如何在C#中去求矩阵的逆矩阵（转载）

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算法的大致思想是通过行列式初等变换来求。

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;
}

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] ) );
    }