fminsearch.js

fminsearch=function(fun,Parm0,x,y,Opt){// fun = function(x,Parm)
	// example
	//
	// 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=jmat.fminsearch(fun,[100,30,10,5000],x,y)
	//
	// Another test:
	// x=[32,37,42,47,52,57,62,67,72,77,82,87,92];y=[0,34,59,77,99,114,121,133,146,159,165,173,170];
	//
	// 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=fminsearch(fun,[100,30,10,5000],x,y,{maxIter:10000,display:false})
	
	if(!Opt){Opt={}};
	if(!Opt.maxIter){Opt.maxIter=1000};
	if(!Opt.step){// initial step is 1/100 of initial value (remember not to use zero in Parm0)
		Opt.step=Parm0.map(function(p){return p/100});
		Opt.step=Opt.step.map(function(si){if(si==0){return 1}else{ return si}}); // convert null steps into 1's
	};
	if(typeof(Opt.display)=='undefined'){Opt.display=true};
	if(!Opt.objFun){Opt.objFun=function(y,yp){return y.map(function(yi,i){return Math.pow((yi-yp[i]),2)}).reduce(function(a,b){return a+b})}} //SSD
	
	var cloneVector=function(V){return V.map(function(v){return v})};
	var ya,y0,yb,fP0,fP1;
	var P0=cloneVector(Parm0),P1=cloneVector(Parm0);
	var n = P0.length;
	var step=Opt.step;
	var funParm=function(P){return Opt.objFun(y,fun(x,P))}//function (of Parameters) to minimize
	// silly multi-univariate screening
	for(var i=0;i<Opt.maxIter;i++){
		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]; // then go a little faster
				P0=cloneVector(P1);
			}
			else{
				step[j]=-(0.5*step[j]); // otherwiese reverse and go slower
			}	
		}
		if(Opt.display){if(i>(Opt.maxIter-10)){console.log(i+1,funParm(P0),P0)}}
	}
	if (!!document.getElementById('plot')){ // if there is then use it
		fminsearch.plot(x,y,fun(x,P0),P0);
	}
	return P0
};

fminsearch.load=function(src){ // script loading
	// example: fminsearch.load('http://localhost:8888/jmat/jmat.js')
	var s = document.createElement('script');
	s.src = src;
	document.head.appendChild(s);
	s.parentElement.removeChild(s);
};

fminsearch.plot=function(x,y,yp,Parms){ // ploting results using <script type="text/javascript" src="https://www.google.com/jsapi"></script>
	// create Array in Google's format
	var data = new google.visualization.DataTable();
	data.addColumn('number', 'X');
	data.addColumn('number', 'Observed');
	data.addColumn('number', 'Model fit');
	var n = x.length;
	for (var i=0;i<n;i++){
		data.addRow([x[i],y[i],yp[i]]);
	};
	//var chart = new google.visualization.ScatterChart(
	var titulo='Model fitting';
	if(!!Parms){titulo='Model parameters: '+Parms};
	var chart = new google.visualization.ComboChart(
		document.getElementById('plot'));
	    chart.draw(data, {title: titulo,
	                      width: 600, height: 400,
	                      vAxis: {title: "Y", titleTextStyle: {color: "green"}},
	                      hAxis: {title: "X", titleTextStyle: {color: "green"}},
						  seriesType: "scatter",
						  series: {1: {type: "line"}}}
	              );
}