ZHBEV computes all the eigenvalues and, optionally, eigenvectors of


 a complex Hermitian band matrix A.

JOBZ

          JOBZ is CHARACTER*1


          = 'N':  Compute eigenvalues only;


          = 'V':  Compute eigenvalues and eigenvectors.

UPLO

          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER


          The order of the matrix A.  N >= 0.

KD

          KD is INTEGER


          The number of superdiagonals of the matrix A if UPLO = 'U',


          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

AB

          AB is COMPLEX*16 array, dimension (LDAB, N)


          On entry, the upper or lower triangle of the Hermitian band


          matrix A, stored in the first KD+1 rows of the array.  The


          j-th column of A is stored in the j-th column of the array AB


          as follows:


          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;


          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).


          On exit, AB is overwritten by values generated during the


          reduction to tridiagonal form.  If UPLO = 'U', the first


          superdiagonal and the diagonal of the tridiagonal matrix T


          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',


          the diagonal and first subdiagonal of T are returned in the


          first two rows of AB.

LDAB

          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD + 1.

W

          W is DOUBLE PRECISION array, dimension (N)


          If INFO = 0, the eigenvalues in ascending order.

Z

          Z is COMPLEX*16 array, dimension (LDZ, N)


          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal


          eigenvectors of the matrix A, with the i-th column of Z


          holding the eigenvector associated with W(i).


          If JOBZ = 'N', then Z is not referenced.

LDZ

          LDZ is INTEGER


          The leading dimension of the array Z.  LDZ >= 1, and if


          JOBZ = 'V', LDZ >= max(1,N).

WORK

          WORK is COMPLEX*16 array, dimension (N)

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:  if INFO = i, the algorithm failed to converge; i


                off-diagonal elements of an intermediate tridiagonal


                form did not converge to zero.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016