如何在C#去求矩阵的逆矩阵

最近有网友问我，怎么去求矩阵的逆，当时就按照以前线性代数上面方法告诉他算法，例如先求矩阵行列式的值，然后再求每一项的代数余子式，然后按照矩阵逆的公式去计算。但是等他向我求代码的时候，发现做法并不是那么简单，甚至用上面的思路，很难做出来。于是我参考网上求行列式值的算法，在上面的基础上完成了矩阵逆的算法。

 

算法的大致思想是通过行列式初等变换来求。

 

大致的代码如下：

private double[,] ReverseMatrix( double[,] dMatrix, int Level )

{

    double dMatrixValue = MatrixValue( dMatrix, Level );

    if( dMatrixValue == 0 ) return null;

           

    double[,] dReverseMatrix = new double[Level,2*Level];

    double x, c;

    // Init Reverse matrix

    for( int i = 0; i < Level; i++ )

    {

        for( int j = 0; j < 2 * Level; j++ )

        {

            if( j < Level )

                dReverseMatrix[i,j] = dMatrix[i,j];

            else

                dReverseMatrix[i,j] = 0;

        }

 

        dReverseMatrix[i,Level + i ] = 1;

    }

 

    for( int i = 0, j = 0; i < Level && j < Level; i++, j++ )

    {

        if( dReverseMatrix[i,j] == 0 )

        {

            int m = i;

            for( ; dMatrix[m,j] == 0; m++ );

            if( m == Level )

                return null;

            else

            {

                // Add i-row with m-row

                for( int n = j; n < 2 * Level; n++ )

                    dReverseMatrix[i,n] += dReverseMatrix[m,n];

            }

        }

 

        // Format the i-row with "1" start

        x = dReverseMatrix[i,j];

        if( x != 1 )

        {

            for( int n = j; n < 2 * Level; n++ )

                if( dReverseMatrix[i,n] != 0 )

                    dReverseMatrix[i,n] /= x;

        }

 

        // Set 0 to the current column in the rows after current row

        for( int s = Level - 1; s > i;s-- )

        {

            x = dReverseMatrix[s,j];

            for( int t = j; t < 2 * Level; t++ )

                dReverseMatrix[s,t] -= ( dReverseMatrix[i,t]* x );

        }

    }

 

    // Format the first matrix into unit-matrix

    for( int i = Level - 2; i >= 0; i-- )

    {

        for( int j = i + 1 ; j < Level; j++ )

            if( dReverseMatrix[i,j] != 0 )

            {

                c = dReverseMatrix[i,j];

                for( int n = j; n < 2*Level; n++ )

                    dReverseMatrix[i,n] -= ( c * dReverseMatrix[j,n] );

            }

    }

 

    double[,] dReturn = new double[Level, Level];

    for( int i = 0; i < Level; i++ )

        for( int j = 0; j < Level; j++ )

            dReturn[i,j] = dReverseMatrix[i,j+Level];

    return dReturn;

}

 

private double MatrixValue( double[,] MatrixList, int Level )

{

    double[,] dMatrix = new double[Level, Level];

    for( int i = 0; i < Level; i++ )

        for( int j = 0; j < Level; j++ )

            dMatrix[i,j] = MatrixList[i,j];

    double c, x;

    int k = 1;

    for( int i = 0, j = 0; i < Level && j < Level; i++, j++ )

    {

        if( dMatrix[i,j] == 0 )

        {

            int m = i;

            for( ; dMatrix[m,j] == 0; m++ );

            if( m == Level )

                return 0;

            else

            {

                // Row change between i-row and m-row

                for( int n = j; n < Level; n++ )

                {

                    c = dMatrix[i,n];

                    dMatrix[i,n] = dMatrix[m,n];

                    dMatrix[m,n] = c;

                }

 

                // Change value pre-value

                k *= (-1);

            }

        }

 

        // Set 0 to the current column in the rows after current row

        for( int s = Level - 1; s > i;s-- )

        {

            x = dMatrix[s,j];

            for( int t = j; t < Level; t++ )

                dMatrix[s,t] -= dMatrix[i,t]* ( x/dMatrix[i,j] );

        }

    }

 

    double sn = 1;

    for( int i = 0; i < Level; i++ )

    {

        if( dMatrix[i,i] != 0 )

            sn *= dMatrix[i,i];

        else

            return 0;

    }

    return k*sn;

}

 

       函数的调用如下：

    double[,] dMatrix = new double[3,3]{{0,1,2},{1,0,1},{4,2,1}};

    double[,] dReturn = ReverseMatrix( dMatrix, 3 );

    if( dReturn != null )

    {

        for( int i=0; i < 3; i++ )

            Debug.WriteLine( string.Format( "{0} {1} {2}",

                dReturn[i,0], dReturn[i,1],dReturn[i,2] ) );

    }