Zhbev Zhbevd Zhbevx Zheev Zheevd Zheevr Zheevx Zhpev Zhpevd Zhpevx

Zhpev() Sub Zhpev ( Jobz As  String, Uplo As  String, N As  Long, Ap() As  Complex, W() As  Double, Z() As  Complex, Info As  Long  ) (Simple driver) Eigenvalues and eigenvectors of a Hermitian matrix in packed form Purpose This routine computes all the eigenvalues and, optionally, eigenvectors of a Hermitian matrix A in packed form. Parameters [in] Jobz = "N": Compute eigenvalues only. = "V": Compute eigenvalues and eigenvectors. [in] Uplo = "U": Upper triangle of A is stored. = "L": Lower triangle of A is stored. [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] N x N Hermitian matrix A in packed form. The upper or lower part is to be stored in accordance with Uplo. [out] Ap() is overwritten by values generated during the reduction to tridiagonal form.   Uplo = "U": The diagonal and first super-diagonal of the tridiagonal matrix T overwrite the corresponding elements of A.   Uplo = "L": The diagonal and first sub-diagonal of T overwrite the corresponding elements of A. [out] W() Array W(LW - 1) (LW >= N) If Info = 0, the eigenvalues in ascending order. [out] Z() Array Z(LZ1 - 1, LZ2 - 1) (LZ1 >= N, LZ2 >= N) Jobz = "V": If Info = 0, Z() contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z() holding the eigenvector associated with W(i). Jobz = "N": Z() is not referenced. [out] Info = 0: Successful exit. = -1: The argument Jobz had an illegal value. (Jobz <> "V" nor "N") = -2: The argument Uplo had an illegal value. (Uplo <> "U" nor "L") = -3: The argument N had an illegal value. (N < 0) = -4: The argument Ap() is invalid. = -5: The argument W() is invalid. = -6: The argument Z() is invalid. = i > 0: The algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. Reference LAPACK Example Program Compute all eigenvalues and eigenvectors of the Hermitian matrix 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_Zhpev() Const N = 3 Dim Ap(N * (N + 1) / 2) As Complex, W(N - 1) As Double, Z(N - 1, N - 1) As Complex Dim 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 Zhpev("V", "L", N, Ap(), W(), Z(), Info) Debug.Print "Eigenvalues =", W(0), W(1), W(2) Debug.Print "Eigenvectors =" Debug.Print Creal(Z(0, 0)), Cimag(Z(0, 0)), Creal(Z(0, 1)), Cimag(Z(0, 1)) Debug.Print Creal(Z(1, 0)), Cimag(Z(1, 0)), Creal(Z(1, 1)), Cimag(Z(1, 1)) Debug.Print Creal(Z(2, 0)), Cimag(Z(2, 0)), Creal(Z(2, 1)), Cimag(Z(2, 1)) Debug.Print Creal(Z(0, 2)), Cimag(Z(0, 2)) Debug.Print Creal(Z(1, 2)), Cimag(Z(1, 2)) Debug.Print Creal(Z(2, 2)), Cimag(Z(2, 2)) Debug.Print "Info =", Info End Sub Example Results Eigenvalues = -2.05348849668514 0.124622388617308 1.51886610806783 Eigenvectors = 0.449276526719113 0 0.654793596518192 -0 -0.227247885813611 0.597641779578735 0.519997178670921 -3.19846835072552E-02 -0.621236109316913 5.83009495222984E-02 0.204907317474214 -0.507777757881847 0.607779522934083 0 -0.392237107311198 -0.407323787101333 0.23846608290599 0.503959683819116 Info = 0