chpgv(3F)

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 matrices A and B.  N >= 0.

     AP      (input/output) 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      (input/output) 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       (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 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 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 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.