# ?hbgvd

Computes all eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian positive-definite eigenproblem with banded matrices. If eigenvectors are desired, it uses a divide and conquer method.

## Syntax

lapack_int LAPACKE_chbgvd( int matrix_layout, char jobz, char uplo, lapack_int n, lapack_int ka, lapack_int kb, lapack_complex_float* ab, lapack_int ldab, lapack_complex_float* bb, lapack_int ldbb, float* w, lapack_complex_float* z, lapack_int ldz );

lapack_int LAPACKE_zhbgvd( int matrix_layout, char jobz, char uplo, lapack_int n, lapack_int ka, lapack_int kb, lapack_complex_double* ab, lapack_int ldab, lapack_complex_double* bb, lapack_int ldbb, double* w, lapack_complex_double* z, lapack_int ldz );

• mkl.h

## Description

The routine computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian positive-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.

If eigenvectors are desired, it uses a divide and conquer algorithm.

## Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

jobz

Must be 'N' or 'V'.

If jobz = 'N', then compute eigenvalues only.

If jobz = 'V', then compute eigenvalues and eigenvectors.

uplo

Must be 'U' or 'L'.

If uplo = 'U', arrays ab and bb store the upper triangles of A and B;

If uplo = 'L', arrays ab and bb store the lower triangles of A and B.

n

The order of the matrices A and B (n 0).

ka

The number of super- or sub-diagonals in A

(ka0).

kb

The number of super- or sub-diagonals in B (kb 0).

ab, bb

Arrays:

ab(size at least max(1, ldab*n) for column major layout and max(1, ldab*(ka + 1)) for row major layout) is an array containing either upper or lower triangular part of the Hermitian matrix A (as specified by uplo) in band storage format.

bb(size at least max(1, ldbb*n) for column major layout and max(1, ldbb*(kb + 1)) for row major layout) is an array containing either upper or lower triangular part of the Hermitian matrix B (as specified by uplo) in band storage format.

ldab

The leading dimension of the array ab; must be at least ka+1.

ldbb

The leading dimension of the array bb; must be at least kb+1.

ldz

The leading dimension of the output array z; ldz 1. If jobz = 'V', ldz max(1, n).

## Output Parameters

ab

On exit, the contents of ab are overwritten.

bb

On exit, contains the factor S from the split Cholesky factorization B = SH*S, as returned by pbstf/pbstf.

w

Array, size at least max(1, n) .

If info = 0, contains the eigenvalues in ascending order.

z

Array z (size at least max(1, ldz*n)).

If jobz = 'V', then if info = 0, z contains the matrix Z of eigenvectors, with the i-th column of z holding the eigenvector associated with w(i). The eigenvectors are normalized so that ZH*B*Z = I.

If jobz = 'N', then z is not referenced.

## Return Values

This function returns a value info.

If info=0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

If info > 0, and

if in, the algorithm failed to converge, and i off-diagonal elements of an intermediate tridiagonal did not converge to zero;

if info = n + i, for 1 in, then pbstf/pbstf returned info = i and B is not positive-definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

For more complete information about compiler optimizations, see our Optimization Notice.