i), model, df_i.shape[0], R_fb_i, CI[i][0],
C_fb_i, CI[i][1], F, (1e3 * np.sqrt(chi2r)),
p_value])
calibration_df = pd.DataFrame(feedback_records,
columns=['fb_resistor', 'Model', 'N', 'R_fb', 'R-CI %',
'C_fb', 'C-CI %', 'F',
'sqrt(Chi2r*sigma^2)', 'p-value'])
return calibration_df"
1439,"def apply_calibration(df, calibration_df, calibration):