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 Post subject: Non-linear curve fit using a split gaussian function
PostPosted: Fri Dec 06, 2019 8:19 am 
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Joined: Fri Dec 06, 2019 7:49 am
Posts: 1
I am trying to implement a non-linear curve fit for asymmetric peaks using a split gaussian function. It uses separate variances for the left and right side of the peak (see https://arxiv.org/pdf/1405.4995.pdf).

A symmetric gaussian is straight forward, but I am stuck with implementing the conditional statement of the split function using different variances (c[2] or c[3]) for x<=c[1] and x>c[1], respectively. The code below shows the two sides of the gaussian in the callback, but I don't know how to go about using one for the part of the x array <= c[1], and the other one for x array > c[1].

Any ideas how this can be implemented?
Nic

Code:
#include "stdafx.h"
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "interpolation.h"

using namespace alglib;
void function_cx_1_func(const real_1d_array &c, const real_1d_array &x, double &func, void *ptr)
{
    // c[0]: scale factor
    // c[1]: center position mu
    // c[2]: variance left side (sigma1)
    // c[3]: variance right side (sigma2)

    // for x <= c[1]:
    func = c[0]*sqrt(2.0/M_PI)/(c[2]+c[3])*exp(-0.5*pow(x[0]-c[1],2.0)/pow(c[2],2.0));

    // for x > c[1]:
    func = c[0]*sqrt(2.0/M_PI)/(c[2]+c[3])*exp(-0.5*pow(x[0]-c[1],2.0)/pow(c[3],2.0));
}

int main(int argc, char **argv)
{
    real_2d_array x = "[[0.0],[0.1],[0.2],[0.3],[0.4],[0.5],[0.6],[0.7],[0.8],[0.9],[1.0],[1.1],[1.2],[1.3],[1.4],[1.5]]";
    real_1d_array y = "[0.00, 0.00, 0.01, 0.05, 0.12, 0.31, 0.63, 1.10, 1.65, 2.10, 2.28, 1.38, 0.31, 0.03, 0.00, 0.00]";
    real_1d_array c = "[1.0, 1.0, 0.25, 0.10]";
    double epsx = 0.000001;
    ae_int_t maxits = 0;
    ae_int_t info;
    lsfitstate state;
    lsfitreport rep;
    double diffstep = 0.0001;

    lsfitcreatef(x, y, c, diffstep, state);
    lsfitsetcond(state, epsx, maxits);
    alglib::lsfitfit(state, function_cx_1_func);
    lsfitresults(state, info, c, rep);
}


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