TODO
in this iteration, we use the ckmeans algorithm from the simple-statistics package to cluster our data. we pick the minimum value of each cluster as a break. we then use these breaks with a quantile scale to map values in the data to colors on the choropleth map.
this is method is my current favorite way to create breaks, or color thresholds, for a choropleth map.
🎩 @Elijah_Meeks for the idea to try the ckmeans algorithm, as it seems to be the new hotness in the choropleth map breaks scene
a further 🙏 to @recifs for talking through where in the ckmeans clusters its reasonable to pick breaks from.
tl;dr any number between max(class n) and min(class n+1) is OK
do check out the other examples in this world map series:
world map 00 original example
world map 01 fix tooltip value
world map 02 d3 v4
world map 03 es2015 + update code style
world map 04 manual breaks + threshold scale
world map 05 linear breaks + quantize scale
world map 06 linear breaks + quantiles scale
world map 07 Jenks natural breaks
world map 08 ckmeans cluster max breaks
world map 09 ckmeans cluster min breaks
// configuration
const colorVariable = 'Home ownership rate(%)'
const geoIDVariable = 'id'
const format = d3.format(',')
// Set tooltips
const tip = d3
.tip()
.attr('class', 'd3-tip')
.offset([-10, 0])
.html(
d =>
`<strong>Country: </strong><span class='details'>${
d.properties.name
}<br></span><strong>Population: </strong><span class='details'>${format(
d[colorVariable]
)}</span>`
)
tip.direction(function(d) {
if (d.properties.name === 'Antarctica') return 'n'
// Americas
if (d.properties.name === 'Greenland') return 's'
if (d.properties.name === 'Canada') return 'e'
if (d.properties.name === 'USA') return 'e'
if (d.properties.name === 'Mexico') return 'e'
// Europe
if (d.properties.name === 'Iceland') return 's'
if (d.properties.name === 'Norway') return 's'
if (d.properties.name === 'Sweden') return 's'
if (d.properties.name === 'Finland') return 's'
if (d.properties.name === 'Russia') return 'w'
// Asia
if (d.properties.name === 'China') return 'w'
if (d.properties.name === 'Japan') return 's'
// Oceania
if (d.properties.name === 'Indonesia') return 'w'
if (d.properties.name === 'Papua New Guinea') return 'w'
if (d.properties.name === 'Australia') return 'w'
if (d.properties.name === 'New Zealand') return 'w'
// otherwise if not specified
return 'n'
})
tip.offset(function(d) {
// [top, left]
if (d.properties.name === 'Antarctica') return [0, 0]
// Americas
if (d.properties.name === 'Greenland') return [10, -10]
if (d.properties.name === 'Canada') return [24, -28]
if (d.properties.name === 'USA') return [-5, 8]
if (d.properties.name === 'Mexico') return [12, 10]
if (d.properties.name === 'Chile') return [0, -15]
// Europe
if (d.properties.name === 'Iceland') return [15, 0]
if (d.properties.name === 'Norway') return [10, -28]
if (d.properties.name === 'Sweden') return [10, -8]
if (d.properties.name === 'Finland') return [10, 0]
if (d.properties.name === 'France') return [-9, 66]
if (d.properties.name === 'Italy') return [-8, -6]
if (d.properties.name === 'Russia') return [5, 385]
// Africa
if (d.properties.name === 'Madagascar') return [-10, 10]
// Asia
if (d.properties.name === 'China') return [-16, -8]
if (d.properties.name === 'Mongolia') return [-5, 0]
if (d.properties.name === 'Pakistan') return [-10, 13]
if (d.properties.name === 'India') return [-11, -18]
if (d.properties.name === 'Nepal') return [-8, 1]
if (d.properties.name === 'Myanmar') return [-12, 0]
if (d.properties.name === 'Laos') return [-12, -8]
if (d.properties.name === 'Vietnam') return [-12, -4]
if (d.properties.name === 'Japan') return [5, 5]
// Oceania
if (d.properties.name === 'Indonesia') return [0, -5]
