文章目录

  • 正态分布(vue 实现)
    • 在线生成正态分布曲线
    • GitHub源码下载
    • 效果图
    • Html 代码
    • 原数据

正态分布(vue 实现)

在线生成正态分布曲线

GitHub源码下载

效果图

Html 代码

<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"><meta http-equiv="refresh" content=""><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Echarts 绘制正态分布曲线</title><!-- 引入数据文件 --><script src="json/data.js"></script><!-- 引入 vue.js --><!-- 工作环境禁止访问该链接，更换为 cdn 资源 --><!-- <script src="https://cdn.jsdelivr.net/npm/vue/dist/vue.js"></script> --><script src="https://cdn.bootcdn.net/ajax/libs/vue/2.6.12/vue.js"></script><!-- 引入 echarts.js --><script src="https://cdn.staticfile.org/echarts/4.3.0/echarts.min.js"></script><!-- 引入 mathJax.js --><script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=AM_HTMLorMML-full"> </script>
</head><body><div id="app"><div style="height: 90px; width: 36%; float: left; ">正态分布曲线函数： {{mathJax}}<span style="color:blue">其中:`\mu` ：数学期望`\sigma` ：标准差</span></div><div style=" height: 90px; float: left; padding-left: 450px; "><p>总长度：{{ data.length}}</p><p>总 和： {{sum}}</p><p>平均值：{{average}}</p><p>最大值：{{max}}</p><p>最小值：{{min}}</p><p>{{isSample ? '样本' : '总体' }}方差：{{  variance}}</p><p>{{isSample ? '样本' : '总体' }}标准差：{{ standardDeviation}}</p><p>一倍标准差范围：{{ standarDevRangeOfOne.low  +" ~ "+ standarDevRangeOfOne.up}}</p><p>二倍标准差范围：{{ standarDevRangeOfTwo.low +" ~ "+ standarDevRangeOfTwo.up}}</p><p>三倍标准差范围：{{ standarDevRangeOfThree.low +" ~ "+ standarDevRangeOfThree.up}}</p><!-- {{ dataAfterCleanX }} --><!-- {{ normalDistribution }} --></div><div style="height: 90px; clear: both;">在这里输入你的数据（用英文逗号隔开）：<input type="text" v-model="input" style="margin: 24px; width: 36%; height: 16px;"></div><div ref="chart" id="chart" style="width: 1866px;height:762px;"></div><div></div></div><script>var app = new Vue({el: '#app',data: {// 首页正态曲线的计算公式mathJax: '`f(x) = (1 / (\sqrt {2\pi} \sigma)) e^(-(x-\mu)^2/(2\sigma^2))`',// 数据源（从隔壁的 js 文件中引入）json: {},// 页面中输入的数据。初始默认为 json 文件input: '', // 数组的 watch 监听不太方便处理// 是否为样本数据isSample: true,},watch: {// 监听输入框，即时更新图形input: function (val) {this.input = val;this.loadChartsSeried() // 加载数据this.initChartsData('chart') // 生成 Echarts 图 },},computed: {/*** @Description： 获取数据源* @Author： ChengduMeng* @Date： 2020-11-27 14:56:07* */data: {get() {// 因为数组的监听不太好处理，所以多转换一次return this.input.split(',').map(t => parseFloat(t))},set(v) {// 如果给 data 赋值，只能是数组类型if (!(v instanceof Array)) return// 同步更新 input 的值this.input = v.join(',')}},/*** @Description： 有序数据源（方便操作）* @Author： ChengduMeng* @Date： 2020-11-28 14:17:24* */dataOrderBy() {const data = this.data.concat([]); // 为防止 sort 方法修改原数组，对原数组进行拷贝，操作副本。return data.sort((a, b) => a - b)},/*** @Description： 数据整理。原数据整理为：{数据值 : 数据频率}* @Author： ChengduMeng* @Date： 2020-11-28 13:59:12* */dataAfterClean() {let res = {}const data = this.dataOrderByfor (let i = 0; i < this.data.length; i++) {let key = parseFloat(this.data[i]).toFixed(1) // 这里保留 1 位小数if (key !