WZggev WZggev2 WZhbgv WZhbgv2 WZhegv WZhegv2

WZhegv() Function WZhegv ( IType As  Long, Jobz As  String, Uplo As  String, N As  Long, A As  Variant, B As  Variant  ) Generalized eigenvalue problem of Hermitian matrices (complex number representation in Excel format) Purpose WZhegv computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x = λ*B*x, A*B*x = λ*x, or B*A*x = λ*x. Here A and B are assumed to be Hermitian 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 as follows: If IType = 1 or 2: (Z^H)BZ = I If IType = 3: (Z^H)B^(-1)Z = 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] IType Specifies the problem type to be solved. = 1: Ax = λBx = 2: ABx = λx = 3: BAx = λx [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] A (N x N) Hermitian matrix A. [in] B (N x N) Hermitian positive definite matrix B. 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 matrix and B is an Hermitian positive definite matrix. ( 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 ) ( 2.20 -0.11+0.93i 0.81-0.37i ) B = ( -0.11-0.93i 2.32 -0.80+0.92i ) ( 0.81+0.37i -0.80-0.92i 2.29 )