if (d.properties.name === 'Papua New Guinea') return [-5, -10]
if (d.properties.name === 'Australia') return [-15, 0]
if (d.properties.name === 'New Zealand') return [-15, 0]
// otherwise if not specified
return [-10, 0]
})
d3.select('body').style('overflow', 'hidden')
const parentWidth = d3
.select('body')
.node()
.getBoundingClientRect().width
const margin = { top: 0, right: 0, bottom: 0, left: 0 }
const width = 960 - margin.left - margin.right
const height = 500 - margin.top - margin.bottom
const color = d3
.scaleQuantile()
.range([
'rgb(247,251,255)',
'rgb(222,235,247)',
'rgb(198,219,239)',
'rgb(158,202,225)',
'rgb(107,174,214)',
'rgb(66,146,198)',
'rgb(33,113,181)',
'rgb(8,81,156)',
'rgb(8,48,107)',
'rgb(3,19,43)'
])
const svg = d3
.select('body')
.append('svg')
.attr('width', width)
.attr('height', height)
.append('g')
.attr('class', 'map')
const projection = d3
.geoRobinson()
.scale(148)
.rotate([352, 0, 0])
.translate([width / 2, height / 2])
const path = d3.geoPath().projection(projection)
svg.call(tip)
queue()
.defer(d3.json, 'world_countries.json')
.defer(d3.tsv, 'home-ownership-by-country-wikipedia.tsv')
.await(ready)
function ready(error, geography, data) {
console.log('data', data)
data.forEach(d => {
console.log('d', d)
console.log('d[colorVariable]', d[colorVariable])
d[colorVariable] = Number(d[colorVariable].replace(',', ''))
})
const colorVariableValueByID = {}
data.forEach(d => {
colorVariableValueByID[d[geoIDVariable]] = d[colorVariable]
})
geography.features.forEach(d => {
d[colorVariable] = colorVariableValueByID[d.id]
})
// calculate ckmeans clusters
// then use the max value of each cluster
// as a break
const numberOfClasses = color.range().length - 1
const ckmeansClusters = ss.ckmeans(
data.map(d => d[colorVariable]),
numberOfClasses
)
const ckmeansBreaks = ckmeansClusters.map(d => d3.min(d))
console.log('numberOfClasses', numberOfClasses)
console.log('ckmeansClusters', ckmeansClusters)
console.log('ckmeansBreaks', ckmeansBreaks)
// set the domain of the color scale based on our data
color.domain(ckmeansBreaks)
//
// .domain(jenksNaturalBreaks)
//
// .domain(d3.extent(data, d => d[colorVariable]));
//
// .domain([
// 10000,
// 100000,
// 500000,
// 1000000,
// 5000000,
// 10000000,
// 50000000,
// 100000000,
// 500000000,
// 1500000000
// ]);
svg
.append('g')
.attr('class', 'countries')
.selectAll('path')
.data(geography.features)
.enter()
.append('path')
.attr('d', path)
.style('fill', d => {
if (typeof colorVariableValueByID[d.id] !== 'undefined') {
return color(colorVariableValueByID[d.id])
}
return 'white'
})
.style('fill-opacity', 0.8)
.style('stroke', d => {
if (d[colorVariable] !== 0) {
return 'white'
}
return 'lightgray'
})
.style('stroke-width', 1)
.style('stroke-opacity', 0.5)
// tooltips
.on('mouseover', function(d) {
tip.show(d)
d3.select(this)
.style('fill-opacity', 1)
.style('stroke-opacity', 1)
.style('stroke-width', 2)
})
.on('mouseout', function(d) {
tip.hide(d)
d3.select(this)
.style('fill-opacity', 0.8)
.style('stroke-opacity', 0.5)
.style('stroke-width', 1)
})
svg
.append('path')
.datum(topojson.mesh(geography.features, (a, b) => a.id !== b.id))
.attr('class', 'names')
.attr('d', path)
}
<!DOCTYPE html>
<meta charset="utf-8">
<style>
.names {
fill: none;
stroke: #fff;
stroke-linejoin: round;
}
/* Tooltip CSS */
.d3-tip {
line-height: 1.5;
font-weight: 400;
font-family:"avenir next", Arial, sans-serif;
padding: 6px;
background: rgba(0, 0, 0, 0.6);
color: #FFA500;
border-radius: 1px;
pointer-events: none;
}
/* Creates a small triangle extender for the tooltip */
.d3-tip:after {
box-sizing: border-box;
display: inline;
font-size: 8px;
width: 100%;
line-height: 1.5;
color: rgba(0, 0, 0, 0.6);
position: absolute;
pointer-events: none;
}
