cait.fit

cait.fit.baseline_template_cubic(t, c0, c1, c2, c3)[source]

Template for the baseline fit, with constant linear, quadratic and cubic component.

Parameters

  • t (1D array) – The time grid.

  • c0 (float) – Constant component.

  • c1 (float) – Linear component.

  • c2 (float) – Quadratic component.

  • c3 (float) – Cubic component.

Returns

The cubic polynomial evaluated on the time grid.

Return type

1D array

cait.fit.baseline_template_quad(t, c0, c1, c2)[source]

Template for the baseline fit, with constant linear and quadratic component.

Parameters

  • t (1D array) – The time grid.

  • c0 (float) – Constant component.

  • c1 (float) – Linear component.

  • c2 (float) – Quadratic component.

Returns

The parabola evaluated on the time grid.

Return type

1D array

cait.fit.fit_pulse_shape(event, x0=None, sample_length=0.04, down=1, t0_start=- 3, t0_bounds=(- 10, 5), opt_start=False)[source]

Fits the pulse shape model to a given event and returns the fit parameters.

Parameters

  • event (1D array) – The event to fit.

  • x0 (None or 1D array) – The start values for the fit: (t0, An, At, tau_n, tau_in, tau_t).

  • sample_length (float) – The length of one sample in milliseconds.

  • down (int) – Should be power of 2, downsample rate during the fit.

  • t0_start (float) – The start value for t0.

  • t0_bounds (tuple) – Lower and upper bound for the t0 value.

  • opt_start (bool) – If activated the start values are searched with a differential evolution algorithm.

Returns

The fitted parameters.

Return type

1D array length 6

cait.fit.fit_quadratic_baseline(event)[source]

Fits a quadratic baseline template the to given event

Parameters

event – 1D array, the event to fit the baseline template

Returns

list of 3 floats (offset, linear_drift, quadratic_drift)

cait.fit.fit_trigger_efficiency(binned_energies, survived_fraction, a1_0, a0_0=1, a2_0=0.01, plot=False, title=None, xlim=None)[source]

Fit and plot the trigger efficiency.

Parameters

  • binned_energies (list of length nmbr_bins + 1) – The bin edges, in keV.

  • survived_fraction (list) – The number of survived events per bin, in keV.

  • a0_0 (float) – Start Value for estimated constant survival probability above threshold.

  • a1_0 (float) – Start Value for estimated threshold value, in keV.

  • a2_0 (float) – Start Value for estimator for the energy resolution, in keV.

  • plot (bool) – Plot the fitted function.

  • title (str) – The title for the plot.

  • xlim (tuple) – The x limits for the plot.

Returns

The fitted values a0, a1, a2.

Return type

list

>>> import cait as ai
>>> import numpy as np
>>> # create mock data
>>> X = np.random.uniform(low=0, high=1, size=10000)
>>> randoms = np.random.uniform(low=0.3, high=0.5, size=10000)
>>> surviving = np.empty(10000, dtype=bool)
>>> surviving[X < 0.3] = False
>>> surviving[X > 0.5] = True
>>> inbet = np.logical_and(X > 0.3, X < 0.5)
>>> surviving[inbet] = X[inbet] > randoms[inbet]
>>> hist, bins = np.histogram(X[surviving], bins=100, range=(0, 1))
>>> hist_all, _ = np.histogram(X, bins=100, range=(0, 1))
>>> # do the fit
>>> a0, a1, a2 = ai.fit.fit_trigger_efficiency(binned_energies=bins,
...                                            survived_fraction=hist/hist_all,
...                                            a1_0=0.4,
...                                            a0_0=0.9,
...                                            a2_0=0.1,
...                                            plot=True,
...                                            title='Trigger Efficiency',
...                                            xlim=(0.2, 0.9))
Estimated constant survival probability:  1.0029709355728647
Estimated energy threshold (keV):  0.4002443060404336
Estimated energy resolution (keV):  0.06203246371547854
../_images/efficiency.png
cait.fit.generate_standard_event(events, main_parameters, labels=None, correct_label=1, pulse_height_interval=None, left_right_cutoff=None, rise_time_interval=None, decay_time_interval=None, onset_interval=None, remove_offset=True, verb=False, scale_fit_height=True, scale_to_unit=True, sample_length=0.04, t0_start=None, opt_start=False)[source]

Calculates the standard event and fits the pulse shape model.

