Zgbcon Zgbtrf Zgbtrs Zgecon Zgetrf Zgetri Zgetrs Zgtcon Zgttrf Zgttrs Zspcon Zsptrf Zsptri Zsptrs Zsycon Zsytrf Zsytri Zsytrs

Zsptri() Sub Zsptri ( Uplo As  String, N As  Long, Ap() As  Complex, IPiv() As  Long, Info As  Long  ) Inverse of a complex symmetric matrix in packed form Purpose This routine computes the inverse of a complex symmetric indefinite matrix A in packed form using the factorization A = U*D*U^T or A = L*D*L^T computed by zsptrf. 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,out] Ap() Array Ap(LAp - 1) (LAp >= N(N + 1)/2) [in] The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by Zsptrf, stored as a packed triangular matrix. [out] If Info = 0, the (symmetric) inverse of the original matrix, stored as a packed triangular matrix. The upper or lower triangular part of the inverse is stored 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 Zsptrf. [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 Ap() 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 ( 0.20-0.11i -0.93-0.32i -0.80-0.92i ) A = ( -0.93-0.32i 0.81+0.37i -0.29+0.86i ) ( -0.80-0.92i -0.29+0.86i 0.64+0.51i ) Sub Ex_Zsptri() Const N = 3 Dim Ap(N * (N + 1) / 2) As Complex, IPiv(N - 1) As Long, Info As Long Ap(0) = Cmplx(0.2, -0.11) Ap(1) = Cmplx(-0.93, -0.32): Ap(3) = Cmplx(0.81, 0.37) Ap(2) = Cmplx(-0.8, -0.92): Ap(4) = Cmplx(-0.29, 0.86): Ap(5) = Cmplx(0.64, 0.51) Call Zsptrf("L", N, Ap(), IPiv(), Info) If Info = 0 Then Call Zsptri("L", N, Ap(), IPiv(), Info) Debug.Print "Inv(A) =" Debug.Print Creal(Ap(0)), Cimag(Ap(0)) Debug.Print Creal(Ap(1)), Cimag(Ap(1)), Creal(Ap(3)), Cimag(Ap(3)) Debug.Print Creal(Ap(2)), Cimag(Ap(2)), Creal(Ap(4)), Cimag(Ap(4)) Debug.Print Creal(Ap(5)), Cimag(Ap(5)) Debug.Print "Info =", Info End Sub Example Results Inv(A) = -0.719227845649432 2.10409854531818E-02 -0.530264806881645 0.461068985285655 0.415967871341667 0.574878197201315 -0.378362108041106 0.215383726745448 -0.459100384344751 -0.118538953519092 0.392991440632119 -2.46277479810784E-02 Info = 0