JS求解三元一次方程组值的方法


Posted in Javascript onJanuary 03, 2017

本文实例讲述了JS求解三元一次方程组值的方法。分享给大家供大家参考,具体如下:

// 求用js 码一段代码求 三元一次方程组的值!
// a1 = y * b1 + z * c1 - d1 * x; (1)
// a2 = y * b2 + z * c2 - d2 * x; (2)
// a3 = y * b3 + z * c3 - d3 * x; (3)
// (1) - (2)
// a1 - a2 = y * (c1 - c2) + z * (d1 - d2)  (4)
// (1) - (3)
// a1 - a3 = y * (c1 - c3) + z * (d1 - d3)  (5)
// (4) * (c1 - c3)/(c1 - c2)
// (a1 - a2) * ((c1 - c3)/(c1 - c2)) = y * (c1 - c3) + z * (d1 - d2) * ((c1 - c3)/(c1 - c2));  (6)
// (6) - (5)
// (a1 - a2) * ((c1 - c3)/(c1 - c2)) - (a1 - a3) = z * ((d1 - d2) * ((c1 - c3)/(c1 - c2)) - (d1 - d3));  (7)
//
//==================================================================================================
// (1) * (d2/d1)
// ( a1 * (d2/d1) ) = y * b1 * (d2/d1) + z * c1 * (d2/d1) - d1 * x * (d2/d1)  (4)
// ( a1 * (d2/d1) ) = y * b1 * (d2/d1) + z * c1 * (d2/d1) - d2 * x       (4.1)
// (4.1) - (2)
// ( ( a1 * (d2/d1) ) - a2 ) = y * ( (b1 * (d2/d1)) - b2 ) + z * ( (c1 * (d2/d1)) - c2 );  (5)
// (1) * (d3/d1)
// ( a1 * (d3/d1) ) = y * ( b1 * (d3/d1) ) + z * ( c1 * (d3/d1) ) - d1 * x * (d3/d1)  (6)
// ( a1 * (d3/d1) ) = y * ( b1 * (d3/d1) ) + z * ( c1 * (d3/d1) ) - d3 * x       (6.1)
// (6.1) - (3)
// ( ( a1 * (d3/d1) ) - a3 ) = y * ( ( b1 * (d3/d1) ) - b3 ) + z * ( ( c1 * (d3/d1) ) - c3 )  (7)
// (5) * ( ( (b1 * (d3/d1)) - b3 ) / ( ( b1 * (d2/d1) ) - b2 ) )
// ( ( ( a1 * (d2/d1) ) - a2 ) * ( ( (b1 * (d3/d1)) - b3 ) / ( ( b1 * (d2/d1) ) - b2 ) ) ) = y * ( (b1 * (d3/d1)) - b3 ) + z * ( ( (c1 * (d2/d1)) - c2 ) * ( ( (b1 * (d3/d1)) - b3 ) / ( ( b1 * (d2/d1) ) - b2 ) ) )  (8)
// (8) - (7)
// ( ( ( ( a1 * (d2/d1) ) - a2 ) * ( ( (b1 * (d3/d1)) - b3 ) / ( ( b1 * (d2/d1) ) - b2 ) ) ) - ( ( a1 * (d3/d1) ) - a3 ) )
// =
// z * ( ( ( (c1 * (d2/d1)) - c2 ) * ( ( (b1 * (d3/d1)) - b3 ) / ( ( b1 * (d2/d1) ) - b2 ) ) ) - ( ( c1 * (d3/d1) ) - c3 ) )
//var a1 = 41778.58102, a2 = 60925.87223, a3 = 88229.03849,
//b1 = 72931.77839, b2 = 61296.01212, b3 = 67138.30916,
//c1 = 120.1318412, c2 = 120.1308286, c3 = 120.1573771,
//d1 = 30.27345376, d2 = 30.30174637, d3 = 30.32151101;
//var a1 = 1, a2 = -9, a3 = -3,
//b1 = -1, b2 = 3, b3 = -3,
//c1 = 1, c2 = -2, c3 = -5,
//d1 = -2, d2 = -1, d3 = -4;
var a1 = 11, a2 = 0, a3 = -2,
b1 = 3, b2 = 1, b3 = -1,
c1 = 1, c2 = 1, c3 = -1,
d1 = -2, d2 = -1, d3 = -3;
var equations = [
  "a1 = y * b1 + z * c1 - d1 * x",
  "a2 = y * b2 + z * c2 - d2 * x",
  "a3 = y * b3 + z * c3 - d3 * x"
];
for (var i = 0; i < equations.length; i++) {
  equations[i] = equations[i].replace("a1", "(" + a1 + ")").replace("b1", "(" + b1 + ")").replace("c1", "(" + c1 + ")").replace("d1", "(" + d1 + ")")
  .replace("a2", "(" + a2 + ")").replace("b2", "(" + b2 + ")").replace("c2", "(" + c2 + ")").replace("d2", "(" + d2 + ")")
  .replace("a3", "(" + a3 + ")").replace("b3", "(" + b3 + ")").replace("c3", "(" + c3 + ")").replace("d3", "(" + d3 + ")");
}
console.log(equations);
// 计算三元一次方程
// 确保常量和未知数分开在2边,逻辑安装这样处理的
var LEquat = {
