Zhecon Zhetrf Zhetri Zhetrs Zhpcon Zhptrf Zhptri Zhptrs

Zhptri() Sub Zhptri ( Uplo As  String, N As  Long, Ap() As  Complex, IPiv() As  Long, Info As  Long  ) Inverse of a Hermitian matrix in packed form Purpose This routine computes the inverse of a Hermitian indefinite matrix A in packed form using the factorization A = U*D*U^H or A = L*D*L^H computed by Zhptrf. 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^H. = "L": Lower triangular, form is A = L*D*L^H. [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 Zhptrf, 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 Zhptrf. [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 -0.11+0.93i 0.81-0.37i ) A = ( -0.11-0.93i -0.32 -0.80+0.92i ) ( 0.81+0.37i -0.80-0.92i -0.29 ) Sub Ex_Zhptri() 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) Ap(1) = Cmplx(-0.11, -0.93): Ap(3) = Cmplx(-0.32, 0) Ap(2) = Cmplx(0.81, 0.37): Ap(4) = Cmplx(-0.8, -0.92): Ap(5) = Cmplx(-0.29, 0) Call Zhptrf("L", N, Ap(), IPiv(), Info) If Info = 0 Then Call Zhptri("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) = 3.5853396244861 0 2.62494404338631 -0.461802857775011 2.18938290789155 0 1.30796976541958 -2.47907094012256 0.702866522251437 -2.3066988427915 2.42092751624671 0 Info = 0