java Gauss消元法 怎样基于java实现Gauss消元法过程解析

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();
    }    
  }
}

//交换两个整数
  private static void swap(int[] source, int i, int j) {

    int temp = source[i];
    source[i] = source[j];
    source[j] = temp;
  }