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JavaScript 方程求解器库

发布于 2024-10-09 11:57:53 字数 98 浏览 1 评论 0原文

是否有 JavaScript 库或函数可以求解变量方程？

例如9 = 3 + x并求解x。但它还应该求解更高级的方程，包括正弦、余弦和正切。

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山人契 2024-10-16 11:57:53

我想推荐 nerdamer。它可以代数求解四次函数，并且可以数值求解一系列函数。另一个需要考虑的库是 Algebrite。

//solve linear equations
var x = nerdamer.solve('(x+1)*3=x-6', 'x');
console.log(x.toString());
//quadratic
var x2 = nerdamer.solve('x^2-8x+15', 'x');
console.log(x2.toString());
//quadratic algebraically
var x3 = nerdamer.solve('x^2-ax+3*b', 'x');
console.log(x3.toString());
//multiple roots
var x4 = nerdamer.solve('x^6+41*x^5+652*x^4+5102*x^3+20581*x^2+40361*x+30030', 'x');
console.log(x4.toString());
//functions - numerically around to zero up to a predefined range
var x5 = nerdamer.solve('cos(x)^2+sin(x-1)', 'x');
console.log(x5.toString());
//solve a system of linear equations
var x6 = nerdamer.solveEquations(['2x+y=7', 'x-y+3z=11', 'y-z=-1']);
console.log(x6.toString());
//solve a system of nonlinear equations
var x7 = nerdamer.solveEquations(['3*x^2/y=2', 'z*x*y-1=35', '5*z^2+7=52']);
console.log(x7.toString());

<script src="https://cdn.jsdelivr.net/npm/nerdamer@latest/nerdamer.core.js"></script>
<script src="https://cdn.jsdelivr.net/npm/nerdamer@latest/Algebra.js"></script>
<script src="https://cdn.jsdelivr.net/npm/nerdamer@latest/Calculus.js"></script>
<script src="https://cdn.jsdelivr.net/npm/nerdamer@latest/Solve.js"></script>

I'd like to propose nerdamer. It can algebraically solve up to quartic functions and it can numerically solve a range of functions. Another library to consider is Algebrite.

//solve linear equations
var x = nerdamer.solve('(x+1)*3=x-6', 'x');
console.log(x.toString());
//quadratic
var x2 = nerdamer.solve('x^2-8x+15', 'x');
console.log(x2.toString());
//quadratic algebraically
var x3 = nerdamer.solve('x^2-ax+3*b', 'x');
console.log(x3.toString());
//multiple roots
var x4 = nerdamer.solve('x^6+41*x^5+652*x^4+5102*x^3+20581*x^2+40361*x+30030', 'x');
console.log(x4.toString());
//functions - numerically around to zero up to a predefined range
var x5 = nerdamer.solve('cos(x)^2+sin(x-1)', 'x');
console.log(x5.toString());
//solve a system of linear equations
var x6 = nerdamer.solveEquations(['2x+y=7', 'x-y+3z=11', 'y-z=-1']);
console.log(x6.toString());
//solve a system of nonlinear equations
var x7 = nerdamer.solveEquations(['3*x^2/y=2', 'z*x*y-1=35', '5*z^2+7=52']);
console.log(x7.toString());

<script src="https://cdn.jsdelivr.net/npm/nerdamer@latest/nerdamer.core.js"></script>
<script src="https://cdn.jsdelivr.net/npm/nerdamer@latest/Algebra.js"></script>
<script src="https://cdn.jsdelivr.net/npm/nerdamer@latest/Calculus.js"></script>
<script src="https://cdn.jsdelivr.net/npm/nerdamer@latest/Solve.js"></script>

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↙温凉少女 2024-10-16 11:57:53

您可以通过执行 Excel 所谓的“目标寻求”来近似解决方案 - 测试 x 的值，直到等式两边近似匹配。您可以通过用 "=" 符号拆分方程，将每次出现的 x 替换为一个值，对两边进行 eval 来实现此目的，并确定差异是否低于某个阈值。虽然相对简单，但这种方法存在缺陷（除了它是近似值这一事实之外），例如，算法可能认为两侧正在收敛，而实际上它只是局部最小值/最大值，并且在差异正好低于您的阈值。您还需要测试多个起点来求解具有多个解的方程。

对于一个像人类一样求解方程的程序来说（通过重新排列方程的两侧并应用反函数、导数/积分等等）要复杂得多，并且不知何故感觉完全是专有的；）

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山川志 2024-10-16 11:57:53

快速搜索会发现 algebra.js 和 js 解算器。我对他们一无所知，但他们看起来很合法。 algebra.js 有一个很好的 OOP API，但似乎无法处理三角函数。

