Multi-peak fitting

This example demonstrates how to use the kontrast.fit() function to extract the position and width of three peaks from their superposition. Please refer to documentation on the fit function for details on all individual input and output properties.

Interactive examples

let mean0 = 1
let mean1 = 4
let mean2 = 6

let variance0 = 3
let variance1 = 4
let variance2 = 1

let N = 100
let min = 0
let max = 10

let x = new Float64Array(N)
let y = new Float64Array(N)
let yFit0 = new Float64Array(N)
let yFit1 = new Float64Array(N)
let yFit2 = new Float64Array(N)
let yFit = new Float64Array(N)

function gaussian(x, mean, variance) {
  return (
    (1 / Math.sqrt(Math.PI * 2 * variance)) *
    Math.exp(-Math.pow(x - mean, 2) / (2 * variance))
  )
}

for (let i = 0; i < N; i++) {
  x[i] = (i / N) * (max - min) + min
  y[i] =
    gaussian(x[i], mean0, variance0) +
    gaussian(x[i], mean1, variance1) +
    gaussian(x[i], mean2, variance2)
}

let fitEquation = function (x, m0, v0, m1, v1, m2, v2) {
  return gaussian(x, m0, v0) + gaussian(x, m1, v1) + gaussian(x, m2, v2)
}

let fit = kontrast.fit({
  numberType: 'real',
  quantities: {
    x: { type: 'constant', data: x },
    y: { type: 'constant', data: y },
    m0: { type: 'parameter', initial: 1 },
    v0: { type: 'parameter', initial: 1 },
    m1: { type: 'parameter', initial: 3 },
    v1: { type: 'parameter', initial: 1 },
    m2: { type: 'parameter', initial: 5 },
    v2: { type: 'parameter', initial: 1 },
  },
  residuals:
    'exp(-((x - m0) ^ 2) / (2 * v0)) / sqrt(2 * pi * v0) + exp(-((x - m1) ^ 2) / (2 * v1)) / sqrt(2 * pi * v1) + exp(-((x - m2) ^ 2) / (2 * v2)) / sqrt(2 * pi * v2) - y',
})

for (let i = 0; i < N; i++) {
  yFit[i] = fitEquation(
    x[i],
    fit.quantities.m0.value,
    fit.quantities.v0.value,
    fit.quantities.m1.value,
    fit.quantities.v1.value,
    fit.quantities.m2.value,
    fit.quantities.v2.value
  )
  yFit0[i] = gaussian(x[i], fit.quantities.m0.value, fit.quantities.v0.value)
  yFit1[i] = gaussian(x[i], fit.quantities.m1.value, fit.quantities.v1.value)
  yFit2[i] = gaussian(x[i], fit.quantities.m2.value, fit.quantities.v2.value)
}

let graph = kontrast.figures.figure0.graphs.graph

graph.points.dataPlot.data = { x: x, y: y }
graph.lines.fitPlot.data = { x: x, y: yFit }
graph.lines.fitPlot0.data = { x: x, y: yFit0 }
graph.lines.fitPlot1.data = { x: x, y: yFit1 }
graph.lines.fitPlot2.data = { x: x, y: yFit2 }

graph.showEverything()