Example does not converge on RunKit

[carstenschwede]

Running the included example on RunKit only converges in ~15% of cases and depends strongly on the chosen initial values.

const LM = require("ml-levenberg-marquardt");

// function that receives the parameters and returns
// a function with the independent variable as a parameter
function sinFunction([a, b]) {
  return (t) => a * Math.sin(b * t);
}

let data = {
  x: [],
  y: []
};
let trueParams = [2, 2];
let sampleFunction = sinFunction(trueParams);

let numSamples = 1000;

for (let i = 0; i < numSamples; i++) {
  let x = i / numSamples * 2 * Math.PI;
  data.x[i] = x;
  data.y[i] = sampleFunction(x);
}

let success = 0;
let counter = 0;

let maxSampleRuns = 250;
while (maxSampleRuns--) {
  let initialValues = [Math.random() - 0.5, Math.random() - 0.5];

  const options = {
    damping: 1.5,
    initialValues,
    gradientDifference: 10e-2,
    maxIterations: 100,
    errorTolerance: 10e-3,
  };

  let fittedParams = LM(data, sinFunction, options);
  if (fittedParams.parameterError < 0.01) {
    success++;
  }
  counter++;
  if (counter % 10 === 0) {
    console.log(`Convergence Rate ${(100*success/counter).toFixed(1)}%`);
  }
}

results in

Convergence Rate 10.0%
Convergence Rate 7.5%
Convergence Rate 12.9%
Convergence Rate 12.5%
...
Convergence Rate 14.8%
Convergence Rate 15.0%

[jobo322]

Thanks, as soon as possible I will have a look at this.

[carstenschwede]

Convergence is very susceptible to initialValues, please see my edit.

[jobo322]

Hello @carstenschwede do you have the way to keep the initial values for which the algorithm converges?

[carstenschwede]

Please see my code, it runs 250 iterations with random initial values in each, in about 15% of cases the random initial values lead to convergence.