// load Google Visualization API
google.load("visualization", "1", {packages:["linechart"]}); 
google.load("visualization", "1", {packages:["columnchart"]}); 
 
// function to demonstrate a scaled symmetric random walk
// m is the number of paths
// n is the number of steps per period
// t is the number of periods
function scaledSymRandomWalkDemo(m, n, t) {
 
  // create and populate 2D array of random walk paths
  var w = new Array(m)
  for(var i=0; i<m; i++){        
    w[i] = scaledSymRandomWalk(n, t); 
  }
 
  // create DataTables for paths and histogram
  var path = new google.visualization.DataTable(); 
  var hist = new google.visualization.DataTable(); 
  path.addColumn('string', 'n');
  for(var i=0; i<m; i=i+1){
    path.addColumn('number', i);  
  }   
  hist.addColumn('string', 'h');
  hist.addColumn('number', 'count');  
 
  // populate DataTable path
  path.addRows(n*t+1); 
  var label = '';
  for(var i=0; i<(n*t+1); i++){
    label = Math.round(i/n*1000)/1000+'';
    path.setValue(i, 0, label);
    for(var j=0; j<m; j++){
      path.setValue(i, j+1, Math.round(w[j][i]*1000)/1000);  
    } 
  }
 
  // populate histogram bucket boundry array
  var buckets = 20;
  var bucketSize = 0.25*Math.sqrt(t);
  var bucketLower = -2.5*Math.sqrt(t);
  var histBounds = new Array(buckets);
  for(var k=0; k<(buckets+1); k++){
    histBounds[k] = k*bucketSize + bucketLower;
  }
 
  // initialize array to hold bucket frequency counts
  var v=new Array(buckets);
  for(var k=0; k<buckets; k++){
    v[k]=0;
  }
 
  // populate bucket frequency count array
  var x=new Array(m);
  for(var i=0; i<m; i++){
    x[i] = w[i][n*t];
    for(var k=0; k<buckets; k++){
      if(x[i]>histBounds[k] && x[i]<=histBounds[k+1]){
        v[k] = v[k] + 1;
      }
    }
  }   
 
  // populate DataTable hist
  hist.addRows(buckets);
  for(var k=0; k<buckets; k++){
    hist.setValue(k, 0, Math.round(histBounds[k]*100)/100 +' to '+ Math.round(histBounds[k+1]*100)/100); 
    hist.setValue(k, 1, v[k]); 
  }
 
  // Draw charts using Google Visualization API
  var chartPath = new google.visualization.LineChart(document.getElementById('scaledSymRandomWalk_div')); 
  var chartHist = new google.visualization.ColumnChart(document.getElementById('histogram_div')); 
  chartPath.draw(path, {width:700, height:400, enableTooltip:false, pointSize:0, legend:'none', lineSize:1, title:'Scaled Symmetric Random Walk', titleX:'t', titleY:'W(t)', axisFontSize:10, titleFontSize:15}); 
  chartHist.draw(hist, {width:400, height:250, is3D:false, enableTooltip:false, pointSize:0, legend:'none', title:'Histogram of Final Values W(T)', titleY:'Counts', axisFontSize:10, titleFontSize:15}); 
 
  // Calculate sample mean and sample variance
  var sampleMean = Math.round(mean(x)*100)/100;
  var sampleVar = Math.round(variance(x)*100)/100;
 
  // Show sample stats
  document.getElementById('sampleStats_div').innerHTML="W(T) Sample Mean: "+ sampleMean +"<br />W(T) Sample Variance: "+ sampleVar;
} 
 
// function to perform a scaled symmetric random walk
// n is the number of steps per period
// t is the number of periods
function scaledSymRandomWalk(n, t) {
  var w=new Array(n*t+1); 
  w[0] = 0;
  var u = 0;
  for(var i=1; i<(n*t+1); i++){
    u = Math.random();
    if(u>0.5){
      w[i] = w[i-1] - 1/Math.sqrt(n);
    } else {
      w[i] = w[i-1] + 1/Math.sqrt(n);          
    }
  }
  return w;
}
 
// function to calculate the sample mean
// x is an array of values
function mean(x) {
  var n=x.length;
  var s=0;
  for(var i=0; i<n; i++){
    s = s + x[i];
  }  
  return s/n;
}
 
// function to calculate sample variance
// x is an array of values
function variance(x) {
  var n=x.length;
  var xbar=mean(x);
  var s=0;
  for(var i=0; i<n; i++){
    s = s + (x[i]-xbar)*(x[i]-xbar);
  }  
  return s/(n-1);
}