WZgeev WZgeev2 WZhbev WZhbev2 WZheev WZheev2

WZhbev() Function WZhbev ( Jobz As  String, Uplo As  String, N As  Long, Kd As  Long, Ab As  Variant  ) Eigenvalues and eigenvectors of a Hermitian band matrix (complex number representation in Excel format) Purpose WZhbev computes all the eigenvalues and, optionally, eigenvectors of a Hermitian band matrix A. To represent complex numbers in Excel cells, complex number format in Excel (e.g. 2.5+1i) is used. Worksheet function Complex can be used to input complex numbers into cells. Returns N+1 x 1 (if Jobz = "N"), N+1 x N+1 (if Jobz = "V" and Info = 0) Column 1 Columns 2 to N+1 Rows 1 to N Eigenvalues in ascending order Eigenvectors (if Jobz = "V" and Info = 0) Row N+1 Return code 0 Return code = 0: Successful exit = i > 0): The i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. 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 >= 1) [in] Kd Number of superdiagonals or subdiagonals of the matrix A. (Kd >= 0) [in] Ab (Kd+1 x N) N x N symmetric band matrix A. (Symmetric band matrix form. See below for details) Further Details The symmetric band matrix form is illustrated by the following example, when n = 6, kd = 2, and uplo = "U": * * a13 a24 a35 a46 * a12 a23 a34 a45 a56 a11 a22 a33 a44 a55 a66 Similarly, if uplo = "L" the format of A is as follows: a11 a22 a33 a44 a55 a66 a21 a32 a43 a54 a65 * a31 a42 a53 a64 * * Array elements marked * are not used by the routine. Reference LAPACK Example Compute all eigenvalues and eigenvectors of the Hermitian band matrix A, where ( 2.20 -0.32-0.81i 0 ) A = ( -0.32+0.81i 2.11 0.37+0.80i ) ( 0 0.37-0.80i 2.93 )