Routines to compute the background from an array of timestamps. This module
is normally imported as bg
when fretbursts is imported.
The important functions are exp_fit()
and exp_cdf_fit()
that
provide two (fast) algorithms to estimate the background without binning.
These functions are not usually called directly but passed to
Data.calc_bg()
to compute the background of a measurement.
See also exp_hist_fit()
for background estimation using an histogram fit.
fretbursts.background.
exp_fit
(ph, tail_min_us=None, clk_p=1.25e08, error_metrics=None)¶Return a background rate using the MLE of mean waitingtimes.
Compute the background rate, selecting waitingtimes (delays) larger than a minimum threshold.
This function performs a Maximum Likelihood (ML) fit. For exponentiallydistributed waitingtimes this is the empirical mean.
Parameters: 


Returns:  2Tuple – Estimated background rate in cps, and a “quality of fit” index (the lower the better) according to the chosen metric. If error_metrics==None, the returned “quality of fit” is None. 
See also
fretbursts.background.
exp_cdf_fit
(ph, tail_min_us=None, clk_p=1.25e08, error_metrics=None)¶Return a background rate fitting the empirical CDF of waitingtimes.
Compute the background rate, selecting waitingtimes (delays) larger than a minimum threshold.
This function performs a least square fit of an exponential Cumulative Distribution Function (CDF) to the empirical CDF of waitingtimes.
Parameters: 


Returns:  2Tuple – Estimated background rate in cps, and a “quality of fit” index (the lower the better) according to the chosen metric. If error_metrics==None, the returned “quality of fit” is None. 
See also
fretbursts.background.
exp_hist_fit
(ph, tail_min_us, binw=5e05, clk_p=1.25e08, weights='hist_counts', error_metrics=None)¶Compute background rate with WLS histogram fit of waitingtimes.
Compute the background rate, selecting waitingtimes (delays) larger than a minimum threshold.
This function performs a Weighed Least Squares (WLS) fit of the histogram of waiting times to an exponential decay.
Parameters: 


Returns:  2Tuple – Estimated background rate in cps, and a “quality of fit” index (the lower the better) according to the chosen metric. If error_metrics==None, the returned “quality of fit” is None. 
See also
Generic functions to fit exponential populations.
These functions can be used directly, or, in a typical FRETBursts workflow they are passed to higher level methods.
See also:
fretbursts.fit.exp_fitting.
expon_fit
(s, s_min=0, offset=0.5, calc_residuals=True)¶Fit sample s
to an exponential distribution using the ML estimator.
This function computes the rate (Lambda) using the maximum likelihood (ML) estimator of the mean waitingtime (Tau), that for an exponentially distributed sample is the samplemean.
Parameters: 


Returns:  A 4tuple of the fitted rate (1/lifetime), residuals array, residuals xaxis array, sample size after threshold. 
fretbursts.fit.exp_fitting.
expon_fit_cdf
(s, s_min=0, offset=0.5, calc_residuals=True)¶Fit of an exponential model to the empirical CDF of s
.
This function computes the rate (Lambda) fitting a line (linear regression) to the log of the empirical CDF.
Parameters: 


Returns:  A 4tuple of the fitted rate (1/lifetime), residuals array, residuals xaxis array, sample size after threshold. 
fretbursts.fit.exp_fitting.
expon_fit_hist
(s, bins, s_min=0, weights=None, offset=0.5, calc_residuals=True)¶Fit of an exponential model to the histogram of s
using least squares.
Parameters: 


Returns:  A 4tuple of the fitted rate (1/lifetime), residuals array, residuals xaxis array, sample size after threshold. 
fretbursts.fit.exp_fitting.
get_ecdf
(s, offset=0.5)¶Return arrays (x, y) for the empirical CDF curve of sample s
.
See the code for more info (is a oneliner!).
Parameters: 


Returns:  (x, y) (tuple of arrays) – the x and y values of the empirical CDF 
fretbursts.fit.exp_fitting.
get_residuals
(s, tau_fit, offset=0.5)¶Returns residuals of sample s
CDF vs an exponential CDF.
Parameters: 


Returns:  residuals (array) – residuals of empirical CDF compared with analytical
CDF with time constant 