CXML
        	    
LAPACK version 3.0
dsbevd(3)

PURPOSE
  DSBEVD - compute all the eigenvalues and, optionally, eigenvectors of a
  real symmetric band matrix A

SYNTAX
  SUBROUTINE DSBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK,
		     IWORK, LIWORK, INFO )

      CHARACTER	     JOBZ, UPLO

      INTEGER	     INFO, KD, LDAB, LDZ, LIWORK, LWORK, N

      INTEGER	     IWORK( * )

      DOUBLE	     PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )

DESCRIPTION
  DSBEVD computes all the eigenvalues and, optionally, eigenvectors of a real
  symmetric band matrix A. If eigenvectors are desired, it uses a divide and
  conquer algorithm.

  The divide and conquer algorithm makes very mild assumptions about floating
  point arithmetic. It will work on machines with a guard digit in
  add/subtract, or on those binary machines without guard digits which
  subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
  conceivably fail on hexadecimal or decimal machines without guard digits,
  but we know of none.

ARGUMENTS
  JOBZ	  (input) CHARACTER*1
	  = 'N':  Compute eigenvalues only;
	  = 'V':  Compute eigenvalues and eigenvectors.

  UPLO	  (input) CHARACTER*1
	  = 'U':  Upper triangle of A is stored;
	  = 'L':  Lower triangle of A is stored.

  N	  (input) INTEGER
	  The order of the matrix A.  N >= 0.

  KD	  (input) INTEGER
	  The number of superdiagonals of the matrix A if UPLO = 'U', or the
	  number of subdiagonals if UPLO = 'L'.	 KD >= 0.

  AB	  (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
	  On entry, the upper or lower triangle of the symmetric 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	  (input) INTEGER
	  The leading dimension of the array AB.  LDAB >= KD + 1.

  W	  (output) DOUBLE PRECISION array, dimension (N)
	  If INFO = 0, the eigenvalues in ascending order.

  Z	  (output) DOUBLE PRECISION 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	  (input) INTEGER
	  The leading dimension of the array Z.	 LDZ >= 1, and if JOBZ = 'V',
	  LDZ >= max(1,N).

  WORK	  (workspace/output) DOUBLE PRECISION array,
	  dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal
	  LWORK.

  LWORK	  (input) INTEGER
	  The dimension of the array WORK.  IF N <= 1,		      LWORK
	  must be at least 1.  If JOBZ	= 'N' and N > 2, LWORK must be at
	  least 2*N.  If JOBZ  = 'V' and N > 2, LWORK must be at least ( 1 +
	  5*N + 2*N**2 ).

	  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.

  IWORK	  (workspace/output) INTEGER array, dimension (LIWORK)
	  On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

  LIWORK  (input) INTEGER
	  The dimension of the array LIWORK.  If JOBZ  = 'N' or N <= 1,
	  LIWORK must be at least 1.  If JOBZ  = 'V' and N > 2, LIWORK must
	  be at least 3 + 5*N.

	  If LIWORK = -1, then a workspace query is assumed; the routine only
	  calculates the optimal size of the IWORK array, returns this value
	  as the first entry of the IWORK array, and no error message related
	  to LIWORK is issued by XERBLA.

  INFO	  (output) 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.