Zhbev Zhbevd Zhbevx Zheev Zheevd Zheevr Zheevx Zhpev Zhpevd Zhpevx

Zheevd() Sub Zheevd ( Jobz As  String, Uplo As  String, N As  Long, A() As  Complex, W() As  Double, Info As  Long  ) (Divide and conquer driver) Eigenvalues and eigenvectors of a Hermitian matrix Purpose This routine computes all eigenvalues and, optionally, eigenvectors of a Hermitian matrix A. If only eigenvalues are desired, it uses a QL or QR method. If eigenvectors are also desired, it uses a divide and conquer algorithm. 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] The Hermitian matrix A. If Uplo = "U", the leading N x N upper triangular part of A() contains the upper triangular part of the matrix A. If Uplo = "L", the leading N x N lower triangular part of A() contains the lower triangular part of the matrix A. [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_Zheevd() 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 Zheevd("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 -3.19846835072552E-02 0.621236109316912 -5.83009495222983E-02 0.204907317474214 -0.507777757881847 -0.607779522934083 0 0.392237107311198 0.407323787101333 -0.23846608290599 -0.503959683819116 Info = 0