/* Northward tooltips */
.d3-tip.n:after {
content: "\25BC";
margin: -1px 0 0 0;
top: 100%;
left: 0;
text-align: center;
}
/* Eastward tooltips */
.d3-tip.e:after {
content: "\25C0";
margin: -4px 0 0 0;
top: 50%;
left: -8px;
}
/* Southward tooltips */
.d3-tip.s:after {
content: "\25B2";
margin: 0 0 1px 0;
top: -8px;
left: 0;
text-align: center;
}
/* Westward tooltips */
.d3-tip.w:after {
content: "\25B6";
margin: -4px 0 0 -1px;
top: 50%;
left: 100%;
}
/*
text{
pointer-events:none;
}
*/
.details{
color: white;
}
</style>
<body>
<script src="https://d3js.org/d3.v4.min.js"></script>
<script src="https://d3js.org/queue.v1.min.js"></script>
<script src="https://d3js.org/topojson.v1.min.js"></script>
<script src="https://d3js.org/d3-geo-projection.v1.min.js"></script>
<script src="d3-tip.js"></script>
<script src='https://unpkg.com/simple-statistics@2.0.0/dist/simple-statistics.min.js'></script>
<script src='https://cdnjs.cloudflare.com/ajax/libs/babel-standalone/6.10.3/babel.min.js'></script>
<script src='./index.js' lang='babel' type='text/babel'>
</script>
</body>
</html>/**
* d3.tip
* Copyright (c) 2013 Justin Palmer
*
* Tooltips for d3.js SVG visualizations
*/
// eslint-disable-next-line no-extra-semi
;(function(root, factory) {
if (typeof define === 'function' && define.amd) {
// AMD. Register as an anonymous module with d3 as a dependency.
define([
'd3-collection',
'd3-selection'
], factory)
} else if (typeof module === 'object' && module.exports) {
/* eslint-disable global-require */
// CommonJS
var d3Collection = require('d3-collection'),
d3Selection = require('d3-selection')
module.exports = factory(d3Collection, d3Selection)
/* eslint-enable global-require */
} else {
// Browser global.
var d3 = root.d3
// eslint-disable-next-line no-param-reassign
root.d3.tip = factory(d3, d3)
}
}(this, function(d3Collection, d3Selection) {
// Public - contructs a new tooltip
//
// Returns a tip
return function() {
var direction = d3TipDirection,
offset = d3TipOffset,
html = d3TipHTML,
node = initNode(),
svg = null,
point = null,
target = null
function tip(vis) {
svg = getSVGNode(vis)
if (!svg) return
point = svg.createSVGPoint()
document.body.appendChild(node)
}
// Public - show the tooltip on the screen
//
// Returns a tip
tip.show = function() {
var args = Array.prototype.slice.call(arguments)
if (args[args.length - 1] instanceof SVGElement) target = args.pop()
var content = html.apply(this, args),
poffset = offset.apply(this, args),
dir = direction.apply(this, args),
nodel = getNodeEl(),
i = directions.length,
coords,
scrollTop = document.documentElement.scrollTop ||
document.body.scrollTop,
scrollLeft = document.documentElement.scrollLeft ||
document.body.scrollLeft
nodel.html(content)
.style('opacity', 1).style('pointer-events', 'all')
while (i--) nodel.classed(directions[i], false)
coords = directionCallbacks.get(dir).apply(this)
nodel.classed(dir, true)
.style('top', (coords.top + poffset[0]) + scrollTop + 'px')
.style('left', (coords.left + poffset[1]) + scrollLeft + 'px')
return tip
}
// Public - hide the tooltip
//
// Returns a tip
tip.hide = function() {
var nodel = getNodeEl()
nodel.style('opacity', 0).style('pointer-events', 'none')
return tip
}
// Public: Proxy attr calls to the d3 tip container.
// Sets or gets attribute value.
//
// n - name of the attribute
// v - value of the attribute
//
// Returns tip or attribute value
// eslint-disable-next-line no-unused-vars
tip.attr = function(n, v) {
if (arguments.length < 2 && typeof n === 'string') {
return getNodeEl().attr(n)
}
var args = Array.prototype.slice.call(arguments)
d3Selection.selection.prototype.attr.apply(getNodeEl(), args)
return tip
}
// Public: Proxy style calls to the d3 tip container.
// Sets or gets a style value.
