CHEGS2  -  reduce a complex Hermitian-definite generalized
       eigenproblem to standard form


SYNOPSIS

       SUBROUTINE CHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, ITYPE, LDA, LDB, N

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


PURPOSE

       CHEGS2 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')*A*inv(U)    or
       inv(L)*A*inv(L')

       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` or
       L'*A*L.

       B must have been previously factorized as U'*U or L*L'  by
       CPOTRF.


ARGUMENTS

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

       UPLO    (input) CHARACTER
               Specifies whether the upper  or  lower  triangular
               part  of the Hermitian matrix A is stored, and how
               B has been factorized.  = 'U':  Upper triangular
               = 'L':  Lower triangular

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

       A       (input/output) COMPLEX 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 array, dimension (LDB,N)
               The triangular factor from the Cholesky factoriza­
               tion of B, as returned by CPOTRF.

       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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