#include <cmath>
#include <numeric>
#include <iostream>
#include <vector>
#include <algorithm>
#include <string.h>

Functions
void	rescale (double fit, double decay, double *scale, int start, int stop)
	Scale model function to the data (old version)

void	rescale_w (double fit, double decay, double w_sq, double scale, int start, int stop)
	Scale model function to the data (with weights)

void	rescale_w_bg (double fit, double decay, double w_sq, double bg, double scale, int start, int stop)
	Scale the model function to the data considering weights and background.

void	fconv (double fit, double x, double *lamp, int numexp, int start, int stop, double dt=0.05)
	Convolve lifetime spectrum with instrument response (fast convolution, low repetition rate)

void	fconv_avx (double fit, double x, double *lamp, int numexp, int start, int stop, double dt=0.05)
	Convolve lifetime spectrum with instrument response (fast convolution, AVX optimized for large lifetime spectra)

void	fconv_per (double fit, double x, double *lamp, int numexp, int start, int stop, int n_points, double period, double dt=0.05)
	Convolve lifetime spectrum with instrument response (fast convolution, high repetition rate)

void	fconv_per_avx (double fit, double x, double *lamp, int numexp, int start, int stop, int n_points, double period, double dt=0.05)
	Convolve lifetime spectrum with instrument response (fast convolution, high repetition rate), AVX optimized version.

void	fconv_per_cs (double fit, double x, double *lamp, int numexp, int stop, int n_points, double period, int conv_stop, double dt)
	Convolve lifetime spectrum - fast convolution, high repetition rate, with convolution stop.

void	fconv_ref (double fit, double x, double *lamp, int numexp, int start, int stop, double tauref, double dt=0.05)
	Convolve lifetime spectrum - fast convolution with reference compound decay.

void	sconv (double fit, double p, double *lamp, int start, int stop)
	Convolve fluorescence decay curve with irf.

void	shift_lamp (double lampsh, double lamp, double ts, int n_points, double out_value=0.0)
	shift instrumnet response function

void	add_pile_up_to_model (double model, int n_model, double data, int n_data, double repetition_rate, double instrument_dead_time, double measurement_time, std::string pile_up_model="coates", int start=0, int stop=-1)
	Add a pile-up distortion to the model function.

void	discriminate_small_amplitudes (double *lifetime_spectrum, int n_lifetime_spectrum, double amplitude_threshold)
	Threshold the amplitudes in the interleaved lifetime spectrum.

void	fconv_per_cs_time_axis (double model, int n_model, double time_axis, int n_time_axis, double irf, int n_irf, double lifetime_spectrum, int n_lifetime_spectrum, int convolution_start=0, int convolution_stop=-1, double period=100.0)
	Compute the fluorescence decay for a lifetime spectrum and an instrument response function considering periodic excitation.

void	fconv_cs_time_axis (double inplace_output, int n_output, double time_axis, int n_time_axis, double instrument_response_function, int n_instrument_response_function, double lifetime_spectrum, int n_lifetime_spectrum, int convolution_start=0, int convolution_stop=-1)
	Compute the fluorescence decay for a lifetime spectrum and an instrument response function.

Function Documentation

◆ add_pile_up_to_model()

void add_pile_up_to_model	(	double *	model,
		int	n_model,
		double *	data,
		int	n_data,
		double	repetition_rate,
		double	instrument_dead_time,
		double	measurement_time,
		std::string	pile_up_model = "coates",
		int	start = 0,
		int	stop = -1 )

Add a pile-up distortion to the model function.

This function adds a pile up distortion to a model fluorescence decay. The model used to compute the pile-up distortion follows the description of Coates (1968, eq. 2 and eq. 4)

Reference: Coates, P.: The correction for photonpile-up in the measurement of radiative lifetimes. J. Phys. E: Sci. Instrum. 1(8), 878–879 (1968)

Parameters

model[in,out]	The array containing the model function
n_model[in]	Number of elements in the model array
data[in]	The array containing the experimental decay
n_data[in]	number of elements in experimental decay
repetition_rate[in]	The repetition-rate (excitation rate) in MHz
instrument_dead_time[in]	The overall dead-time of the detection system in nanoseconds
measurement_time[in]	The measurement time in seconds
pile_up_model[in]	The model used to compute the pile up distortion.
start	Start index for pile up
stop	Stop index for pile up (default "coates")

◆ discriminate_small_amplitudes()

void discriminate_small_amplitudes	(	double *	lifetime_spectrum,
		int	n_lifetime_spectrum,
		double	amplitude_threshold )

Threshold the amplitudes in the interleaved lifetime spectrum.

