SSBEV  -  compute  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, eigen­
       vectors 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 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.

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

       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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