/*	pl simulator.js
	062008 hac	v1.0
	071308 hac	v1.1	x, y std dev bias fix

	Processes a form containg the mean and std dev of historical trades,
	forecasts the next 100 trades based on the Axiom of the Small Edge (even prob of win/loss), 
	and returns the URL for a google chart representing the trades

*/


//polar version of =SQRT(-2*LN(A6))*COS(2*PI()*B6)
function getrandomnumber3(count, r, winpct){
	var flipper;
	var i = 0;
    var x1, x2, y1, y2;
    var w = 999;
 
 	while (i < count) {
 	
 		finished 	= false;
 		flipper		= Math.random();
 	
		while (w >= 1.0) {
		
			x1 		= 2.0 * Math.random() - 1.0;
			x2 		= 2.0 * Math.random() - 1.0;
			w  		= (x1 * x1) + (x2 * x2);
		}
		
		w  = Math.sqrt((-2.0 * Math.log(w))/w);
		y1 = x1 * w;
		y2 = x2 * w;
		
		if (flipper >= 1 - winpct){
			if (y1 >= 0) {
				r[i] 	= y1; i++; finished = true;
				
			} else if (y2 >= 0) {
				r[i] 	= y2; i++; finished = true;
				
			}
		} else {
			if (y1 < 0) {
				r[i] = y1; i++; finished = true;
				
			} else if (y2 < 0) {
				r[i] = y2; i++; finished = true;
				
			}
		
		}
 	
 	}
}


//returns an array of count random numbers, normally distributed through winloss percentage
//use a to simulate winpct and x or y to be the result if it has the same sign
//for example, if winpct = 60, and a >=.6 and x is pos, then r[i] = x
function getrandomnumber2(count, r, winpct){
	var a, b, x, y 	= 0;
	var i 			= 0;
	var finished 	= false;
	var flipper		= 0;
	var wins 		= 0;
	var losses 		= 0;
	
	while (i < count) {
	
		finished = false;
	
		while (finished == false) {
		
			flipper = Math.random();
			a 		= Math.random();
			b 		= Math.random();
			
			//=SQRT(-2*LN(A6))*COS(2*PI()*B6)
			x = Math.sqrt(-2*Math.log(a))*Math.cos(2*Math.PI*b);
			y = Math.sqrt(-2*Math.log(a))*Math.sin(2*Math.PI*b);
			
			if (flipper >= 1 - winpct){
				//x/y bias?
				if (x >= 0) {
					r[i] 	= x; i++; finished = true;
					
				} else if (y >= 0) {
					r[i] 	= y; i++; finished = true;
					
				}
			} else {
				if (x < 0) {
					r[i] = x; i++; finished = true;
					
				} else if (y < 0) {
					r[i] = y; i++; finished = true;
					
				}
			
			}
			
		}

	}
	
}


//returns an array of count normally distr random numbers
function getrandomnumber(count, r) {
	var a = 0;
	var b = 0;
	var x = 0;
	var y = 0;
	
	for (var i = 0; i < count;) {
	
		a = Math.random();
		b = Math.random();
		
		//=SQRT(-2*LN(A6))*COS(2*PI()*B6)
		x = Math.sqrt(-2*Math.log(a))*Math.cos(2*Math.PI*b);
		y = Math.sqrt(-2*Math.log(a))*Math.sin(2*Math.PI*b);
		
		r[i] 	= x; i++;
		r[i] 	= y; i++;
		
		/*if (window.console)
			window.console.log(i.toString());*/
	}
}


//Init simulation arrays
function initsimulationarrays(sim, notrades, pctwins) {

	var winpct = 0;
	
	if (pctwins != "") {
		winpct = parseFloat(pctwins);
		if (winpct > 1) {
			winpct = winpct/100;
		}
	}

	for (var i = 0; i < sim.length; i++) {
		
		sim[i] = new Array(notrades);
		
		// fill the array w/ simulated, normally distributed random numbers
		if (winpct == 0) {
			getrandomnumber(sim[i].length, sim[i]);
		} else 
			getrandomnumber3(sim[i].length, sim[i], winpct);
			
	}
}


//creates the trades in place from the 
// normally distributed random vars
function buildtradeseries(mean, stddev, sim) {

	var dx, z = 0;
	
	for (var i = 0; i < sim.length; i++){
		z = 0;
		dx = 0; //running sum of trades
	
		for (var j=0; j<sim[i].length; j++){
		
			// start each series at 0
			// otherwise add each trade
			if (j > 0) {
				z = sim[i][j];  //get the z for this trade
			
				dx = dx + mean + (stddev * z); //calc the trade and add to sum of trades
			}

			sim[i][j] = dx;
		}
		
		
		/*if (window.console) {
			window.console.log(sim[i][0].toString());
			window.console.log(sim[i][sim[i].length-1].toString());
		}*/
		
