qetpy.fitting package

Submodules

qetpy.fitting.fitting module

qetpy.fitting.fitting.ofamp(signal, template, psd, fs, withdelay=True, coupling='AC', lgcsigma=False, nconstrain=None, lgcoutsidewindow=False, integralnorm=False)

Function for calculating the optimum amplitude of a pulse in data. Supports optimum filtering with and without time delay.

Parameters:

signal : ndarray

The signal that we want to apply the optimum filter to (units should be Amps). Can be an array of traces.

template : ndarray

The pulse template to be used for the optimum filter (should be normalized beforehand).

psd : ndarray

The two-sided psd that will be used to describe the noise in the signal (in Amps^2/Hz)

fs : float

The sample rate of the data being taken (in Hz).

withdelay : bool, optional

Determines whether or not the optimum amplitude should be calculate with (True) or without (False) using a time delay. With the time delay, the pulse is assumed to be at any time in the trace. Without the time delay, the pulse is assumed to be directly in the middle of the trace. Default is True.

coupling : str, optional

String that determines if the zero frequency bin of the psd should be ignored (i.e. set to infinity) when calculating the optimum amplitude. If set to ‘AC’, then ths zero frequency bin is ignored. If set to anything else, then the zero frequency bin is kept. Default is ‘AC’.

lgcsigma : Boolean, optional

If True, the estimated optimal filter energy resolution will be calculated and returned.

nconstrain : int, NoneType, optional

The length of the window (in bins) to constrain the possible t0 values to, centered on the unshifted trigger. If left as None, then t0 is uncontrained. If nconstrain is larger than nbins, then the function sets nconstrain to nbins, as this is the maximum number of values that t0 can vary over.

lgcoutsidewindow : bool, optional

Boolean flag that is used to specify whether ofamp should look inside nconstrain or outside it. If False, ofamp will minimize the chi^2 in the bins specified by nconstrain, which is the default behavior. If True, then ofamp will minimize the chi^2 in the bins that do not contain the constrained window.

integralnorm : bool, optional

If set to True, then ofamp will normalize the template to an integral of 1, and ofamp will instead return the optimal integral in units of Coulombs. If lgcsigma is set to True, then it will be returned in units of Coulombs as well. If set to False, then the usual optimal filter amplitude will be returned (in units of Amps).

Returns:

amp : float

The optimum amplitude calculated for the trace (in Amps).

t0 : float

The time shift calculated for the pulse (in s). Set to zero if withdelay is False.

chi2 : float

The chi^2 value calculated from the optimum filter.

sigma : float, optional

The optimal filter energy resolution (in Amps)

qetpy.fitting.fitting.ofamp_pileup(signal, template, psd, fs, a1=None, t1=None, coupling='AC', nconstrain1=None, nconstrain2=None, lgcoutsidewindow=True)

Function for calculating the optimum amplitude of a pileup pulse in data. Supports inputted the values of a previously known pulse for increased computational speed, but can be used on its own.

Parameters:

signal : ndarray

The signal that we want to apply the optimum filter to (units should be Amps).

template : ndarray

The pulse template to be used for the optimum filter (should be normalized beforehand).

psd : ndarray

The two-sided psd that will be used to describe the noise in the signal (in Amps^2/Hz)

fs : float

The sample rate of the data being taken (in Hz).

a1 : float, optional

The OF amplitude (in Amps) to use for the “main” pulse, e.g. the triggered pulse. This should be calculated beforehand using ofamp. This is only used if t1 is also inputted.

t1 : float, optional

The corresponding time offset (in seconds) to use for the “main” pulse, e.g. the triggered pulse. As with a1, this should be calculated beforehand using ofamp. This is only used if a1 is also inputted.

coupling : str, optional

String that determines if the zero frequency bin of the psd should be ignored (i.e. set to infinity) when calculating the optimum amplitude. If set to ‘AC’, then ths zero frequency bin is ignored. If set to anything else, then the zero frequency bin is kept. Default is ‘AC’.

nconstrain1 : int, NoneType, optional

If t1 is left as None, this is the length of the window (in bins) to constrain the possible t1 values to for the first pulse, centered on the unshifted trigger. If left as None, then t1 is uncontrained. If nconstrain1 is larger than nbins, then the function sets nconstrain1 to nbins, as this is the maximum number of values that t1 can vary over. This is only used if a1 or t1 is not given.

nconstrain2 : int, NoneType, optional

This is the length of the window (in bins) out of which to constrain the possible t2 values to for the pileup pulse, centered on the unshifted trigger. If left as None, then t2 is uncontrained. The value of nconstrain2 should be less than nbins.

lgcoutsidewindow : bool, optional

Boolean flag that is used to specify whether ofamp_pileup should look for the pileup pulse inside the bins specified by nconstrain2 or outside them. If True, ofamp will minimize the chi^2 in the bins ouside the range specified by nconstrain2, which is the default behavior. If False, then ofamp will minimize the chi^2 in the bins inside the constrained window specified by nconstrain2.

