高斯消去法java代码_GaussianElimination 高斯消去法java（求逆，求解）

importjava.util.Scanner;public classGaussianElimination{public static void Input(int n, double[][] A, double[] b, intlength){

Scanner in= newScanner(System.in);

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]=in.nextDouble();

}

}if(length == 1){

System.out.println("输入方程组矩阵b：");for (int i = 0; i < n; i++) {

b[i]=in.nextDouble();

}

}

}public static void Merge1(int n, double[][] A, double[] b){for (int i = 0; i < n; i++) {

A[i][n]=b[i];

}

Print(n, A,1);return;

}public static void Merge2(int n, double[][] A){for (int i = 0; i < n; i++) {for (int j = n; j < 2*n; j++) {

A[i][j]= 0;

}

A[i][n+i] = 1;

}

Print(n, A, n);return;

};public static void Print(int n, double[][] A, intlength){

System.out.println("##################手 动 分 割 线#####################");

System.out.println("增广矩阵：");for (int i = 0; i < n; i++) {for (int j = 0; j < n + length; j++) {

System.out.printf("%-11.4f", A[i][j]);

}

System.out.print("\n");

}

}//length为1，求逆为n

public static void Swap(int n, double[][]A, int i, int pivotrow, intlength){double temp = 0;for (int k = 0; k < n+length; k++) {

temp=A[i][k];

A[i][k]=A[pivotrow][k];

A[pivotrow][k]=temp;

}

}//交换行

public static int SelectPivotrow(int n, double[][]A, inti) {int pivotrow =i;for (int j = i + 1; j < n; j++) {if (Math.abs(A[j][i]) >Math.abs(A[pivotrow][i]))

pivotrow=j;

}if (A[pivotrow][i] == 0)return -1;else

returnpivotrow;

}//选择主元

public static void ForwardElimination(int n, double[][]A, intlength){for (int i = 0; i < n-1; i++) {int pivotrow =SelectPivotrow(n, A, i);if(pivotrow == -1){

System.out.println("输出结果不唯一");break;

}

Swap(n, A, i, pivotrow, length);for (int j = i+1; j < n; j++) {double temp = A[j][i]/A[i][i];for (int k = i; k < n+length; k++) {

A[j][k]= A[j][k] - A[i][k] *temp;

}

}

Print(n, A, length);

}

}//前向消去，求length为1，求逆为n

public static void BackElimination(int n, double[][]A, intlength){for (int i = n-1; i > 0; i--) {for (int j = i-1; j >= 0; j--) {double temp = A[j][i]/A[i][i];for (int k = n+length-1; k > j; k--) {

A[j][k]= A[j][k] - A[i][k] *temp;

}

}

Print(n, A, length);

}

}//反向替换，求length为1，求逆为n

public static void Normalization(int n, double[][]A, intlength){for (int i = 0; i < n; i++) {for (int j = n; j < 2*n; j++) {

A[i][j]= A[i][j]/A[i][i];

}

A[i][i]= 1;

}

Print(n, A, length);

}//归一化,length为1，求逆为n

public static void PrintResult(int n, double[][] A, intlength){

System.out.println("##################手 动 分 割 线#####################");

System.out.println("最终结果为：");if(length == 1){for (int i = 0; i < n; i++) {

System.out.println("x"+(i+1)+" = "+A[i][n+length-1]);

}

}else if(n ==length){

System.out.println("矩阵的逆：");for (int i = 0; i < n; i++) {for (int j = n; j < 2*n; j++) {

System.out.printf("%-11.2f", A[i][j]);

}

System.out.print("\n");

}

}return;

}public static void Do(int n, double[][]A, intlength){

ForwardElimination(n, A, length);

BackElimination(n, A, length);

Normalization(n, A, length);

PrintResult(n, A, length);

}public static voidmain(String[] args) {

Scanner in= newScanner(System.in);while(true){

System.out.println("-----------------高 斯 消 元 法------------------");

System.out.println("求逆矩阵请输入1，求解请输入2，退出请输入0。");int flag =in.nextInt();if(flag != 0){

System.out.println("输入方程组的元数：");int n =in.nextInt();double[][] A = new double[n][2*n];double[] b = new double[n];double[] x = new double[n];double[][] A_I = new double[n][n];if(flag ==1){

Input(n, A, b, n);

Merge2(n, A);

Do(n, A, n);

}else{

Input(n, A, b ,1);

Merge1(n, A, b);

Do(n, A,1);

}

}else break;

}

System.out.println("-----------------程 序 结 束 !!------------------");

}

}