/// <summary>
/// Calculate the determinant of a Matrix
/// </summary>
/// <returns>The determinant</returns>
/// <exception cref="GeometryException">Thrown, if the Matrix is not a Square Matrix</exception>
/// <remarks>Based on code by Rajitha Wimalasooriya (http://www.thecodeproject.com/csharp/rtwmatrix.asp)</remarks>
public double Determinant()
{
if (this.Rows != this.Columns)
{
throw new GeometryException("You can only compute the Determinant of a Square Matrix. (" + ToString() + ")");
}
double d = 0;
//get the determinent of a 2x2 matrix
if (this.Rows == 2 && this.Columns == 2)
{
d = (this[0, 0] * this[1, 1]) - (this[0, 1] * this[1, 0]);
return(d);
}
//get the determinent of a 3x3 matrix
if (this.Rows == 3 && this.Columns == 3)
{
d = (this[0, 0] * this[1, 1] * this[2, 2])
+ (this[0, 1] * this[1, 2] * this[2, 0])
+ (this[0, 2] * this[1, 0] * this[2, 1])
- (this[0, 2] * this[1, 1] * this[2, 0])
- (this[0, 1] * this[1, 0] * this[2, 2])
- (this[0, 0] * this[1, 2] * this[2, 1]);
return(d);
}
Matrixd tempMtx = new Matrixd(this.Rows - 1, this.Columns - 1);
//find the determinent with respect to the first row
for (int j = 0; j < this.Columns; j++)
{
tempMtx = this.Minor(0, j);
//recursively add the determinents
d += (int)Math.Pow(-1, j) * this[0, j] * tempMtx.Determinant();
}
return(d);
}
/// <summary>
/// Calculate the Adjoint of a Matrix
/// </summary>
/// <returns>The adjoint</returns>
/// <exception cref="GeometryException">Thrown if <see cref="Rows"/> or <see cref="Columns"/> is less than 2.</exception>
/// <remarks>Based on code by Rajitha Wimalasooriya (http://www.thecodeproject.com/csharp/rtwmatrix.asp)</remarks>
public Matrixd Adjoint()
{
if (this.Rows < 2 || this.Columns < 2)
{
throw new GeometryException("Adjoint matrix is not available. (" + ToString() + ")");
}
Matrixd tempMtx = new Matrixd(this.Rows - 1, this.Columns - 1);
Matrixd adjMtx = new Matrixd(this.Columns, this.Rows);
for (int i = 0; i < this.Rows; i++)
{
for (int j = 0; j < this.Columns; j++)
{
tempMtx = this.Minor(i, j);
//put the determinent of the minor in the transposed position
adjMtx[j, i] = (int)Math.Pow(-1, i + j) * tempMtx.Determinant();
}
}
return(adjMtx);
}
