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

ZHPGV(l)					)					 ZHPGV(l)

NAME
       ZHPGV  - 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 ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, RWORK, INFO )

	   CHARACTER	 JOBZ, UPLO

	   INTEGER	 INFO, ITYPE, LDZ, N

	   DOUBLE	 PRECISION RWORK( * ), W( * )

	   COMPLEX*16	 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       ZHPGV 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, 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*16 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*16 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) DOUBLE PRECISION array, dimension (N)
	       If INFO = 0, the eigenvalues in ascending order.

       Z       (output) COMPLEX*16 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*16 array, dimension (max(1, 2*N-1))

       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:  ZPPTRF or ZHPEV returned an error code:
	       <= N:  if INFO = i, ZHPEV failed to converge; i off-diagonal elements of an inter-
	       mediate 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 fac-
	       torization  of  B  could  not be completed and no eigenvalues or eigenvectors were
	       computed.

LAPACK version 3.0			   15 June 2000 				 ZHPGV(l)


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