
ZHPGV(l) ) ZHPGV(l)
NAME
ZHPGV  compute all the eigenvalues and, optionally, the eigenvectors of a complex gener
alized Hermitiandefinite 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 Hermitiandefinite 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 jth column of A is stored in the array AP as follows: if
UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
(j1)*(2*nj)/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 jth column of B is stored in the array BP as follows: if
UPLO = 'U', BP(i + (j1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i +
(j1)*(2*nj)/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*N1))
RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N2))
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: ZPPTRF or ZHPEV returned an error code:
<= N: if INFO = i, ZHPEV failed to converge; i offdiagonal 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) 
