背景
我正在尝试为可汗学院写一个练习。他们的代码都可以在这里找到：https ://github.com/Khan/khan-exercises 。这是我第一次真正编程任何东西，我基本上只是通过查看示例代码来学习 html 和 js。
作为本练习的一部分，我需要绘制一个“随机函数”，并找到它的零点。我写了一个找零算法（将间隔重复减半以放大零。）。我知道牛顿方法的某些变体可能更快，但我想确保收敛。我的“随机函数”采用一组点值并用多项式样条插值这些点。这些中的每一个都独立工作：我可以绘制我的“随机函数”，并且可以使用我的寻零算法来逼近 2 的平方根（x^2 - 2 在区间 (1,2) 上的零）。当我试图找到我的“随机函数”的零点时，我遇到了麻烦：我的浏览器进入了无限循环或其他东西。我什至看不到开发人员工具中的错误。
所以我的问题基本上是：
- 我犯了什么错误，在这里消耗了如此多的计算能力？
- 这些功能如何独立工作而不是一起工作？
- 如何修复我的代码？
由于我在整个 knhan academy 框架内工作，我的程序中有太多内容无法发布所有相关代码（它使用 Raphael 来处理图像，预先编写代码以使练习都具有相同的风格等）。我可以给你我写的 html 代码和我写的函数的 .js 文件。
<!DOCTYPE html>
<html data-require="math graphie graphie-helpers steveMath8">
<head>
<title>Piecewise-defined function</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id = "n">randRange(2,4)</var>
<var id = "abscissas">makeXList()</var>
<var id = "ordinates">makeYList(-8,8,abscissas.length)</var>
<var id = "points">makeCoordinates(abscissas,ordinates)</var>
<var id = "f">(function(x){return niceFunction(x,points)})</var>
<!-- <var id = "f">(function(x){return x*x-n})</var>-->
<var id = zeros>locateZeros(f,abscissas)</var>
</div>
<div class="problems">
<div id="problem-type-or-description">
<p class="problem">You are going to have to answer 5</p>
<p class="question">Answer 5</p>
<div class="graphie" id="grid">
graphInit({
range: 10,
scale: 20,
tickStep: 1,
axisArrows: "<->"
});
a =style({
stroke: "red",
strokeWidth: 2
}, function() {
plot( function( x ) { return niceFunction(x,points);
}, [ -10, 10 ] );
});;
a.plot();
</div>
<p class="solution">5</p>
</div>
</div>
<div class="hints">
<!-- Any hints to show to the student. -->
</div>
</div>
</body>
$.extend(KhanUtil, {
//takes num and returns +1 if num>0 or -1 if num<0
steveSign: function(num){
return num && num/Math.abs(num)
},
// Approximates a root of f on the interval (xmin,xmax) by successively halving the interval.
steveRoot: function(f,xmin,xmax){
var l = xmin
var r = xmax
var z = 0
for (i=0;i<10;i++){
z = (l + r)/2
if (KhanUtil.steveSign(f(l)) == KhanUtil.steveSign(f(z))){ l = z}
else{r = z}
}
return z
},
//takes a function and a list of abscissas, and returns an array of zeros - one zero between each pair of abscissas that are of
//opposite sign
locateZeros: function(f,abscissas){
var len = abscissas.length
var list = []
var z = 0
for(i=0;i<len-1;i++){
var x0 = abscissas[i]
var x1 = abscissas[i+1]
var y0 = f(x0)
var y1 = f(y0)
if (KhanUtil.steveSign(y0) !== KhanUtil.steveSign(y1)){
z = KhanUtil.steveRoot(f,x0,x1)
list.push(KhanUtil.steveSign(f(x0)))
}
}
return list
},
steveCubic: function(x){return -Math.pow(x,3)/2+3*x/2},
//niceFunction is a C^1 function which connects the points in "points". It is designed to be used
//in my "curveSketchingIntuition" exercise. Every point in the "points" will have 0 slope, except the first and last point.
niceFunction: function(x,points){
len = points.length
var x1 = points[0][0]
var x2 = points[1][0]
var y1 = points[0][1]
var y2 = points[1][1]
var k = (y1 - y2)/Math.pow(x1-x2,2)
if (x<x2){return k*Math.pow(x-x2,2)+y2}
for (i=1;i<len-2;i++){
var x1 = points[i][0]
var x2 = points[i+1][0]
var y1 = points[i][1]
var y2 = points[i+1][1]
xNew = (x-x1)*2/(x2-x1)-1
yNew = (KhanUtil.steveCubic(xNew)+1)*(y2-y1)/2+y1
if (x>=x1 && x<x2){return yNew}
}
var x1 = points[len-2][0]
var x2 = points[len-1][0]
var y1 = points[len-2][1]
var y2 = points[len-1][1]
var k = (y2 - y1)/Math.pow(x1-x2,2)
if (x>=x1){return k*Math.pow(x-x1,2)+y1}
},
makeXList: function(){
array = [-10]
i=0
while(array[i]<10){
x = array[i]+3*KhanUtil.randRange(1,3)
if (x<10){array.push(x)}
i=i+1
}
array.push(10)
return array
},
makeYList:function(min,max,n){
excluded = [0]
array = [KhanUtil.randRangeExclude(min,max,excluded)]
excluded.push(array[0])
array.push[KhanUtil.randRangeExclude(min,max,excluded)]
excluded = [0]
for (i=1;i<n;i++){
if (array[i-2]<array[i-1]){
array.push(KhanUtil.randRangeExclude(min,array[i-1]-1,excluded))
}
else{array.push(KhanUtil.randRangeExclude(array[i-1]+1,max,excluded))}
}
return array
},
makeCoordinates: function(array1,array2){
array = []
for (i=0;i<array1.length;i++){
array.push([array1[i],array2[i]])
}
return array
},
});