.TH ZHPGV 1 "November 2006" " LAPACK driver routine (version 3.1) " " LAPACK driver routine (version 3.1) "
.SH NAME
ZHPGV - 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
.SH SYNOPSIS
.TP 18
SUBROUTINE ZHPGV(
ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
RWORK, INFO )
.TP 18
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CHARACTER
JOBZ, UPLO
.TP 18
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INTEGER
INFO, ITYPE, LDZ, N
.TP 18
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DOUBLE
PRECISION RWORK( * ), W( * )
.TP 18
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COMPLEX*16
AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
.SH PURPOSE
ZHPGV 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.
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.SH ARGUMENTS
.TP 8
ITYPE (input) INTEGER
Specifies the problem type to be solved:
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= 1: A*x = (lambda)*B*x
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= 2: A*B*x = (lambda)*x
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= 3: B*A*x = (lambda)*x
.TP 8
JOBZ (input) CHARACTER*1
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= \(aqN\(aq: Compute eigenvalues only;
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= \(aqV\(aq: Compute eigenvalues and eigenvectors.
.TP 8
UPLO (input) CHARACTER*1
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= \(aqU\(aq: Upper triangles of A and B are stored;
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= \(aqL\(aq: Lower triangles of A and B are stored.
.TP 8
N (input) INTEGER
The order of the matrices A and B. N >= 0.
.TP 8
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 = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = \(aqL\(aq, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, the contents of AP are destroyed.
.TP 8
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 = \(aqU\(aq, BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
if UPLO = \(aqL\(aq, 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.
.TP 8
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
.TP 8
Z (output) COMPLEX*16 array, dimension (LDZ, N)
If JOBZ = \(aqV\(aq, 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 = \(aqN\(aq, then Z is not referenced.
.TP 8
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = \(aqV\(aq, LDZ >= max(1,N).
.TP 8
WORK (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1))
.TP 8
RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))
.TP 8
INFO (output) INTEGER
= 0: successful exit
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< 0: if INFO = -i, the i-th argument had an illegal value
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> 0: ZPPTRF or ZHPEV returned an error code:
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<= N: if INFO = i, ZHPEV 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.