JS求解三元一次方程组值的方法
作者：lilili123
这篇文章主要介绍了JS求解三元一次方程组值的方法,涉及JS数学运算的相关操作技巧,需要的朋友可以参考下
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.jb51.net/jisuanqi/equ_jisuanqi
科学计算器在线使用_高级计算器在线计算：
http://tools.jb51.net/jisuanqi/jsqkexue
在线计算器_标准计算器：
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希望本文所述对大家JavaScript程序设计有所帮助。