zhpgv (l)  Linux Man Pages
zhpgv: computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
Command to display zhpgv
manual in Linux: $ man l zhpgv
NAME
ZHPGV  computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized 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 generalized 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

= aqNaq: Compute eigenvalues only;
= aqVaq: Compute eigenvalues and eigenvectors.
 UPLO (input) CHARACTER*1

= aqUaq: Upper triangles of A and B are stored;
= aqLaq: 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 = aqUaq, AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = aqLaq, 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 = aqUaq, BP(i + (j1)*j/2) = B(i,j) for 1<=i<=j;
if UPLO = aqLaq, 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 = aqVaq, 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 = aqNaq, then Z is not referenced.
 LDZ (input) INTEGER

The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = aqVaq, 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 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.
Pages related to zhpgv
 zhpgv (3)
 zhpgvd (l)  computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
 zhpgvx (l)  computes selected eigenvalues and, optionally, eigenvectors of a complex generalized Hermitiandefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
 zhpgst (l)  reduces a complex Hermitiandefinite generalized eigenproblem to standard form, using packed storage
 zhpcon (l)  estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF
 zhpev (l)  computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage
 zhpevd (l)  computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
 zhpevx (l)  computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
 zhpmv (l)  performs the matrixvector operation y := alpha*A*x + beta*y,