高斯定理求线性代数方程java

高斯定理可以用于求解线性代数方程组。下面是一个用Java实现高斯定理求解线性代数方程组的例子：

public class GaussJordanElimination {

    public static void main(String[] args) {
        double[][] a = {{1, 2, 1}, {2, -1, 1}, {1, 1, -2}};
        double[] b = {8, 3, -2};

        double[] x = solveLinearEquations(a, b);

        for (int i = 0; i < x.length; i++) {
            System.out.println("x" + (i + 1) + " = " + x[i]);
        }
    }

    public static double[] solveLinearEquations(double[][] a, double[] b) {
        int n = b.length;
        double[][] ab = new double[n][n + 1];

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                ab[i][j] = a[i][j];
            }
            ab[i][n] = b[i];
        }

        for (int i = 0; i < n; i++) {
            // Find pivot row
            int pivot = i;
            for (int j = i + 1; j < n; j++) {
                if (Math.abs(ab[j][i]) > Math.abs(ab[pivot][i])) {
                    pivot = j;
                }
            }

            // Swap pivot row with current row
            double[] temp = ab[i];
            ab[i] = ab[pivot];
            ab[pivot] = temp;

            // Eliminate current column
            for (int j = i + 1; j < n; j++) {
                double factor = ab[j][i] / ab[i][i];
                for (int k = i; k <= n; k++) {
                    ab[j][k] -= factor * ab[i][k];
                }
            }
        }

        // Back substitution
        double[] x = new double[n];
        for (int i = n - 1; i >= 0; i--) {
            double sum = 0;
            for (int j = i + 1; j < n; j++) {
                sum += ab[i][j] * x[j];
            }
            x[i] = (ab[i][n] - sum) / ab[i][i];
        }

        return x;
    }
}

在这个例子中，我们使用了一个3x3的矩阵和一个长度为3的向量作为输入，在`solveLinearEquations`函数中实现了高斯定理求解线性代数方程组的算法。最后输出求解结果。