Returns:

a1 : float

The optimum amplitude (in Amps) calculated for the first pulse that was found, which is generally the triggered pulse.

t1 : float

The time shift calculated for the first pulse that was found (in s)

a2 : float

The optimum amplitude calculated for the pileup pulse (in Amps).

t2 : float

The time shift calculated for the pileup pulse (in s)

chi2 : float

The chi^2 value calculated for the pileup optimum filter.

qetpy.fitting.fitting.ofamp_pileup_stationary(signal, template, psd, fs, coupling='AC', nconstrain=None, lgcoutsidewindow=False)

Function for calculating the optimum amplitude of a pileup pulse in data, with the assumption that the triggered pulse is centered in the trace.

Parameters:

signal : ndarray

The signal that we want to apply the optimum filter to (units should be Amps).

template : ndarray

The pulse template to be used for the optimum filter (should be normalized beforehand).

psd : ndarray

The two-sided psd that will be used to describe the noise in the signal (in Amps^2/Hz)

fs : float

The sample rate of the data being taken (in Hz).

coupling : str, optional

String that determines if the zero frequency bin of the psd should be ignored (i.e. set to infinity) when calculating the optimum amplitude. If set to ‘AC’, then ths zero frequency bin is ignored. If set to anything else, then the zero frequency bin is kept. Default is ‘AC’.

nconstrain : int, NoneType, optional

This is the length of the window (in bins) out of which to constrain the possible t2 values to for the pileup pulse, centered on the unshifted trigger. If left as None, then t2 is uncontrained. The value of nconstrain should be less than nbins.

lgcoutsidewindow : bool, optional

Boolean flag that is used to specify whether the function should look for the pileup pulse inside the bins specified by nconstrain or outside them. If True, ofamp will minimize the chi^2 in the bins ouside the range specified by nconstrain, which is the default behavior. If False, then ofamp will minimize the chi^2 in the bins inside the constrained window specified by nconstrain.

Returns:

a1 : float

The optimum amplitude (in Amps) calculated for the first pulse that was found, which is the triggered pulse.

a2 : float

The optimum amplitude calculated for the pileup pulse (in Amps).

t2 : float

The time shift calculated for the pileup pulse (in s)

chi2 : float

The reduced chi^2 value of the fit.

qetpy.fitting.fitting.chi2lowfreq(signal, template, amp, t0, psd, fs, fcutoff=10000)

Function for calculating the low frequency chi^2 of the optimum filter, given some cut off frequency. This function does not calculate the optimum amplitude - it requires that ofamp has been run, and the fit has been loaded to this function.

Parameters:

signal : ndarray

The signal that we want to calculate the low frequency chi^2 of (units should be Amps).

template : ndarray

The pulse template to be used for the low frequency chi^2 calculation (should be normalized beforehand).

amp : float

The optimum amplitude calculated for the trace (in Amps).

t0 : float

The time shift calculated for the pulse (in s).

psd : ndarray

The two-sided psd that will be used to describe the noise in the signal (in Amps^2/Hz).

fs : float

The sample rate of the data being taken (in Hz).

fcutoff : float, optional

The frequency (in Hz) that we should cut off the chi^2 when calculating the low frequency chi^2.

Returns:

chi2low : float

The low frequency chi^2 value (cut off at fcutoff) for the inputted values.

qetpy.fitting.fitting.chi2_nopulse(signal, psd, fs, coupling='AC')

Function for calculating the chi^2 of a trace with the assumption that there is no pulse.

Parameters:

signal : ndarray

The signal that we want to calculate the no pulse chi^2 of (units should be Amps).

psd : ndarray

The two-sided psd that will be used to describe the noise in the signal (in Amps^2/Hz).

fs : float

The sample rate of the data being taken (in Hz).

coupling : str, optional

String that determines if the zero frequency bin of the psd should be ignored (i.e. set to infinity) when calculating the no pulse chi^2 . If set to ‘AC’, then the zero frequency bin is ignored. If set to anything else, then the zero frequency bin is kept. Default is ‘AC’.

Returns:

chi2_0 : float

The chi^2 value for there being no pulse.

class qetpy.fitting.fitting.OFnonlin(psd, fs, template=None)

Bases: object

This class provides the user with a non-linear optimum filter to estimate the amplitude, rise time (optional), fall time, and time offset of a pulse.

