laboneq_applications.analysis.fitting_helpers

This module contains helper function for experiment analyses.

cosine_oscillatory_decay(x, frequency, phase, decay_time, amplitude=1.0, oscillation_offset=0.0, exponential_offset=0.0, decay_exponent=1.0)

A function for modelling decaying oscillations such as Ramsey and Echo decay.

Parameters:

Name	Type	Description	Default
x	ArrayLike	An array of values to evaluate the function at.	required
frequency	float	The frequency of the cosine.	required
phase	float	The phase of the cosine.	required
decay_time	float	The exponential decay time.	required
amplitude	float	The amplitude of the cosine.	1.0
oscillation_offset	float	The offset of the oscillatory part of the function.	0.0
exponential_offset	float	The offset of the exponential-decay part of the function.	0.0
decay_exponent	float	Exponential decay exponent power	1.0

Returns:

Name	Type	Description
values	ArrayLike	The values of the decaying oscillation function at the values x.

cosine_oscillatory_decay_fit(x, data, param_hints=None)

Performs a fit of an exponentially decaying cosine model to data.

Parameters:

Name	Type	Description	Default
data	ArrayLike	the data to be fitted	required
x	ArrayLike	the independent variable	required
param_hints	dict[str, dict[str, float | bool | str]] | None	dictionary of guesses for the fit parameters. See the lmfit docstring for details on the form of the parameter hints dictionary: https://lmfit.github.io/lmfit-py/model.html#lmfit.model.Model.set_param_hint	None

Returns:

Type	Description
ModelResult	The lmfit result

cosine_oscillatory_fit(x, data, param_hints=None)

Performs a fit of a cosine model to data.

Parameters:

Name	Type	Description	Default
data	ArrayLike	the data to be fitted	required
x	ArrayLike	the independent variable	required
param_hints	dict | None	dictionary of guesses for the fit parameters. See the lmfit docstring for details on the form of the parameter hints dictionary: https://lmfit.github.io/lmfit-py/model.html#lmfit.model.Model.set_param_hint	None

Returns:

Type	Description
ModelResult	The lmfit result

exponential_decay_fit(x, data, param_hints=None)

Performs a fit of an exponential-decay model to data.

Parameters:

Name	Type	Description	Default
data	ArrayLike	the data to be fitted	required
x	ArrayLike	the independent variable	required
param_hints	dict[str, dict[str, float | bool | str]] | None	dictionary of guesses for the fit parameters. See the lmfit docstring for details on the form of the parameter hints dictionary: https://lmfit.github.io/lmfit-py/model.html#lmfit.model.Model.set_param_hint	None

Returns:

Type	Description
ModelResult	The lmfit result

find_oscillation_frequency_and_phase(time, data)

Extracts the frequency and phase of an oscillatory data set.

The frequency and phase are extracted using a fast-Fourier analysis.

Parameters:

Name	Type	Description	Default
data	ArrayLike	the data describing the oscillation	required
time	ArrayLike	the independent variable	required

Returns:

Type	Description
tuple[ArrayLike, ArrayLike]	the frequency and phase values

fit_data_lmfit(model, x, y, param_hints)

Performs a fit of model to the data (x,y).

Parameters:

Name	Type	Description	Default
model	Model | Callable | str	the model to fit to	required
x	ArrayLike	the independent variable	required
y	ArrayLike	the data to fit	required
param_hints	dict	dictionary of guesses for the fit parameters. See the lmfit docstring for details on the form of the parameter hints dictionary: https://lmfit.github.io/lmfit-py/model.html#lmfit.model.Model.set_param_hint	required

Returns:

Type	Description
ModelResult	the lmfit result

get_pi_pi2_xvalues_on_cos(x, frequency, phase)

Calculate the useful x-values of a cosine function.

Calculate the x-values of a cosine function of the form cos(x * frequency + phase) at which x * frequency + phase = n * pi and x * frequency + phase = n * pi + pi/2.

Only the values that are inside the interval [min(x), max(x)] are returned. Note: To achieve this, we have heuristically chosen n=+/-20 periods of the fitted cosine to make sure the entire range spanned by x. Then we use a mask to return only the pi and pi/2 values of the cosine within this range.

Parameters:

Name	Type	Description	Default
x	ArrayLike	array of x-values of the cosine function, corresponding for example to: - amplitudes in an amplitude-Rabi measurement - voltages in a resonator-spectroscopy-vs-dc-voltage measurement - phases in a dynamic-phase measurement	required
frequency	float | ArrayLike	the frequency of the cosine oscillation in angular units	required
phase	float | ArrayLike	the phase of the cosine oscillation in radians	required

the following array in the following order

Type	Description
float | ArrayLike	x-values for which cos(x * frequency + phase) = 1
float | ArrayLike	x-values for which cos(x * frequency + phase) = - 1
float | ArrayLike	x-values for which cos(x * frequency + phase) = 0 on the rising edge
float | ArrayLike	x-values for which cos(x * frequency + phase) = 0 on the falling edge

linear(x, gradient, intercept)

A function for modelling linear.

Parameters:

Name	Type	Description	Default
x	ArrayLike	An array of values to evaluate the function at.	required
gradient	float	The gradient.	required
intercept	float	The offset.	required

Returns:

Name	Type	Description
ArrayLike	ArrayLike	The values of the linear function at the times x.

linear_fit(x, data, param_hints=None)

Performs a fit of a linear model to the data.

Parameters:

Name	Type	Description	Default
data	ArrayLike	the data to be fitted	required
x	ArrayLike	the independent variable	required
param_hints	dict[str, dict[str, float | bool | str]] | None	dictionary of guesses for the fit parameters. See the lmfit docstring for details on the form of the parameter hints dictionary: https://lmfit.github.io/lmfit-py/model.html#lmfit.model.Model.set_param_hint	None

Returns:

Type	Description
ModelResult	The lmfit result

lorentzian_fit(x, data, param_hints=None)

Fit a Lorentzian model to the data as a function of sweep_points.

This function determines whether the Lorentzian structure has a peak or a dip by performing two fits with two guess values, the min and the max of the data. To determine whether there is a peak or a dip, the distance between the value at the fitted peak/dip is compared to the mean of the data array: the larger distance is the true spectroscopy signal.

Parameters:

Name	Type	Description	Default
x	ArrayLike	numpy array of the independent variable	required
data	ArrayLike	numpy array of data to fit	required
param_hints	dict[str, dict[str, float | bool | str]] | None	dict with parameter hints for the fit (see fit_data_lmfit)	None

Returns:

Type	Description
ModelResult	an instance of lmfit.model.ModelResult