为什么我的 Javascript 高斯消元程序在我输入矩阵时不起作用？

Question

我在 Javascript 中有一个程序可以执行高斯消元来求解方程组。我的问题是，当用户尝试输入系数矩阵和解向量时，程序根本无法运行。现在，我知道它有效，因为如果在代码中输入数据，例如

var A = [[1, 1, 1], [2, 1, 2], [1, 2, 3]];
var x = [6, 10, 14];

程序会正确输出答案。当手动输入数据时，我的问题就来了。老实说，我找不到它有什么问题，因为我已经检查过输入工作正常并且处理工作正常。

<html>
<head>
  <title>
    Solving a system of equations
  </title>
</head>

<body>
  <script type="text/javascript">
    var abs = Math.abs;

    function array_fill(i, n, v) {
      var a = [];
      for (; i < n; i++) {
        a.push(v);
      }
      return a;
    }
    /**
     * Gaussian elimination
     * @param  array A matrix
     * @param  array x vector
     * @return array x solution vector
     */
    function gauss(A, x) {

      //Index variables
      var i, k, j;

      var A_copy = [];
      var x_copy = [];

      //Copy A
      for (var i = 0; i < A.length; ++i) {
        A_copy[i] = A[i].slice();
      }

      //Copy b
      for (var i = 0; i < x.length; ++i) {
        x_copy[i] = x[i];
      }
      // Just make a single matrix
      for (i = 0; i < A_copy.length; i++) {
        A_copy[i].push(x_copy[i]);
      }
      var n = A_copy.length;

      for (i = 0; i < n; i++) {
        // Search for maximum in this column
        var maxEl = abs(A_copy[i][i]),
          maxRow = i;
        for (k = i + 1; k < n; k++) {
          if (abs(A_copy[k][i]) > maxEl) {
            maxEl = abs(A_copy[k][i]);
            maxRow = k;
          }
        }
        // Swap maximum row with current row (column by column)
        for (k = i; k < n + 1; k++) {
          var tmp = A_copy[maxRow][k];
          A_copy[maxRow][k] = A_copy[i][k];
          A_copy[i][k] = tmp;
        }
        // Make all rows below this one 0 in current column
        for (k = i + 1; k < n; k++) {
          var c = -A_copy[k][i] / A_copy[i][i];
          for (j = i; j < n + 1; j++) {
            if (i === j) {
              A_copy[k][j] = 0;
            } else {
              A_copy[k][j] += c * A_copy[i][j];
            }
          }
        }
      }
      // Solve equation Ax=b for an upper triangular matrix A
      x_copy = array_fill(0, n, 0);
      for (i = n - 1; i > -1; i--) {
        x_copy[i] = A_copy[i][n] / A_copy[i][i];
        for (k = i - 1; k > -1; k--) {
          A_copy[k][n] -= A_copy[k][i] * x_copy[i];
        }
      }
      return x_copy;
    }

    alert("Solving a System of equations")
    var rows = prompt("Enter the number of variables of the system");
    var A = [];
    alert("Enter the equations´ coefficients");
    for (var i = 0; i < rows; i++) {
      A.push([]);
      A[i].push(new Array(rows));
      for (var j = 0; j < rows; j++) {
        A[i][j] = prompt()
      }
    }
    alert("Now enter the solutions of each respective equation");
    x = new Array(rows)
    for (i = 0; i < rows; i++) {
      x[i] = prompt()
    }
    result = gauss(A, x);
    document.write(result);
  </script>
</body>
</html>

输出应该只是求解系统的浮点数，但是当我尝试手动输入矩阵时它会显示 NaN

Answer 1

问题是您从 prompt 函数输入的是一个字符串。您必须先将其转换为数值。最简单的方法是在 prompt:

前面加上 +

A[i][j] = +prompt()

x[i] = +prompt()

为什么我的 Javascript 高斯消元程序在我输入矩阵时不起作用？

Why is my Javascript Gauss Elimination program not working when I input the matrix?

javascript

equation

algebra

matrix