	}
	
}


//creates the trades in place from the 
// normally distributed random vars
function buildtradeseriespct(avgwin, wlratio, sim) {

	var dx, trade, z = 0;
	
	for (var i = 0; i < sim.length; i++){
		z = 0;
		dx = 0; //running sum of trades
	
		for (var j=0; j<sim[i].length; j++){
		
			// start each series at 0
			// otherwise add each trade
			// the series is normally distributed so the bumps are a bit more realistic
			if (j > 0) {
				z		= sim[i][j];			//get the z for this trade
				if (z > 0) {
					z = 1
				} else if (z <= 0) {
					z = -1
				}
				
				//calc trades adjusting for w/l ratio
				if (z > 0) 
					trade	= avgwin * z
				else if (z < 0)
					trade	= avgwin/wlratio * z
			 	else
			 		trade= 0;
			
				dx = dx + trade;				//running sum of trades
			}

			sim[i][j] = dx;
		}
		
		
		/*if (window.console) {
			window.console.log(sim[i][0].toString());
			window.console.log(sim[i][sim[i].length-1].toString());
		}*/
		
	}
	
}

// returns best, worst and average series indices
function gettradeindices(sim, indices){
	var avgindex	= 0;
	var avgtrade	= new Array(sim.length);	// for sorting and finding avg series
	var dx			= 0;
	var lastentry 	= sim[0].length - 1;
	var lookup		= false;
	var max, maxindex	= 0;
	var min, minindex	= 0;

	// get max and min series
	for (var i=0; i < sim.length; i++) {
		
		if (sim[i][lastentry] > max) {
			
			max 		= sim[i][lastentry];
			maxindex 	= i;
		} else if (sim[i][lastentry] < min) {
			
			min			= sim[i][lastentry];
			minindex	= i;
		}
		
		avgtrade[i]		= sim[i][lastentry];	// populate by net result
	}
	
	// find the median series
	avgtrade.sort( function (a,b) { return a-b }); 	//sort min to max
	
	dx = avgtrade[Math.floor(sim.length/2)+2];		//median series - NOTE: adjusted up to there's a funny downside bias...
	
	lookup = false;
	avgindex = 0;
	while(!lookup) {
		if (sim[avgindex][lastentry] == dx || avgindex >= sim.length) {
			lookup = true;	
		} else {
			avgindex++;
		}
	}
	
	indices[0] = maxindex;
	indices[1] = minindex;
	indices[2] = avgindex;
	
	/*if (window.console) {
		window.console.log("max index: "+maxindex.toString());
		window.console.log("min index: "+minindex.toString());
		window.console.log("avg index: "+avgindex.toString());
	}*/
}

//get trade stats
// outputs 3 arrays - best, worst and average
function gettradestats(sim, stats){

	var avgtrade	= new Array(sim.length);
	var dx, i		= 0;
	var indices		= new Array(3);	// for best, worst and average series
	var lookup		= false;
	var maxindex, minindex = 0;
	
	// get indices for best, worst and average series
	gettradeindices(sim, indices);
	
	// set pointers to series
	stats[0] = sim[indices[0]]; //best
	stats[1] = sim[indices[1]]; //worst
	stats[2] = sim[indices[2]]; //avg
	
}

//get the max and min for each series
function getseriesmaxmin(stats, max, min){

	for (var i=0; i < stats.length; i++){
	
		min[i] = 9999;
		max[i] = -9999;
		
		for (var j=0; j<stats[i].length; j++){
			
			if (stats[i][j] > max[i]) {
				max[i] = stats[i][j];
			}
			else if (stats[i][j] < min[i]) {
				min[i] = stats[i][j];
			}
			
		}
		
		/*if (window.console) {
			window.console.log("max: " + max[i].toString());
			window.console.log("min: " + min[i].toString());
		}*/
		
	}
	
}


//scale series for charting
//all we do here is truncate the median series to 1 decimal place
function scale(stats, seriesindex) {

	for (var j=0; j<stats[0].length; j++) {
			
		stats[seriesindex][j] = stats[seriesindex][j].toFixed(1);	//one decimal place
	}
}


//add white space, rounds max, min for plotting
function addwhitespace(min, max, index){

	min[index] = min[index] - Math.abs(.1 * min[index]);
	min[index] = Math.floor(min[index]);
	min[index] = min[index].toFixed(0);
	
	max[index] = max[index] * 1.1;
	max[index] = Math.ceil(max[index]);
	max[index] = max[index].toFixed(0);
}


