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# chpgv

```
NAME
CHPGV - compute 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

SYNOPSIS
SUBROUTINE CHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ,
WORK, RWORK, INFO )

CHARACTER     JOBZ, UPLO

INTEGER       INFO, ITYPE, LDZ, N

REAL          RWORK( * ), W( * )

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

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.

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 matrix A.  N >= 0.

AP      (input/workspace) COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermi-
tian 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)*(2n-j)/2) =
A(i,j) for j<=i<=n.

On exit, the contents of AP are destroyed.

BP      (input/output) COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermi-
tian 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)*(2n-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) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z       (output) COMPLEX array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the
matrix Z of eigenvectors.  The eigenvectors are nor-
malized 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 array, dimension (max(1, 2*N-1))

RWORK   (workspace) REAL 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:  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 converge to 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.
```