ZHEGV computes all the eigenvalues, and optionally, the eigenvectors


 of a complex generalized Hermitian-definite eigenproblem, of the form


 A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.


 Here A and B are assumed to be Hermitian and B is also


 positive definite.

ITYPE

          ITYPE is INTEGER


          Specifies the problem type to be solved:


          = 1:  A*x = (lambda)*B*x


          = 2:  A*B*x = (lambda)*x


          = 3:  B*A*x = (lambda)*x

JOBZ

          JOBZ is CHARACTER*1


          = 'N':  Compute eigenvalues only;


          = 'V':  Compute eigenvalues and eigenvectors.

UPLO

          UPLO is CHARACTER*1


          = 'U':  Upper triangles of A and B are stored;


          = 'L':  Lower triangles of A and B are stored.

N

          N is INTEGER


          The order of the matrices A and B.  N >= 0.

A

          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.  If UPLO = 'L',


          the leading N-by-N lower triangular part of A contains


          the lower triangular part of the matrix A.


          On exit, if JOBZ = 'V', then if INFO = 0, A contains the


          matrix Z of eigenvectors.  The eigenvectors are normalized


          as follows:


          if ITYPE = 1 or 2, Z**H*B*Z = I;


          if ITYPE = 3, Z**H*inv(B)*Z = I.


          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')


          or the lower triangle (if UPLO='L') of A, including the


          diagonal, is destroyed.

LDA

          LDA is INTEGER


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

B

          B is COMPLEX*16 array, dimension (LDB, N)


          On entry, the Hermitian positive definite matrix B.


          If UPLO = 'U', the leading N-by-N upper triangular part of B


          contains the upper triangular part of the matrix B.


          If UPLO = 'L', the leading N-by-N lower triangular part of B


          contains the lower triangular part of the matrix B.


          On exit, if INFO <= N, the part of B containing the matrix is


          overwritten by the triangular factor U or L from the Cholesky


          factorization B = U**H*U or B = L*L**H.

LDB

          LDB is INTEGER


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

W

          W is DOUBLE PRECISION array, dimension (N)


          If INFO = 0, the eigenvalues in ascending order.

WORK

          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))


          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER


          The length of the array WORK.  LWORK >= max(1,2*N-1).


          For optimal efficiency, LWORK >= (NB+1)*N,


          where NB is the blocksize for ZHETRD returned by ILAENV.


          If LWORK = -1, then a workspace query is assumed; the routine


          only calculates the optimal size of the WORK array, returns


          this value as the first entry of the WORK array, and no error


          message related to LWORK is issued by XERBLA.

RWORK

          RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))

INFO

          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value


          > 0:  ZPOTRF or ZHEEV returned an error code:


             <= N:  if INFO = i, ZHEEV failed to converge;


                    i off-diagonal elements of an intermediate


                    tridiagonal form did not converge to zero;


             > N:   if INFO = N + i, for 1 <= i <= N, then the leading


                    minor of order i of B is not positive definite.


                    The factorization of B could not be completed and


                    no eigenvalues or eigenvectors were computed.

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NAG Ltd.

November 2011