ZHEGST  -  reduce a complex Hermitian-definite generalized
       eigenproblem to standard form


SYNOPSIS

       SUBROUTINE ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, ITYPE, LDA, LDB, N

           COMPLEX*16     A( LDA, * ), B( LDB, * )


PURPOSE

       ZHEGST reduces a  complex  Hermitian-definite  generalized
       eigenproblem  to standard form.  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 ZPOTRF.


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.

       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
               On  entry, the Hermitian matrix A.  If UPLO = 'U',
               the leading N-by-N upper triangular part of A con­
               tains  the  upper triangular part of the matrix A,
               and the strictly lower triangular part of A is not
               referenced.   If  UPLO  =  'L', the leading N-by-N
               lower triangular part of A contains the lower tri­
               angular  part  of  the  matrix A, and the strictly
               upper triangular part of A is not referenced.

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

               The  leading  dimension  of  the  array A.  LDA >=
               max(1,N).

       B       (input) COMPLEX*16 array, dimension (LDB,N)
               The triangular factor from the Cholesky factoriza­
               tion of B, as returned by ZPOTRF.

       LDB     (input) INTEGER
               The  leading  dimension  of  the  array B.  LDB >=
               max(1,N).

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


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