//encode chart url
function encodecharturl(stats, min, max, index){
	var chartstr	= "";
	var chs, chd, chds, cht, chtt, chco, chdl, chls	="";
	var chxt, chxl, chg, chm	= "";
	var dx, dy;
	
	chs			= "chs=600x400";
	
    chd 		= "chd=t:" + stats[index].toString();
    
    chds 		= "chds=" + min[index].toString() + "," + max[index].toString();
    
    dx 			= Math.floor(stats[index].length/10);
    dx			= dx.toFixed(0);
    dy			= Math.floor((max[index] - min[index])/10);
    dy			= dy.toFixed(0);
    chg			= "chg=" + dx.toString() + "," + dy.toString() + ",1,5";				//grid - y not working
    
    dx			= stats[index][stats[index].length-1].toString();
    chm			= "chm=t" + dx + ",0000ff,0," + dx + ",13,1";							// marker - not working

    cht			= "cht=lc";
    
    chtt		= "chtt=Forecast";
    
   	chco		= "chco=0000ff"; 				// colors
    chdl		= "chdl=Median";				//legend
    chls		= "chls=1,1,0";					// lines
    chxt		= "chxt=x,y";					// axes
    
    chxl		= "chxl=0:|0|" + stats[2].length.toString() + "|" 			
    					+"1:|" + min[2].toString() + "|" + max[2].toString();	//axes scales
    
    chartstr 	= "http://chart.apis.google.com/chart?" + chs + "&amp;" + chd + "&amp;" + chds + "&amp;" 
    					+ chco + "&amp;" /*+ chdl + "&amp;"*/ + chls + "&amp;" + chxt + "&amp;" + chxl + "&amp;" 
    					+ cht + "&amp;" + chtt + "&amp;" + chg /*+ "&amp;" + chm*/;
	
	return chartstr;
}


//returns the url to fetch the chart from google
function getcharturl(stats){
	var chs, chd, cht, chl, chartstr = "";
	var min		= new Array(stats.length);
	var max		= new Array(stats.length);
	
	// get the max and min for each series
	getseriesmaxmin(stats, max, min);
	
	// scale the average series for charting
	scale(stats, 2);
	scale(min, 2);
	scale(max, 2);

	
	//add some white space to the median series max and min
	addwhitespace(min, max, 2);
	
    
    //encode url from the median series for plotting
    chartstr = encodecharturl(stats, min, max, 2);
    
    if (window.console) {
			window.console.log("url length: " + chartstr);
	}
    
    return chartstr;
}


function plsimulator (form) {
	var dx;
    var mean 	= form.mean.value;
    var sim		= new Array(100);		//holds 100 simulations
    var stats	= new Array(3);			//arrays of best, worst and median series
    var stddev 	= form.stddev.value;
    var t		= "";
    
	// init simulation array w/ size of test
	initsimulationarrays(sim, 100, "");
    
    //using the mean and std dev from the form, simulate trades
    buildtradeseries(parseFloat(mean), parseFloat(stddev), sim);
    
    // build out each trade series, accumulating each trade
    gettradestats(sim, stats);
    
    // build out the url to get a chart from google
	charturl = getcharturl(stats);
	
	// display the chart
	t = "<img src=" + charturl + " />"
			+ "<br /><br />"
			+ "Forecast = $" + stats[2][stats[2].length-1].toString();
	document.getElementById("chart").innerHTML = t;
    
}


//for calling the simulator from a mac widget
//widget uses 100 arrays of length 50 instead of length 100 in simulator
function plsimulatorpctwins (form) {
	var avgwin		= form.avgwin.value;
	var charturl	= ""
	var dx;
	var pctwins		= form.pctwins.value;
    var sim			= new Array(100);		//holds 100 simulations
    var stats		= new Array(3);			//arrays of best, worst and median series
    var t			= "";
    var wlratio		= form.wlratio.value;
    
	// init simulation array w/ size of test
	initsimulationarrays(sim, 100, pctwins);
    
    //using the mean and std dev from the form, simulate trades
    buildtradeseriespct(parseFloat(avgwin), parseFloat(wlratio), sim);
    
    // build out each trade series, accumulating each trade
    gettradestats(sim, stats);
    
    // build out the url to get a chart from google
	charturl = getcharturl(stats);
	
	// display the chart
	t = "<img src=" + charturl + " />"
			+ "<br /><br />"
			+ "Forecast = $" + stats[2][stats[2].length-1].toString();
	document.getElementById("chart").innerHTML = t;
    
}