numl.Math.LinearAlgebra.Matrix.Det C# (CSharp) Method

        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 = QR(x);
                return qr.Item1.Diag().Prod() * qr.Item2.Diag().Prod();

            }
        }

 /// <summary>
 /// computes matrix determinant NOTE: currently using cholesky factorization to save time so non
 /// symmetric positive semi-definite matrices will cause problems...
 /// </summary>
 /// <param name="m">Matrix.</param>
 /// <returns>Determinant.</returns>
 public static double Det(this Matrix m)
 {
     return(Matrix.Det(m));
 }