# chpgv.f - Man Page

SRC/chpgv.f

## Synopsis

### Functions/Subroutines

subroutine chpgv (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, rwork, info)
CHPGV

## Function/Subroutine Documentation

### subroutine chpgv (integer itype, character jobz, character uplo, integer n, complex, dimension( * ) ap, complex, dimension( * ) bp, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CHPGV

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.
Parameters

ITYPE

ITYPE is 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

JOBZ is CHARACTER*1
= 'N':  Compute eigenvalues only;
= 'V':  Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= 'U':  Upper triangles of A and B are stored;
= 'L':  Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B.  N >= 0.

AP

AP is 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

BP is 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
factorization B = U**H*U or B = L*L**H, in the same storage
format as B.

W

W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is 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

LDZ is INTEGER
The leading dimension of the array Z.  LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N).

WORK

WORK is COMPLEX array, dimension (max(1, 2*N-1))

RWORK

RWORK is REAL array, dimension (max(1, 3*N-2))

INFO

INFO is 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
principal minor of order i of B is not positive.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 163 of file chpgv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page chpgv(3) is an alias of chpgv.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK