Detailed Description

Function for fitting PID mass spectra.

This class is used by KVIDZAFromZGrid (and in the GUI for determining identified isotopes with such grids, KVItvFinderDialog) in order to fit PID mass spectra for a given \(Z\) with a set of gaussians and a background function. The fit can then be used to calculate yields of each isotope, probability that a given PID value is associated with a certain \(A\), mean/most probable \(A\) for a given PID, mass distribution \(P(A|PID)\) for given PID, etc. etc.

The function used to fit the PID spectrum is

\[ N(PID) = \exp(b_0 + b_1*PID) + \sum_{i=1}^{N_{iso}} N_i \mathcal{G}(PID,f(A_i),\sigma) \]

where:

\(N_{iso}\) is the number of isotopes \(A_i\) in the spectrum;
\(b_0 , b_1\) are the parameters of the exponential background;
\(\mathcal{G}(x,\bar{x},\sigma)\) is a normalized gaussian distribution with mean \(\bar{x}\) and standard deviation \(\sigma\);
\(N_i\) is the yield of each isotope;
\(f(A_i)\) is a function which parameterizes the PID coordinate of the centroid of the gaussian for mass \(A_i\),

\[ f(A_i) = a_0 + a_1 A_i + a_2 A_i^2 \]

Note that the same width \(\sigma\) is used for all isotopes \(A_i\) of a given element \(Z\).

The probability that a given PID value is associated with the mass number \(A_i\) is then given by

\[ P(A_i|PID) = \frac{N_i \mathcal{G}(PID,f(A_i),\sigma)}{N(PID)} \]

Author: eindra

Date: Wed Jun 15 10:56:41 2022

Definition at line 51 of file KVMultiGaussIsotopeFit.h.

#include <KVMultiGaussIsotopeFit.h>

Inheritance diagram for KVMultiGaussIsotopeFit:

[legend]

Private Types
enum	fit_param_index { bkg_cst = 1 , bkg_slp = 2 , gauss_wid = 3 , pidvsA_a0 = 4 , pidvsA_a1 = 5 , pidvsA_a2 = 6 }

Private Member Functions
double	centroid_fit (double x, double p)

double	FitFunc (double x, double p)

Member Enumeration Documentation

◆ fit_param_index

enum KVMultiGaussIsotopeFit::fit_param_index

private

Enumerator
bkg_cst
bkg_slp
gauss_wid
pidvsA_a0
pidvsA_a1
pidvsA_a2

Definition at line 52 of file KVMultiGaussIsotopeFit.h.

Member Function Documentation

◆ centroid_fit()

double KVMultiGaussIsotopeFit::centroid_fit	(	double *	x,
		double *	p
	)

inlineprivate

centroids of gaussians are expected to increase linearly with mass A but we allow a quadratic dependence

x[0]=A
p[0]=offset
p[1]=slope
p[2]=quadratic term

Definition at line 60 of file KVMultiGaussIsotopeFit.h.

◆ FitFunc()

double KVMultiGaussIsotopeFit::FitFunc	(	double *	x,
		double *	p
	)