Amplitudes with absolute values smaller than the specified threshold are set to zero.

Parameters

lifetime_spectrum	[in,out] Interleaved lifetime spectrum (amplitude, lifetime).
n_lifetime_spectrum	[in] Number of elements in the lifetime spectrum.
amplitude_threshold	[in] Threshold value for amplitude discrimination.

◆ fconv()

void fconv	(	double *	fit,
		double *	x,
		double *	lamp,
		int	numexp,
		int	start,
		int	stop,
		double	dt = 0.05 )

Convolve lifetime spectrum with instrument response (fast convolution, low repetition rate)

This function computes the convolution of a lifetime spectrum (a set of lifetimes with corresponding amplitudes) with a instrument response function (irf). This function does not consider periodic excitation and is suited for experiments at low repetition rate.

Parameters

fit[out]	model function. The convoluted decay is written to this array
x[in]	lifetime spectrum (amplitude1, lifetime1, amplitude2, lifetime2, ...)
lamp[in]	instrument response function
numexp[in]	number of fluorescence lifetimes
start[in]	start micro time index for convolution (not used)
stop[in]	stop micro time index for convolution.
dt[in]	time difference between two micro time channels

◆ fconv_avx()

void fconv_avx	(	double *	fit,
		double *	x,
		double *	lamp,
		int	numexp,
		int	start,
		int	stop,
		double	dt = 0.05 )

Convolve lifetime spectrum with instrument response (fast convolution, AVX optimized for large lifetime spectra)

This function is a modification of fconv for large lifetime spectra. The lifetime spectrum is processed by AVX intrinsics. Four lifetimes are convolved at once. Spectra with lifetimes that are not multiple of four are zero padded.

Parameters

fit
x
lamp
numexp
start
stop
n_points
dt

◆ fconv_cs_time_axis()

void fconv_cs_time_axis	(	double *	inplace_output,
		int	n_output,
		double *	time_axis,
		int	n_time_axis,
		double *	instrument_response_function,
		int	n_instrument_response_function,
		double *	lifetime_spectrum,
		int	n_lifetime_spectrum,
		int	convolution_start = 0,
		int	convolution_stop = -1 )

Compute the fluorescence decay for a lifetime spectrum and an instrument response function.

Fills the pre-allocated output array inplace_output with a fluorescence intensity decay defined by a set of fluorescence lifetimes specified in the lifetime_spectrum parameter. The fluorescence decay is convolved (non-periodically) with an instrumental response function defined by instrument_response_function.

This function calculates a fluorescence intensity decay model that is convolved with an instrument response function (IRF). The fluorescence intensity decay model is specified by its fluorescence lifetime spectrum, represented by an interleaved array containing fluorescence lifetimes with corresponding amplitudes.

The convolution supports unevenly spaced time axes.

Parameters

inplace_output	[in,out] In-place output array that is filled with the values of the computed fluorescence intensity decay model.
n_output	[in] Number of elements in the output array.
time_axis	[in] Time-axis of the fluorescence intensity decay model.
n_time_axis	[in] Length of the time axis.
instrument_response_function	[in] Instrument response function array.
n_instrument_response_function	[in] Length of the instrument response function array.
lifetime_spectrum	[in] Interleaved array of amplitudes and fluorescence lifetimes in the form (amplitude, lifetime, amplitude, lifetime, ...).
n_lifetime_spectrum	[in] Number of elements in the lifetime spectrum.
convolution_start	[in] Start channel of convolution (position in array of IRF).
convolution_stop	[in] Convolution stop channel (the index on the time-axis).

◆ fconv_per()

void fconv_per	(	double *	fit,
		double *	x,
		double *	lamp,
		int	numexp,
		int	start,
		int	stop,
		int	n_points,
		double	period,
		double	dt = 0.05 )

Convolve lifetime spectrum with instrument response (fast convolution, high repetition rate)

This function computes the convolution of a lifetime spectrum (a set of lifetimes with corresponding amplitudes) with a instrument response function (irf). This function does consider periodic excitation and is suited for experiments at high repetition rate.