//
// n - name of the property
// v - value of the property
//
// Returns tip or style property value
// eslint-disable-next-line no-unused-vars
tip.style = function(n, v) {
if (arguments.length < 2 && typeof n === 'string') {
return getNodeEl().style(n)
}
var args = Array.prototype.slice.call(arguments)
d3Selection.selection.prototype.style.apply(getNodeEl(), args)
return tip
}
// Public: Set or get the direction of the tooltip
//
// v - One of n(north), s(south), e(east), or w(west), nw(northwest),
// sw(southwest), ne(northeast) or se(southeast)
//
// Returns tip or direction
tip.direction = function(v) {
if (!arguments.length) return direction
direction = v == null ? v : functor(v)
return tip
}
// Public: Sets or gets the offset of the tip
//
// v - Array of [x, y] offset
//
// Returns offset or
tip.offset = function(v) {
if (!arguments.length) return offset
offset = v == null ? v : functor(v)
return tip
}
// Public: sets or gets the html value of the tooltip
//
// v - String value of the tip
//
// Returns html value or tip
tip.html = function(v) {
if (!arguments.length) return html
html = v == null ? v : functor(v)
return tip
}
// Public: destroys the tooltip and removes it from the DOM
//
// Returns a tip
tip.destroy = function() {
if (node) {
getNodeEl().remove()
node = null
}
return tip
}
function d3TipDirection() { return 'n' }
function d3TipOffset() { return [0, 0] }
function d3TipHTML() { return ' ' }
var directionCallbacks = d3Collection.map({
n: directionNorth,
s: directionSouth,
e: directionEast,
w: directionWest,
nw: directionNorthWest,
ne: directionNorthEast,
sw: directionSouthWest,
se: directionSouthEast
}),
directions = directionCallbacks.keys()
function directionNorth() {
var bbox = getScreenBBox()
return {
top: bbox.n.y - node.offsetHeight,
left: bbox.n.x - node.offsetWidth / 2
}
}
function directionSouth() {
var bbox = getScreenBBox()
return {
top: bbox.s.y,
left: bbox.s.x - node.offsetWidth / 2
}
}
function directionEast() {
var bbox = getScreenBBox()
return {
top: bbox.e.y - node.offsetHeight / 2,
left: bbox.e.x
}
}
function directionWest() {
var bbox = getScreenBBox()
return {
top: bbox.w.y - node.offsetHeight / 2,
left: bbox.w.x - node.offsetWidth
}
}
function directionNorthWest() {
var bbox = getScreenBBox()
return {
top: bbox.nw.y - node.offsetHeight,
left: bbox.nw.x - node.offsetWidth
}
}
function directionNorthEast() {
var bbox = getScreenBBox()
return {
top: bbox.ne.y - node.offsetHeight,
left: bbox.ne.x
}
}
function directionSouthWest() {
var bbox = getScreenBBox()
return {
top: bbox.sw.y,
left: bbox.sw.x - node.offsetWidth
}
}
function directionSouthEast() {
var bbox = getScreenBBox()
return {
top: bbox.se.y,
left: bbox.se.x
}
}
function initNode() {
var div = d3Selection.select(document.createElement('div'))
div
.style('position', 'absolute')
.style('top', 0)
.style('opacity', 0)
.style('pointer-events', 'none')
.style('box-sizing', 'border-box')
return div.node()
}
function getSVGNode(element) {
var svgNode = element.node()
if (!svgNode) return null
if (svgNode.tagName.toLowerCase() === 'svg') return svgNode
return svgNode.ownerSVGElement
}
function getNodeEl() {
if (node == null) {
node = initNode()
// re-add node to DOM
document.body.appendChild(node)
}
return d3Selection.select(node)
}
// Private - gets the screen coordinates of a shape
//
// Given a shape on the screen, will return an SVGPoint for the directions
// n(north), s(south), e(east), w(west), ne(northeast), se(southeast),
// nw(northwest), sw(southwest).