  formatFloat: function(f, digit) {
    var m = Math.pow(10, digit);
    return parseInt(f * m, 10) / m;
  },
  // 是否常量一边, 返回0常量的一边索引,1变量一边的索引,返回一个数组
  separateSide: function(equations) {
    var arr = [], equa = equations.split("=");
    if (equa[0].search(/x|y|z/) == -1) {
      arr = equa.slice(0);
    } else {
      arr[0] = equa[1];
      arr[1] = equa[0];
    }
    return arr;
  },
  // 分隔变量的一边,把x,y,z分隔
  // x 是索引0,y是索引1,z是索引2
  separateVariableSide: function(variableSide) {
    var variables = variableSide.split(/\s+(\+|\-)\s+/);
    var arr = [];
    for (var i = 0; i < variables.length; i++) {
      if (variables[i].search(/x/) != -1) {
        arr[0] = variables[i];
      } else if (variables[i].search(/y/) != -1) {
        arr[1] = variables[i];
      } else if (variables[i].search(/z/) != -1) {
        arr[2] = variables[i];
      }
    }
    return arr;
  },
  // 取出方程里面变量一边对应x,y,z的常量系数
  // 0: x的系数,1:y的系数,2:z的系数
  getCoefficient: function(variableSideArray) {
    var me = LEquat;
    var arr = [];
    for (var i = 0; i < variableSideArray.length; i++) {
      var coeffs = variableSideArray[i].split("*");
      if (coeffs[0].search(/x|y|z/) == -1) {
        arr[i] = coeffs[0];
      } else {
        arr[i] = coeffs[1];
      }
    }
    return arr;
  },
  step: function() {
    var me = LEquat;
    // 分隔第一个方程
    var equation1 = me.separateSide(equations[0]);
    // 分隔第二个方程
    var equation2 = me.separateSide(equations[1]);
    // 分隔第三个方程
    var equation3 = me.separateSide(equations[2]);
    // 第一个方程的常量一边
    var a1 = equation1[0];
    // 第一个方程x系数
    var equa1 = me.getCoefficient(me.separateVariableSide(equation1[1]));
    // y的系数     z的系数     x的系数
    var b1 = equa1[1], c1 = equa1[2], d1 = equa1[0];
    // 第二个方程的常量一边
    var a2 = equation2[0];
    // 第二个方程变量一边系数
    var equa2 = me.getCoefficient(me.separateVariableSide(equation2[1]));
    var b2 = equa2[1], c2 = equa2[2], d2 = equa2[0];
    // 第三个方程的常量一边
    var a3 = equation3[0];
    // 第三个方程变量一边系数
    var equa3 = me.getCoefficient(me.separateVariableSide(equation3[1]));
    var b3 = equa3[1], c3 = equa3[2], d3 = equa3[0];
    // ( a1 * (d2/d1) )
    var left4_1 = " ( " + a1 + " * ( " + d2 + " / " + d1 + " ) ) ";
    // (4.1) 右边
    var right4_1 = " y " + " * " + b1 + " * ( " + d2 + " / " + d1 + " ) + z * " + c1 + " * ( " + d2 + " / " + d1 + " ) - " + d2 + " * x ";
    // 消x (4.1) - (2)
    // ( ( a1 * (d2/d1) ) - a2 ) = y * ( (b1 * (d2/d1)) - b2 ) + z * ( (c1 * (d2/d1)) - c2 );  (5)
    // (5) 中常量的一边
    var left5_1 = " ( " + left4_1 + " - " + a2 + " ) ";
    // (5) 中变量一边
    var right5_1 = " y * ( ( " + b1 + " * ( " + d2 + " / " + d1 + " ) ) - " + b2 + " ) + z * ( ( " + c1 + " * ( " + d2 + " / " + d1 + " ) ) - " + c2 + " ) ";
    // (1) * (d3/d1)
    // ( a1 * (d3/d1) ) = y * ( b1 * (d3/d1) ) + z * ( c1 * (d3/d1) ) - d1 * x * (d3/d1)  (6)
    // ( a1 * (d3/d1) ) = y * ( b1 * (d3/d1) ) + z * ( c1 * (d3/d1) ) - d3 * x       (6.1)
