232 lines
7.2 KiB
HTML
232 lines
7.2 KiB
HTML
<!DOCTYPE html>
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<!-- vdc.js (C) 2013-present SheetJS http://sheetjs.com -->
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<!-- vim: set ts=2: -->
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
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<title>VDC Live Demo</title>
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</head>
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<body>
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<b>VDC Live Demo</b><br />
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<a href="https://github.com/SheetJS/js-vdc">Source Code</a><br />
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<a href="https://github.com/SheetJS/js-vdc/issues">Issues? Something look weird? Click here and report an issue</a><br />
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<br />
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<div>
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Using the van der Corput sequences for bases 2,3 we can generate a sequence of
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quasirandom points in the unit square. The sequence is said to be
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<a href="https://en.wikipedia.org/wiki/Low-discrepancy_sequence">low-discrepancy</a>
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(basically the points are somewhat more uniformly spread across the square; you
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would expect a truly random sequence of points to have some concentrated lumps
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and small areas with no points).
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<br /><br />
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quasi-Monte Carlo methods generally have better error properties compared to the
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standard random and pseudo-random MC methods. As a demonstration, we will
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estimate π by sampling points in the unit square. The left side shows the
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VDC estimate using bases 2 (x) and 3 (y). The right side shows the random
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estimate by repeatedly calling Math.random.
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<br /><br />
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The graphs show the results of sampling many points and estimating PI. Below
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the graphs, the PI value shows the calculated estimate, "err %" shows the
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relative error (smaller is better) and "ln err" shows the natural log of the
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error (smaller is better).
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<br /><br />
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VDC sequences can be "seeded" by setting the starting index for the calculation.
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In this demo a random integer is chosen using Math.random.
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<br /><br />
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The values and graphs are calculated in your browser window. If the graphs do
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not appear or the values are not calculated, please report the issue!
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</div>
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<br />
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<div width=620>
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<div style="float:left">
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<b><center id="ltext">VDC (2,3) Sampling </center></b>
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<br />
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<canvas id="canvas1" width=300 height=300></canvas>
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<br />
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<b><center id="lout">Estimate of PI: </center></b>
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</div>
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<div style="float:right">
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<b><center id="rtext">Math.random Sampling </center></b>
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<br />
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<canvas id="canvas2" width=300 height=300></canvas>
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<br />
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<b><center id="rout">Estimate of PI: </center></b>
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</div>
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</div>
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</body>
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<script src="http://d3js.org/d3.v2.js"></script>
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<script src="vdc.js"></script>
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<script src="https://cdn.rawgit.com/SheetJS/printj/master/printj.js"></script>
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<script>
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/*jshint browser:true */
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var PTS = 10000;
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var seed = (Math.random()*100000)|0;
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document.getElementById("ltext").innerHTML += PTS + " points; seed " + seed;
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document.getElementById("rtext").innerHTML += PTS + " points";
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var canvas1, canvas2;
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// from http://bl.ocks.org/syntagmatic/3341641 (WTFPL)
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var renderQueue = (function(func) {
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var _queue = [], // data to be rendered
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_rate = 1000, // number of calls per frame
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_invalidate = function() {}, // invalidate last render queue
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_clear = function() {}; // clearing function
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var rq = function(data) {
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if (data) rq.data(data);
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_invalidate();
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_clear();
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rq.render();
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};
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rq.render = function() {
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var valid = true;
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_invalidate = rq.invalidate = function() {
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valid = false;
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};
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function doFrame() {
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if (!valid) return true;
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var chunk = _queue.splice(0,_rate);
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chunk.map(func);
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timer_frame(doFrame);
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}
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doFrame();
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};
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rq.data = function(data) {
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_invalidate();
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_queue = data.slice(0); // creates a copy of the data
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return rq;
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};
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rq.add = function(data) {
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_queue = _queue.concat(data);
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};
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rq.rate = function(value) {
