zhegv(3)

NAME

ZHEGV - compute all the eigenvalues, and optionally, the

eigenvectors of a complex generalized Hermitian-definite eigen

problem, 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 eigen

problem, 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 matrices A and B. 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 contains 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 con

tains the matrix Z of eigenvectors. The eigenvectors are normal

ized 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 trian

gle (if UPLO='U') or the lower triangle (if UPLO='L') of A, in

cluding 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 positive definite matrix

B. If UPLO = 'U', the leading N-by-N upper triangular part of B

contains 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/output) 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.

If LWORK = -1, then a workspace query is assumed;

the routine only calculates the optimal size of the WORK array,

returns this value as the first entry of the WORK array, and no

error message related to LWORK is issued by XERBLA.

RWORK (workspace) DOUBLE PRECISION array, dimension

(max(1, 3*N-2))

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal 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.

LAPACK version 3.0 15 June 2000

ZHEGV(3)