Methods

calcchi2(model)	Function to calculate the reduced chi square
fit_falltimes(pulse[, lgcdouble, errscale, …])	Function to do the fit
onepole(A, tau_f, t0)	Functional form of pulse in time domain with the amplitude, fall time, and time offset allowed to float, and the rise time held constant
residuals(params)	Function ot calculate the weighted residuals to be minimized
twopole(A, tau_r, tau_f, t0)	Functional form of pulse in frequency domain with the amplitude, rise time, fall time, and time offset allowed to float.
twopoletime(A, tau_r, tau_f, t0)	Functional form of pulse in time domain with the amplitude, rise time, fall time, and time offset allowed to float

calcchi2(model)

Function to calculate the reduced chi square

Parameters:

model: ndarray

Array corresponding to pulse function (twopole or onepole) evaluated at the optimum values

Returns:

chi2: float

The reduced chi squared statistic

fit_falltimes(pulse, lgcdouble=False, errscale=1, guess=None, taurise=None, lgcfullrtn=False, lgcplot=False)

Function to do the fit

Parameters:

pulse: ndarray

Time series traces to be fit

lgcdouble: bool, optional

If False, the twopole fit is done, if True, the one pole fit it done. Note, if True, the user must provide the value of taurise.

errscale: float or int, optional

A scale factor for the psd. Ex: if fitting an average, the errscale should be set to the number of traces used in the average

guess: tuple, optional

Guess of initial values for fit, must be the same size as the model being used for fit

taurise: float, optional

The value of the rise time of the pulse if the single pole function is being use for fit

lgcfullrtn: bool, optional

If False, only the best fit parameters are returned. If True, the errors in the fit parameters, the covariance matrix, and chi squared statistic are returned as well.

lgcplot: bool, optional

If True, diagnostic plots are returned.

Returns:

variables: tuple

The best fit parameters

errors: tuple

The corresponding fit errors for the best fit parameters

cov: ndarray

The convariance matrix returned from the fit

chi2: float

The reduced chi squared statistic evaluated at the optimum point of the fit

Raises:

ValueError

if length of guess does not match the number of parameters needed in fit

onepole(A, tau_f, t0)

Functional form of pulse in time domain with the amplitude, fall time, and time offset allowed to float, and the rise time held constant

Parameters:

A: float

Amplitude of pulse

tau_f: float

Fall time of two-pole pulse

t0: float

Time offset of two pole pulse

Returns:

pulse: ndarray, complex

Array of amplitude values as a function of freuqncy

residuals(params)

Function ot calculate the weighted residuals to be minimized

Parameters:

params: tuple

Tuple containing fit parameters

Returns:

z1d: ndarray

Array containing residuals per frequency bin. The complex data is flatted into single array

twopole(A, tau_r, tau_f, t0)

Functional form of pulse in frequency domain with the amplitude, rise time, fall time, and time offset allowed to float. This is meant to be a private function

Parameters:

A: float

Amplitude of pulse

tau_r: float

Rise time of two-pole pulse

tau_f: float

Fall time of two-pole pulse

t0: float

Time offset of two pole pulse

Returns:

pulse: ndarray, complex

Array of amplitude values as a function of frequency

twopoletime(A, tau_r, tau_f, t0)

Functional form of pulse in time domain with the amplitude, rise time, fall time, and time offset allowed to float

Parameters:

A: float

Amplitude of pulse

tau_r: float

Rise time of two-pole pulse

tau_f: float

Fall time of two-pole pulse

t0: float

Time offset of two pole pulse

Returns:

pulse: ndarray

Array of amplitude values as a function of time

class qetpy.fitting.fitting.MuonTailFit(psd, fs)

Bases: object

This class provides the user with a fitting routine to estimate the thermal muon tail fall time.

Methods

calcchi2(model)	Function to calculate the chi square
fitmuontail(signal[, lgcfullrtn, errscale])	Function to do the fit
muontailfcn(A, tau)	Functional form of a thermal muon tail in time domain with the amplitude and fall time allowed to float.
residuals(params)	Function to calculate the weighted residuals to be minimized.

calcchi2(model)

Function to calculate the chi square

Parameters:

model: ndarray

Array corresponding to pulse function evaluated at the fitted values

Returns:

chi2: float

The chi squared statistic

fitmuontail(signal, lgcfullrtn=False, errscale=1)

Function to do the fit

Parameters:

signal: ndarray

Time series traces to be fit

lgcfullrtn: bool, optional

If False, only the best fit parameters are returned. If True, the errors in the fit parameters, the covariance matrix, and chi squared statistic are returned as well.

errscale: float or int, optional

A scale factor for the psd. Ex: if fitting an average, the errscale should be set to the number of traces used in the average

Returns:

variables: tuple

The best fit parameters

errors: tuple

The corresponding fit errors for the best fit parameters

cov: ndarray

The convariance matrix returned from the fit

chi2: float

The chi squared statistic evaluated at the fit

muontailfcn(A, tau)

Functional form of a thermal muon tail in time domain with the amplitude and fall time allowed to float.

Parameters:

A: float

Amplitude of pulse

tau: float

Fall time of muon tail

Returns:

pulse: ndarray

Array of amplitude values as a function of time

residuals(params)

Function to calculate the weighted residuals to be minimized.

Parameters:

params: tuple

Tuple containing fit parameters

Returns:

z1d: ndarray

Array containing residuals per frequency bin. The complex data is flatted into single array.

Module contents