//
// +-+-+
// | |
// + +
// | |
// +-+-+
//
// Returns an Object {n, s, e, w, nw, sw, ne, se}
function getScreenBBox() {
var targetel = target || d3Selection.event.target
while (targetel.getScreenCTM == null && targetel.parentNode == null) {
targetel = targetel.parentNode
}
var bbox = {},
matrix = targetel.getScreenCTM(),
tbbox = targetel.getBBox(),
width = tbbox.width,
height = tbbox.height,
x = tbbox.x,
y = tbbox.y
point.x = x
point.y = y
bbox.nw = point.matrixTransform(matrix)
point.x += width
bbox.ne = point.matrixTransform(matrix)
point.y += height
bbox.se = point.matrixTransform(matrix)
point.x -= width
bbox.sw = point.matrixTransform(matrix)
point.y -= height / 2
bbox.w = point.matrixTransform(matrix)
point.x += width
bbox.e = point.matrixTransform(matrix)
point.x -= width / 2
point.y -= height / 2
bbox.n = point.matrixTransform(matrix)
point.y += height
bbox.s = point.matrixTransform(matrix)
return bbox
}
// Private - replace D3JS 3.X d3.functor() function
function functor(v) {
return typeof v === 'function' ? v : function() {
return v
}
}
return tip
}
// eslint-disable-next-line semi
}));Rank Country Home ownership rate(%) Date of Information id link
1 Romania 96.4 2015[2] ROU Romania
2 Singapore 90.7 2017[3] SGP Singapore
3 Slovakia 90.3 2014[2] SVK Slovakia
4 China 90 2014[4] CHN China
5 Cuba 90 2014[5] CUB Cuba
6 Croatia 89.7 2014[2] HRV Croatia
7 Lithuania 89.4 2015[2] LTU Lithuania
8 India 86.6 2011[6] IND India
9 Hungary 86.3 2015[2] HUN Hungary
10 Russia 84 2012[7] RUS Russia
11 Poland 83.5 2014[2] POL Poland
12 Oman 83 2014[8] OMN Oman
13 Norway 82.8 2015[2] NOR Norway
14 Bulgaria 82.3 2015[2] BGR Bulgaria
15 Serbia 82 2017[9] SRB Serbia
16 Estonia 81.5 2015[2] EST Estonia
17 Latvia 80.2 2015[2] LVA Latvia
18 Malta 80 2014[2] 173 Malta
19 Mexico 80 2009[10] MEX Mexico
20 Thailand 80 2002[11] THA Thailand
21 Spain 78.2 2015[2] ESP Spain
22 Czech Republic 78 2015[2] CZE Czech Republic
23 Iceland 77.8 2015[2] ISL Iceland
24 Slovenia 76.2 2015[2] SVN Slovenia
25 Trinidad and Tobago 76 2013[12] TTO Trinidad and Tobago
26 Portugal 74.9 2014[2] PRT Portugal
27 Brazil 74.4 2008[13] BRA Brazil
28 Greece 74 2014[2] GRC Greece
29 Cyprus 73.1 2014[2] CYP Cyprus
30 Italy 72.9 2014[2] ITA Italy
31 Finland 72.7 2015[2] FIN Finland
32 Luxembourg 72.5 2014[2] LUX Luxembourg
33 Belgium 71.3 2016[2] BEL Belgium
34 Sweden 70.6 2015[2] SWE Sweden
35 Ireland 68.6 2014[14] IRL Ireland
36 Netherlands 67.8 2015[2] NLD Netherlands
37 Canada 67.6 2013[15] CAN Canada
38 Israel 67.3 2014[16] ISR Israel
39 Turkey 67.3 2011[17] TUR Turkey
40 Australia 65.5 2016[18] AUS Australia
41 France 65 2014[2] FRA France
42 United States 64.5 2014[19] USA United States
43 United Kingdom 63.5 2015[2] GBR United Kingdom
44 New Zealand 63.2 2017[20] NZL New Zealand
45 Denmark 62.7 2015[2] DNK Denmark
46 Japan 61.6 2008[21] JPN Japan
47 South Korea 56.8 2015[22] KOR South Korea
48 Austria 55 2016[2] AUT Austria
49 Germany 51.9 2015[2] DEU Germany
50 Hong Kong 51 2014[23] HKG Hong Kong
51 Switzerland 43.4 2015[2] CHE Switzerland// # [Jenks natural breaks optimization](http://en.wikipedia.org/wiki/Jenks_natural_breaks_optimization)
//
// Implementations: [1](http://danieljlewis.org/files/2010/06/Jenks.pdf) (python),
// [2](https://github.com/vvoovv/djeo-jenks/blob/master/main.js) (buggy),
// [3](https://github.com/simogeo/geostats/blob/master/lib/geostats.js#L407) (works)
function jenks(data, n_classes) {
// Compute the matrices required for Jenks breaks. These matrices
// can be used for any classing of data with `classes <= n_classes`
function getMatrices(data, n_classes) {
// in the original implementation, these matrices are referred to
// as `LC` and `OP`
//
// * lower_class_limits (LC): optimal lower class limits
// * variance_combinations (OP): optimal variance combinations for all classes
var lower_class_limits = [],
variance_combinations = [],
// loop counters
i, j,
// the variance, as computed at each step in the calculation
variance = 0;
// Initialize and fill each matrix with zeroes
for (i = 0; i < data.length + 1; i++) {
var tmp1 = [], tmp2 = [];
for (j = 0; j < n_classes + 1; j++) {
tmp1.push(0);
tmp2.push(0);
}
lower_class_limits.push(tmp1);
variance_combinations.push(tmp2);
}
for (i = 1; i < n_classes + 1; i++) {
lower_class_limits[1][i] = 1;
variance_combinations[1][i] = 0;
// in the original implementation, 9999999 is used but
// since Javascript has `Infinity`, we use that.
