WDgeev WDsbev WDstev WDsyev

WDsbev() Function WDsbev ( Jobz As  String, Uplo As  String, N As  Long, Kd As  Long, Ab As  Variant  ) Eigenvalues and eigenvectors of a symmetric band matrix Purpose WDsbev computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A. 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 symmetric band matrix A, where ( 0.61 0.79 0 ) A = ( 0.79 2.23 0.25 ) ( 0 0.25 2.87 )