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CHPGV(l)			       )			      CHPGV(l)

NAME
       CHPGV  -	 compute 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

SYNOPSIS
       SUBROUTINE CHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, RWORK,
			 INFO )

	   CHARACTER	 JOBZ, UPLO

	   INTEGER	 INFO, ITYPE, LDZ, N

	   REAL		 RWORK( * ), W( * )

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

PURPOSE
       CHPGV 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, stored in packed format, 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.

       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 factor‐
	       ization 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 (max(1, 2*N-1))

       RWORK   (workspace) REAL 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:  CPPTRF or CHPEV returned an error code:
	       <= N:  if INFO = i, CHPEV 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 factoriza‐
	       tion of B could not be completed and no eigenvalues  or	eigen‐
	       vectors were computed.

LAPACK version 3.0		 15 June 2000			      CHPGV(l)
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