ZHPGV  -  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 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 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*16 array, dimension
               (N*(N+1)/2)
               On entry, the upper or lower triangle of the  Her­
               mitian  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.


       BP      (input/output) COMPLEX*16 array, dimension
               (N*(N+1)/2)
               On entry, the upper or lower triangle of the  Her­
               mitian  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) DOUBLE PRECISION array, dimension (N)
               If INFO = 0, the eigenvalues in ascending order.

       Z       (output) COMPLEX*16 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*16 array, dimension (max(1,
               2*N-1))

       RWORK    (workspace)  DOUBLE  PRECISION  array, dimension
               (max(1, 3*N-2))

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value
               > 0:  ZPPTRF or ZHPEV returned an error code:
               <= N:  if INFO = i, ZHPEV failed  to  converge;  i
               off-diagonal elements of an intermediate tridiago­
               nal 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  fac­
               torization  of  B  could  not  be completed and no
               eigenvalues or eigenvectors were computed.


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