    var left6_1 = " ( " + a1 + " * ( " + d3 + " / " + d1 + " ) ) ";
    var right6_1 = " y * ( " + b1 + " * ( " + d3 + " / " + d1 + " ) ) + z * ( " + c1 + " * ( " + d3 + " / " + d1 + " ) ) - " + d3 + " * x ";
    // (6.1) - (3)
    // ( ( a1 * (d3/d1) ) - a3 ) = y * ( ( b1 * (d3/d1) ) - b3 ) + z * ( ( c1 * (d3/d1) ) - c3 )  (7)
    var left7_1 = " ( " + left6_1 + " - " + a3 + " ) ";
    var right7_1 = " y * ( ( " + b1 + " * ( " + d3 + " / " + d1 + " ) ) - " + b3 + " ) + z * ( ( " + c1 + " * ( " + d3 + " / " + d1 + " ) ) - " + c3 + " ) ";
    // (5) * ( ( (b1 * (d3/d1)) - b3 ) / ( ( b1 * (d2/d1) ) - b2 ) )
    // ( ( ( a1 * (d2/d1) ) - a2 ) * ( ( (b1 * (d3/d1)) - b3 ) / ( ( b1 * (d2/d1) ) - b2 ) ) )
    // = y * ( (b1 * (d3/d1)) - b3 ) + z * ( ( (c1 * (d2/d1)) - c2 ) * ( ( (b1 * (d3/d1)) - b3 ) / ( ( b1 * (d2/d1) ) - b2 ) ) )  (8)
    var left8_1 = " ( " + left5_1 + " * ( ( ( " + b1 + " * ( " + d3 + " / " + d1 + " ) ) - " + b3 + " ) / ( ( " + b1 + " * ( " + d2 + " / " + d1 + " ) ) - " + b2 + " ) ) ) ";
    var right8_1 = " y * ( ( " + b1 + " * ( " + d3 + " / " + d1 + " ) ) - " + b3 + " ) + z * ( ( ( " + c1 + " * ( " + d2 + " / " + d1 + " ) ) - " + c2 + " ) * ( ( ( " + b1 + " * ( " + d3 + " / " + d1 + " ) ) - " + b3 + " ) / ( ( " + b1 + " * ( " + d2 + " / " + d1 + " ) ) - " + b2 + " ) ) ) ";
    // (8) - (7)
    // ( ( ( ( a1 * (d2/d1) ) - a2 ) * ( ( (b1 * (d3/d1)) - b3 ) / ( ( b1 * (d2/d1) ) - b2 ) ) ) - ( ( a1 * (d3/d1) ) - a3 ) )
    // =
    // z * ( ( ( (c1 * (d2/d1)) - c2 ) * ( ( (b1 * (d3/d1)) - b3 ) / ( ( b1 * (d2/d1) ) - b2 ) ) ) - ( ( c1 * (d3/d1) ) - c3 ) )  (9)
    var left9_1 = " ( " + left8_1 + " - " + left7_1 + " ) ";
    var right9_1 = " z * ( ( ( ( " + c1 + " * ( " + d2 + " / " + d1 + " ) ) - " + c2 + " ) * ( ( ( " + b1 + " * ( " + d3 + " / " + d1 + " ) ) - " + b3 + " ) / ( ( " + b1 + " * ( " + d2 + " / " + d1 + " ) ) - " + b2 + " ) ) ) - ( ( " + c1 + " * ( " + d3 + " / " + d1 + " ) ) - " + c3 + " ) ) ";
    var z = left9_1 + " / " + " ( ( ( ( " + c1 + " * ( " + d2 + " / " + d1 + " ) ) - " + c2 + " ) * ( ( ( " + b1 + " * ( " + d3 + " / " + d1 + " ) ) - " + b3 + " ) / ( ( " + b1 + " * ( " + d2 + " / " + d1 + " ) ) - " + b2 + " ) ) ) - ( ( " + c1 + " * ( " + d3 + " / " + d1 + " ) ) - " + c3 + " ) ) ";
    // ( ( a1 * (d2/d1) ) - a2 ) = y * ( (b1 * (d2/d1)) - b2 ) + z * ( (c1 * (d2/d1)) - c2 );
    var y = " ( " + left5_1 + " - " + " z * ( ( " + c1 + " * ( " + d2 + " / " + d1 + " ) ) - " + c2 + " ) ) " + " / " + " ( ( " + b1 + " * ( " + d2 + " / " + d1 + " ) ) - " + b2 + " ) ";
    // 把z代入到(5)中
    y = y.replace("z", z);
    // 把y,z代入方程1
    // a1 = y * b1 + z * c1 - d1 * x
    var x = " ( y * " + b1 + " + z * " + c1 + " - " + a1 + " ) / " + d1;
    x = x.replace("z", z).replace("y", y);
    x = me.formatFloat(eval(x), 2);
    y = me.formatFloat(eval(y), 2);
    z = me.formatFloat(eval(z), 2);
    return {x: x,y: y,z: z};
  }
};
console.log("-----------计算结果--------------");
console.log(LEquat.step());

