矩阵逆变器返回错误的逆

Question

此代码用于查找矩阵的逆，几乎可以做到这一点。最后一行数字不正确，我不确定为什么。这不是找到逆数的最佳方法，但是这是我需要做的作业。我已经多次修改了幂函数，所以现在应该是正确的。使用的方法是B = I-A，A ^ -1 = I + B + B ^ 2 + B ^ 3 ...（一直到B ^ 20）。

#include <iostream>
#include <iomanip>

using namespace std;

void multiplinator(double invA[][3], double A[][3], double y[][3]) //multiplies the matrix
{
    for(int i = 0; i < 3; i++)
    {
            for(int j = 0; j < 3; j++)
            {
                y[i][j] = 0;
                    for(int k = 0; k < 3; k++)
                    {
                            y[i][j] += invA[i][k] * A[k][j];
                    }
            }
    }
}

void printinator(double a[3][3]) //prints a matrix
{
for(int i=0; i<=2; i++)
    {
    for(int j=0; j<=2; j++)
        cout << fixed << setprecision(2) << setw(12) << a[i][j] << "  ";
    cout << endl;
    }
        cout << endl;
}

void substitinator(double I[][3], double A[][3], double B[][3]) //Matrix subtraction
{
   for (int i = 0; i < 3; i++)
        for (int j = 0; j < 3; j++)
            B[i][j] = I[i][j] - A[i][j];
}

void additinator(double I[3][3], double B[][3], double invA[][3]) //Matrix addition
{
   for (int i = 0; i < 3; i++)
        for (int j = 0; j < 3; j++)
            invA[i][j] = I[i][j] + B[i][j];
}

void powernator(double B[][3],double pB[][3], int p) //function which is supposed to raise a matrix to a certain power
{
    double temp[3][3] = { {0, 0, 0} , {0, 0, 0} , {0, 0, 0} };
    int i,j,w,k;

    for(i = 0 ; i < 2 ; ++ i )
          for(j = 0 ; j < 2 ; ++ j )
           pB[i][j] = ( i == j ) ;
    for(w = 0; w < p; w++)
    {
        for(i=0;i<2;i++)
        {
            for(j=0;j<2;j++)
            {
                temp[i][j]=0;
                for(k=0;k<2;k++)
                {
                    temp[i][j] += pB[i][k] * B[k][j];
                }
            }
        }

        for(i = 0; i < 2; i++){
            for(j = 0; j < 2; j++)
            {
                pB[i][j] = temp[i][j];
            }
        }
    }
}

void gettem(double pB[][3], double invA[][3]) //Matrix addition of power of B
{
   for (int i = 0; i < 3; i++)
        for (int j = 0; j < 3; j++)
            invA[i][j] += pB[i][j];
}

int main()
{

double A[3][3] = { {1./2, 1, 0} , {0, 2./3, 0} , {-1./2, -1, 2./3} };
double invA[3][3] = { {0, 0, 0} , {0, 0, 0} , {0, 0, 0} };
double I[3][3] = { {1, 0, 0} , {0, 1, 0} , {0, 0, 1} };

double B[3][3] = { {0, 0, 0} , {0, 0, 0} , {0, 0, 0} };
double pB[3][3] = { {0, 0, 0} , {0, 0, 0} , {0, 0, 0} };
double y[3][3] = { {0, 0, 0} , {0, 0, 0} , {0, 0, 0} };

    substitinator(I,A,B);
    additinator(I,B,invA);

        for(int p = 2; p <= 20; p++)
        {
            powernator(B,pB,p);
            gettem(pB, invA);
        }

    cout << "\n\t\t   Inverse:" << endl;
        printinator(invA);

    cout << "\n\t\t   invA * A:" << endl;
        multiplinator(invA, A, y);
        printinator(y);
}

Answer 1

我同意@ 1201ProgramAlarm，您的powernator()函数错误，应确保所有for循环条件都是< 3而不是< 2

void powernator(double B[3][3],double pB[3][3], int p) //function which is supposed to raise a matrix to a certain power
{
    double temp[3][3] = { {0, 0, 0} , {0, 0, 0} , {0, 0, 0} };
    int i,j,w,k;

    for(i = 0 ; i < 3 ; ++ i )
          for(j = 0 ; j < 3 ; ++ j )
           pB[i][j] = ( i == j ) ;
    for(w = 0; w < p; w++)
    {
        for(i=0;i<3;i++)
        {
            for(j=0;j<3;j++)
            {
                temp[i][j]=0;
                for(k=0;k<3;k++)
                {
                    temp[i][j] += pB[i][k] * B[k][j];
                }
            }
        }

        for(i = 0; i < 3; i++){
            for(j = 0; j < 3; j++)
            {
                pB[i][j] = temp[i][j];
            }
        }
    }
}

结果是：

   Inverse:
2.00         -3.00          0.00  
0.00          1.50          0.00  
1.50          0.00          1.50  


   invA * A:
1.00          0.00          0.00  
0.00          1.00          0.00  
   -0.00          0.00          1.00  

希望这会有所帮助。