Gauss消元法的原理及Java实现

package peterxiazhe;

import java.util.Scanner;

public class Gauss {
    /**
     * 列主元高斯消去法
     */
    static double A[][];
    static double b[];
    static double x[];
    
    static int n;    //n表示未知数的个数
    static int n_2;    //记录换行的次数
    
    public static void main(String[] args) {
        System.out.println("--------------输入方程组未知数的个数---------------");
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        
        A = new double[n][n];
        b = new double[n];
        x = new double[n];
        
        System.out.println("--------------输入方程组的系数矩阵A:---------------");
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < n; j++) {
                A[i][j] = sc.nextDouble();
            }
        }
        
        System.out.println("--------------输入方程组的常量向量b:---------------");
        for(int i = 0; i < n; i++) {
                b[i] = sc.nextDouble();
            }
        
        Elimination();
        BackSubstitution();
        PrintRoot();
    }
    
    
    //消元法
    public static void Elimination() {
        PrintA();
        for(int k = 0; k < n; k++) {
            WrapRow(k);
            for(int i = k+1; i < n; i++) {
                double l = A[i][k] / A[k][k];
                A[i][k] = 0;
                
                for(int j = k+1; j < n; j++) {
                    A[i][j] = A[i][j] - l * A[k][j];
                }
                b[i] = b[i] - l * b[k];
            }
            //System.out.println("第" + k + "次消元后:");
            //PrintA();
        }
    }
    
    //回代法
    public static void    BackSubstitution() {
        x[n-1] = b[n-1] / A[n-1][n-1];
        for(int i = n - 2; i >= 0; i--) {
            x[i] = (b[i] - solve(i)) / A[i][i];
        }
    }
    
    public static double solve(int i) {
        double result = 0.0;
        for(int j = i; j < n; j++)
            result += A[i][j] * x[j];
        return result;
    }
    
    
    //输出方程组的根
    public static void PrintRoot() {
        System.out.println("--------------方程组的根为---------------");
        for(int  i = 0; i < n; i++) {
            System.out.println("x" + (i+1) + " = " + x[i]);
        }
    }
    
    //交换Swap函数???
    public static void Swap(double[] ar, int x, int y) {
        Double tmp = ar[x];
        ar[x] = ar[y];
        ar[y] = tmp;
    }
    
    public static void PrintA() {    //输出A的增广矩阵
        //System.out.println("--------------增广矩阵---------------");
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < n; j++) {
                System.out.print(A[i][j] + " ");
            }
            System.out.println(b[i]);
        }
    }
    
    //交换矩阵的行
    public static void WrapRow(int k) {    //k表示第k+1轮消元
        double maxElement = Math.abs(A[k][k]);
        
        int WrapRowIndex = k;    //    记住要交换的行
        for(int i = k + 1; i < n; i++) {
            if (Math.abs(A[i][k]) > maxElement) {
                WrapRowIndex = i;
                maxElement = A[i][k];
            }
        }
        if (WrapRowIndex != k) {    //交换求得最大主元
            n_2 += 1;
            System.out.println("k = " + k + "时，" + "要交换的行为" + k + "和"+ WrapRowIndex);
            
            //先交换A
            for(int j = k; j < n; j++) {
                double[] arr = {A[k][j], A[WrapRowIndex][j]};
                Swap(arr, 0, 1);
                A[k][j] = arr[0]; A[WrapRowIndex][j] = arr[1];
//                double tmp = A[k][j];
//                A[k][j] = A[WrapRowIndex][j];
//                A[WrapRowIndex][j] = tmp;
            }
            
            //再交换b
            double[] arr = {b[k], b[WrapRowIndex]};
            Swap(arr, 0, 1);
            b[k] = arr[0]; b[WrapRowIndex] = arr[1];
//            double tmp = b[k];
//            b[k] = b[WrapRowIndex];
//            b[WrapRowIndex] = tmp;
            System.out.println("--------------交换后---------------");
            PrintA();
        }        
    }
}