Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3  -  computes  all  the eigenvalues, and optionally, the eigenvectors of a complex
generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x

```

#### SYNOPSIS

```       SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, RWORK,  INFO
)

CHARACTER     JOBZ, UPLO

INTEGER       INFO, KA, KB, LDAB, LDBB, LDZ, N

DOUBLE        PRECISION RWORK( * ), W( * )

COMPLEX*16    AB( LDAB, * ), BB( LDBB, * ), WORK( * ), Z( LDZ, * )

```

#### PURPOSE

```       ZHBGV  computes  all  the  eigenvalues,  and  optionally,  the  eigenvectors  of a complex
generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x.  Here  A
and B are assumed to be Hermitian
and banded, and B is also positive definite.

```

#### ARGUMENTS

```        JOBZ    (input) CHARACTER*1
= 'N':  Compute eigenvalues only;
= 'V':  Compute eigenvalues and eigenvectors.

UPLO    (input) CHARACTER*1
= 'U':  Upper triangles of A and B are stored;
= 'L':  Lower triangles of A and B are stored.

N       (input) INTEGER
The order of the matrices A and B.  N >= 0.

KA      (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KA >= 0.

KB      (input) INTEGER
The number of superdiagonals of the matrix B if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KB >= 0.

AB      (input/output) COMPLEX*16 array, dimension (LDAB, N)
On entry, the upper or lower triangle of the Hermitian band
matrix A, stored in the first ka+1 rows of the array.  The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).
On exit, the contents of AB are destroyed.

LDAB    (input) INTEGER
The leading dimension of the array AB.  LDAB >= KA+1.

BB      (input/output) COMPLEX*16 array, dimension (LDBB, N)
On entry, the upper or lower triangle of the Hermitian band
matrix B, stored in the first kb+1 rows of the array.  The
j-th column of B is stored in the j-th column of the array BB
as follows:
if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).
On exit, the factor S from the split Cholesky factorization
B = S**H*S, as returned by ZPBSTF.

LDBB    (input) INTEGER
The leading dimension of the array BB.  LDBB >= KB+1.

W       (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z       (output) COMPLEX*16 array, dimension (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 Z**H*B*Z = I.
If JOBZ = 'N', then Z is not referenced.

LDZ     (input) INTEGER
The leading dimension of the array Z.  LDZ >= 1, and if
JOBZ = 'V', LDZ >= N.

WORK    (workspace) COMPLEX*16 array, dimension (N)

RWORK   (workspace) DOUBLE PRECISION array, dimension (3*N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, and i is:
<= N:  the algorithm failed to converge:
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
> N:   if INFO = N + i, for 1 <= i <= N, then ZPBSTF
returned INFO = i: B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

LAPACK driver routine (version 3.2)        April 2011                             ZHBGV(3lapack)
```