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CHPGVD(l)					)					CHPGVD(l)

NAME
       CHPGVD - 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 CHPGVD( ITYPE,  JOBZ,  UPLO,	N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK,
			  IWORK, LIWORK, INFO )

	   CHARACTER	  JOBZ, UPLO

	   INTEGER	  INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N

	   INTEGER	  IWORK( * )

	   REAL 	  RWORK( * ), W( * )

	   COMPLEX	  AP( * ), BP( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       CHPGVD 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, stored in packed format, 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 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.

       AP      (input/output) COMPLEX array, dimension (N*(N+1)/2)
	       On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise
	       in a linear array.  The j-th column of A is stored in the array AP as follows:  if
	       UPLO  =	'U',  AP(i  +  (j-1)*j/2)  =  A(i,j)  for  1<=i<=j; if UPLO = 'L', AP(i +
	       (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

	       On exit, the contents of AP are destroyed.

       BP      (input/output) COMPLEX array, dimension (N*(N+1)/2)
	       On entry, the upper or lower triangle of the Hermitian matrix B, packed columnwise
	       in  a linear array.  The j-th column of B is stored in the array BP as follows: if
	       UPLO = 'U', BP(i + (j-1)*j/2) =	B(i,j)	for  1<=i<=j;  if  UPLO  =  'L',  BP(i	+
	       (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.

	       On  exit,  the triangular factor U or L from the Cholesky factorization B = U**H*U
	       or B = L*L**H, in the same storage format as B.

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

       Z       (output) COMPLEX array, dimension (LDZ, N)
	       If JOBZ = 'V', then if INFO = 0, Z 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 Z is not referenced.

       LDZ     (input) INTEGER
	       The leading dimension of the array Z.  LDZ >=  1,  and  if  JOBZ  =  'V',  LDZ  >=
	       max(1,N).

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

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

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

       LRWORK  (input) INTEGER
	       The dimension of 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 array IWORK.  If JOBZ	= 'N' or 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	size  of  the  IWORK  array, returns this value as the first entry of the
	       IWORK array, and no error message related to LIWORK is issued by XERBLA.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       > 0:  CPPTRF or CHPEVD returned an error code:
	       <= N:  if INFO = i, CHPEVD failed to  converge;	i  off-diagonal  elements  of  an
	       intermediate tridiagonal form did not convergeto 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 				CHPGVD(l)
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