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ml-spectra-fitting

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Readme

ml-spectra-fitting

Curve fitting method in javascript.

This is spectra fitting package optimize the position (x), max intensity (y), full width at half maximum (width) and the percent of gaussian (mu). It supports three kind of shapes:

Name	Equation
Gaussian	$y \cdot exp \left[\frac{\delta}{2 \sigma^2}\right]$
Lorentzian	$y\cdot\frac{\gamma}{\delta + \gamma}$
Pseudo Voigt	$y * \left[\mu \cdot exp \left[\frac{\delta}{2 \sigma^2}\right] + (1 - \mu) \cdot \frac{\gamma}{\delta + \gamma} \right]$

where

$\delta = \left(t - x\right)^2$	$\sigma = \frac{width}{2\sqrt{2 \cdot Log(2)}}$	$\gamma=\left(width\right)^2$

It is a wrapper of ml-levenberg-marquardt

API Documentation

Installation

$ npm install ml-spectra-fitting

Example

// import library
import { optimizeSum } from 'ml-spectra-fitting';
import { generateSpectrum } from 'spectrum-generator';

const peaks = [
  { x: 0.5, y: 0.2, width: 0.2 },
  { x: -0.5, y: 0.2, width: 0.3 },
];
const data = generateSpectrum(peaks, {from: -1, to: 1, nbPoints: 41});


//the approximate values to be optimized, It could come from a peak picking with ml-gsd
let peakList = [
  {
    x: -0.5,
    y: 0.18,
    width: 0.18,
  },
  {
    x: 0.52,
    y: 0.17,
    width: 0.37,
  },
];

// the function recive a peaklist with {x, y, width} as a guess
// and return a list of objects

let fittedParams = optimize(data, peakList);
console.log(fittedParams);
/**
 {
    error: 0.010502794375558983,
    iterations: 15,
    peaks: [
      {
        x: -0.49999760133593774,
        y: 0.1999880261075537,
        width: 0.3000369491704072
      },
      {
        x: 0.5000084944744884,
        y: 0.20004144804853427,
        width: 0.1999731186595336
      }
    ]
  }
 */

For data with and combination of signals with shapes between gaussian and lorentzians, we could use the kind pseudovoigt to fit the data.

import { optimize } from 'ml-spectra-fitting';
import { SpectrumGenerator } from 'spectrum-generator';

const generator = new SpectrumGenerator({
  nbPoints: 101,
  from: -1,
  to: 1,
});

// by default the kind of shape is gaussian;
generator.addPeak({ x: 0.5, y: 0.2 }, { width: 0.2 });
generator.addPeak(
  { x: -0.5, y: 0.2 },
  {
    width: 0.1,
    shape: {
      kind: 'lorentzian',
      options: {
        fwhm: 1000,
        length: 50001,
        factor: 5
      },
    },
  },
);

//points to fit {x, y};
let data = generator.getSpectrum();
console.log(JSON.stringify({x: Array.from(data.x), y: Array.from(data.y)}))
//the approximate values to be optimized, It could coming from a peak picking with ml-gsd
let peakList = [
  {
    x: -0.5,
    y: 0.22,
    width: 0.25,
  },
  {
    x: 0.52,
    y: 0.18,
    width: 0.18,
  },
];

// the function recive a peaklist with {x, y, width} as a guess
// and return a list of objects
let fittedParams = optimize(data, peakList, { kind: 'pseudovoigt' });

console.log(fittedParams);
/**
{
  error: 0.12361588652854476,
  iterations: 100,
  peaks: [
    {
      x: -0.5000014532421942,
      y: 0.19995307937326137,
      width: 0.10007670374735196,
      mu: 0.004731136777288483
    },
    {
      x: 0.5001051783652894,
      y: 0.19960010175400406,
      width: 0.19935932346969124,
      mu: 1
    }
  ]
}
*/

License

MIT