Dspcon Dsptrf Dsptri Dsptrs Dsycon Dsytrf Dsytri Dsytrs

Dsytri() Sub Dsytri ( Uplo As  String, N As  Long, A() As  Double, IPiv() As  Long, Info As  Long  ) Inverse of a symmetric matrix Purpose This routine computes the inverse of a real symmetric matrix A using the factorization A = U*D*U^T or A = L*D*L^T computed by Dsytrf. Parameters [in] Uplo Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = "U": Upper triangular, form is A = U*D*U^T. = "L": Lower triangular, form is A = L*D*L^T. [in] N Order of the matrix A. (N >= 0) (If N = 0, returns without computation) [in] A() Array A(LA1 - 1, LA2 - 1) (LA1 >= N, LA2 >= N) [in] The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by Dsytrf. [out] If Info = 0, the (symmetric) inverse of the original matrix A. The upper or lower triangular part of the inverse is formed and the other part of A() below or above the diagonal is not referenced in accordance with Uplo. [in] IPiv() Array IPiv(LIPiv - 1) (LIPiv >= N) Details of the interchanges and the block structure of D as determined by Dsytrf. [out] Info = 0: Successful exit. = -1: The argument Uplo had an illegal value. (Uplo <> "U" nor "L") = -2: The argument N had an illegal value. (N < 0) = -3: The argument A() is invalid. = -4: The argument IPiv() is invalid. = i > 0: The i-th element of D is exactly zero; the matrix is singular and its inverse could not be computed. Reference LAPACK Example Program Compute the inverse matrix of A, where ( 2.2 -0.11 -0.32 ) A = ( -0.11 2.93 0.81 ) ( -0.32 0.81 -2.37 ) Sub Ex_Dsytri() Const N = 3 Dim A(N - 1, N - 1) As Double, IPiv(N - 1) As Long, Info As Long A(0, 0) = 2.2 A(1, 0) = -0.11: A(1, 1) = 2.93 A(2, 0) = -0.32: A(2, 1) = 0.81: A(2, 2) = 2.37: Call Dsytrf("L", N, A(), IPiv(), Info) If Info = 0 Then Call Dsytri("L", N, A(), IPiv(), Info) Debug.Print "Inv(A) =" Debug.Print A(0, 0), A(0, 1), A(0, 2) Debug.Print A(1, 0), A(1, 1), A(1, 2) Debug.Print A(2, 0), A(2, 1), A(2, 2) Debug.Print "Info =", Info End Sub Example Results Inv(A) = 0.463651335375572 0 0 1.10603849087679E-04 0.376908423331071 0 6.25649106339333E-02 -0.128801869057578 0.474409403096834 Info = 0