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

CHEGVD(l)					)					CHEGVD(l)

NAME
       CHEGVD - 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 CHEGVD( ITYPE,  JOBZ,  UPLO,	N, A, LDA, B, LDB, W, WORK, LWORK, RWORK, LRWORK,
			  IWORK, LIWORK, INFO )

	   CHARACTER	  JOBZ, UPLO

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

	   INTEGER	  IWORK( * )

	   REAL 	  RWORK( * ), W( * )

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

PURPOSE
       CHEGVD computes 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. Here A and B are assumed to be Hermitian and B is  also  positive  defi-
       nite.  If eigenvectors are desired, it uses a divide and conquer algorithm.

       The  divide  and conquer algorithm makes very mild assumptions about floating point arith-
       metic. It will work on machines with a guard digit in add/subtract,  or	on  those  binary
       machines  without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
       Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits,
       but we know of none.

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 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 array, dimension (LDB, N)
	       On entry, the Hermitian matrix B.  If UPLO = 'U', the leading N-by-N upper  trian-
	       gular  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) REAL array, dimension (N)
	       If INFO = 0, the eigenvalues in ascending order.

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

       LWORK   (input) INTEGER
	       The length of the array WORK.  If N <= 1,		LWORK >= 1.  If  JOBZ	=
	       'N' and N > 1, LWORK >= N + 1.  If JOBZ	= 'V' and N > 1, LWORK >= 2*N + N**2.

	       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/output) REAL array, dimension (LRWORK)
	       On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

       LRWORK  (input) INTEGER
	       The dimension of the array RWORK.  If N <= 1,		    LRWORK >= 1.  If JOBZ
	       = 'N' and N > 1, LRWORK >= N.  If JOBZ  = 'V' and N > 1,  LRWORK  >=  1	+  5*N	+
	       2*N**2.

	       If LRWORK = -1, then a workspace query is assumed; the routine only calculates the
	       optimal size of the RWORK array, returns this value as  the  first  entry  of  the
	       RWORK array, and no error message related to LRWORK is issued by XERBLA.

       IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
	       On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

       LIWORK  (input) INTEGER
	       The dimension of the array IWORK.  If N <= 1,		    LIWORK >= 1.  If JOBZ
	       = 'N' and N > 1, LIWORK >= 1.  If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       > 0:  CPOTRF or CHEEVD returned an error code:
	       <= N:  if INFO = i, CHEEVD 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.

FURTHER DETAILS
       Based on contributions by
	  Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

LAPACK version 3.0			   15 June 2000 				CHEGVD(l)


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