MatrixInversion.h

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// calculate the cofactor of element (row,col)
int GetMinor(std::complex<float> **src, std::complex<float> **dest, int row, int col, int order)
{
    // indicate which col and row is being copied to dest
    int colCount=0,rowCount=0;
 
    for(int i = 0; i < order; i++ )
    {
        if( i != row )
        {
            colCount = 0;
            for(int j = 0; j < order; j++ )
            {
                // when j is not the element
                if( j != col )
                {
                    dest[rowCount][colCount] = src[i][j];
                    colCount++;
                }
            }
            rowCount++;
        }
    }
 
    return 1;
}
 
// Calculate the determinant recursively.
std::complex<float> CalcDeterminant( std::complex<float> **mat, int order)
{
    // order must be >= 0
    // stop the recursion when matrix is a single element
    if( order == 1 )
        return mat[0][0];
 
    // the determinant value
    std::complex<float> det = 0;
 
    // allocate the cofactor matrix
    std::complex<float> **minor;
    minor = new std::complex<float>*[order-1];
    for(int i=0;i<order-1;i++)
        minor[i] = new std::complex<float>[order-1];
 
    for(int i = 0; i < order; i++ )
    {
        // get minor of element (0,i)
        GetMinor( mat, minor, 0, i , order);
        // the recusion is here!
 
  std::complex<float> neg = {-1.0,-1.0};
  std::complex<float> pos = {1.0,1.0};
  std::complex<float> sign = (i%2==1) ? neg : pos;
        det += sign * mat[0][i] * CalcDeterminant(minor,order-1);
        //det += pow( -1.0, i ) * mat[0][i] * CalcDeterminant( minor,order-1 );
    }
 
    // release memory
    for(int i=0;i<order-1;i++)
        delete [] minor[i];
    delete [] minor;
 
    return det;
}
 
// matrix inversioon
// the result is put in Y
void MatrixInversion(std::complex<float> **A, int order, std::complex<float> **Y)
{
    // get the determinant of a
    std::complex<float> unit = {1.0, 1.0};
    std::complex<float> det = unit/CalcDeterminant(A,order);
 
    // memory allocation
    std::complex<float> *temp = new std::complex<float>[(order-1)*(order-1)];
    std::complex<float> **minor = new std::complex<float>*[order-1];
    for(int i=0;i<order-1;i++)
        minor[i] = temp+(i*(order-1));
 
    for(int j=0;j<order;j++)
    {
        for(int i=0;i<order;i++)
        {
            // get the co-factor (matrix) of A(j,i)
            GetMinor(A,minor,j,i,order);
            Y[i][j] = det*CalcDeterminant(minor,order-1);
            if( (i+j)%2 == 1)
                Y[i][j] = -Y[i][j];
        }
    }
 
    // release memory
    //delete [] minor[0];
    delete [] temp;
    delete [] minor;
}