== "NaN" && parseFloat(key) === 0)key = "0.0" //这个判断用来处理保留小数位后 -0.0 和 0.0 判定为不同 key 的 bugif (res[key])res[key] += 1elseres[key] = 1}console.log(res)return res},/*** @Description： 数据整理。返回源数据所有值（排序后）* @Author： ChengduMeng* @Date： 2020-11-28 14:35:52* */dataAfterCleanX() {return Object.keys(this.dataAfterClean).sort((a, b) => a - b).map(t => parseFloat(t).toFixed(1)) // 保留 1 位小数// return Object.keys(this.dataAfterClean) // 不保证顺序一致},/*** @Description： 数据整理。返回源数据所有值对应的频率（排序后） -- 与 dataAfterCleanX 顺序一致* @Author： ChengduMeng* @Date： 2020-11-28 13:59:12* */dataAfterCleanY() {let r = []for (let i = 0; i < this.dataAfterCleanX.length; i++) {r.push(this.dataAfterClean[this.dataAfterCleanX[i]])}return r},/*** @Description： 数据整理。返回源数据所有值对应的频率，刻度更细致（保留 2 位小数） -- 与 dataAfterCleanX 顺序一致* @Author： ChengduMeng* @Date： 2020-11-29 13:59:22* */dataAfterCleanXSub() {let r = []for (let i = parseFloat(this.min.toFixed(1)); i <= parseFloat(this.max.toFixed(1)); i +=0.01)r.push(i.toFixed(2))console.log(r)return r},/*** @Description： 计算平均数。这里的平均数指的是数学期望、算术平均数* @Author： ChengduMeng* @Date： 2020-11-27 15:24:14* */sum() {if (this.data.length === 0) return 0return this.data.reduce((prev, curr) => prev + curr)},/*** @Description： 计算平均数。这里的平均数指的是数学期望、算术平均数* @Author： ChengduMeng* @Date： 2020-11-27 15:26:03* */average() {return this.sum / this.data.length},/*** @Description： 计算众数* @Author： ChengduMeng* @Date： 2020-11-27 15:26:03* */mode() {return 0},/*** @Description： 计算中位数* @Author： ChengduMeng* @Date： 2020-11-27 15:26:03* */median() {const data = this.dataOrderByreturn (data[(data.length - 1) >> 1] + data[data.length >> 1]) / 2},/*** @Description： 计算偏差* @Author： ChengduMeng* @Date： 2020-11-27 15:26:03* */deviation() {// 1、求平均数const avg = this.average// 2、返回偏差。 f(x) = x - avgreturn this.data.map(x => x - avg)},/*** @Description： 计算总体/样本方差* @Author： ChengduMeng* @Date： 2020-11-27 15:26:03* */variance() {if (this.data.length === 0) return 0// 1、求偏差const dev = this.deviation// 2、求偏差平方和const sumOfSquOfDev = dev.map(x => x * x).reduce((x, y) => x + y)// 3、返回方差return sumOfSquOfDev / (this.isSample ? (this.data.length - 1) : this.data.length)},/*** @Description： 计算总体/样本标准差* @Author： ChengduMeng* @Date： 2020-11-27 15:26:03* */standardDeviation() {return Math.sqrt(this.variance)},/*** @Description： 计算一倍标准差范围* @Author： ChengduMeng* @Date： 2020-11-27 15:26:03* */standarDevRangeOfOne() {return {low: this.average - 1 * this.standardDeviation,up: this.average + 1 * this.standardDeviation}},/*** @Description： 计算三倍标准差范围* @Author： ChengduMeng* @Date： 2020-11-27 15:29:43* */standarDevRangeOfTwo() {return {low: this.average - 2 * this.standardDeviation,up: this.average + 2 * this.standardDeviation}},/*** @Description： 计算三倍标准差范围* @Author： ChengduMeng* @Date： 2020-11-27 15:30:49* */standarDevRangeOfThree() {return {low: this.average - 3 * this.standardDeviation,up: this.average + 3 * this.standardDeviation}},/*** @Description： 计算最小值* @Author： ChengduMeng* @Date： 2020-11-28 13:19:06* */min() {return Math.min.apply(null, this.data)},/*** @Description： 计算最大值* @Author： ChengduMeng* @Date： 2020-11-28 13:21:16* */max() {return Math.max.apply(null, this.data)},/*** @Description： 正态分布(高斯分布)计算公式* @Author： ChengduMeng* @Date： 2020-11-28 13:46:18* */normalDistribution() {// 计算公式： `f(x) = (1 / (\sqrt {2\pi} \sigma)) e^(-(x-\mu)^2/(2\sigma^2))`// return (1 / Math.sqrt(2 * Math.PI) * a) * (Math.exp(-1 * ((x - u) * (x - u)) / (2 * a * a)))let res = []for (let i = 0; i < this.dataAfterCleanX.length; i++) {const x = this.dataAfterCleanX[i]const a = this.standardDeviationconst u = this.averageconst y = (1 / (Math.sqrt(2 * Math.PI) * a)) * (Math.exp(-1 * ((x - u) * (x - u)) / (2 *a * a)))res.push(y)if (x == 11.8)console.log(y) // 正态分布峰值，用于验证}return res},},created() {},mounted() {// 示例中提供了 3 组数据。所以这里随机生成 1~3 的数字，用于随机展示数据const r = Math.floor(Math.random() * (3 - 1 + 1)) + 1;switch (r) {case 1:this.data = json.R1break;case 2:this.data = json.R2break;case 3:this.data = json.R3breakdefault:this.data = json.R1break;}this.loadChartsSeried() // 加载数据this.initChartsData('chart') // 生成 Echarts 图console.log(`总长度： ${this.data.length}`)console.log(`总  和： ${this.sum}`)console.log(`平均值： ${this.average}`)console.log(`最大值： ${this.max}`)console.log(`最小值： ${this.min}`)console.log(`${this.isSample ? '样本' : '总体'}方差 ${this.variance}`)console.log(`${this.isSample ? '样本' : '总体'}标准差： ${this.standardDeviation}`)//console.log(`正态分布频率： ${this.normalDistribution}`)console.log(`一倍标准差范围： ${this.standarDevRangeOfOne.low }>>> ${this.standarDevRangeOfOne.up}`)console.log(`二倍标准差范围： ${this.standarDevRangeOfTwo.low }>>> ${this.standarDevRangeOfTwo.up}`)console.log(`三倍标准差范围： ${this.standarDevRangeOfThree.low} >>>${this.standarDevRangeOfThree.up}`)},methods: {/*** @Description： 加载 Echarts 图所需数据** @Params url* * @return* @Author： ChengduMeng* @Date： 2020-11-27 13:24:26* */loadChartsSeried() {this.json = json},/*** @Description： 生成 Echarts 图** @Params ref：容器* * @return* @Author： ChengduMeng* @Date： 2020-11-27 13:23:26* */initChartsData(ref) {let chart = this.$refs[ref]if (!chart) returnchart = echarts.init(chart)// Echarts 图的配置let options = {// Echarts 图 -- 标题title: {text: 'Echarts 绘制正态分布曲线（有 3 组示例数据，刷新随机显示）'},// Echarts 图 -- 工具tooltip: {},// Echarts 图 -- 图例legend: {data: ['f(x)']},// Echarts 图 -- x 坐标轴刻度 -- 正态分布数值xAxis: [{// name : "标准刻度(0.1)",data: this.dataAfterCleanX,// min: this.min,// max: this.max}],// Echarts 图 -- y 坐标轴刻度yAxis: [{type: 'value',name: '频数',position: 'left',// 