Fitting data with functions

let N = 1000
let min = -10
let max = 10

let x = new Float64Array(N)
let y = new Float64Array(N)
let yFit = new Float64Array(N)

let random = kontrast.generateRandomNumbers({
  distribution: 'gaussian',
  count: N,
  mean: 0,
  standardDeviation: 100,
})

for (let i = 0; i < N; i++) {
  x[i] = (i / N) * (max - min) + min
  y[i] = 5 + 2 * x[i] + 8 * Math.pow(x[i], 2) + random.values[i]
}

let fit = kontrast.fit({
  numberType: 'real',
  quantities: {
    x: { type: 'constant', data: x },
    y: { type: 'constant', data: y },
    a0: { type: 'parameter', initial: 1 },
    a1: { type: 'parameter', initial: 1 },
    a2: { type: 'parameter', initial: 1 },
  },
  residualCallback: function (scope) {
    return scope.a0 + scope.a1 * scope.x + scope.a2 * scope.x ** 2 - scope.y
  },
})

for (let i = 0; i < N; i++) {
  yFit[i] =
    fit.quantities.a0.value +
    fit.quantities.a1.value * x[i] +
    fit.quantities.a2.value * x[i] * x[i]
}

let graph = kontrast.figures.figure0.graphs.graph
graph.points.dataPlot.data = { x: x, y: y }
graph.lines.fitPlot.data = { x: x, y: yFit }
graph.showEverything()

let N = 1000
let min = -10
let max = 10

let x = new Float64Array(N)
let y = new Float64Array(N)
let yFit = new Float64Array(N)

let random = kontrast.generateRandomNumbers({
  distribution: 'gaussian',
  count: N,
  mean: 0,
  standardDeviation: 100,
})

for (let i = 0; i < N; i++) {
  x[i] = (i / N) * (max - min) + min
  y[i] = 5 + 2 * x[i] + 8 * Math.pow(x[i], 2) + random.values[i]
}

let fit = kontrast.fit({
  numberType: 'real',
  quantities: {
    x: { type: 'constant', data: x },
    y: { type: 'constant', data: y },
    a0: { type: 'parameter', initial: 1 },
    a1: { type: 'parameter', initial: 1 },
    a2: { type: 'parameter', initial: 1 },
  },
  residuals: '(a0 + a1 * x + a2 * x ^ 2) - y',
})

for (let i = 0; i < N; i++) {
  yFit[i] =
    fit.quantities.a0.value +
    fit.quantities.a1.value * x[i] +
    fit.quantities.a2.value * x[i] * x[i]
}

let graph = kontrast.figures.figure0.graphs.graph
graph.points.dataPlot.data = { x: x, y: y }
graph.lines.fitPlot.data = { x: x, y: yFit }
graph.showEverything()

let N = 1000
let minE = -1
let maxE = 1

let x = new Float64Array(N)
let y = new Float64Array(N)
let yFit = new Float64Array(N)

let random = kontrast.generateRandomNumbers({
  distribution: 'gaussian',
  count: N,
  mean: 0,
  standardDeviation: 0.01,
})

for (let i = 0; i < N; i++) {
  x[i] = Math.pow(10, (i / N) * (maxE - minE) + minE)
  y[i] = 1 + Math.exp(-3 * x[i]) + random.values[i]
}

let fit = kontrast.fit({
  numberType: 'real',
  quantities: {
    x: { type: 'constant', data: x },
    y: { type: 'constant', data: y },
    offset: { type: 'parameter', initial: 1 },
    lambda: { type: 'parameter', initial: 1 },
  },
  residualCallback: function (scope) {
    return scope.offset + Math.exp(-scope.lambda * scope.x) - scope.y
  },
})

for (let i = 0; i < N; i++) {
  yFit[i] =
    fit.quantities.offset.value + Math.exp(-fit.quantities.lambda.value * x[i])
}

let graph = kontrast.figures.figure0.graphs.graph
graph.points.dataPlot.data = { x: x, y: y }
graph.lines.fitPlot.data = { x: x, y: yFit }
graph.showEverything()

let N = 1000
let min = 60e3
let max = 140e3

let x = new Float64Array(N)
let y = new Float64Array(N)
let yFit = new Float64Array(N)

let gainFunction = function (
  frequency,
  qualityFactor,
  eigenFrequency,
  springConstant
) {
  let r = Math.pow(frequency / eigenFrequency, 2)
  return (
    1 /
    (springConstant *
      Math.sqrt(Math.pow(1 - r, 2) + r / (qualityFactor * qualityFactor)))
  )
}

let random = kontrast.generateRandomNumbers({
  distribution: 'gaussian',
  count: N,
  mean: 0,
  standardDeviation: 0.01,
})

for (let i = 0; i < N; i++) {
  x[i] = (i / N) * (max - min) + min
  y[i] = gainFunction(x[i], 50, 100e3, 10) + random.values[i]
}

let fit = kontrast.fit({
  numberType: 'real',
  quantities: {
    frequency: { type: 'constant', data: x },
    gainFunction: { type: 'constant', data: y },
    qualityFactor: { type: 'parameter', initial: 50 },
    eigenFrequency: { type: 'parameter', initial: 100e3 },
    springConstant: { type: 'parameter', initial: 8 },
  },
  residualCallback: function (scope) {
    return (
      gainFunction(
        scope.frequency,
        scope.qualityFactor,
        scope.eigenFrequency,
        scope.springConstant
      ) - scope.gainFunction
    )
  },
})

for (let i = 0; i < N; i++) {
  yFit[i] = gainFunction(
    x[i],
    fit.quantities.qualityFactor.value,
    fit.quantities.eigenFrequency.value,
    fit.quantities.springConstant.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.showEverything()

let N = 1000
let min = 60e3
let max = 140e3

let x = new Float64Array(N)
let y = new Float64Array(N)
let yFit = new Float64Array(N)

let gainFunction = function (
  frequency,
  qualityFactor,
  eigenFrequency,
  springConstant
) {
  let r = Math.pow(frequency / eigenFrequency, 2)
  return (
    1 /
    (springConstant *
      Math.sqrt(Math.pow(1 - r, 2) + r / (qualityFactor * qualityFactor)))
  )
}

let random = kontrast.generateRandomNumbers({
  distribution: 'gaussian',
  count: N,
  mean: 0,
  standardDeviation: 0.01,
})

for (let i = 0; i < N; i++) {
  x[i] = (i / N) * (max - min) + min
  y[i] = gainFunction(x[i], 50, 100e3, 10) + random.values[i]
}

let fit = kontrast.fit({
  numberType: 'real',
  quantities: {
    frequency: { type: 'constant', data: x },
    gainFunction: { type: 'constant', data: y },
    qualityFactor: { type: 'parameter', initial: 50 },
    eigenFrequency: { type: 'parameter', initial: 100e3 },
    springConstant: { type: 'parameter', initial: 8 },
  },
  residuals:
    '1 / (springConstant * sqrt((1 - (frequency / eigenFrequency) ^ 2) ^ 2 + ((frequency / eigenFrequency) / qualityFactor) ^ 2)) - gainFunction',
})

for (let i = 0; i < N; i++) {
  yFit[i] = gainFunction(
    x[i],
    fit.quantities.qualityFactor.value,
    fit.quantities.eigenFrequency.value,
    fit.quantities.springConstant.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.showEverything()

Interactive examples