Parameters

  • events (2D array of shape (nmbr_events, record_length)) – The events to calculate the SEV from.

  • main_parameters (2D array of shape (nmbr_events, nmbr_mp=10)) – The main parameters of the events.

  • labels (None or 1D array of shape (nmbr_events)) – The labels of the events, if set only the correct labels are included in the SEV generation.

  • correct_label (int) – The correct label to calc SEV from, 1==events, 2==testpulses.

  • pulse_height_interval (None or 2-tuple or list) – The interval in which the PH may be to be included.

  • left_right_cutoff (None or float) – The maximal abs(R - L) baseline difference of the event.

  • rise_time_interval (None or 2-tuple or list) – The interval in ms in which the rise time may be to be included.

  • decay_time_interval (None or 2-tuple or list) – The interval in ms in which the decay time may be to be included.

  • onset_interval (None or 2-tuple or list) – The interval in which the onset time in ms may be to be included.

  • remove_offset (bool) – If True the offset of the events is removed before building mean for SEV; highly recommended!

  • verb (bool) – If True verbal feedback about the progress of the program is provided.

  • scale_fit_height (bool) – If True the fitpar of the sev are scaled to height 1 after the fit.

  • sample_length (float) – The length of one sample in milliseconds –> needed for the fit!

  • t0_start (float) – The start value for t0.

  • opt_start (bool) – If activated the starting values are searched with a differential evolution algorithm.

Returns

The calculated sev, the fit parameters.

Return type

tuple of two 1D arrays with shape (record_length, nmbr_fitpar)

cait.fit.get_noise_parameters_binned(counts, bins)[source]

Return the least squares fit parameters to the purely Gaussian noise model. You need to calculate a histogram of the maxima of the empty baselines before already, e.g. with np.hist.

Parameters

  • counts (1D array) – The counts within the bins.

  • bins (1D array) – The bin edges. This array is one number longer than the counts array.

Returns

The fitted parameters (d, sigma).

Return type

2-tuple

cait.fit.get_noise_parameters_unbinned(events, model='gauss', sigma_x0=2)[source]

Find the maximum likelihood estimators of all noise trigger model parameters in an unbinned maximum likelihood fit.

Parameters

  • events (1D array) – The array of the unbinned noise baseline maxima.

  • model (string) – The model that is used to fit the noise maxima. - ‘gauss’: Purely Gaussian noise model. - ‘pollution_exponential’: Gaussian noise model with an exponentially distributed pollution. - ‘fraction_exponential’: Gaussian-exponential mixture noise model. - ‘pollution_gauss’: Gaussian noise model with an Gaussian distributed pollution. - ‘fraction_gauss’: Gaussian mixture noise model.

  • sigma_x0 (float) – The start value for the baseline resolution.

Returns

The fitted parameters. These are different for each model and compatible with the functions gauss_noise, pollution_exponential_noise, fraction_exponential_noise and pollution_gauss_noise.

Return type

1D array

cait.fit.logistic_curve(x, A, K, C, Q, B, nu)[source]

Returns the evaluated logistics curve at x.

Parameters

  • x (scalar or 1D numpy array) – The x value or grid.

  • A (float) – A parameter of the generalized logistics curve.

  • K (float) – A parameter of the generalized logistics curve.

  • C (float) – A parameter of the generalized logistics curve.

  • Q (float) – A parameter of the generalized logistics curve.

  • B (float) – A parameter of the generalized logistics curve.