网格线splitLine: {show: false},axisLine: {lineStyle: {color: 'orange'}},axisLabel: {formatter: '{value}'}},{type: 'value',name: '概率',position: 'right',// 网格线splitLine: {show: false},axisLine: {lineStyle: {color: 'black'}},axisLabel: {formatter: '{value}'}},],// Echarts 图 -- y 轴数据series: [{name: '源数据', // y 轴名称type: 'bar', // y 轴类型yAxisIndex: 0,barGap: 0,barWidth: 27,itemStyle: {normal: {show: true,color: 'rgba(255, 204, 0,.3)', //柱子颜色borderColor: '#FF7F50' //边框颜色}},data: this.dataAfterCleanY, // y 轴数据 -- 源数据}, {name: '正态分布', // y 轴名称type: 'line', // y 轴类型// symbol: 'none', //去掉折线图中的节点smooth: true, //true 为平滑曲线yAxisIndex: 1,data: this.normalDistribution, // y 轴数据 -- 正态分布// 警示线markLine: {symbol: ['none'], // 箭头方向lineStyle: {type: "silent",color: "green",},itemStyle: {normal: {show: true,color: 'black'}},label: {show: true,position: "middle"},data: [{name: '一倍标准差',xAxis: this.standarDevRangeOfOne.low.toFixed(1),// 当 n 倍标准差在坐标轴外时，将其隐藏，否则它会默认显示在最小值部分，容易引起混淆lineStyle: {opacity: (this.min > this.standarDevRangeOfOne.low) ? 0 : 1},label: {show: !(this.min > this.standarDevRangeOfOne.low)}}, {name: '一倍标准差',xAxis: this.standarDevRangeOfOne.up.toFixed(1),lineStyle: {opacity: (this.max < this.standarDevRangeOfOne.up) ?0 : 1},label: {show: !(this.max < this.standarDevRangeOfOne.up)}}, {name: '二倍标准差',xAxis: this.standarDevRangeOfTwo.low.toFixed(1),lineStyle: {opacity: (this.min > this.standarDevRangeOfTwo.low) ? 0 : 1},label: {show: !(this.min > this.standarDevRangeOfTwo.low)}}, {name: '二倍标准差',xAxis: this.standarDevRangeOfTwo.up.toFixed(1),lineStyle: {opacity: (this.max < this.standarDevRangeOfTwo.up) ? 0 : 1},label: {show: !(this.max < this.standarDevRangeOfTwo.up)}}, {name: '三倍标准差',xAxis: this.standarDevRangeOfThree.low.toFixed(1),lineStyle: {opacity: (this.min > this.standarDevRangeOfThree.low) ? 0 : 1},label: {show: !(this.min > this.standarDevRangeOfThree.low)}}, {name: '三倍标准差',xAxis: this.standarDevRangeOfThree.up.toFixed(1),lineStyle: {opacity: (this.max < this.standarDevRangeOfThree.up) ? 0 : 1},label: {show: !(this.max < this.standarDevRangeOfThree.up)}}, {name: '平均值',// type: 'average',xAxis: this.average.toFixed(1),lineStyle: {color: 'red'}}, ]}}],}chart.setOption(options)window.addEventListener("resize", () => {chart.resize()})},/*** @Description： 正态分布(高斯分布)计算公式（已将其移动到计算属性中自行计算，该方法暂做保留用于手动传参计算）** @Params x: 未知数* @Params u: 代替 `\mu`，意为 数学期望，长的像，好区分  *-^* @Params a: 代替 `\sigma`，意为 标准差* * @return* @Author： ChengduMeng* @Date： 2020-11-27 15:09:01* */// normalDistribution(x, u, a) {//     // 计算公式： `f(x) = (1 / (\sqrt {2\pi} \sigma)) e^(-(x-\mu)^2/(2\sigma^2))`//     return (1 / (Math.sqrt(2 * Math.PI) * a)) * (Math.exp(-1 * ((x - u) * (x - u)) / (2 * a * a)))// },}})</script>
</body></html>

原数据

json = {"R1": 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