WDsbgv WDsygv

WDsbgv() Function WDsbgv ( Jobz As  String, Uplo As  String, N As  Long, Ka As  Long, Kb As  Long, Ab As  Variant, Bb As  Variant  ) Generalized eigenvalue problem of symmetric band matrices Purpose WDsbgv computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x = λ*B*x. Here A and B are assumed to be symmetric and banded, and B is also positive definite. 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). The eigenvectors are normalized so that (Z^T)BZ = I. Row N+1 Return code 0 Return code = 0: Successful exit = i (0 < i <= N): The i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. = i (N < i): The leading minor of order (i - N) of B is not positive definite. The factorization of B could not be completed. Parameters [in] Jobz = "N": Compute eigenvalues only. = "V": Compute eigenvalues and eigenvectors. [in] Uplo = "U": Upper triangles of A and B are stored. = "L": Lower triangles of A and B are stored. [in] N Order of the matrices A and B. (N >= 1) [in] Ka The number of superdiagonals or subdiagonals of the matrix A. (Ka >= 0) [in] Kb The number of superdiagonals or subdiagonals of the matrix B. (Kb >= 0) [in] Ab (Ka + 1 x N) Symmetric band matrix A. (Symmetric band matrix form) [in] Bb (Kb + 1 x N) Symmetric positive definite band matrix B. (Symmetric band matrix form) Reference LAPACK Example Compute the eigenvalues and the eigenvectors of a generalized symmetric-definite eigenproblem of the form Ax = λBx, where A is a symmetric matrix and B is a symmetric positive definite matrix. ( 0.31 0.69 0 ) ( 2.58 -0.99 0 ) A = ( 0.69 2.71 0.57 ) B = ( -0.99 0.69 -0.03 ) ( 0 0.57 -0.13 ) ( 0 -0.03 0.18 )