options.errorTolerance doesn't recognize function minimum

[MontyThibault]

I ran into a problem and had to make a source modification for the convergence criteria. The currently-implemented convergence criterion operates in absolute terms of the squared residuals. Real data sets with noise may have a minimal curve with an arbitrarily-large error, and convergence in those cases will not be recognized.

https://github.com/mljs/levenberg-marquardt/blob/master/src/index.js#L106

I modified the convergence criteria to be the relative change based on the previous error, as described here: https://en.wikipedia.org/wiki/Non-linear_least_squares#Convergence_criteria.

...

error = errorCalculation(
      data,
      parameters,
      parameterizedFunction,
      weightSquare,
    );

converged = (previousError - error) / error <= errorTolerance;  // <<<

if (isNaN(error)) break;

...

[jobo322]

Hello @MontyThibault, Many thanks for it, I will check it soon.

[MontyThibault]

If the curve can be fit exactly, I've gotten the inverse problem where convergence isn't recognized because the proportion of the change in error to the error itself has a lower bound. A combination of the relative and absolute approaches seems to work well in practice. Not an exact science in any case.

converged = (Math.abs(previousError - error) / error <= errorTolerance) || (error <= errorTolerance)