public static QR ( Matrix A ) : Matrix>.Tuple |
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A | Matrix | Matrix A. |
Résultat | 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()); } }