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NAME
     ssbevd - compute all the eigenvalues and, optionally, eigen-
     vectors 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, * )



     #include <sunperf.h>

     void ssbevd(char jobz, char uplo, int n, int kd, float *sab,
               int ldab, float *w, float *sz, int ldz, int *info)
               ;

PURPOSE
     SSBEVD computes all the eigenvalues and, optionally,  eigen-
     vectors  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) 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
               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) 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
               referenced.

     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 LWORK >  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 + 4*N + 2*N*lg N
               + 3*N**2 ), where lg( N )  =  smallest  integer  k
               such that 2**k >= N.

     IWORK     (workspace/output)   INTEGER   array,    dimension
               (LIWORK)
               On exit, if  LIWORK  >  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 2 + 5*N.

     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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