for (j = 2; j < data.length + 1; j++) {
variance_combinations[j][i] = Infinity;
}
}
for (var l = 2; l < data.length + 1; l++) {
// `SZ` originally. this is the sum of the values seen thus
// far when calculating variance.
var sum = 0,
// `ZSQ` originally. the sum of squares of values seen
// thus far
sum_squares = 0,
// `WT` originally. This is the number of
w = 0,
// `IV` originally
i4 = 0;
// in several instances, you could say `Math.pow(x, 2)`
// instead of `x * x`, but this is slower in some browsers
// introduces an unnecessary concept.
for (var m = 1; m < l + 1; m++) {
// `III` originally
var lower_class_limit = l - m + 1,
val = data[lower_class_limit - 1];
// here we're estimating variance for each potential classing
// of the data, for each potential number of classes. `w`
// is the number of data points considered so far.
w++;
// increase the current sum and sum-of-squares
sum += val;
sum_squares += val * val;
// the variance at this point in the sequence is the difference
// between the sum of squares and the total x 2, over the number
// of samples.
variance = sum_squares - (sum * sum) / w;
i4 = lower_class_limit - 1;
if (i4 !== 0) {
for (j = 2; j < n_classes + 1; j++) {
// if adding this element to an existing class
// will increase its variance beyond the limit, break
// the class at this point, setting the lower_class_limit
// at this point.
if (variance_combinations[l][j] >=
(variance + variance_combinations[i4][j - 1])) {
lower_class_limits[l][j] = lower_class_limit;
variance_combinations[l][j] = variance +
variance_combinations[i4][j - 1];
}
}
}
}
lower_class_limits[l][1] = 1;
variance_combinations[l][1] = variance;
}
// return the two matrices. for just providing breaks, only
// `lower_class_limits` is needed, but variances can be useful to
// evaluage goodness of fit.
return {
lower_class_limits: lower_class_limits,
variance_combinations: variance_combinations
};
}
// the second part of the jenks recipe: take the calculated matrices
// and derive an array of n breaks.
function breaks(data, lower_class_limits, n_classes) {
var k = data.length - 1,
kclass = [],
countNum = n_classes;
// the calculation of classes will never include the upper and
// lower bounds, so we need to explicitly set them
kclass[n_classes] = data[data.length - 1];
kclass[0] = data[0];
// the lower_class_limits matrix is used as indexes into itself
// here: the `k` variable is reused in each iteration.
