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Sobol Low Discrepancy Sequence
Raw
.block
license: bsd-3-clause
Raw
README.md

Visualisation of the first 10 dimensions of the Sobol low discrepancy sequence.

Low-discrepancy sequences are also called quasi-random sequences, due to their common use as a replacement of uniformly distributed random numbers. Quasi-random numbers have an advantage over pure random numbers in that they cover the domain of interest quickly and evenly. This is an important feature when performing numerical integration via Monte Carlo techniques.

The Sobol sequence preserves low discrepancy properties in multi dimensions which makes it a good candidate for quasi Monte Carlo methods on random paths.

Sobol implementation in d3-quant, single code base visualisations on svg and canvas thanks to d3-canvas-transition module.

Raw
index.html
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Sobol Low Discrepancy Sequence</title>
<script src="https://d3js.org/d3.v4.js"></script>
<script src="https://giottojs.org/d3-canvas-transition/0.3.4/d3-canvas-transition.js"></script>
<script src="https://giottojs.org/d3-quant/0.4.2/d3-quant.js"></script>
<style>
#panel {
background-color: rgba(245,245,245,0.9);
padding: 5px;
position: absolute;
display: block;
}
</style>
</head>
<body>
<div id="panel">
<div id="paper">
<label>
<input id='svg' name="type" type="radio" checked>
<span>svg</span>
</label>
<label>
<input id='canvas' name="type" type="radio">
<span>canvas</span>
</label>
</div>
<button>Randomise</button>
<label>Dimensions</label>
<select>Dimensions
<option value="1">1-2</option>
<option value="2">2-3</option>
<option value="3">3-4</option>
<option value="4">4-5</option>
<option value="5">5-6</option>
<option value="6">6-7</option>
<option value="7">7-8</option>
<option value="8">8-9</option>
</select>
</div>
<div id="example" style="max-width: 960px"></div>
<script src="./script.js">
</script>
</body>
Raw
script.js
(function () {
d3.select('#svg').on('click', function () {
draw('svg');
});
d3.select('#canvas').on('click', function () {
draw('canvas');
});
if (d3.resolution() > 1) {
d3.select('#paper').append('label').html(
"<input id='canvas-low' name='type' type='radio'><span>canvas low resolution</span>"
);
d3.select('#canvas-low').on('click', function () {
draw('canvas', 1);
});
}
var N = 2000,
sobol = d3.sobol(10),
data = sobol.generate(N),
dim = 0,
currentType,
currentRes,
paper, x, y;
d3.select('button').on('click.randomise', function () {
data = sobol.generate(N);
refresh();
});
d3.select('select').on('change.dimension', function () {
dim = d3.select(this).property('value') - 1;
refresh();
});
draw('svg');
function draw(type, r) {
var example = d3.select("#example"),
width = d3.getSize(example.style('width')),
height = Math.min(500, width);
x = d3.scaleLinear().range([0, width]);
y = d3.scaleLinear().range([height, 0]);
currentRes = r;
currentType = type;
example.select('.paper').remove();
paper = example
.append(type)
.classed('paper', true)
.attr('width', width).attr('height', height).canvasResolution(r).canvas(true);
paper.append('rect')
.attr('width', width)
.attr('height', height)
.style('fill', '#fff');
refresh();
}
function refresh () {
var points = paper.selectAll('circle').data(data);
points
.enter()
.append('circle')
.style('fill', '#999')
.style('stroke', '#333')
.style('stroke-width', '1px')
.attr('r', 2)
.attr('cx', x(0.5))
.attr('cy', y(0.5))
.merge(points)
.transition()
.duration(1000)
.attr('cx', function (d) {return x(d[dim]);})
.attr('cy', function (d) {return y(d[dim+1]);});
}
}());
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