|
public static QR ( Matrix A ) : Matrix>.Tuple |
||
| A | Matrix | Matrix A. |
| return | Matrix>.Tuple | |
/// <summary>Dets the given x coordinate.</summary>
/// <exception cref="InvalidOperationException">Thrown when the requested operation is invalid.</exception>
/// <param name="x">Matrix x.</param>
/// <returns>A double.</returns>
public static double Det(Matrix x)
{
// 0, 1, 2
// --------
// 0 | a, b, c
// 1 | d, e, f
// 2 | g, h, i
if (x.Rows != x.Cols)
{
throw new InvalidOperationException("Can only compute determinants of square matrices");
}
int n = x.Rows;
if (n == 1)
{
return(x[0, 0]);
}
else if (n == 2)
{
return(x[0, 0] * x[1, 1] - x[0, 1] * x[1, 0]);
}
else if (n == 3) // aei + bfg + cdh - ceg - bdi - afh
{
return(x[0, 0] * x[1, 1] * x[2, 2] +
x[0, 1] * x[1, 2] * x[2, 0] +
x[0, 2] * x[1, 0] * x[2, 1] -
x[0, 2] * x[1, 1] * x[2, 0] -
x[0, 1] * x[1, 0] * x[2, 2] -
x[0, 0] * x[1, 2] * x[2, 1]);
}
else
{
// ruh roh, time for generalized determinant
// to save time we'll do a cholesky factorization
// (note, this requires a symmetric positive-semidefinite
// matrix or it might explode....)
// and square the product of the diagonals
//return System.Math.Pow(x.Cholesky().Diag().Prod(), 2);
// switched to QR since it is safer...
// fyi: determinant of a triangular matrix is the
// product of its diagonals
// also: det(AB) = det(A) * det(B)
// that's how we come up with this crazy thing
var qr = Matrix.QR(x);
return(qr.Item1.Diag().Prod() * qr.Item2.Diag().Prod());
}
}