fminsearch ·

fminsearch(fun,Parm0,x,y,Opt)

Source code at https://github.com/jonasalmeida/fminsearch, can be loaded into web application with

<script src="https://jonasalmeida.github.io/fminsearch/fminsearch.js"></script>

Multiparametric nonlinear regression in javascript.

I developed this function originally at http://jmat.googlecode.com, i.e. https://jmat.googlecode.com/git/jmat.js, which Google has since discontinued, so I moved it here 8 years ago. The purpose of fminsearch is to provide a simple heuristic for non-linear regression that makes the most of javascript's functional style, and specifically of Map-Reduce patterns, while demanding as little as possible from the browser, or from developers using it as part of their own work. The steepest descent proceedure has a core regression thread with optional parameters (Opt). These options range from the basic of setting the display and controlling the number of iterations, all the way to configuring the output variable, setting the cost function to applying a paralelized Genetic Algorithm-style penalty on divergent parameter vectors.

Core algorithm

The core algorithm is a variation on the golden rule of speeding changes in the values of the parameters that decrease the objective function (cost function), while reversing and slowing it down otherwiese. Accordingly, the core algorithm only really has two lines

for(var j=0;j<n;j++){ // take a step for each parameter
	P1=cloneVector(P0);
	P1[j]+=step[j];
	if(funParm(P1)<funParm(P0)){ // if parm value going in the righ direction
		step[j]=1.2*step[j]; // go a little faster
		P0=cloneVector(P1);
	}
	else{ // if not
		step[j]=-(0.5*step[j]); // reverse and go slower
	}	
} 

(...)

Example - the core thread applied to a 4 variable function

x = [32,37,42,47,52,57,62,67,72,77,82,87,92]
y=[749,1525,1947,2201,2380,2537,2671,2758,2803,2943,3007,2979,2992]
fun = function(x,P){return x.map(function(xi){return (P[0]+1/(1/(P[1]*(xi-P[2]))+1/P[3]))})}
Parms=fminsearch(fun,[100,30,10,5000],x,y)

Opt is an object will all other parameters, from the objective function (cost function), to the number of iterations, initial step vector and the display switch, for example

Parms=jmat.fminsearch(fun,[100,30,10,5000],x,y),{maxIter:10000,display:false})

License

fminsearch is MIT licensed.