java - 我的 3x3 矩阵程序的逆部分？

Question

我有一个 3x3 矩阵程序，我想找到矩阵的逆矩阵。说明说 C 是 B 的倒数；即，C*B = B*C = 1，其中 1 是单位矩阵。我知道这可能很简单，但我只需要一些帮助或指导即可

代码如下:

import java.util.Scanner;
import java.lang.*;
import java.io.*;
import java.text.*;
import java.lang.Math.*;
import java.text.DecimalFormat;
import java.lang.String;

public class Program9
{
   static Scanner scan= new Scanner(System.in);
   public static void main(String[] args)
   {    
      Scanner scan= new Scanner(System.in);
      int[][]A=new int[3][3];
      int[][]B=new int[3][3];
      int[][]C=new int[3][3];
      int i, j, num;

      do
      {
         System.out.println("--------------------------------------");
         System.out.println("-           MAIN MENU                -"); 
         System.out.println("- 1.  INPUT FOR MATRIX A & B         -");
         System.out.println("- 2.  REPLACE MATRIX A=C             -");
         System.out.println("- 3.  ADD MATRIX A+B=C               -");
         System.out.println("- 4.  SUBTRACT MATRIX A+B=C          -");
         System.out.println("- 5.  MULTIPLY 3 TO MATRIX A         -");
         System.out.println("- 6.  MULTIPLY MATRIX A*B            -");
         System.out.println("- 7.  REPLACE MATRIX C=0             -");
         System.out.println("- 8.  REPLACE MATRIX C=1             -");
         System.out.println("- 9.  IDENTITY MATRIX                -");
         System.out.println("- 10. TRANSPOSE MATRIX A             -");
         System.out.println("- 11. QUIT                           -");
         System.out.println("--------------------------------------");
         System.out.println();

         System.out.print("Please enter a number: ");
         num= scan.nextInt();

         switch(num)
         {
            case 1: input(A, B);
               break;
            case 2: replaceA (A);
               break;
            case 3: add(A, B);
               break;
            case 4: subtract(A, B);
               break;
            case 5: multiply3(A);
               break;
            case 6: multiplyAB(A,B);
               break;
            case 7: replace0();
               break;
            case 8: replace1();
               break;
            case 9: identity();
               break;
            case 10: trans(A);
               break;
            case 11: inverse(B);
               break;
            case 12: System.out.println("Hope you enjoyed the program");
               break;
            default: System.out.println("Please enter a number");
               break;
         }
      }
      while(num !=11);
   }
   public static void input(int[][] a, int[][] b)
   {
      int i;
      int j;
      System.out.print("Enter numbers into the matrix for matrix A: ");
      for(i=0;i<3;i++)
         for(j=0;j<3;j++)
            a[i][j]=scan.nextInt();
      System.out.println();

      System.out.print("Enter numbers into the matrix for matrix B: ");

      for(i=0;i<3;i++)
         for(j=0;j<3;j++)
            b[i][j]=scan.nextInt();

      System.out.printf("%15s%n", "Matrix A");

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", a[i][j]);
         }
         System.out.println();
      }
      System.out.printf("%15s%n", "Matrix B");

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", b[i][j]);
         }
         System.out.println();
      }
   }
   public static void replaceA(int[][] a)
   {
      int[][] C= new int[3][3];
      int i, j;

      System.out.printf("%15s%n", "Matrix C");

      for(i=0;i<3;i++)
         for(j=0;j<3;j++)
            C[i][j]=a[i][j];

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", C[i][j]);
         }
         System.out.println();
      }
   }
   public static void add(int[][] a, int[][] b)
   {
      int[][] C= new int[3][3];
      int i, j;

      for(i=0;i<3;i++)
         for(j=0;j<3;j++)
            C[i][j]=a[i][j] + b[i][j];

      System.out.printf("%15s%n", "Matrix A");

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", a[i][j]);
         }
         System.out.println();
      }

      System.out.printf("%15s%n", "Matrix B");

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", b[i][j]);
         }
         System.out.println();
      }
      System.out.printf("%15s%n", "Matrix C");

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", C[i][j]);
         }
         System.out.println();
      }
   }
   public static void subtract(int[][] a, int[][] b)
   {
      int[][] C= new int[3][3];
      int i, j;

      for(i=0;i<3;i++)
         for(j=0;j<3;j++)
            C[i][j]=a[i][j] - b[i][j];