while (countNum > 1) {
kclass[countNum - 1] = data[lower_class_limits[k][countNum] - 2];
k = lower_class_limits[k][countNum] - 1;
countNum--;
}
return kclass;
}
if (n_classes > data.length) return null;
// sort data in numerical order, since this is expected
// by the matrices function
data = data.slice().sort(function (a, b) { return a - b; });
// get our basic matrices
var matrices = getMatrices(data, n_classes),
// we only need lower class limits here
lower_class_limits = matrices.lower_class_limits;
// extract n_classes out of the computed matrices
return breaks(data, lower_class_limits, n_classes);
}id name population
CHN China "1330141295"
IND India "1173108018"
USA United States "310232863"
IDN Indonesia "242968342"
BRA Brazil "201103330"
PAK Pakistan "177276594"
BGD Bangladesh "158065841"
NGA Nigeria "152217341"
RUS Russia "139390205"
JPN Japan "126804433"
MEX Mexico "112468855"
PHL Philippines "99900177"
VNM Vietnam "89571130"
ETH Ethiopia "88013491"
DEU Germany "82282988"
EGY Egypt "80471869"
TUR Turkey "77804122"
COD "Congo, Democratic Republic of the" "70916439"
IRN Iran "67037517"
THA Thailand "66404688"
FRA France "64057792"
GBR United Kingdom "61284806"
ITA Italy "58090681"
MMR Burma "53414374"
ZAF South Africa "49109107"
KOR "Korea, South" "48636068"
UKR Ukraine "45415596"
COL Colombia "44205293"
SDN Sudan "41980182"
TZA Tanzania "41892895"
ARG Argentina "41343201"
ESP Spain "40548753"
KEN Kenya "40046566"
POL Poland "38463689"
DZA Algeria "34586184"
CAN Canada "33759742"
UGA Uganda "33398682"
MAR Morocco "31627428"
PER Peru "29907003"
IRQ Iraq "29671605"
SAU Saudi Arabia "29207277"
AFG Afghanistan "29121286"
NPL Nepal "28951852"
UZB Uzbekistan "27865738"
VEN Venezuela "27223228"
MYS Malaysia "26160256"
GHA Ghana "24339838"
YEM Yemen "23495361"
TWN Taiwan "23024956"
PRK "Korea, North" "22757275"
SYR Syria "22198110"
ROU Romania "22181287"
MOZ Mozambique "22061451"
AUS Australia "21515754"
LKA Sri Lanka "21513990"
MDG Madagascar "21281844"
CIV Cote d'Ivoire "21058798"
CMR Cameroon "19294149"
NLD Netherlands "16783092"
CHL Chile "16746491"
BFA Burkina Faso "16241811"
NER Niger "15878271"
KAZ Kazakhstan "15460484"
MWI Malawi "15447500"
ECU Ecuador "14790608"
KHM Cambodia "14753320"
SEN Senegal "14086103"
MLI Mali "13796354"
GTM Guatemala "13550440"
AGO Angola "13068161"
ZMB Zambia "12056923"
ZWE Zimbabwe "11651858"
CUB Cuba "11477459"
RWA Rwanda "11055976"
GRC Greece "10749943"
PRT Portugal "10735765"
TUN Tunisia "10589025"
TCD Chad "10543464"
BEL Belgium "10423493"
GIN Guinea "10324025"
CZE Czech Republic "10201707"
SOM Somalia "10112453"
BOL Bolivia "9947418"
HUN Hungary "9880059"
BDI Burundi "9863117"
DOM Dominican Republic "9794487"
BLR Belarus "9612632"
HTI Haiti "9203083"
SWE Sweden "9074055"
BEN Benin "9056010"
AZE Azerbaijan "8303512"
AUT Austria "8214160"
HND Honduras "7989415"
CHE Switzerland "7623438"
TJK Tajikistan "7487489"
ISR Israel "7353985"
SRB Serbia "7344847"
BGR Bulgaria "7148785"
HKG Hong Kong "7089705"
LAO Laos "6993767"
LBY Libya "6461454"
JOR Jordan "6407085"
PRY Paraguay "6375830"
TGO Togo "6199841"
PNG Papua New Guinea "6064515"
SLV El Salvador "6052064"
NIC Nicaragua "5995928"
ERI Eritrea "5792984"
DNK Denmark "5515575"
KGZ Kyrgyzstan "5508626"
SVK Slovakia "5470306"
FIN Finland "5255068"
SLE Sierra Leone "5245695"
ARE United Arab Emirates "4975593"
TKM Turkmenistan "4940916"
CAF Central African Republic "4844927"
SGP Singapore "4701069" not listed
NOR Norway "4676305"
BIH Bosnia and Herzegovina "4621598"
GEO Georgia "4600825"
CRI Costa Rica "4516220"
HRV Croatia "4486881"
MDA Moldova "4317483"
NZL New Zealand "4252277"
