rpgove/.block

## .block
license: gpl-3.0
height: 300
scrolling: no
border: yes


## README.md

      
    Raw
  

              README.md
            
          
    Kernel smoothing is a method to estimate a smooth line from several discrete points, which is in contrast with kernel density estimation which is used to estimate a probability distribution from discrete points. This example uses the Nadaraya-Watson kernel-weighted average with a Gaussian kernel on random data that follows a noisey sine wave.
The smoothness is controlled by a bandwidth parameter. If the bandwidth is too small, the line essentially connects the existing data points. If the bandwidth is too large, then the line essentially becomes a straight line.
This method is usually fast if there are a small number of data points, but a tree structure can speed up the calculation if there is a lot of data.

  
## index.html
<!DOCTYPE html>
<meta charset="utf-8">
<style>

html, body {
  margin: 0;
}

circle {
  fill: #666;
}

path {
  fill: none;
  stroke: teal;
  stroke-width: 2px;
  opacity: 0.5;
}

</style>

<div>
Bandwidth: <span id="current-bandwidth">15</span><br>
1<input type="range" min="1" max="200" value="15" class="slider" id="bandwidth-slider">200
</div>
<svg></svg>

<script src="https://d3js.org/d3.v4.min.js"></script>
<script>

var margin = {left: 10, top: 10, right: 10, bottom: 10};
var width = 960 - margin.left - margin.right;
var height = 220 - margin.top - margin.bottom;

// Generate source particles in a sine wave with random noise
var numbers = d3.range(0, width, 10).map(function (d,i) {
  return [d, height * (0.4 * Math.sin(d/(0.075*width)) + 0.4 + Math.random()/5)];
});

var line = d3.line();

var svg = d3.select('svg')
  .attr('width', width + margin.left + margin.right)
  .attr('height', height + margin.top + margin.bottom)
  .append('g')
  .attr('transform', 'translate(' + margin.left +',' + margin.top + ')');

// Plot a circle for each source particle
svg.append('g')
  .attr('class', 'data')
  .selectAll('circle').data(numbers)
  .enter().append('circle')
  .attr('r', 2)
  .attr('cx', function (d) { return d[0]; })
  .attr('cy', function (d) { return d[1]; });

svg.append('g')
  .attr('class', 'smoothed')
  .append('path');

d3.select('#bandwidth-slider')
  .on('input', renderLine);

renderLine();

function renderLine() {
  // Get the value of the slider
  var bandwidth = +document.getElementById('bandwidth-slider').value;

  d3.select('#current-bandwidth').text(bandwidth)

  svg.select('.smoothed path')
    .datum(smoothedNumbers(d3.range(0, width, 10), numbers, bandwidth))
    .attr('d', line);
}

// Compute estimated value at each target x coordinate using the
// source particles (the samples).
function smoothedNumbers (targets, sources, bandwidth) {
  return targets.map(function (t) {
    var numerator = d3.sum(sources, function (s) {
      return gaussian(s[0], t, bandwidth) * s[1];
    });

    var denominator = d3.sum(sources, function (s) {
      return gaussian(s[0], t, bandwidth);
    });

    return [t, numerator / denominator];
  });
}

function gaussian (target, source, bandwidth) {
  return Math.exp(-Math.pow(target - source, 2) / (2*bandwidth*bandwidth));
}

</script>

## preview.png

      
    Raw
  

              preview.png
            
          
## thumbnail.png

      
    Raw
  

              thumbnail.png
	<!DOCTYPE html>
	<meta charset="utf-8">
	<style>

	html, body {
	margin: 0;
	}

	circle {
	fill: #666;
	}

	path {
	fill: none;
	stroke: teal;
	stroke-width: 2px;
	opacity: 0.5;
	}

	</style>

	<div>
	Bandwidth: <span id="current-bandwidth">15</span><br>
	1<input type="range" min="1" max="200" value="15" class="slider" id="bandwidth-slider">200
	</div>
	<svg></svg>

	<script src="https://d3js.org/d3.v4.min.js"></script>
	<script>

	var margin = {left: 10, top: 10, right: 10, bottom: 10};
	var width = 960 - margin.left - margin.right;
	var height = 220 - margin.top - margin.bottom;

	// Generate source particles in a sine wave with random noise
	var numbers = d3.range(0, width, 10).map(function (d,i) {
	return [d, height * (0.4 * Math.sin(d/(0.075*width)) + 0.4 + Math.random()/5)];
	});

	var line = d3.line();

	var svg = d3.select('svg')
	.attr('width', width + margin.left + margin.right)
	.attr('height', height + margin.top + margin.bottom)
	.append('g')
	.attr('transform', 'translate(' + margin.left +',' + margin.top + ')');

	// Plot a circle for each source particle
	svg.append('g')
	.attr('class', 'data')
	.selectAll('circle').data(numbers)
	.enter().append('circle')
	.attr('r', 2)
	.attr('cx', function (d) { return d[0]; })
	.attr('cy', function (d) { return d[1]; });

	svg.append('g')
	.attr('class', 'smoothed')
	.append('path');

	d3.select('#bandwidth-slider')
	.on('input', renderLine);

	renderLine();

	function renderLine() {
	// Get the value of the slider
	var bandwidth = +document.getElementById('bandwidth-slider').value;

	d3.select('#current-bandwidth').text(bandwidth)

	svg.select('.smoothed path')
	.datum(smoothedNumbers(d3.range(0, width, 10), numbers, bandwidth))
	.attr('d', line);
	}

	// Compute estimated value at each target x coordinate using the
	// source particles (the samples).
	function smoothedNumbers (targets, sources, bandwidth) {
	return targets.map(function (t) {
	var numerator = d3.sum(sources, function (s) {
	return gaussian(s[0], t, bandwidth) * s[1];
	});

	var denominator = d3.sum(sources, function (s) {
	return gaussian(s[0], t, bandwidth);
	});

	return [t, numerator / denominator];
	});
	}

	function gaussian (target, source, bandwidth) {
	return Math.exp(-Math.pow(target - source, 2) / (2bandwidthbandwidth));
	}

	</script>
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