numl.Math.LinearAlgebra.Matrix.QR C# (CSharp) Метод

        public static Tuple<Matrix, Matrix> QR(Matrix A)
        {
            int n = A.Rows;
            Matrix R = Zeros(n);
            Matrix Q = A.Copy();
            for (int k = 0; k < n; k++)
            {
                R[k, k] = Q[k, VectorType.Col].Norm();
                Q[k, VectorType.Col] = Q[k, VectorType.Col] / R[k, k];

                for (int j = k + 1; j < n; j++)
                {
                    R[k, j] = Vector.Dot(Q[k, VectorType.Col], A[j, VectorType.Col]);
                    Q[j, VectorType.Col] = Q[j, VectorType.Col] - (R[k, j] * Q[k, VectorType.Col]);
                }
            }

            return new Tuple<Matrix, Matrix>(Q, R);
        }

        /// <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());
            }
        }