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早茶月光 2024-10-16 11:57:53

查看脚本 f(x)= 的牛顿方法程序0。它使用牛顿切线法求解方程。

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第七度阳光i 2024-10-16 11:57:53

Ceres.js 可以找到 f(x) = 形式的方程组的解0. 使用 Emscripten 从 C++ 移植到 JavaScript。该文件有点大，但如果您需要真正高性能的求解器，这是您最好的选择。它以网络组装方式运行，因此速度很高。
这是一个例子：

<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8"/>
</head>
<body>

<h3>Powell Function</h3>
    <p>This is an example of the solution of the powell function using Ceres.js</p>
    <pre><code id="powell_demo_code" class="language-js"></code></pre>
    <textarea id="powell_demo" rows="40" cols="110"></textarea>
    <script id="powell_demo_code_source">
        async function ceresSolvePowell() {
            const {Ceres} = await import('https://cdn.jsdelivr.net/gh/Pterodactylus/Ceres.js@latest/dist/ceres.min.js');
    
            var fn1 = function f1(x){
                return (x[0]+10*x[1]);
            }
    
            var fn2 = function f2(x){
                return (Math.sqrt(5)*(x[2]-x[3]));
            }
            
            var fn3 = function f3(x){
                return Math.pow(x[1]-2*x[2],2);
            }
            
            var fn4 = function f4(x){
                return Math.sqrt(10)*Math.pow(x[0]-x[3],2);
            }
            
            let solver = new Ceres()
            solver.addFunction(fn1) //Add the first equation to the solver.
            solver.addFunction(fn2) //Add the second equation to the solver.
            solver.addFunction(fn3) //Add the third equation to the solver.
            solver.addFunction(fn4) //Add the forth equation to the solver.
            //solver.addCallback(c1) //Add the callback to the solver.
            //solver.addLowerbound(0,1.6) //Add a lower bound to the x[0] variable
            //solver.addUpperbound(1,1.7) //Add a upper bound to the x[1] variable
            
            var x_guess = [1,2,3,4] //Guess the initial values of the solution.
            let s = await solver.solve(x_guess) //Solve the equation
            var x = s.x //assign the calculated solution array to the variable x
            document.getElementById("powell_demo").value = s.report //Print solver report
            solver.remove() //required to free the memory in C++
            
        }
        ceresSolvePowell();
    </script>
</body>
</html>

Ceres.js can find the solution to an array of equations of the form f(x) = 0. It is ported from C++ to JavaScript with Emscripten. The file is a bit large but if you need a really high performance solver this is your best bet. It runs in web-assembly so the speed is high.
Here is an example:

<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8"/>
</head>
<body>

<h3>Powell Function</h3>
    <p>This is an example of the solution of the powell function using Ceres.js</p>
    <pre><code id="powell_demo_code" class="language-js"></code></pre>
    <textarea id="powell_demo" rows="40" cols="110"></textarea>
    <script id="powell_demo_code_source">
        async function ceresSolvePowell() {
            const {Ceres} = await import('https://cdn.jsdelivr.net/gh/Pterodactylus/Ceres.js@latest/dist/ceres.min.js');
    
            var fn1 = function f1(x){
                return (x[0]+10*x[1]);
            }
    
            var fn2 = function f2(x){
                return (Math.sqrt(5)*(x[2]-x[3]));
            }
            
            var fn3 = function f3(x){
                return Math.pow(x[1]-2*x[2],2);
            }
            
            var fn4 = function f4(x){
                return Math.sqrt(10)*Math.pow(x[0]-x[3],2);
            }
            
            let solver = new Ceres()
            solver.addFunction(fn1) //Add the first equation to the solver.
            solver.addFunction(fn2) //Add the second equation to the solver.
            solver.addFunction(fn3) //Add the third equation to the solver.
            solver.addFunction(fn4) //Add the forth equation to the solver.
            //solver.addCallback(c1) //Add the callback to the solver.
            //solver.addLowerbound(0,1.6) //Add a lower bound to the x[0] variable
            //solver.addUpperbound(1,1.7) //Add a upper bound to the x[1] variable
            
            var x_guess = [1,2,3,4] //Guess the initial values of the solution.
            let s = await solver.solve(x_guess) //Solve the equation
            var x = s.x //assign the calculated solution array to the variable x
            document.getElementById("powell_demo").value = s.report //Print solver report
            solver.remove() //required to free the memory in C++
            
        }
        ceresSolvePowell();
    </script>
</body>
</html>

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