      System.out.printf("%15s%n", "Matrix A");

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", a[i][j]);
         }
         System.out.println();
      }

      System.out.printf("%15s%n", "Matrix B");

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", b[i][j]);
         }
         System.out.println();
      }
      System.out.printf("%15s%n", "Matrix C");

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", C[i][j]);
         }
         System.out.println();
      }
   }
   public static void multiply3(int[][] a)
   {
      int[][] C= new int[3][3];
      int i, j;

      for(i=0;i<3;i++)
         for(j=0;j<3;j++)
            C[i][j]=a[i][j] * 3;

      System.out.printf("%15s%n", "Matrix A");

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", a[i][j]);
         }
         System.out.println();
      }

      System.out.printf("%15s%n", "Matrix A times 3");

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", C[i][j]);
         }
         System.out.println();
      }
   }
   public static void multiplyAB(int[][] a, int[][] b)
   {
      int[][] C= new int[3][3];
      int i, j;

      for(i=0;i<3;i++)
         C[i][0] = (a[0][0]*b[0][i]) + (a[i][1]*b[1][0]) + (a[i][2]*b[2][0]);
      for(i=0;i<3;i++)
         C[i][1] = (a[1][0]*b[0][i]) + (a[1][1]*b[1][i]) + (a[1][2]*b[2][i]);
      for(i=0;i<3;i++)
         C[i][0] = (a[2][0]*b[0][i]) + (a[2][1]*b[1][i]) + (a[2][2]*b[2][i]);


      System.out.printf("%15s%n", "Matrix A");

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", a[i][j]);
         }
         System.out.println();
      }

      System.out.printf("%15s%n", "Matrix B");

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", b[i][j]);
         }
         System.out.println();
      }
      System.out.printf("%15s%n", "Matrix A*B");

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", C[i][j]);
         }
         System.out.println();
      }
   }
   public static void replace0()
   {
      int[][] C= new int[3][3];
      int i, j;
      System.out.printf("%15s%n", "Matrix C");

      for(i=0;i<3;i++)
         for(j=0;j<3;j++)
            C[i][j]=0;

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", C[i][j]);
         }
         System.out.println();
      }
   }
   public static void replace1()
   {
      int[][] C= new int[3][3];
      int i, j;
      System.out.printf("%15s%n", "Matrix C");

      for(i=0;i<3;i++)
         for(j=0;j<3;j++)
            C[i][j]=1;

      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", C[i][j]);
         }
         System.out.println();
      }
   }
   public static void identity()
   {
      int[][] C = new int[3][3];
      int i, j;
      System.out.printf("%15s%n", "Matrix C");

      for(i=0; i<3; i++)
      {
         for(j=0; j<3; j++)
         {
            if(i == 0 && j == 0)
               C[0][0]=1;
            else if(i == 1 && j == 1)
               C[1][1]=1;
            else if(i == 2 && j == 2)
               C[2][2]=1;
            else
               C[i][j]=0;
         }
      }
      for(i=0;i<3;i++)
      {
         for(j=0;j<3;j++)
         {
            System.out.printf("%5d", C[i][j]);
         }
         System.out.println();
      }
   }
   public static void trans(int[][] a)
   {
      int[][] C= new int[3][3];
      int i,j;
      int temp=0;

      for(i=0;i<3;i++)
      {
         temp= a[i][0];
         a[i][0] = a[0][i];
         a[0][i]=temp;
      }
      for(i=1;i<=2;i++)
      {
         temp=a[i][1];
         a[i][1]= a[1][i];
         a[1][i]= temp;
      }
      System.out.printf("%15s%n", "Matrix C");
      for(i=0; i<3; i++)
         for(j=0; j<3; j++)
            C[i][j]= a[i][j];
      for(i=0; i<3; i++)
      {
         for(j=0; j<3; j++)
         {
            System.out.printf("%5d", C[i][j]);
         }
         System.out.println();
      }
   }
   public static void inverse(int[][] b)
   {
      int[][] C= new int[3][3];
      int i, j;
   }
}

Answer 1

一行就够了。

System.out.println(new LUDecompositionImpl(
MatrixUtils.createRealMatrix(new double[][] { { 1, 2 }, { 3, 4 } })
).getSolver().getInverse());