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# zhegv

```
NAME
ZHEGV - compute all the eigenvalues, and optionally, the
eigenvectors of a complex generalized Hermitian-definite
eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x,
or B*A*x=(lambda)*x

SYNOPSIS
SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
WORK, LWORK, RWORK, INFO )

CHARACTER     JOBZ, UPLO

INTEGER       INFO, ITYPE, LDA, LDB, LWORK, N

DOUBLE        PRECISION RWORK( * ), W( * )

COMPLEX*16    A( LDA, * ), B( LDB, * ), WORK( * )

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

ARGUMENTS
ITYPE   (input) INTEGER
Specifies the problem type to be solved:
= 1:  A*x = (lambda)*B*x
= 2:  A*B*x = (lambda)*x
= 3:  B*A*x = (lambda)*x

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 matrix A.  N >= 0.

A       (input/output) COMPLEX*16 array, dimension (LDA, N)
On entry, the Hermitian matrix A.  If UPLO = 'U',
the leading N-by-N upper triangular part of A con-
tains the upper triangular part of the matrix A.  If
UPLO = 'L', the leading N-by-N lower triangular part
of A contains the lower triangular part of the
matrix A.

On exit, if JOBZ = 'V', then if INFO = 0, A contains
the matrix Z of eigenvectors.  The eigenvectors are
normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z =
I; if ITYPE = 3, Z**H*inv(B)*Z = I.  If JOBZ = 'N',
then on exit the upper triangle (if UPLO='U') or the
lower triangle (if UPLO='L') of A, including the
diagonal, is destroyed.

LDA     (input) INTEGER
The leading dimension of the array A.  LDA >=
max(1,N).

B       (input/output) COMPLEX*16 array, dimension (LDB, N)
On entry, the Hermitian matrix B.  If UPLO = 'U',
the leading N-by-N upper triangular part of B con-
tains the upper triangular part of the matrix B.  If
UPLO = 'L', the leading N-by-N lower triangular part
of B contains the lower triangular part of the
matrix B.

On exit, if INFO <= N, the part of B containing the
matrix is overwritten by the triangular factor U or
L from the Cholesky factorization B = U**H*U or B =
L*L**H.

LDB     (input) INTEGER
The leading dimension of the array B.  LDB >=
max(1,N).

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

WORK    (workspace) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.

LWORK   (input) INTEGER
The length of the array WORK.  LWORK >= max(1,2*N-
1).  For optimal efficiency, LWORK >= (NB+1)*N,
where NB is the blocksize for ZHETRD returned by
ILAENV.

3*N-2))
RWORK   (workspace) DOUBLE PRECISION array, dimension (max(1,

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value
> 0:  ZPOTRF or ZHEEV returned an error code:
<= N:  if INFO = i, ZHEEV 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 the leading minor of order
i of B is not positive definite.  The factorization
of B could not be completed and no eigenvalues or
eigenvectors were computed.
```