Parameters

fit[out]	model function. The convoluted decay is written to this array
x[in]	lifetime spectrum (amplitude1, lifetime1, amplitude2, lifetime2, ...)
lamp[in]	instrument response function
numexp[in]	number of fluorescence lifetimes
start[in]	start micro time index for convolution (not used)
stop[in]	stop micro time index for convolution.
n_points	number of points in the model function.
period	excitation period in units of the fluorescence lifetimes (typically nanoseconds)
dt[in]	time difference between two micro time channels

◆ fconv_per_avx()

void fconv_per_avx	(	double *	fit,
		double *	x,
		double *	lamp,
		int	numexp,
		int	start,
		int	stop,
		int	n_points,
		double	period,
		double	dt = 0.05 )

Convolve lifetime spectrum with instrument response (fast convolution, high repetition rate), AVX optimized version.

This function computes the convolution of a lifetime spectrum (a set of lifetimes with corresponding amplitudes) with a instrument response function (irf). This function does consider periodic excitation and is suited for experiments at high repetition rate.

Parameters

fit[out]	model function. The convoluted decay is written to this array
x[in]	lifetime spectrum (amplitude1, lifetime1, amplitude2, lifetime2, ...)
lamp[in]	instrument response function
numexp[in]	number of fluorescence lifetimes
start[in]	start micro time index for convolution (not used)
stop[in]	stop micro time index for convolution.
n_points	number of points in the model function.
period	excitation period in units of the fluorescence lifetimes (typically nanoseconds)
dt[in]	time difference between two micro time channels

◆ fconv_per_cs()

void fconv_per_cs	(	double *	fit,
		double *	x,
		double *	lamp,
		int	numexp,
		int	stop,
		int	n_points,
		double	period,
		int	conv_stop,
		double	dt )

Convolve lifetime spectrum - fast convolution, high repetition rate, with convolution stop.

fast convolution, high repetition rate, with convolution stop for Paris

Parameters

fit[out]	model function. The convoluted decay is written to this array
x[in]	lifetime spectrum (amplitude1, lifetime1, amplitude2, lifetime2, ...)
lamp[in]	instrument response function
numexp[in]	number of fluorescence lifetimes
stop[in]	stop micro time index for convolution.
n_points	number of points in the model function.
period	excitation period in units of the fluorescence lifetimes (typically nanoseconds)
conv_stop	convolution stop micro channel number
dt[in]	time difference between two micro time channels

◆ fconv_per_cs_time_axis()

void fconv_per_cs_time_axis	(	double *	model,
		int	n_model,
		double *	time_axis,
		int	n_time_axis,
		double *	irf,
		int	n_irf,
		double *	lifetime_spectrum,
		int	n_lifetime_spectrum,
		int	convolution_start = 0,
		int	convolution_stop = -1,
		double	period = 100.0 )

Compute the fluorescence decay for a lifetime spectrum and an instrument response function considering periodic excitation.

Fills the pre-allocated output array model with a fluorescence intensity decay defined by a set of fluorescence lifetimes specified in the lifetime_spectrum parameter. The fluorescence decay is convolved (non-periodically) with an instrumental response function defined by irf.

This function calculates a fluorescence intensity model that is convolved with an instrument response function (IRF). The fluorescence intensity model is specified by its fluorescence lifetime spectrum, represented by an interleaved array containing fluorescence lifetimes with corresponding amplitudes.

This convolution only works with evenly linear spaced time axes.

Parameters

model	[in,out] In-place output array that is filled with the values of the computed fluorescence intensity decay model.
n_model	[in] Number of elements in the output array.
time_axis	[in] Time-axis of the model.
n_time_axis	[in] Length of the time axis.
irf	[in] Instrument response function array.
n_irf	[in] Length of the instrument response function array.
lifetime_spectrum	[in] Interleaved array of amplitudes and fluorescence lifetimes in the form (amplitude, lifetime, amplitude, lifetime, ...).
n_lifetime_spectrum	[in] Number of elements in the lifetime spectrum.
convolution_start	[in] Start channel of convolution (position in array of IRF).
convolution_stop	[in] Convolution stop channel (the index on the time-axis).
period	[in] Period of repetition in units of the lifetime (usually, nano-seconds). Default value is 100.0.

◆ fconv_ref()

void fconv_ref	(	double *	fit,
		double *	x,
		double *	lamp,
		int	numexp,
		int	start,
		int	stop,
		double	tauref,
		double	dt = 0.05 )

Convolve lifetime spectrum - fast convolution with reference compound decay.

