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


SYNOPSIS

       SUBROUTINE SSBEVD( 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( * )

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


PURPOSE

       SSBEVD  computes  all  the  eigenvalues  and,  optionally,
       eigenvectors  of a real symmetric band matrix A. If eigen­
       vectors are desired, it uses a divide  and  conquer  algo­
       rithm.

       The  divide  and conquer algorithm makes very mild assump­
       tions 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  with­
       out 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) REAL array, dimension (LDAB, N)
               On  entry, the upper or lower triangle of the sym­
               metric 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

               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) 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  associ­
               ated with W(i).  If JOBZ = 'N', then Z is not ref­
               erenced.

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

       WORK    (workspace/output) REAL 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'

               '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 ille­
               gal value
               >  0:   if  INFO = i, the algorithm failed to con­
               verge; i off-diagonal elements of an  intermediate
               tridiagonal form did not converge to zero.


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