WZggev WZggev2 WZhbgv WZhbgv2 WZhegv WZhegv2

WZhbgv() Function WZhbgv ( 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 Hermitian band matrices (complex number representation in Excel format) Purpose WZhbgv computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x = λ*B*x. Here A and B are assumed to be Hermitian and banded, and B is also positive definite. 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). The eigenvectors are normalized so that (Z^H)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) Hermitian band matrix A. (Symmetric band matrix form) [in] Bb (Kb + 1 x N) Hermitian positive definite band matrix B. (Symmetric band matrix form) Reference LAPACK Example Compute the eigenvalues and the eigenvectors of a generalized Hermitian-definite eigenproblem of the form Ax = λBx, where A is an Hermitian band matrix and B is an Hermitian positive definite band matrix. ( -0.20 -0.32-0.81i 0 ) A = ( -0.32+0.81i 0.11 0.37+0.80i ) ( 0 0.37-0.80i -0.93 ) ( 2.20 -0.32-0.81i 0 ) B = ( -0.32+0.81i 2.11 0.37-0.80i ) ( 0 0.37-0.80i 2.93 )