This function convolves a set of fluorescence lifetimes and with associated amplitudes with an instrument response function. The provided amplitudes are scaled prior to the convolution by area using a reference fluorescence lifetime. The amplitudes are computed by

amplitude_corrected = a * ( 1 /tauref - 1 / tau)

where a and tau are provided amplitudes.

Parameters

fit[out]	model function. The convoluted decay is written to this array
x[in]	lifetime spectrum (amplitude1, lifetime1, amplitude2, lifetime2, ...)
lamp[in]	instrument response function
numexp[in]	number of fluorescence lifetimes
start[in]	start micro time index for convolution (not used)
stop[in]	stop micro time index for convolution.
tauref	a reference lifetime used to rescale the amplitudes of the fluorescence lifetime spectrum
dt[in]	time difference between two micro time channels

◆ rescale()

void rescale	(	double *	fit,
		double *	decay,
		double *	scale,
		int	start,
		int	stop )

Scale model function to the data (old version)

This function rescales the model function (fit) to the data by the number of photons between a start and a stop micro time counting channel. The number of photons between start and stop are counted and the model function is scaled to match the data by area.

This rescaling function does not consider the noise in the data when rescaling the model.

Parameters

fit[in,out]	model function that is scaled (modified in-place)
decay[in]	the experimental data to which the model function is scaled
scale[out]	the scaling parameter (the factor) by which the model function is multiplied.
start[in]	The start micro time channel
stop[in]	The stop micro time channel

◆ rescale_w()

void rescale_w	(	double *	fit,
		double *	decay,
		double *	w_sq,
		double *	scale,
		int	start,
		int	stop )

Scale model function to the data (with weights)

This function rescales the model function (fit) to the data by the number of photons between a start and a stop micro time counting channel. The number of photons between start and stop are counted and the model function is scaled to match the data by area considering the noise of the data.

The scaling factor is computed by:

scale = sum(fit*decay/w^2)/sum(fit^2/w^2)

Parameters

fit[in,out]	model function that is scaled (modified in-place)
decay[in]	the experimental data to which the model function is scaled
w_sq[in]	squared weights of the data.
scale[out]	the scaling parameter (the factor) by which the model function is multiplied.
start[in]	The start micro time channel
stop[in]	The stop micro time channel

◆ rescale_w_bg()

void rescale_w_bg	(	double *	fit,
		double *	decay,
		double *	w_sq,
		double	bg,
		double *	scale,
		int	start,
		int	stop )

Scale the model function to the data considering weights and background.

This function scales the model function (fit) to the data by counting the number of photons between a start and a stop micro time counting channel. The number of photons between start and stop is counted, and the model function is scaled to match the data by area, considering the noise of the data and a constant offset of the data.

The scaling parameter (scale) is calculated using the formula: $\text{scale} = \frac{\sum (\text{fit} \cdot (\text{decay} - \text{bg}) / w^2)}{\sum (\text{fit}^2 / w^2)}$

Parameters

fit	[in,out] Model function that is scaled (modified in-place).
decay	[in] Experimental data to which the model function is scaled.
w_sq	[in] Squared weights of the data.
bg	[in] Constant background of the data.
scale	[out] The scaling parameter (the factor) by which the model function is multiplied.
start	[in] The start micro time channel.
stop	[in] The stop micro time channel.

◆ sconv()

void sconv	(	double *	fit,
		double *	p,
		double *	lamp,
		int	start,
		int	stop )

Convolve fluorescence decay curve with irf.

This function computes a convolved model function for a fluorescence decay curve.

Parameters

fit	convolved model function
p	model function before convolution - fluorescence decay curve
lamp	instrument response function
start	start index of the convolution
stop	stop index of the convolution

◆ shift_lamp()

void shift_lamp	(	double *	lampsh,
		double *	lamp,
		double	ts,
		int	n_points,
		double	out_value = 0.0 )

shift instrumnet response function

Parameters

lampsh
lamp
ts
n_points
out_value	the value of the shifted response function outside of the valid indices

Functions

Function Documentation

◆ add_pile_up_to_model()

◆ discriminate_small_amplitudes()

◆ fconv()

◆ fconv_avx()

◆ fconv_cs_time_axis()

◆ fconv_per()

◆ fconv_per_avx()

◆ fconv_per_cs()

◆ fconv_per_cs_time_axis()

◆ fconv_ref()

◆ rescale()

◆ rescale_w()

◆ rescale_w_bg()

◆ sconv()

◆ shift_lamp()