SSBEV(3)              LAPACK driver routine (version 3.1)             SSBEV(3)



NAME
       SSBEV  -  all  the  eigenvalues and, optionally, eigenvectors of a real
       symmetric band matrix A

SYNOPSIS
       SUBROUTINE SSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, INFO )

           CHARACTER     JOBZ, UPLO

           INTEGER       INFO, KD, LDAB, LDZ, N

           REAL          AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       SSBEV computes all the eigenvalues and, optionally, eigenvectors  of  a
       real symmetric band matrix A.


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) REAL 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 super-
               diagonal  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) REAL array, dimension (N)
               If INFO = 0, the eigenvalues in ascending order.

       Z       (output) REAL 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) REAL array, dimension (max(1,3*N-2))

       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.



 LAPACK driver routine (version 3.N1o)vember 2006                        SSBEV(3)