ZHEGS2(3)      LAPACK routine of NEC Numeric Library Collection      ZHEGS2(3)



NAME
       ZHEGS2

SYNOPSIS
       SUBROUTINE ZHEGS2 (ITYPE, UPLO, N, A, LDA, B, LDB, INFO)



PURPOSE
            ZHEGS2 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)
                     ITYPE is 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)
                     UPLO is CHARACTER*1
                     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)
                     N is INTEGER
                     The order of the matrices A and B.  N >= 0.

           A         (input/output)
                     A is 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 contains 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
                     triangular 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.

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

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

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

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



LAPACK routine                  31 October 2017                      ZHEGS2(3)