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



NAME
       ZHPGST

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



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)
                     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
                     = '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)
                     N is INTEGER
                     The order of the matrices A and B.  N >= 0.

           AP        (input/output)
                     AP is COMPLEX*16 array, dimension (N*(N+1)/2)
                     On entry, the upper or lower triangle of the Hermitian 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.

           BP        (input)
                     BP is COMPLEX*16 array, dimension (N*(N+1)/2)
                     The triangular factor from the Cholesky factorization of B,
                     stored in the same format as A, as returned by ZPPTRF.

           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                      ZHPGST(3)