ZHPGST  -  reduce a complex Hermitian-definite generalized
       eigenproblem to standard form, using packed storage


SYNOPSIS

       SUBROUTINE ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, ITYPE, N

           COMPLEX*16     AP( * ), BP( * )


PURPOSE

       ZHPGST reduces a  complex  Hermitian-definite  generalized
       eigenproblem  to  standard form, using packed storage.  If
       ITYPE = 1, the problem is A*x = lambda*B*x,
       and   A   is   overwritten   by   inv(U**H)*A*inv(U)    or
       inv(L)*A*inv(L**H)

       If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
       B*A*x  =  lambda*x,  and  A  is overwritten by U*A*U**H or
       L**H*A*L.

       B must have been previously factorized as U**H*U or L*L**H
       by ZPPTRF.


ARGUMENTS

       ITYPE   (input) INTEGER
               =     1:     compute     inv(U**H)*A*inv(U)     or
               inv(L)*A*inv(L**H);
               = 2 or 3: compute U*A*U**H or L**H*A*L.

       UPLO    (input) CHARACTER
               = 'U':  Upper triangle of A is  stored  and  B  is
               factored as U**H*U; = 'L':  Lower triangle of A is
               stored and B is factored as L*L**H.

       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)*(2n-j)/2) = A(i,j) for j<=i<=n.

               On exit, if INFO  =  0,  the  transformed  matrix,
               stored in the same format as A.

               The triangular factor from the Cholesky factoriza­
               tion of B, stored in the  same  format  as  A,  as
               returned by ZPPTRF.

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value


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