  • nu (float) – A parameter of the generalized logistics curve.

Returns

The evaluated log curve at x.

Return type

scalar or 1D numpy array

cait.fit.pulse_template(t, t0, An, At, tau_n, tau_in, tau_t)[source]

Parametric model for the pulse shape, 6 parameters.

This method was described in “(1995) F. Pröbst et. al., Model for cryogenic particle detectors with superconducting phase transition thermometers.”

Parameters

  • t – 1D array, the time grid; attention, this needs to be provided in compatible units with the fit parameters!

  • t0 (float) – The pulse onset time.

  • An (float) – Amplitude of the first nonthermal pulse component.

  • At (float) – Amplitude of the thermal pulse component.

  • tau_n (float) – Parameter for decay 1. comp and rise 2. comp.

  • tau_in (float) – Parameter for rise 1. comp.

  • tau_t (float) – Parameter for decay 2. comp.

Returns

The pulse model evaluated on the time grid.

Return type

1D array

class cait.fit.sev_fit_template(pm_par, t, down=1, t0_bounds=(- 20, 20), truncation_level=None, interval_restriction_factor=None, saturation_pars=None)[source]

Bases: object

Class to store pulse fit models for individual detectors.

This method was described in “F. Reindl, Exploring Light Dark Matter With CRESST-II Low-Threshold Detector”, available via http://mediatum.ub.tum.de/?id=1294132 (accessed on the 9.7.2021).

Parameters

  • par (1D array with size 6) – 1D array with size 6, the fit parameter of the sev (t0, An, At, tau_n, tau_in, tau_t).

  • t (1D array) – The time grid on which the pulse shape model is evaluated.

  • down (int) – Power of 2, the downsample rate of the event for fitting.

  • t0_bounds (tuple) – The lower and upper bounds for the t0 value.

  • truncation_level (float) – All values above this are excluded from the fit.

  • interval_restriction_factor (float) – Value between 0 and 1, the inverval of the event is restricted around 1/4 by this factor.

  • saturation_pars – The fit parameter of the saturation curve (A, K, C, Q, B, nu).

Rtype saturation_pars

1D array with size 6

fit_cubic(pars)[source]

Calculates the standard event fit parameters with a cubic baseline model.

Parameters

pars (list of (1D array, float, float)) – The event to fit, the fixed onset value, a start value for the onset.

Returns

The sev fit parameters.

Return type

1D array of length 6

sef(h, t0, a0)[source]

Standard Event Model with Flat Baseline.

Parameters

  • h (float) – Height of pulse shape.

  • t0 (float) – Onset of pulse shape.

  • a0 (float) – Offset of the baseline.

Returns

The pulse model evaluated on the time grid.

Return type

1D array

sel(h, t0, a0, a1)[source]

Standard Event Model with Linear Baseline.

Parameters

  • h (float) – Height of pulse shape.

  • t0 (float) – Onset of pulse shape.

  • a0 (float) – Offset of the baseline.

  • a1 (float) – Linear drift component of the baseline.

Returns

The pulse model evaluated on the time grid.

Return type

1D array

seq(h, t0, a0, a1, a2)[source]

Standard Event Model with Quadradtic Baseline.

Parameters

  • h (float) – Height of pulse shape.

  • t0 (float) – Onset of pulse shape.

  • a0 (float) – Offset of the baseline.

  • a1 (float) – Linear drift component of the baseline.

  • a2 (float) – Quadratic drift component of the baseline.

Returns

The pulse model evaluated on the time grid.

Return type

1D array

cait.fit.threshold_model(x, a0, a1, a2)[source]

Fit model for the threshold

Parameters

  • x (array) – The grid on which the model is evaluated.

  • a0 (float) – Estimated constant survival probability above threshold.

  • a1 (float) – Estimated threshold value.

  • a2 (float) – Estimator for the energy resolution.

Returns

The evaluated error function

Return type

array