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chegvd.f(3)				      LAPACK				      chegvd.f(3)

NAME
       chegvd.f -

SYNOPSIS
   Functions/Subroutines
       subroutine chegvd (ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, RWORK, LRWORK,
	   IWORK, LIWORK, INFO)
	   CHEGST

Function/Subroutine Documentation
   subroutine chegvd (integerITYPE, characterJOBZ, characterUPLO, integerN, complex, dimension(
       lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, real, dimension( * )W,
       complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, integerLRWORK,
       integer, dimension( * )IWORK, integerLIWORK, integerINFO)
       CHEGST

       Purpose:

	    CHEGVD 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.
	    If eigenvectors are desired, it uses a divide and conquer algorithm.

	    The divide and conquer algorithm makes very mild assumptions about
	    floating point arithmetic. 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.

       Parameters:
	   ITYPE

		     ITYPE is 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

		     JOBZ is CHARACTER*1
		     = 'N':  Compute eigenvalues only;
		     = 'V':  Compute eigenvalues and eigenvectors.

	   UPLO

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

	   N

		     N is INTEGER
		     The order of the matrices A and B.  N >= 0.

	   A

		     A is COMPLEX 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 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

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

	   B

		     B is COMPLEX array, dimension (LDB, N)
		     On entry, the Hermitian 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

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

	   W

		     W is REAL array, dimension (N)
		     If INFO = 0, the eigenvalues in ascending order.

	   WORK

		     WORK is COMPLEX array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

	   LWORK

		     LWORK is 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 sizes of the WORK, RWORK and
		     IWORK arrays, returns these values as the first entries of
		     the WORK, RWORK and IWORK arrays, and no error message
		     related to LWORK or LRWORK or LIWORK is issued by XERBLA.

	   RWORK

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

	   LRWORK

		     LRWORK is 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 sizes of the WORK, RWORK
		     and IWORK arrays, returns these values as the first entries
		     of the WORK, RWORK and IWORK arrays, and no error message
		     related to LWORK or LRWORK or LIWORK is issued by XERBLA.

	   IWORK

		     IWORK is INTEGER array, dimension (MAX(1,LIWORK))
		     On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

	   LIWORK

		     LIWORK is 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.

		     If LIWORK = -1, then a workspace query is assumed; the
		     routine only calculates the optimal sizes of the WORK, RWORK
		     and IWORK arrays, returns these values as the first entries
		     of the WORK, RWORK and IWORK arrays, and no error message
		     related to LWORK or LRWORK or LIWORK is issued by XERBLA.

	   INFO

		     INFO is 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 and JOBZ = 'N', then the algorithm
			       failed to converge; i off-diagonal elements of an
			       intermediate tridiagonal form did not converge to
			       zero;
			       if INFO = i and JOBZ = 'V', then the algorithm
			       failed to compute an eigenvalue while working on
			       the submatrix lying in rows and columns INFO/(N+1)
			       through mod(INFO,N+1);
			> 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Further Details:

	     Modified so that no backsubstitution is performed if CHEEVD fails to
	     converge (NEIG in old code could be greater than N causing out of
	     bounds reference to A - reported by Ralf Meyer).  Also corrected the
	     description of INFO and the test on ITYPE. Sven, 16 Feb 05.

       Contributors:
	   Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

       Definition at line 249 of file chegvd.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      chegvd.f(3)
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