CHPGV(3)       LAPACK routine of NEC Numeric Library Collection       CHPGV(3)



NAME
       CHPGV

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



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

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

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

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

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

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

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

           INFO      (output)
                     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
                               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.



LAPACK routine                  31 October 2017                       CHPGV(3)