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if (!arguments.length) return _rate;
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_rate = value;
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return rq;
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};
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rq.remaining = function() {
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return _queue.length;
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};
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// clear the canvas
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rq.clear = function(func) {
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if (!arguments.length) {
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_clear();
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return rq;
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}
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_clear = func;
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return rq;
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};
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rq.invalidate = _invalidate;
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var timer_frame = window.requestAnimationFrame || window.webkitRequestAnimationFrame || window.oRequestAnimationFrame || window.msRequestAnimationFrame || function(callback) { setTimeout(callback, 17); };
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return rq;
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});
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// ---
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var color = d3.scale.linear()
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.domain([0, 0.5, 1])
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.range(["#ef2212", "#e7c767", "#2799df"])
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.interpolate(d3.interpolateHcl);
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var VDC2 = VDC({b:2,n:seed});
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var VDC3 = VDC({b:3,n:seed});
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var VDC5 = VDC({b:5,n:seed});
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var in1 = 0, in2 = 0, out1 = 0, out2 = 0;
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function update1() {
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var mypi = (in1 / (in1 + out1))*4, err = Math.abs(mypi - Math.PI)/Math.PI, lnerr = Math.log(err);
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document.getElementById("lout").innerHTML = PRINTJ.sprintf("PI = %f <br />err%% = %f<br />ln err = %f", mypi, err, lnerr);
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}
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function update2() {
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var mypi = (in2 / (in2 + out2))*4, err = Math.abs(mypi - Math.PI)/Math.PI, lnerr = Math.log(err);
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document.getElementById("rout").innerHTML = PRINTJ.sprintf("PI = %f <br />err%% = %f<br />ln err = %f", mypi, err, lnerr);
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}
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function generate1(n) {
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return d3.range(n).map(function(i) {
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var x = VDC2.next(), y = VDC3.next();
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if(x*x + y*y <= 1) in1++; else out1++;
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if((in1 + out1) % 100 === 0) update1();
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return [ canvas1.width*x, canvas1.height*y, color(VDC5.next()) ];
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});
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}
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function generate2(n) {
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return d3.range(n).map(function(i) {
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var x = Math.random(), y = Math.random();
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if(x*x + y*y <= 1) in2++; else out2++;
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if((in2 + out2) % 100 === 0) update2();
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return [ canvas2.width*x, canvas2.height*y, color(Math.random()) ];
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});
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}
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function make_dot(ctx) {
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return function(pos) {
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ctx.fillStyle = pos[2];
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ctx.beginPath();
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ctx.fillRect(pos[0]-1,pos[1]-1,2,2);
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ctx.stroke();
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ctx.fill();
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};
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}
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function make_clear_canvas(ctx, canvas) {
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return function() { ctx.clearRect(0,0,canvas.width,canvas.height); make_boundary(canvas, ctx); };
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}
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function make_boundary(canvas, ctx) {
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ctx.beginPath();
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ctx.arc(0, canvas.height, canvas.width, 0, 2*Math.PI);
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ctx.stroke();
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}
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window.onload = function() {
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canvas1 = document.getElementById("canvas1");
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var ctx1 = canvas1.getContext("2d");
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ctx1.globalCompositeOperation = "destination-over";
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canvas2 = document.getElementById("canvas2");
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var ctx2 = canvas2.getContext("2d");
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ctx2.globalCompositeOperation = "destination-over";
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make_boundary(canvas1, ctx1);
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make_boundary(canvas2, ctx2);
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var dot1 = make_dot(ctx1);
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var dot2 = make_dot(ctx2);
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var clear_canvas1 = make_clear_canvas(ctx1, canvas1);
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var clear_canvas2 = make_clear_canvas(ctx2, canvas2);
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var render1 = renderQueue(dot1).clear(clear_canvas1);
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var render2 = renderQueue(dot2).clear(clear_canvas2);
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render1(generate1(PTS));
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render2(generate2(PTS));
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};
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</script>
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<script type="text/javascript">
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var _gaq = _gaq || [];
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_gaq.push(['_setAccount', 'UA-36810333-1']);
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_gaq.push(['_trackPageview']);
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(function() {
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var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true;
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ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
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var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s);
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})();
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</script>
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</html>
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