ml-spectra-fitting

This is a spectra fitting package to optimize the position (x), max intensity (y), full width at half-maximum (FWHM = width) and the ratio of gaussian contribution (mu) if it's required.

It supports the gaussian, lorentzian, pseudoVoigt, pseudoVoigtTCH, lorentzianDispersive, generalizedLorentzian and splitGaussian shapes of ml-peak-shape-generator. The splitGaussian shape is asymmetric: it is parameterized by fwhmLow and fwhmHigh instead of fwhm, and both are optimized independently. The three most common ones are:

Name	Equation
Gaussian
Lorentzian
Pseudo Voigt

where

It is a wrapper of ml-levenberg-marquardt

API Documentation

Installation

npm i ml-spectra-fitting

Example

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

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

generator.addPeak(
  { x: 0.5, y: 0.2 },
  { shape: { kind: 'gaussian', fwhm: 0.2 } },
);
generator.addPeak(
  { x: -0.5, y: 0.2 },
  { shape: { kind: 'lorentzian', fwhm: 0.1 } },
);

//points to fit {x, y};
const data = generator.getSpectrum();

//the approximate values to be optimized, it could come from a peak picking with ml-gsd
const peaks = [
  {
    x: -0.5,
    y: 0.22,
    shape: {
      kind: 'pseudoVoigt',
      fwhm: 0.25,
    },
  },
  {
    x: 0.52,
    y: 0.18,
    shape: {
      kind: 'pseudoVoigt',
      fwhm: 0.18,
    },
  },
];

// the function receives an array of peaks with {x, y, shape} as a guess
// and returns the optimized peaks
const fittedParams = optimize(data, peaks);

console.log(fittedParams);
// {
//   error: 3.689192965926774e-8,
//   iterations: 100,
//   peaks: [
//     {
//       x: -0.49999998364851705,
//       y: 0.2000001018716569,
//       shape: { kind: 'pseudoVoigt', fwhm: 0.10000007214964078, mu: 0 },
//     },
//     {
//       x: 0.500000000861883,
//       y: 0.1999983363407256,
//       shape: { kind: 'pseudoVoigt', fwhm: 0.20000322106167928, mu: 1 },
//     },
//   ],
// }

A pseudoVoigt fit recovers mu = 0 for the lorentzian peak and mu = 1 for the gaussian one. Each peak's own shape.kind wins over the shape passed in the options, which only applies to peaks that do not define one.

Linked parameters

You can link one parameter across multiple peaks so they share one optimization variable.

For each linked peak, the actual parameter value is reconstructed as:

actualValue = sharedVariable * factor + offset

By default, factor = 1 and offset = 0.

import { optimize } from 'ml-spectra-fitting';

const result = optimize(data, peaks, {
  parameters: {
    x: { optimize: false },
  },
  linkedParameters: [
    {
      parameter: 'fwhm',
      peaks: [{ id: 'left' }, { id: 'right' }],
    },
    {
      parameter: 'y',
      peaks: [
        { id: 'left', factor: 1 },
        { id: 'right', factor: 2 },
      ],
    },
  ],
});

linkedParameters.peaks[].id accepts either the peak index or peak id.

If the linked parameter is y, offset is interpreted in the original Y scale.

License

MIT