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RedHat 9 (Linux i386) - man page for zhegv (redhat section l)

ZHEGV(l)					)					 ZHEGV(l)

NAME
       ZHEGV  - compute all the eigenvalues, and optionally, the eigenvectors of a complex gener-
       alized 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 general-
       ized 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 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 trian-
	       gular 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 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 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 illegal value
	       > 0:  ZPOTRF or ZHEEV returned an error code:
	       <= N:  if INFO = i, ZHEEV failed to converge; i off-diagonal elements of an inter-
	       mediate 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(l)


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