PS:这里再为大家推荐几款计算工具供大家进一步参考借鉴:

在线一元函数(方程)求解计算工具:
http://tools.3water.com/jisuanqi/equ_jisuanqi

科学计算器在线使用_高级计算器在线计算:
http://tools.3water.com/jisuanqi/jsqkexue

在线计算器_标准计算器:
http://tools.3water.com/jisuanqi/jsq

希望本文所述对大家JavaScript程序设计有所帮助。

Javascript 相关文章推荐
基于jquery实现的可以编辑选择的下拉框的代码
Nov 19 Javascript
JQuery Highcharts 动态生成图表的方法
Nov 15 Javascript
js实现无缝滚动特效
Dec 20 Javascript
js实现颜色阶梯渐变效果(Gradient算法)
Mar 21 Javascript
Bootstrap3.3.7导航栏下拉菜单鼠标滑过展开效果
Oct 31 Javascript
JS扩展String.prototype.format字符串拼接的功能
Mar 09 Javascript
使用JavaScript中的lodash编写双色球效果
Jun 24 Javascript
JS实现动态生成html table表格的方法分析
Jul 11 Javascript
JavaScript实现的级联算法示例【省市二级联动功能】
Dec 25 Javascript
JavaScript中Dom操作实例详解
Jul 08 Javascript
vue项目中使用AES实现密码加密解密(ECB和CBC两种模式)
Aug 12 Javascript
js实现多个标题吸顶效果
Jan 08 Javascript
Vue.js系列之项目结构说明(2)
Jan 03 #Javascript
Vue.js系列之项目搭建(1)
Jan 03 #Javascript
jquery实现下拉框多选方法介绍
Jan 03 #Javascript
jQuery实现可拖拽3D万花筒旋转特效
Jan 03 #Javascript
详解JavaScript常量定义
Jan 03 #Javascript
两种简单的跨域方法(jsonp、php)
Jan 02 #Javascript
JavaScript实现图片瀑布流和底部刷新
Jan 02 #Javascript
You might like
浅析php中抽象类和接口的概念以及区别
2013/06/27 PHP
一个简单且很好用的php分页类
2013/10/26 PHP
Codeigniter实现处理用户登录验证后的URL跳转
2014/06/12 PHP
thinkPHP自定义类实现方法详解
2016/11/30 PHP
PHP simplexml_import_dom()函数讲解
2019/02/03 PHP
javascript add event remove event
2008/04/07 Javascript
JS 创建对象(常见的几种方法)
2008/11/03 Javascript
了解jQuery技巧来提高你的代码(个人觉得那个jquery的手册很不错)
2012/02/10 Javascript
javascript读写json示例
2014/04/11 Javascript
Javascript前端UI框架Kit使用指南之kitjs事件管理
2014/11/28 Javascript
jQuery 3.0中存在问题及解决办法
2016/07/15 Javascript
省市区三级联动jquery实现代码
2020/04/15 Javascript
通过一个简单的例子学会vuex与模块化
2017/11/22 Javascript
在vue中添加Echarts图表的基本使用教程
2017/11/22 Javascript
Vue基础学习之项目整合及优化
2019/06/02 Javascript
JS实现从对象获取对象中单个键值的方法示例
2019/06/05 Javascript
python正则表达式去掉数字中的逗号(python正则匹配逗号)
2013/12/25 Python
python连接mongodb操作数据示例(mongodb数据库配置类)
2013/12/31 Python
Python获取单个程序CPU使用情况趋势图
2015/03/10 Python
基于python爬虫数据处理(详解)
2017/06/10 Python
使用python采集脚本之家电子书资源并自动下载到本地的实例脚本
2018/10/23 Python
django使用xadmin的全局配置详解
2019/11/15 Python
详解Python的三种拷贝方式
2020/02/11 Python
Python3 读取Word文件方式
2020/02/13 Python
Python 解决火狐浏览器不弹出下载框直接下载的问题
2020/03/09 Python
利用python绘制数据曲线图的实现
2020/04/09 Python
python中np是做什么的
2020/07/21 Python
马来西亚排名第一的宠物用品店:Pets Wonderland
2020/04/16 全球购物
软件测试常见笔试题
2012/02/04 面试题
汽车运用工程专业毕业生推荐信
2013/12/25 职场文书
优秀教师先进事迹
2014/01/22 职场文书
运动会解说词100字
2014/01/31 职场文书
2016年五一劳动节专题校园广播稿
2015/12/17 职场文书
用Python爬取某乎手机APP数据
2021/06/15 Python
深入讲解数据库中Decimal类型的使用以及实现方法
2022/02/15 MySQL
Spring依赖注入多种类型数据的示例代码
2022/03/31 Java/Android