馬可夫鏈 (Markov chain) 或稱馬可夫過程 (Markov process)是一種隨機過程，在數學上只要這傳遞矩陣有一些好的性質，就可以證明經由這馬可夫鏈抽樣的分佈會收斂到想要的機率分佈。
這邊我簡單模擬有一群人，分為A和B兩種狀態，並且一開始兩種狀態人數相同，而每回合 A 中的每個人會有 aRate 機率變 B，B 中的每個人會有 bRate 的機率變 A。如此進行多回合。(這是 Agent-Based 而不是直接矩陣運算)
A to B: ( 0 ~ 1 )
B to A: ( 0 ~ 1 )
HTML Code:
B to A: ( 0 ~ 1 )
<!DOCTYPE html>
<html>
<head>
<title>Simulation</title>
<meta charset="utf-8">
<style>
body {
font: 14px sans-serif;
}
.axis path,
.axis line {
fill: none;
stroke: #111;
shape-rendering: crispEdges;
}
.x.axis path {
display: none;
}
</style>
<script src="https://d3js.org/d3.v3.min.js"></script>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.0/jquery.min.js"></script>
</head>
<body>
<p>Exchange System</p>
<p>A to B: ( 0 ~ 1 )</p>
<input type="number" id="aRate" value='0.2' min='0.0' max='1.0'>
<p>B to A: ( 0 ~ 1 )</p>
<input type="number" id="bRate" value='0.1' min='0.0' max='1.0'>
<button>Result</button>
<div id="Res"></div>
<script>
var aRate, bRate;
$(document).ready(function(){
$("button").click(function(){
aRate = $("#aRate").val();
bRate = $("#bRate").val();
f();
});
});
var Pss = { // person state
A: 1,
B: 2
};
function f() {
var res = System.runRounds(), data = [];
for(var i=0; i<= System.NumRounds; i++){
data.push({ Terms: i, A: res[i].A, B: res[i].B});
}
showResult(data);
}
var System = (function (){
var People = [];
var runRounds = function(){
var result = [];
initialize();
result.push({ A: System.NumPeople, B: System.NumPeople}); // initial
for(var i= 0; i< System.NumRounds;i++){
result.push( aRound());
}
return result;
};
var initialize = function(){
People = [];
for(var i= 0; i< System.NumPeople; i++){
People.push(new Person(Pss.A));
People.push(new Person(Pss.B));
}
};
var aRound = function(){
People.forEach(function(ps){
ps.change();
});
return count();
};
var count = function(){
var Pp = People;
var data = { A: 0, B: 0};
for(var i in Pp){
if(Pp[i].State == Pss.A) data.A++;
else data.B++;
}
return data;
};
return{
NumPeople: 10000,
NumRounds: 30,
runRounds: runRounds
};
})();
function Person(state){
this.State = state;
}
Person.prototype.change = function(){
this.Rate = (this.State == Pss.A)? aRate: bRate;
this.State = (Math.random()< this.Rate)? 3^this.State: this.State;
}
function showResult(data) {
var margin = {top: 20, right: 20, bottom: 30, left: 40},
width = 900 - margin.left - margin.right,
height = 500 - margin.top - margin.bottom;
var x0 = d3.scale.ordinal()
.rangeRoundBands([0, width-20], .1);
var x1 = d3.scale.ordinal();
var y = d3.scale.linear()
.range([height, 0]);
var color = d3.scale.ordinal()
.range([ "#aa4748","#ff8c00"]);
var xAxis = d3.svg.axis()
.scale(x0)
.orient("bottom");
var yAxis = d3.svg.axis()
.scale(y)
.orient("left")
.tickFormat(d3.format(".2s"));
$("#Res").empty();
var svg = d3.select("#Res").append("svg")
.attr("width", width + margin.left + margin.right)
.attr("height", height + margin.top + margin.bottom)
.append("g")
.attr("transform", "translate(" + margin.left + "," + margin.top + ")");
var X_Names = ['A','B',];
data.forEach(function(d) {
d.xs = X_Names.map(function(name) { return {name: name, value: +d[name]}; });
});
x0.domain(data.map(function(d) { return d.Terms; }));
x1.domain(X_Names).rangeRoundBands([0, x0.rangeBand()]);
y.domain([0, d3.max(data, function(d) { return d3.max(d.xs, function(d) { return d.value; }); })]);
svg.append("g")
.attr("class", "x axis")
.call(xAxis)
.attr("transform", "translate(0," + height + ")")
.append("text")
.attr("x", width+10)
.attr("y", 18)
.style("text-anchor", "end")
.text("Terms");;
svg.append("g")
.attr("class", "y axis")
.call(yAxis)
.append("text")
.attr("transform", "rotate(-90)")
.attr("y",6)
.attr("dy", ".71em")
.style("text-anchor", "end")
.text("People");
var terms = svg.selectAll(".terms")
.data(data)
.enter().append("g")
.attr("class", "terms")
.attr("transform", function(d) { return "translate(" + x0(d.Terms) + ",0)"; });
terms.selectAll("rect")
.data(function(d) { return d.xs; })
.enter().append("rect")
.attr("width", x1.rangeBand())
.attr("x", function(d) { return x1(d.name); })
.attr("y", function(d) { return y(d.value); })
.attr("height", function(d) { return height - y(d.value); })
.style("fill", function(d) { return color(d.name); });
var legend = svg.selectAll(".legend")
.data(X_Names.slice().reverse())
.enter().append("g")
.attr("class", "legend")
.attr("transform", function(d, i) { return "translate(0," + i * 20 + ")"; });
legend.append("rect")
.attr("x", width - 16)
.attr("width", 18)
.attr("height", 18)
.style("fill", color);
legend.append("text")
.attr("x", width+12 )
.attr("y", 9)
.attr("dy", ".35em")
.style("text-anchor", "end")
.text(function(d) { return d; });
};
</script>
</body>
</html>
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