Zhbev Zhbevd Zhbevx Zheev Zheevd Zheevr Zheevx Zhpev Zhpevd Zhpevx

Zheev() Sub Zheev ( Jobz As  String, Uplo As  String, N As  Long, A() As  Complex, W() As  Double, Info As  Long  ) (Simple driver) Eigenvalues and eigenvectors of a Hermitian matrix Purpose This routine computes all eigenvalues and, optionally, eigenvectors of a Hermitian matrix A. 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] A() Array A(LA1 - 1, LA2 - 1) (LA1 >= N, LA2 >= N) [in] N x N Hermitian matrix A. The upper or lower triangular part is to be stored in accordance with Uplo. [out] Jobz = "V": If Info = 0, A() contains the orthonormal eigenvectors of the matrix A.   Jobz = "N": The lower triangle (if Uplo = "L") or the upper triangle (if Uplo = "U") of A(), including the diagonal, is destroyed. [out] W() Array W(LW - 1) (LW >= N) If Info = 0, the eigenvalues in ascending order. [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 A() is invalid. = -5: The argument W() 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_Zheev() Const N = 3 Dim A(N - 1, N - 1) As Complex, W(N - 1) As Double, Info As Long A(0, 0) = Cmplx(0.2, 0) A(1, 0) = Cmplx(-0.11, -0.93): A(1, 1) = Cmplx(-0.32, 0) A(2, 0) = Cmplx(0.81, 0.37): A(2, 1) = Cmplx(-0.8, -0.92): A(2, 2) = Cmplx(-0.29, 0) Call Zheev("V", "L", N, A(), W(), Info) Debug.Print "Eigenvalues =", W(0), W(1), W(2) Debug.Print "Eigenvectors =" Debug.Print Creal(A(0, 0)), Cimag(A(0, 0)), Creal(A(0, 1)), Cimag(A(0, 1)) Debug.Print Creal(A(1, 0)), Cimag(A(1, 0)), Creal(A(1, 1)), Cimag(A(1, 1)) Debug.Print Creal(A(2, 0)), Cimag(A(2, 0)), Creal(A(2, 1)), Cimag(A(2, 1)) Debug.Print Creal(A(0, 2)), Cimag(A(0, 2)) Debug.Print Creal(A(1, 2)), Cimag(A(1, 2)) Debug.Print Creal(A(2, 2)), Cimag(A(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 -3.19846835072553E-02 -0.621236109316912 5.83009495222984E-02 0.204907317474214 -0.507777757881847 0.607779522934083 0 -0.392237107311198 -0.407323787101333 0.23846608290599 0.503959683819116 Info = 0