IRL Ireland "4250163"
COG "Congo, Republic of the" "4125916"
LBN Lebanon "4125247"
PRI Puerto Rico "3977663"
LBR Liberia "3685076"
ALB Albania "3659616"
LTU Lithuania "3545319"
URY Uruguay "3510386"
PAN Panama "3410676"
MRT Mauritania "3205060"
MNG Mongolia "3086918"
OMN Oman "2967717"
ARM Armenia "2966802"
JAM Jamaica "2847232"
KWT Kuwait "2789132"
PSE West Bank "2514845"
LVA Latvia "2217969"
NAM Namibia "2128471"
MKD Macedonia "2072086"
BWA Botswana "2029307"
SVN Slovenia "2003136"
LSO Lesotho "1919552"
GMB "Gambia, The" "1824158"
KWT Kosovo "1815048"
149 Gaza Strip "1604238" not listed
GNB Guinea-Bissau "1565126"
GAB Gabon "1545255"
SWZ Swaziland "1354051"
153 Mauritius "1294104" not listed
EST Estonia "1291170"
TTO Trinidad and Tobago "1228691"
TLS Timor-Leste "1154625"
CYP Cyprus "1102677"
FJI Fiji "957780"
QAT Qatar "840926"
160 Comoros "773407" not listed
GUY Guyana "748486"
DJI Djibouti "740528"
163 Bahrain "738004" not listed
BTN Bhutan "699847"
MNE Montenegro "666730"
GNQ Equatorial Guinea "650702"
SLB Solomon Islands "609794"
168 Macau "567957" not listed
169 Cape Verde "508659" not listed
LUX Luxembourg "497538"
ESH Western Sahara "491519"
SUR Suriname "486618"
173 Malta "406771" not listed
174 Maldives "395650" not listed
BRN Brunei "395027"
BLZ Belize "314522"
BHS "Bahamas, The" "310426"
ISL Iceland "308910"
179 French Polynesia "291000" not listed
180 Barbados "285653" not listed
181 Mayotte "231139" not listed
NCL New Caledonia "229993"
183 Netherlands Antilles "228693" not listed
VUT Vanuatu "221552"
185 Samoa "192001" not listed
186 Sao Tome and Principe "175808" not listed
187 Saint Lucia "160922" not listed
188 Tonga "122580" not listed
189 Virgin Islands "109775" not listed
190 Grenada "107818" not listed
191 "Micronesia, Federated States of" "107154" not listed
192 Aruba "104589" not listed
193 Saint Vincent and the Grenadines "104217" not listed
194 Kiribati "99482" not listed
195 Jersey "91812" not listed
196 Seychelles "88340" not listed
197 Antigua and Barbuda "86754" not listed
198 Andorra "84525" not listed
199 Isle of Man "76913" not listed
DOM Dominica "72813"
201 Bermuda "68268" not listed
202 American Samoa "66432" not listed
203 Marshall Islands "65859" not listed
204 Guernsey "65632" not listed
GRL Greenland "57637"
206 Cayman Islands "50209" not listed
207 Saint Kitts and Nevis "49898" not listed
208 Faroe Islands "49057" not listed
209 Northern Mariana Islands "48317" not listed
210 Liechtenstein "35002" not listed
211 San Marino "31477" not listed
212 Monaco "30586" not listed
213 Saint Martin "30235" not listed
214 Gibraltar "28877" not listed
215 British Virgin Islands "24939" not listed
216 Turks and Caicos Islands "23528" not listed
217 Palau "20879" not listed
218 Akrotiri "15700" not listed
219 Dhekelia "15700" not listed
220 Wallis and Futuna "15343" not listed
221 Anguilla "14764" not listed
222 Nauru "14264" not listed
223 Cook Islands "11488" not listed
224 Tuvalu "10472" not listed
225 "Saint Helena, Ascension, and Tristan da Cunha" "7670" not listed
226 Saint Barthelemy "7406" not listed
227 Saint Pierre and Miquelon "6010" not listed
228 Montserrat "5118" not listed
FLK Falkland Islands (Islas Malvinas) "3140"
230 Norfolk Island "2155" not listed
231 Svalbard "2067" not listed
232 Christmas Island "1402" not listed
233 Tokelau "1400" not listed
234 Niue "1354" not listed
235 Holy See (Vatican City) 829 not listed
236 Cocos (Keeling) Islands 596 not listed
237 Pitcairn Islands 48 not listed
ATA Antarctica 0
ATF French Southern and Antarctic Lands 0
SDS South Sudan "12152321"
ABV Somaliland "3500000"
OSA Kosovo "1824000"