個體導向馬可夫鍊模擬 Agent-Based Markov Chain Simulation
- 2016-03-19
- Liu, An-Chi 劉安齊
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。
這個程式簡單模擬有一群人，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。
(這邊採用 Agent-Based 而不是直接矩陣運算)
效果如下：
程式碼 (將程式碼複製存為 index.html，並使用瀏覽器打開)
<!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>